material science

Material Science Syllabus

Satish Kailash Vasu/IISc, Bangalore V1/1-6-04/1

MATERIAL SCIENCE

Aim: At the end of the course the student will have an understanding of mechanics,

physical and chemical properties of materials including metals, ceramics, polymers

and composites and the reasons for these properties to exist.

Module 1: Introduction (3)

Historical perspective of Materials Science. Why study properties of materials? Classification of materials. Advanced Materials, Future materials and modern materials

Module 2: Atomic Structure, Interatomic Bonding and Structure of Crystalline Solids (5)

Atomic structure. Atomic bonding in solids, Crystal structures, Crystalline and non-crystalline materials. Miller indices. Anisotropic elasticity. Elastic behavior of composites. Structure and properties of polymers. Structure and properties of ceramics.

Module 3: Imperfections in Solids (2)

Point defects. Theoretical yield point. Line defects and dislocations. Interfacial defects. Bulk or volume defects. Atomic vibrations

Module 4: Mechanical Properties of Metals (3)

Elastic deformation. Plastic deformation. Interpretation of tensile stress-strain curves Yielding under multiaxial stress. Yield criteria and macroscopic aspects of plastic deformation. Property variability and design factors Module 5: Diffusion (2) Diffusion mechanisms. Steady and non-steady state diffusion. Factors that influence diffusion. Non-equilibrium transformation and microstructure

Module 6: Dislocations and Strengthening Mechanisms (3) Dislocation and plastic deformation. Mechanisms of strengthening in metals. Recovery, recrystallization and grain growth. Strengthening by second phase particles. Optimum distribution of particles. Lattice resistance to dislocation motion

Module 7: Phase Diagrams (4) Equilibrium phase diagrams. Particle strengthening by precipitation. Precipitation reactions. Kinetics of nucleation and growth. The iron-carbon system. Phase transformations. Transformation rate effects and TTT diagrams. Microstructure and property changes in iron-carbon system

Module 8: Failure (5) Fracture. Ductile and brittle fracture. Fracture mechanics. Impact fracture. Ductile brittle transition. Fatigue. Crack initiation and propagation. Crack propagation rate. Creep. Generalized creep behavior. Stress and temperature effects

Module 9: Applications and Processing of Metals and Alloys (2) Types of metals and alloys. Fabrication of metals. Thermal processing of metals. Heat treatment. Precipitation hardening.



Module 10: Applications and Processing of Ceramics (1) Types and applications of ceramics. Fabrication and processing of ceramics. Module 11: Applications and Processing of Polymers (2) Mechanical behavior of polymers. Mechanisms of deformation and strengthening of polymers. Crystallization, melting and glass transition. Polymer types. Polymer synthesis and processing.

Module 12: Composites (1) Particle reinforced composites. Fiber reinforced composites. Structural composites Module 13: Corrosion and Degradation of Materials (1) Corrosion of metals. Corrosion of ceramics. Degradation of polymers

Module 14: Electrical Properties (1)

Electrical conduction. Semi conductivity. Super conductivity. Electrical conduction in ionic ceramics and in polymers. Dielectric behavior. Ferroelectricity. Piezoelectricity

Module 15: Thermal Properties (1) Heat capacity. Thermal expansion. Thermal conductivity. Thermal stresses

Module 16: Magnetic Properties (1) Diamagnetism and paramagnetism. Ferromagnetism.Antiferromagnetism and ferrimagnetism. Influence of temperature on magnetic behavior. Domains and Hysteresis

Module 17: Optical Properties (1)

Basic concepts. Optical properties of metals. Optical properties of nonmetals. Application of optical phenomena.

Module 18: Economic, Environmental and Social Issues of Material Usage (2) Economic considerations. Environmental and societal considerations. Recycling issues. Life cycle analysis and its use in design



Lecture Plan Module Learning Units Hours

per topic Total Hours

1. Historic perspective and Materials Science 1 2. Why study properties of materials.

Classification of materials 1

1) Introduction

3. Advanced materials, Future materials and Modern materials

1

3

4. Atomic Structure and atomic bonding in solids

1

5. Crystal structures, Crystalline and non-crystalline materials

1

6. Miller indices, Anisotropic elasticity and elastic behavior of composites

1

7. Structure and properties of polymers 1

2) Atomic Structure, Interatomic Bonding and Structure of Crystalline Solids

8. Structure and properties of Ceramics 1

5

9. Pint defects, theoretical yield point, line defects and dislocations

1 3) Imperfections in Solids

10. Interfacial defects, bulk or volume defects and atomic vibrations

1

2

11. Elastic deformation and plastic deformation 1 12. Interpretation of tensile stress-strain curves 1

4) Mechanical Properties of Metals

13. Yielding under multiaxial stress, Yield criteria and macroscopic aspects of plastic deformation and property variability and design factors

1

3

14. Diffusion Mechanisms and steady state and non-steady state diffusion

1 5) Diffusion

15. Factors that influence diffusion and non-equilibrium transformation and microstructure

1

2

16. Dislocation and plastic deformation and mechanisms of strengthening in metals

1

17. Recovery, recrystallization and grain growth 1

6) Dislocations and Strengthening Mechanisms

18. Strengthening by second phase particles, optimum distribution of particles and lattice resistance to dislocation motion

1

3

19. Equilibrium phase diagrams, Particle strengthening by precipitation and precipitation reactions

1

20. Kinetics of nucleation and growth 1 21. The iron-carbon system, phase

transformations 1

7. Phase Diagrams

22. Transformation rate effects and TTT diagrams, Microstructure and property changes in iron-carbon system

1

4

23. Fracture, ductile and brittle fracture 1 24. Fracture mechanics 1

8. Failure

25. Impact fracture, ductile brittle transition 1



26. Fatigue, crack initiation and propagation, crack propagation rate

1

27. Creep, generalized creep behavior, stress and temperature effects

1

5

28. Types on metals and alloys, fabrication of metals, thermal processing of metals

1 9. Applications and Processing of Metals and Alloys 29. Heat treatment and precipitation hardening 1

2

10. Applications and Processing of Ceramics

30. Types and applications of ceramics, fabrication and processing of ceramics

1

1

31. Mechanical Behavior of polymers, Mechanisms of deformation and strengthening of polymers

1

11. Applications and Processing of Polymers 32. Crystallization, melting and glass transition,

polymer types and polymer synthesis and processing

1

2

12. Composites 33. Particle reinforced composites, fiber reinforced composites, structural composites

1

1

13. Corrosion and Degradation of Materials

34. Corrosion of metals, Corrosion of ceramics, Degradation of polymers

1

1

14. Electrical Properties

35. Electrical conduction, Semi conductivity, Super conductivity, Electrical conduction in ionic ceramics and in polymers, Dielectric behavior, Ferroelectricity, Piezoelectricity

2

1

15. Thermal Properties

36. Heat capacity, Thermal expansion, Thermal conductivity, Thermal stresses

1 1

16. Magnetic Properties

37. Diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism. Influence of temperature on magnetic behavior, domains and hysteresis

1

1

17. Optical Properties

38. Basic concepts, Optical properties of metals, Optical properties of nonmetals, Application of optical phenomena

1

1

39. Economic considerations, Environmental and societal considerations, Recycling issues

1

18. Economic, Environmental and Social Issues of Material Usage

40. Life Cycle analysis and its use in design 1

2

Material Science/Introduction Learning Material

Introduction

Historical Perspective

Materials are so important in the development of civilization that we associate ages with them. In the origin of human life on earth, the Stone Age, people used only natural materials, like stone, clay, skins, and wood. When people found copper and how to make it harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The next big step was the discovery of a cheap process to make steel around 1850, which enabled the railroads and the building of the modern infrastructure of the industrial world.

Materials Science and Engineering

Understanding of how materials behave like they do, and why they differ in properties was only possible with the atomistic understanding allowed by quantum mechanics, that first explained atoms and then solids starting in the 1930s. The combination of physics, chemistry, and the focus on the relationship between the properties of a material and its microstructure is the domain of Materials Science. The development of this science allowed designing materials and provided a knowledge base for the engineering applications (Materials Engineering).

Satish V. Kailas/IISc M1/L1/V1/Aug 2004/1


Why Study Materials Science and Engineering?

• To be able to select a material for a given use based on considerations of cost and performance.

• To understand the limits of materials and the change of their properties with use. • To be able to create a new material that will have some desirable properties.

All engineering disciplines need to know about materials. Even the most "immaterial", like software or system engineering depend on the development of new materials, which in turn alter the economics, like software-hardware trade-offs. Increasing applications of system engineering are in materials manufacturing (industrial engineering) and complex environmental systems.

Classification of Materials

Like many other things, materials are classified in groups, so that our brain can handle the complexity. One could classify them according to structure, or properties, or use. The one that we will use is according to the way the atoms are bound together:

Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together. Metals are usually strong, conduct electricity and heat well and are opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.

Semiconductors: the bonding is covalent (electrons are shared between atoms). Their electrical properties depend extremely strongly on minute proportions of contaminants. They are opaque to visible light but transparent to the infrared. Examples: Si, Ge, GaAs.

Ceramics: atoms behave mostly like either positive or negative ions, and are bound by Coulomb forces between them. They are usually combinations of metals or semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides). Examples: glass, porcelain, many minerals.

Polymers: are bound by covalent forces and also by weak van der Waals forces, and usually based on H, C and other non-metallic elements. They decompose at moderate temperatures (100 – 400 C), and are lightweight. Other properties vary greatly. Examples: plastics (nylon, teflon, polyester) and rubber.

Other categories are not based on bonding. A particular microstructure identifies composites, made of different materials in intimate contact (example: fiberglass, concrete, wood) to achieve specific properties. Biomaterials can be any type of material that is biocompatible and used, for instance, to replace human body parts.




Advanced Materials

Materials used in "High-Tec" applications, usually designed for maximum performance, and normally expensive. Examples are titanium alloys for supersonic airplanes, magnetic alloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.

Modern Material's Needs

• Engine efficiency increases at high temperatures: requires high temperature structural materials

• Use of nuclear energy requires solving problem with residues, or advances in nuclear waste processing.

• Hypersonic flight requires materials that are light, strong and resist high temperatures.

• Optical communications require optical fibers that absorb light negligibly. • Civil construction – materials for unbreakable windows. • Structures: materials that are strong like metals and resist corrosion like plastics.

Satish V. Kailas ME/MS 1

Module-1

Introduction


1. Historic perspective and Materials Science

2. Why study properties of materials, Classification of

materials

3. Advanced materials, Future materials and Modern

materials’ needs

Contents


Historic Perspective

Materials are very important in development of human

civilization. In respect, their names are associated in

history, e.g. stone age, Bronze age, Iron age, etc.

With time humans discovered new materials and also

techniques to produce known materials. This is an

ongoing process for coming centuries, i.e. no end in sight!


Materials Science

It can be defined as science dealing the relationships that exist between the structures and properties of materials, which are useful in practice of engineer’s profession.

Basic components and their interrelationship:

Structure

Properties Processing

Performance


Properties Of Materials

All solid engineering materials are characterized for their properties.Engineering use of a material is reflection of its properties under conditions of use.All important properties can be grouped into six categories: Mechanical, Electrical, Thermal, Magnetic, Optical, and Deteriorative.Each material possess a structure, relevant properties, which dependent on processing and determines the performance.


Why Study Properties Of Materials? - 1

Since there are thousands of materials available it is almost impossible to select a material for a specific task unless otherwise its properties are known.

There are several criteria on which the final decision is based on.

There are less chances of material possessing optimal or idle combination of properties.

A need to trade off between number of factors!


The classic example involves strength and ductility:

Normally material possessing strength have limited ductility.In such cases a reasonable comprise between two or more properties are important.

A second selection consideration is any deterioration of material properties during service operations.

Finally the overriding consideration is economics.

Why Study Properties Of Materials? - 2


Classification Of MaterialsThree basic groups of solid engineering materials based on atomic bonds and structures:

MetalsCeramics

Polymers

Classification can also be done based on either properties (mechanical, electrical, optical), areas of applications (structures, machines, devices). Further we can subdivide these groups.

According to the present engineering needs:Composites, Semiconductors, Biomatrials


Metals

Characteristics are owed to non-localized electrons (metallic bond between atoms) i.e. electrons are not bound to a particular atom.They are characterized by their high thermal and electrical conductivities. They are opaque, can be polished to high luster. The opacity and reflectivity of a metal arise from the response of the unbound electrons to electromagnetic vibrations at light frequencies.Relatively heavier, strong, yet deformable.E.g.: Steel, Aluminium, Brass, Bronze, Lead, Titanium, etc.


CeramicsThey contain both metallic and nonmetallic elements.Characterized by their higher resistance to high temperatures and harsh environments than metals and polymers. Typically good insulators to passage of both heat and electricity.Less dense than most metals and alloys.They are harder and stiffer, but brittle in nature.They are mostly oxides, nitrides, and carbides of metals.Wide range: traditional (clay, silicate glass, cement) to advanced (carbides, pure oxides, non-silicate glasses).E.g.: Glass, Porcelain, Minerals, etc.


Polymers

Commercially called plastics; noted for their low density, flexibility and use as insulators.Mostly are of organic compounds i.e. based on carbon, oxygen and other nonmetallic elements.Consists large molecular structures bonded by covalent and vander Waals forces.They decompose at relatively moderate temperatures (100-400 C).Application: packaging, textiles, biomedical devices, optical devices, ceramics household items, toys, etc.E.g.: Nylon, Teflon, Rubber, Polyester, etc.


CompositesConsist more than one kind of material; tailor made to benefit from combination of best characteristics of each constituent.Available over a very wide range: natural (wood) to synthetic (fiberglass).Many are composed of two phases; one is matrix – which is continuous and surrounds the other, dispersed phase.Classified into many groups: (1) depending on orientation of phases; such as particle reinforced, fiber reinforced, etc. (2) depending on matrix; metal matrix, polymer matrix, ceramic matrix.E.g.: Cement concrete, Fiberglass, special purpose refractory bricks, plywood, etc.


Semiconductors

Their electrical properties are intermediate when compared with electrical conductors and electrical insulators.

These electrical characteristics are extremely sensitive to the presence of minute amounts of foreign atoms.

Found very many applications in electronic devices over decades through integrated circuits. In can be said that semiconductors revolutionized the electronic industry for last few decades.


BiomaterialsThose used for replacement of damaged or diseased body parts.Primary requirements: must be biocompatible with body tissues, must not produce toxic substances.Important materials factors: ability to support the forces, low friction and wear, density, reproducibility and cost.All the above materials can be used depending on the application.A classic example: hip joint.E.g.: Stainless steel, Co-28Cr-6Mo, Ti-6Al-4V, ultra high molecular weight polyethylene, high purity dense Al-oxide, etc.


Advanced MaterialsCan be defined as materials used in high-tech devices i.e. which operates based on relatively intricate and sophisticated principles (e.g. computers, air/space-crafts, electronic gadgets, etc.).These are either traditional materials with enhanced properties or newly developed materials with high-performance capabilities. Thus, these are relatively expensive.Typical applications: integrated circuits, lasers, LCDs, fiber optics, thermal protection for space shuttle, etc.E.g.: Metallic foams, inter-metallic compounds, multi-component alloys, magnetic alloys, special ceramics and high temperature materials, etc.


Future Materials - 1

Group of new and state-of-the-art materials now being developed, and expected to have significant influence on present-day technologies, especially in the fields of medicine, manufacturing and defense.Smart/Intelligent material system consists some type of sensor (detects an input) and an actuator (performs responsive and adaptive function). Actuators may be called upon to change shape, position, natural frequency, mechanical characteristics in response to changes in temperature, electric/magnetic fields, moisture, pH, etc.


Future Materials - 2

Four types of materials used as actuators:Shape memory alloysPiezoelectric ceramicsMagnetostrictive materialsElectro-/Magneto-rheologic fluids

Materials / Devices used as sensors:Optical fibersPiezoelectric materialsMicro-electro-mechanical systems (MEMS)- etc.


Future Materials - 3Typical applications:

1. By incorporating sensors, actuators and chip processors into system, researchers are able to stimulate biological human-like behavior.

2. Fibers for bridges, buildings, and wood utility poles.3. They also help in fast moving and accurate robot parts, high

speed helicopter rotor blades.4. Actuators that control chatter in precision machine tools.5. Small microelectronic circuits in machines ranging from

computers to photolithography prints.6. Health monitoring detecting the success or failure of a

product.


Modern Materials’ Needs

Engine efficiency increases at high temperatures; requires high temperature structural materials.Use of nuclear energy requires solving problems with residue, or advance in nuclear waste processing.Hypersonic flight requires materials that are light, strong and resist high temperatures.Optical communications require optical fibers that absorb light negligibly.Civil construction – materials for unbreakable windows.Structures: materials that are strong like metals and resist corrosion like plastics.

Material Science/Atomic Structure, Inter atomic bonding Learning Material and structure of crystalline solids and atomic bonding in solids


Atomic Structure and atomic Bonding in solids

Atomic Structure:

Atoms are composed of electrons, protons, and neutrons. Electron and protons are negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.

The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same number of electrons and protons, Z.

A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu.

Calculating n, the number of atoms per cm3 in a piece of material of density δ (g/cm3).

n = Nav × δ / M

where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a density δ = 1.8 g/cm3, M =12, we get 6 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 C/cm3.

For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density of 1 g/cm3, one obtains n = 3.3 × 1022 H2O/cm3. Note that since the water molecule contains 3 atoms, this is equivalent to 9.9 × 1022 atoms/cm3.

Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per centimeter, about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids.



Atomic bonding in solids:

Primary Interatomic Bonds

Ionic Bonding

This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding.

Covalent Bonding

In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H2 molecule, where the electrons spend more time in between the nuclei than outside, thus producing bonding.

Metallic Bonding

In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form an electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons.

Secondary Bonding (Van der Waals)

Fluctuating Induced Dipole Bonds

Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is called van der Waals bonding.

Polar Molecule-Induced Dipole Bonds

A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a nearby atom, leading to bonding.

Permanent Dipole Bonds

This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole



Crystal Structures:

Atoms self-organize in crystals, most of the time. The crystalline lattice is a periodic array of the atoms. When the solid is not crystalline, it is called amorphous. Examples of crystalline solids are metals, diamond and other precious stones, ice, graphite. Examples of amorphous solids are glass, amorphous carbon (a-C), amorphous Si, most plastics

To discuss crystalline structures it is useful to consider atoms as being hard spheres, with well-defined radii. In this scheme, the shortest distance between two like atoms is one diameter.

Metallic Crystal Structures

Important properties of the unit cells are

• The type of atoms and their radii R. • Cell dimensions (side a in cubic cells, side of base a and height c in HCP) in

terms of R. • n, number of atoms per unit cell. For an atom that is shared with m adjacent unit

cells, we only count a fraction of the atom, 1/m. • CN, the coordination number, which is the number of closest neighbors to which

an atom is bonded. • APF, the atomic packing factor, which is the fraction of the volume of the cell

actually occupied by the hard spheres. APF = Sum of atomic volumes/Volume of cell.

Unit Cell n CN a/R APF

SC 1 6 2 0.52

BCC 2 8 4√ 3 0.68

FCC 4 12 2√ 2 0.74

HCP 6 12 0.74



Crystalline and Non-crystalline materials:

Single Crystals

Crystals can be single crystals where the whole solid is one crystal. Then it has a regular geometric structure with flat faces.

Polycrystalline Materials

A solid can be composed of many crystalline grains, not aligned with each other. It is called polycrystalline. The grains can be more or less aligned with respect to each other. Where they meet is called a grain boundary.

Non-Crystalline Solids

In amorphous solids, there is no long-range order. But amorphous does not mean random, since the distance between atoms cannot be smaller than the size of the hard spheres. Also, in many cases there is some form of short-range order. For instance, the tetragonal order of crystalline SiO2 (quartz) is still apparent in amorphous SiO2 (silica glass.)



Miller Indices: Rules for Miller Indices:

• Determine the intercepts of the face along the crystallographic axes, in terms of unit cell dimensions.

• Take the reciprocals • Clear fractions • Reduce to lowest terms

For example, if the x-, y-, and z- intercepts are 2, 1, and 3, the Miller indices are calculated as:

• Take reciprocals: 1/2, 1/1, 1/3 • Clear fractions (multiply by 6): 3, 6, 2 • Reduce to lowest terms (already there)

Thus, the Miller indices are 3,6,2. If a plane is parallel to an axis, its intercept is at infinity and its Miller index is zero. A generic Miller index is denoted by (hkl).

If a plane has negative intercept, the negative number is denoted by a bar above the number. Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get 1,1,1. This implies symmetry that the crystal may not have!



Some General Principles

• If a Miller index is zero, the plane is parallel to that axis. • The smaller a Miller index, the more nearly parallel the plane is to the axis. • The larger a Miller index, the more nearly perpendicular a plane is to that axis. • Multiplying or dividing a Miller index by a constant has no effect on the

orientation of the plane • Miller indices are almost always small.

Why Miller Indices?

• Using reciprocals spares us the complication of infinite intercepts. • Formulas involving Miller indices are very similar to related formulas from

analytical geometry. • Specifying dimensions in unit cell terms means that the same label can be applied

to any face with a similar stacking pattern, regardless of the crystal class of the crystal. Face 111 always steps the same way regardless of crystal system.

Anisotropy

Different directions in the crystal have different packing. For instance, atoms along the edge FCC crystals are more separated than along the face diagonal. This causes anisotropy in the properties of crystals; for instance, the deformation depends on the direction in which a stress is applied.

Elastic Behavior of Composites:

The idea is that by combining two or more distinct materials one can engineer a new material with the desired combination of properties (e.g., light, strong, corrosion resistant). The idea that a better combination of properties can be achieved is called the principle of combined action.

A type of composite that has been discussed is perlitic steel, which combines hard, brittle cementite with soft, ductile ferrite to get a superior material.

Natural composites: wood (polymer-polymer), bones (polymer-ceramics).

Usual composites have just two phases:



• matrix (continuous) • dispersed phase (particulates, fibers)

Properties of composites depend on

• Properties of phases • Geometry of dispersed phase (particle size, distribution, orientation) • Amount of phase

Classification of composites: three main categories:

• Particle-reinforced (large-particle and dispersion-strengthened) • Fiber-reinforced (continuous (aligned) and short fibers (aligned or random) • Structural (laminates and sandwich panels)

In many applications, like in aircraft parts, there is a need for high strength per unit weight (specific strength). This can be achieved by composites consisting of a low-density (and soft) matrix reinforced with stiff fibers.

The strength depends on the fiber length and its orientation with respect to the stress direction.

The efficiency of load transfer between matrix and fiber depends on the interfacial bond.



Structure and properties of polymers:

Polymers are common in nature, in the form of wood, rubber, cotton, leather, wood, silk, proteins, enzymes, starches, cellulose. Artificial polymers are made mostly from oil. Their use has grown exponentially, especially after WW2. The key factor is the very low production cost and useful properties (e.g., combination of transparency and flexibility, long elongation).

Hydrocarbon Molecules

Most polymers are organic, and formed from hydrocarbon molecules. These molecules can have single, double, or triple carbon bonds. A saturated hydrocarbon is one where all bonds are single, that is, the number of atoms is maximum (or saturated). Among this type are the paraffin compounds, CnH2n+2 (Table 15.1). In contrast, non-saturated hydrocarbons contain some double and triple bonds.

Isomers are molecules that contain the same molecules but in a different arrangement. An example is butane and isobutane.

Polymer molecules are huge, macromolecules that have internal covalent bonds. For most polymers, these molecules form very long chains. The backbone is a string of carbon atoms, often single bonded.

Polymers are composed of basic structures called mer units. A molecule with just one mer is a monomer.

The Chemistry of Polymer Molecules

Examples of polymers are polyvinyl chloride (PVC), poly-tetra-chloro-ethylene (PTFE or Teflon), polypropylene, nylon and polystyrene. Chains are represented straight but in practice they have a three-dimensional, zig-zag structure (Fig. 15.1b).

When all the mers are the same, the molecule is called a homopolymer. When there is more than one type of mer present, the molecule is a copolymer.

Molecular Weight

The mass of a polymer is not fixed, but is distributed around a mean value, since polymer molecules have different lengths. The average molecular weight can be obtained by averaging the masses with the fraction of times they appear (number-average) or with the mass fraction of the molecules (called, improperly, a weight fraction).



The degree of polymerization is the average number of mer units, and is obtained by dividing the average mass of the polymer by the mass of a mer unit.

Polymers of low mass are liquid or gases, those of very high mass (called high-polymers, are solid). Waxes, paraffins and resins have intermediate masses.

Molecular Shape

Polymers are usually not linear; bending and rotations can occur around single C-C bonds (double and triple bonds are very rigid) (Fig. 15.5). Random kings and coils lead to entanglement, like in the spaghetti structure shown in Fig. 15.6.

Molecular Structure

Typical structures are :

• linear (end-to-end, flexible, like PVC, nylon) • branched • cross-linked (due to radiation, vulcanization, etc.) • network (similar to highly cross-linked structures).

Molecular Configurations

The regularity and symmetry of the side-groups can affect strongly the properties of polymers. Side groups are atoms or molecules with free bonds, called free-radicals, like H, O, methyl, etc.

If the radicals are linked in the same order, the configuration is called isostatic

In a stereoisomer in a syndiotactic configuration, the radical groups alternative sides in the chain.

In the atactic configuration, the radical groups are positioned at random.

Copolymers

Copolymers, polymers with at least two different types of mers can differ in the way the mers are arranged. Fig. 15.9 shows different arrangements: random, alternating, block, and graft.

Polymer Crystallinity



Crystallinity in polymers is more complex than in metals (fig. 15.10). Polymer molecules are often partially crystalline (semicrystalline), with crystalline regions dispersed within amorphous material. .

Chain disorder or misalignment, which is common, leads to amorphous material since twisting, kinking and coiling prevent strict ordering required in the crystalline state. Thus, linear polymers with small side groups, which are not too long form crystalline regions easier than branched, network, random copolymers, or polymers with bulky side groups.

Crystalline polymers are denser than amorphous polymers, so the degree of crystallinity can be obtained from the measurement of density.

Polymer Crystals

Different models have been proposed to describe the arrangement of molecules in semicrytalline polymers. In the fringed-micelle model, the crystallites (micelles) are embedded in an amorphous matrix (Fig.15.11). Polymer single crystals grown are shaped in regular platelets (lamellae) (Fig. 15.12). Spherulites (Fig. 15.4) are chain-folded crystallites in an amorphous matrix that grow radially in spherical shape “grains”.



Structure and properties of ceramics:

Ceramics are inorganic and non-metallic materials that are commonly electrical and thermal insulators, brittle and composed of more than one element (e.g., two in Al2O3)

Ceramic Structures

Ceramic bonds are mixed, ionic and covalent, with a proportion that depends on the particular ceramics. The ionic character is given by the difference of electronegativity between the cations (+) and anions (-). Covalent bonds involve sharing of valence electrons. Very ionic crystals usually involve cations which are alkalis or alkaline-earths (first two columns of the periodic table) and oxygen or halogens as anions.

The building criteria for the crystal structure are two:

• maintain neutrality • charge balance dictates chemical formula • achieve closest packing

the condition for minimum energy implies maximum attraction and minimum repulsion. This leads to contact, configurations where anions have the highest number of cation neighbors and viceversa.

Silicate Ceramics

Oxygen and Silicon are the most abundant elements in Earth’s crust. Their combination (silicates) occur in rocks, soils, clays and sand. The bond is weekly ionic, with Si4+ as the cation and O2- as the anion. rSi = 0.04 nm, rO.= 0.14 nm, so rC/rA = 0.286.

The tetrahedron is charged: Si4+ + 4 O2- ⇒ (Si O4)4-. Silicates differ on how the tetrahedra are arranged. In silica, (SiO2), every oxygen atom is shared by adjacent tetrahedra. Silica can be crystalline (e.g., quartz) or amorphous, as in glass.

Soda glasses melt at lower temperature than amorphous SiO2 because the addition of Na2O (soda) breaks the tetrahedral network. A lower melting point makes it easy to form glass to make, for instance, bottles.

Carbon



Carbon is not really a ceramic, but an allotropic form, diamond, may be thought as a type of ceramic. Diamond has very interesting and even unusual properties:

• diamond-cubic structure (like Si, Ge) • covalent C-C bonds • highest hardness of any material known • very high thermal conductivity (unlike ceramics) • transparent in the visible and infrared, with high index of refraction • semiconductor (can be doped to make electronic devices) • metastable (transforms to carbon when heated)

Synthetic diamonds are made by application of high temperatures and pressures or by chemical vapor deposition. Future applications of this latter, cheaper production method include hard coatings for metal tools, ultra-low friction coatings for space applications, and microelectronics.

Graphite has a layered structure with very strong hexagonal bonding within the planar layers (using 3 of the 3 bonding electrons) and weak, van der Waals bonding between layers using the fourth electron. This leads to easy interplanar cleavage and applications as a lubricant and for writing (pencils). Graphite is a good electrical conductor and chemically stable even at high temperatures. Applications include furnaces, rocket nozzles, electrodes in batteries.

A recently (1985) discovered formed of carbon is the C60 molecule, also known as fullerene or bucky-ball (after the architect Buckminster Fuller who designed the geodesic structure that C60 resembles.) Fullerenes and related structures like bucky-onions amd nanotubes are exceptionally strong. Future applications are as a structural material and possibly in microelectronics, due to the unusual properties that result when fullerenes are doped with other atoms.

Imperfections in Ceramics

Imperfections include point defects and impurities. Their formation is strongly affected by the condition of charge neutrality (creation of unbalanced charges requires the expenditure of a large amount of energy.

Non-stoichiometry refers to a change in composition so that the elements in the ceramic are not in the proportion appropriate for the compound (condition known as stoichiometry). To minimize energy, the effect of non-stoichiometry is a redistribution of the atomic charges (Fig. 13.1).



Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is a vacancy- interstitial pair of cations (placing large anions in an interstitial position requires a lot of energy in lattice distortion). A Schottky-defect is the a pair of nearby cation and anion vacancies.

Introduction of impurity atoms in the lattice is likely in conditions where the charge is maintained. This is the case of electronegative impurities that substitute a lattice anions or electropositive substitutional impurities. This is more likely for similar ionic radii since this minimizes the energy required for lattice distortion. Defects will appear if the charge of the impurities is not balanced.

Brittle Fracture of Ceramics

The brittle fracture of ceramics limits applications. It occurs due to the unavoidable presence of microscopic flaws (micro-cracks, internal pores, and atmospheric contaminants) that result during cooling from the melt. The flaws need to crack formation, and crack propagation (perpendicular to the applied stress) is usually transgranular, along cleavage planes. The flaws cannot be closely controlled in manufacturing; this leads to a large variability (scatter) in the fracture strength of ceramic materials.

The compressive strength is typically ten times the tensile strength. This makes ceramics good structural materials under compression (e.g., bricks in houses, stone blocks in the pyramids), but not in conditions of tensile stress, such as under flexure.

Plastic deformation in crystalline ceramics is by slip, which is difficult due to the structure and the strong local (electrostatic) potentials. There is very little plastic deformation before fracture.

Non-crystalline ceramics, like common glass deform by viscous flow (like very high-density liquids). Viscosity decreases strongly with increases temperature.


Atomic Structures, Interatomic Bonding and Structure of Crystalline Solids

Module 2


1. Atomic Structure and Atomic bonding in solids

2. Crystal structures, Crystalline and Non-crystalline materials

3. Miller indices, Anisotropic elasticity and Elastic behavior

of Composites

4. Structure and properties of polymers

5. Structure and properties of ceramics

Contents


Atomic Structure -1Every atom consists of a small nucleus composed of protons and neutrons, which is encircled by moving electrons in their orbitals, specific energy levels.The top most ortibal electrons, valence electrons, affect most material properties that are of interest to engineer. E.g.: chemical properties, nature of bonding, size of atom, optical/magnetic/electrical properties.Electrons and protons are negative and positive charges of the same magnitude being 1.60x10-19 coulombs.Neutrons are electrically neutral.Protons and neutrons have approximately the mass, 1.67x10-27 kg, which is larger than that of an electron, 9.11x10-31 kg.


Atomic number (Z) - is the number of protons per atoms. Atomic mass (A) - is the sum of the masses of protons and neutrons within the nucleus.Atomic mass is measured in atomic mass unit (amu) where 1amu=(1\12) the mass of most common isotope of carbon atom, measured in grams.A ≅ Z+N, where N is number of neutrons.Isotopes - atoms with same atomic number but different atomic masses.A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus a mole of carbon has a mass of 12 grams.

Atomic Structure -2


The number of atoms or molecules in a mole of substance is called the Avogadro’s number, Nay. Nay=1gram/1amu = 6.023x1023.E.g.: Calculating the number of atoms per cm3, n, in a piece of material of density d (g/cm3)n = Nav × d / M, where M is the atomic mass in amu.Thus, for graphite (carbon) with a density d = 1.8 g/cm3 and M =12, n = 6.023 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol) = 9 × 1022 atoms/cm3.Most solid materials will have atomic density in the order of 6x1022, that’s about 39 million atoms per centimeter.Mean distance between atoms is in the range of 0.25 nm. It gives an idea about scale of atomic structures in solids.

Atomic Structure -3


Atomic Bonding In SolidsTwo questions need to be answered: why the atoms are clustered together?, and how they are arranged?

Bonds are two kinds – Primary, and Secondary

Primary bonds – relatively stronger. Exists in almost all solid materials.

E.g.: Ionic, Covalent, and Metallic bonds.

Secondary bonds – relatively weaker bonds. Exists in many substances like water along with primary bonds.

E.g.: Hydrogen, and Vander Waals forces.


Atomic bonding

Primary bonding

Secondary bondingionic covalent metallic

Fluctuatinginduced

Polarinduced permanent

Atomic Bond In Solids


Primary Inter-Atomic Bonds

These bonds invariably involves valence electrons.

Nature of bond depends on electron arrangement in respective atoms.

Atoms tend to acquire stable electron arrangement in their valence orbitals by transferring (ionic), sharing (covalent, and metallic) valence electrons. This leads to formation of bonds.

Bond energies are in order of 1000 kJ/mol.


Ionic BondThis primary bond exists between two atoms when transfer of electron(s) results in one of the atoms to become negative (has an extra electron) and another positive (has lost an electron).

This bond is a direct consequence of strong Coulomb attraction between charged atoms.

Basically ionic bonds are non-directional in nature.

In real solids, ionic bonding is usually exists along with covalent bonding.

E.g.: NaCl. In the molecule, there are more electrons around Cl, forming Cl- and fewer electrons around Na, forming Na+.


Covalent Bond

This bond comes into existence if valence electrons are shared between a pair of atoms, thus acquire stability by saturating the valence configuration.

Covalent bonds are stereo specific i.e. each bond is between a specific pair of atoms, which share a pair of electrons (of opposite magnetic spins).

Typically, covalent bonds are very strong, and directional in nature.

E.g.: H2 molecule, where an electron from each of the atom shared by the other atom, thus producing the covalent bond.


Metallic Bond

This bond comes into existence if valence electrons are shared between number of atoms, i.e. arranged positive nucleuses are surrounded by electron pool.

Shared electrons are not specific to a pair of atoms, in contrast to Covalent bond, i.e. electrons are delocalized.

As shared electrons are delocalized, metallic bonds are non-directional.

Very characteristic properties of metals like high thermal and electrical conductivities are result of presence of delocalized electron pool.


Secondary Inter-Atomic Bonds - 1

These bonds involves atomic or molecular dipoles.

Bonds can exists between induced and permanent dipoles

(polar molecules).

Bond comes into existence because of Columbic attraction

between positive end of one dipole and negative end of

another dipole.

Bond energies are in order of 10 kJ/mol


Secondary Inter-Atomic Bonds - 2

Existence of these depends on three kinds of dipoles –fluctuating dipoles, Polar-molecule dipoles and Permanent dipoles.

Permanent dipole bonds are also called Hydrogen bonds as covalently bonded hydrogen atoms – for example C-H, O-H, F-H – share single electron becomes positively charged proton that is capable of strong attractive force with the negative end of an adjacent molecule.

Hydrogen bonds is responsible for water t exist in liquid state at room temperature.


Crystal StructuresAll solid materials are made of atoms/molecules, which are arranged in specific order in some materials, called crystalline solids. Otherwise non-crystalline or amorphous solids.

Groups of atoms/molecules specifically arranged – crystal.

Lattice is used to represent a three-dimensional periodic array of points coinciding with atom positions.

Unit cell is smallest repeatable entity that can be used to completely represent a crystal structure. It is the building block of crystal structure.


Unit Cell

It is characterized by:

Type of atom and their radii, R

Cell dimensions, a and c (for hexagonal structures)

Number of atoms per unit cell, n

Coordination number (CN)– closest neighbors to an atom

Atomic packing factor, APF

Most common unit cells – Face-centered cubic, Body-centered cubic and Hexagonal.


Common Crystal Structures

0.74126Hexagonal Close Packed

0.744/Ö 2124Face-Centered Cubic

0.684/Ö 382Body-Centered Cubic

0.524/Ö 461Simple Cubic

APFa/RCNnUnit Cell


Schematic Unit Cells


Miller Indices

A system of notation is required to identify particular direction(s) or plane(s) to characterize the arrangement of atoms in a unit cell

Formulas involving Miller indices are very similar to related formulas from analytical geometry – simple to use

Use of reciprocals avoids the complication of infinite intercepts

Specifying dimensions in unit cell terms means that the same label can be applied to any plane with a similar stacking pattern, regardless of the crystal class of the crystal. Plane (111) always steps the same way regardless of crystal system


Miller Indices - Direction

A vector of convenient length is placed parallel to the required direction

The length of the vector projection on each of three axes are measured in terms of unit cell dimensions

These three numbers are made to smallest integer values, known as indices, by multiplying or dividing by a common factor

The three indices are enclosed in square brackets, [uvw].

A family of directions is represented by <uvw>


Miller Indices - Plane

Determine the intercepts of the plane along the crystallographic axes, in terms of unit cell dimensions. If plane is passing through origin, there is a need to construct a plane parallel to original plane

Take the reciprocals of these intercept numbers

Clear fractions

Reduce to set of smallest integers

The three indices are enclosed in parenthesis, (hkl).

A family of planes is represented by hkl


Miller Indices - Examples


Miller Indices – Useful ConventionsIf a plane is parallel to an axis, its intercept is at infinity and its Miller index will be zeroNever alter negative numbers. This implies symmetry that the crystal may not have! Use bar over the number to represent negative numbers.A plane or direction of family is not necessarily parallel to other planes or directions in the same familyThe smaller the Miller index, more nearly parallel the plane to that axis, and vice versa Multiplying or dividing a Miller index by constant has no effect on the orientation of the planeWhen the integers used in the Miller indices contain more than one digit, the indices must be separated by commas. E.g.: (3,10,13)


Useful Conventions For Cubic Crystals[uvw] is normal to (hkl) if u = h, v = k, and w = l. E.g.: (111) [111][uvw] is parallel to (hkl) if hu + kv + lw = 0Two planes (h1k1l1) and (h2k2l2) are normal if h1h2 + k1k2+ l1l2=0Two directions (u1v1w1) and (u2v2w2) are normal if u1u2 + v1v2 + w1w2=0Inter-planar distance between family of planes hkl is given by:Angle between two planes is given by:

222lkh

ad hkl++

=

22

22

22

21

21

21

212121coslkhlkh

llkkhh

++++

++=θ


Miller-Bravis IndicesMiller indices can describe all possible planes/directions in any crystal. However, Miller-Bravis indices are used in hexagonal systems as they can reveal hexagonal symmetry more clearlyIndices are based on four axes – three are coplanar on basal plane at 120˚ apart, fourth axis is perpendicular to basal planeBoth for planes/directions, extra index is given by

t = -(u+v), i = -(h+k)where plane is represented as [uvtw], and a direction is represented by (hkil)E.g.: Basal plane – (0001), Prismatic plane – (1010)


Polymers - DefinitionPolymers are made of basic units called mersThese are usually Hydrocarbons – where major constituent atoms are Hydrogen and CarbonWhen structure consists of only one mer, it is monomer. If it contains more than one mer, it is called polymerIsomers are molecules those contain same number of similar mers but arrangement will be differentE.g.: Butene and IsobuteneWhen a polumer has ONE kind of mers in its structure, it is called homopolymerPolymer made with more than one kind of mers is called copolymer


Polymer Structures

Linear, where mer units are joined together end to end in single chains. E.g.: PVC, nylon.

Branched, where side-branch chains are connected to main ones. Branching of polymers lowers polymer density because of lower packing efficiency

Cross-linked, where chains are joined one to another at various positions by covalent bonds. This cross-linking is usually achieved at elevated temperatures by additive atoms. E.g.: vulcanization of rubber

Network, trifunctional mer units with 3-D networks comes under this category. E.g.: epoxies, phenol-formaldehyde.


Polymer Structures

Schematic presentation of polymer structures. Individual mers are represented by solid circles.


Thermo-Sets – Thermo-PlastsPolymers mechanical response at elevated temperatures strongly depends their chain configurationBased on this response polymers are grouped in to two -thermo-sets and thermo-plastsThermo-sets: become permanently hard when heated, and do not soften during next heat cycle. During first heating covalent bonds forms thus extensive cross-linking takes place. Stronger and harder than thermo-plasts.E.g.: Vulcanized rubber, epoxies, some polyester resinsThermo-plasts: softens at high temperatures, and becomes hard at ambient temperatures. The process is reversible. Usually made of linear and branched structures.E.g.: Polystyrene, Acrylics, Cellulosics, Vinyls


Polymer Crystallinity

Crystallinity in polymers is more complex than in metals

Polymer crystallinity range from almost crystalline to amorphous in nature

It depends on cooling path and on chain configuration

Crystalline polymers are more denser than amorphous polymers

Many semicrystalline polymers form spherulites. Each spherulite consists of collection of ribbon like chain folded lamellar crystallites.

E.g.: PVC (Poly Vinyl Chloride)


Polymer Properties


Ceramics

Ceramics are inorganic and non-metallic materials

Atomic bonds in ceramics are mixed – covalent + ionic

Proportion of bonds is specific for a ceramic

Ionic bonds exists between alkalis/alkaline-earth metals and

oxygen/halogens.

Mostly oxides, carbides, nitrides of metals are ceramics

E.g.: Sand, Glass, Bricks, Marbles


Ceramic StructuresBuilding criteria for ceramic structures:

- maintain neutrality- closest packing

Packing efficiency can be characterized by coordination number which depends on cation-anion radius ratio (rc/ra)

1286432Coordination number

> 1.00

0

0.732 –

1.000

0.414 –0.732

0.225 –0.414

0.155 –0.225

< 0.15

5

Cation-anion radius ratio

(rc/ra)


Ion Arrangement – Coordination Numbers


Ceramic Crystal StructuresAX-type: most common in ceramics. They assume different structures of varying coordination number (CN).

Rock salt structure – CN=6. E.g.: NaCl, FeO

Cesium Chloride structure – CN=8 E.g.: CsCl

Zinc Blende structure – CN=4 E.g.: ZnS, SiC

AmXp-type: number of anions and cations are different (m≠p). One unit cell is made of eight cubes.

E.g.: CaF2, ThO2

AmBnXp-type: when ceramic contains more then one kind of cations. Also called perovskite crystal structure.

E.g.: BaTiO3


Silicates - 1

Most common ceramic in nature – Silicates, as constituent elements – silicon and oxygen – are most abundant in earth’s crust.

Bond between Si4+ and O2- is weak ionic and very strong covalent in nature. Thus, basic unit of silicates is SiO4

4-

tetrahedron.


Silicates - 2

In Silica (SiO2), every oxygen atom the corner of the tetrahedron is shared by the adjacent tetrahedron.Silica can be both crystalline (quartz) and amorphous (glass)Crystalline forms of silica are complicated, and comparatively open…thus low in density compared with amorphous glassesAddition of network modifiers (Na2O) and intermediates (Al2O3, TiO2)lowers the melting point…thus it is easy to form. E.g.: Bottles.In complicated silicates, corner oxygen is shared by other tetrahedra….thus consists SiO4

4-, Si2O76-, Si3O9

6- groupsClays comprises 2-D sheet layered structures made of Si2O5

2-


CarbonCarbon is not a ceramic, but its allotropic form - Diamond isDiamond:C-C covalent bonds, highest known hardness, Semiconductor, high thermal conductivity, meta-stableGraphite - another allotropic form of carbon layered structure - hexagonal bonding within planar layers, good electrical conductor, solid lubricantAnother allotropic form - C60 - also called Fullerene / Bucky ball. Structure resembles hallow ball made of 20 hexagons and 12 pentagons where no two pentagons share a common edge.Fullerenes and related nanotubes are very strong, ductile -could be one of the important future engineering materials


Imperfections In Ceramics

Imperfections in ceramics – point defects, and impurities. Their formation is strongly affected by charge neutrality

Frenkel-defect is a vacancy-interstitial pair of cations

Schottky-defect is a pair of nearby cation and anion vacancies

Impurities:

Introduction of impurity atoms in the lattice is likely in conditions where the charge is maintained.

E.g.:electronegative impurities that substitute lattice anions or electropositive substitutional impurities


Mechanical Response Of Ceramics 1Engineering applications of ceramics are limited because of

presence of microscopic flaws – generated during cooling stage of processing.However, as ceramics are high with hardness, ceramics are good structural materials under compressive loads.Plastic deformation of crystalline ceramics is limited by strong inter-atomic forces. Little plastic strain is accomplished by process of slip.Non-crystalline ceramics deform by viscous flow.Characteristic parameter of viscous flow – viscosity. Viscosity decreases with increasing temperature. However, at room temperature, viscosity of non-crystalline ceramics is very high.


Mechanical Response Of Ceramics - 2Hardness – one best mechanical property of ceramics which is utilized in many application such as abrasives, grinding mediaHardest materials known are ceramicsCeramics having Knoop hardness about 1000 or greater are used for their abrasive characteristicsCreep – Ceramics experience creep deformation as a result of exposure to stresses at elevated temperatures.Modulus of elasticity, E, as a function of volume fraction of porosity, P: E = E0 (1-1.9 P + 0.9 P2)Porosity is deleterious to the flexural strength for two reasons:- reduces the cross-sectional area across where load is applied- act as stress concentrations

Material Science/Imperfections in Solids Lecture Notes

Satish Kailash Vasu/IISc, Bangalore M3/L1/V1/dec2004/1

Chapter 3. Imperfections in Solids 3.1 Point Defects

Vacancies and Self-Interstitials

A vacancy is a lattice position that is vacant because the atom is missing. It is created when the solid is formed. There are other ways of making a vacancy, but they also occur naturally as a result of thermal vibrations.

An interstitial is an atom that occupies a place outside the normal lattice position. It may be the same type of atom as the others (self interstitial) or an impurity atom.

In the case of vacancies and interstitials, there is a change in the coordination of atoms around the defect. This means that the forces are not balanced in the same way as for other atoms in the solid, which results in lattice distortion around the defect.

The number of vacancies formed by thermal agitation follows the law:

NV = NA × exp(-QV/kT)

where NA is the total number of atoms in the solid, QV is the energy required to form a vacancy, k is Boltzmann constant, and T the temperature in Kelvin (note, not in oC or oF).

When QV is given in joules, k = 1.38 × 10-23 J/atom-K. When using eV as the unit of energy, k = 8.62 × 10-5 eV/atom-K.

Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical vacancy formation energies. For instance, QV(Cu) = 0.9 eV/atom. This means that NV/NA at room temperature is exp(-36) = 2.3 × 10-16, an insignificant number. Thus, a high temperature is needed to have a high thermal concentration of vacancies. Even so, NV/NA is typically only about 0.0001 at the melting point.

3.2 Theoretical yield point:

Theoretical yield is the maximum quantity of a product that could be formed in a chemical reaction if all the limiting reactant reacted to form products (distinguished from actual yield).

3.3 Dislocations—Linear Defects :

Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation line) in the solid. They occur in high density and are very important in mechanical properties of material. They are characterized by the Burgers vector, found by doing a loop around the dislocation line and noticing the extra interatomic spacing needed to close the loop. The Burgers vector in metals points in a close packed direction.

Material Science/Imperfections in Solids Lecture Notes


Edge dislocations occur when an extra plane is inserted. The dislocation line is at the end of the plane. In an edge dislocation, the Burgers vector is perpendicular to the dislocation line.

Screw dislocations result when displacing planes relative to each other through shear. In this case, the Burgers vector is parallel to the dislocation line.

3.4 Interfacial Defects :

The environment of an atom at a surface differs from that of an atom in the bulk, in that the number of neighbors (coordination) decreases. This introduces unbalanced forces which result in relaxation (the lattice spacing is decreased) or reconstruction (the crystal structure changes).

The density of atoms in the region including the grain boundary is smaller than the bulk value, since void space occurs in the interface.

Surfaces and interfaces are very reactive and it is usual that impurities segregate there. Since energy is required to form a surface, grains tend to grow in size at the expense of smaller grains to minimize energy. This occurs by diffusion, which is accelerated at high temperatures.

3.5 Bulk or Volume Defects :

Other defects exist in all solid materials that are much larger than those heretofore discussed. A typical volume defect is porosity, often introduced in the solid during processing. A common example is snow, which is highly porous ice.

3.6 Atomic Vibrations :

Atomic vibrations occur, even at zero temperature (a quantum mechanical effect) and increase in amplitude with temperature. Vibrations displace transiently atoms from their regular lattice site, which destroys the perfect periodicity .In a sense, these atomic vibrations may be thought of as imperfections or defects. At room temperature, a typical vibrational frequency of atoms is of the order of 10^13 vibrations per second, whereas the amplitude is a few thousandths of a nanometer.


Imperfections in Solids

Module-3


1. Theoretical yield strength, Point defects and Line defects

or Dislocations

2. Interfacial defects, Bulk or Volume defects and Atomic

vibrations

Contents


Theoretical Yield Strength - 1Ideal solids are made of atoms arranged in orderly way.


Theoretical Yield Strength – 2Using a sin function to represent the variation in shear stress

bx

mΠ

=2sinττ b

xm

Π≈

2ττa

GxG == γτ

abG

m Π=

2τ

Π=

2G

mτ

(Hooke’s law)

If b≈a

G ≈ 20-150 GPa

Shear strength ≈ 3-30 GPa

(ideal)

Real strength values ≈ 0.5-10 MPa


Theoretical Yield Strength - 3Theoretical strength of solids shall possess an ideal value in the range of 3-30 GPa.

Real values observed in practice are 0.5-10 MPa.

The assumption of perfectly arranged atoms in a solid may not valid…..i.e. atomic order must have been disturbed.

Disordered atomic region is called defect or imperfection.

Based on geometry, defects are: Point defects (zero-D), Line defects (1-D) or Dislocations, Interfacial defects (2-D) and Bulk or Volume defects (3-D).


Point Defects - 1Point defects are of zero-dimensional i.e. atomic disorder is restricted to point-like regions.Thermodynamically stable compared with other kind of defects.


Point Defects - 2Fraction of vacancy sites can be given as follows:

In ionic crystals, defects can form on the condition of charge neutrality. Two possibilities are:

kTQ

eNn −=


Line DefectsLine defects or Dislocations are abrupt change in atomic order along a line.They occur if an incomplete plane inserted between perfect planes of atoms or when vacancies are aligned in a line.A dislocation is the defect responsible for the phenomenon of slip, by which most metals deform plastically.Dislocations occur in high densities (108-1010 m-2 ), and are intimately connected to almost all mechanical properties which are in fact structure-sensitive.Dislocation form during plastic deformation, solidification or due to thermal stresses arising from rapid cooling.


Line Defects – Burger’s VectorA dislocation in characterized by Burger’s vector, b.It is unique to a dislocation, and usually have the direction of close packed lattice direction. It is also the slip direction of a dislocation.It represents the magnitude and direction of distortion associated with that particular dislocation.Two limiting cases of dislocations, edge and screw, are characterized by Burger’s vector perpendicular to the dislocation line (t) and Burger’s vector parallel to the dislocation line respectively. Ordinary dislocation is of mixed character of edge and screw type.


Line Defects – Edge DislocationIt is also called as Taylor-Orowan dislocation.It will have regions of compressive and tensile stresses on either side of the plane containing dislocation.


Line Defects – Screw DislocationIt is also called as Burger’s dislocation.It will have regions of shear stress around the dislocation lineFor positive screw dislocation, dislocation line direction is parallel to Burger’s vector, and vice versa.

A negative dislocation


Line Defects – Dislocation MotionDislocations move under applied stresses, and thus causes plastic deformation in solids.Dislocations can move in three ways – glide/slip, cross-slip and climb – depending on their character. Slip is conservative in nature, while the climb is non-conservative, and is diffusion-controlled.Any dislocation can slip, but in the direction of its burger’s vector.Edge dislocation moves by slip and climb.Screw dislocation moves by slip / cross-slip. Possibility for cross-slip arises as screw dislocation does not have a preferred slip plane as edge dislocation have.


Line Defect – Dislocation CharacteristicsA dislocation line cannot end at abruptly inside a crystal. It can close-on itself as a loop, either end at a node or surface.Burger’s vector for a dislocation line is invariant i.e. it will have same magnitude and direction all along the dislocation line.Energy associated with a dislocation because of presence of stresses is proportional to square of Burger’s vector length. Thus dislocations, at least of same nature, tend to stay away from each other.Dislocations are, thus, two types – full and partial dislocations. For full dislocation, Burger’s vector is integral multiple of inter-atomic distance while for partial dislocation, it is fraction of lattice translation.


Interfacial Defects - 1An interfacial defect is a 2-D imperfection in crystalline

solids, and have different crystallographic orientations on

either side of it.

Region of distortion is about few atomic distances.

They usually arise from clustering of line defects into a

plane.

These imperfections are not thermodynamically stable,

but meta-stable in nature.

E.g.: External surface, Grain boundaries, Stacking faults,

Twin boundaries, Phase boundaries.


Interfacial Defects - 2

Grain boundaries


Bulk or Volume DefectsVolume defects are three-dimensional in nature.These defects are introduced, usually, during processing and fabrication operations like casting, forming etc.E.g.: Pores, Cracks, Foreign particlesThese defects act like stress raisers, thus deleterious to mechanical properties of parent solids.In some instances, foreign particles are added to strengthen the solid – dispersion hardening. Particles added are hindrances to movement of dislocations which have to cut through or bypass the particles thus increasing the strength.


Atomic VibrationsAtoms are orderly arranged, but they are expected to vibrate about their positions where the amplitude of vibration increases with the temperature.After reaching certain temperature, vibrations are vigorous enough to rupture the inter-atomic forces casing melting of solids.Average amplitude of vibration at room temperature is about 10-12m i.e. thousandth of a nanometer.Frequency of vibrations is the range of 1013 Hz.Temperature of a solid body is actually a measure of vibrational activity of atoms and/or molecules.

Material Science/Mechanical Properties of Metals Lecture Notes


Chapter 4. Mechanical Properties of Metals 4.1 Elastic deformation:

When the stress is removed, the material returns to the dimension it had before the load was applied. Valid for small strains (except the case of rubbers).

Deformation is reversible, non permanent

4.2 Plastic deformation:

When the stress is removed, the material does not return to its previous dimension but there is a permanent, irreversible deformation.

In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's law:

σ = E ε

That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of elasticity. In some cases, the relationship is not linear so that E can be defined alternatively as the local slope:

E = dσ/dε

Shear stresses produce strains according to:

τ = G γ

where G is the shear modulus.Elastic moduli measure the stiffness of the material. They are related to the second derivative of the interatomic potential, or the first derivative of the force vs. internuclear distance (Fig. 6.6). By examining these curves we can tell which material has a higher modulus. Due to thermal vibrations the elastic modulus decreases with temperature. E is large for ceramics (stronger ionic bond) and small for polymers (weak covalent bond). Since the interatomic distances depend on direction in the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly oriented policrystals, E is isotropic.

4.4 Yielding under multiaxial stress-strain curves

4.5 Yield criteria and macroscopic aspects of plastic deformation

Gross plastic deformation of a polycrystalline specimen corresponds to the comparable distortion of the individual grains by means of slip. During deformation, mechanical integrity and coherency are maintained along the grain boundaries; that is, the grain boundaries is constrained, to some degree, in the shape it may assume by its neighboring



grains. Before deformation the grains are equiaxed, or have approximately the same dimension in all directions. For this particular deformation, the grains become elongated along the directions. For this particular deformation, the grains become elongated along the direction in which the specimen was extended.

4.6 Property variability and design factors

To take into account variability of properties, designers use, instead of an average value of, say, the tensile strength, the probability that the yield strength is above the minimum value tolerable. This leads to the use of a safety factor N > 1. Thus, a working value for the tensile strength would be σW = σTS / N.

Utilization of design stress is usually preferred since it is based on the anticipated maximum applied stress instead of the yield strength of the material. The choice of an appropriate value of N is necessary. If N is too large, then component over design will result; that is , either too much material or an alloy having a higher than necessary strength will be used. Values normally range between 1.2 and 4.0. Selection of N will depend on a number of factors, including economics, previous experience, the accuracy with which mechanical forces and material properties may be determined and most important, the consequences of failure in terms of loss of life or property damage.



4.3 Interpretation of tensile stress-strain curves:

Tensile Properties

Yield point. If the stress is too large, the strain deviates from being proportional to the stress. The point at which this happens is the yield point because there the material yields, deforming permanently (plastically).

Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point is called yield stress, and is an important measure of the mechanical properties of materials. In practice, the yield stress is chosen as that causing a permanent strain of 0.002

The yield stress measures the resistance to plastic deformation.

The reason for plastic deformation, in normal materials, is not that the atomic bond is stretched beyond repair, but the motion of dislocations, which involves breaking and reforming bonds.

Plastic deformation is caused by the motion of dislocations.

Tensile strength. When stress continues in the plastic regime, the stress-strain passes through a maximum, called the tensile strength (σTS) , and then falls as the material starts to develop a neck and it finally breaks at the fracture point .

For structural applications, the yield stress is usually a more important property than the tensile strength, since once the it is passed, the structure has deformed beyond acceptable limits.

Ductility. The ability to deform before braking. It is the opposite of brittleness. Ductility can be given either as percent maximum elongation εmax or maximum area reduction.

%EL = εmax x 100 %

%AR = (A0 - Af)/A0

These are measured after fracture (repositioning the two pieces back together).

Resilience. Capacity to absorb energy elastically. The energy per unit volume is the

area under the strain-stress curve in the elastic region.

Toughness. Ability to absorb energy up to fracture. The energy per unit volume is the total area under the strain-stress curve. It is measured by an impact test .



True Stress and Strain

When one applies a constant tensile force the material will break after reaching the tensile strength. The material starts necking (the transverse area decreases) but the stress cannot increase beyond σTS. The ratio of the force to the initial area, what we normally do, is called the engineering stress. If the ratio is to the actual area (that changes with stress) one obtains the true stress.



4.4 Yielding under multiaxial stress-strain curves

4.5 Yield criteria and macroscopic aspects of plastic deformation

Gross plastic deformation of a polycrystalline specimen corresponds to the comparable distortion of the individual grains by means of slip. During deformation, mechanical integrity and coherency are maintained along the grain boundaries; that is, the grain boundaries is constrained, to some degree, in the shape it may assume by its neighboring grains. Before deformation the grains are equiaxed, or have approximately the same dimension in all directions. For this particular deformation, the grains become elongated along the directions. For this particular deformation, the grains become elongated along the direction in which the specimen was extended.

4.6 Property variability and design factors

To take into account variability of properties, designers use, instead of an average value of, say, the tensile strength, the probability that the yield strength is above the minimum value tolerable. This leads to the use of a safety factor N > 1. Thus, a working value for the tensile strength would be σW = σTS / N.

Utilization of design stress is usually preferred since it is based on the anticipated maximum applied stress instead of the yield strength of the material. The choice of an appropriate value of N is necessary. If N is too large, then component over design will result; that is , either too much material or an alloy having a higher than necessary strength will be used. Values normally range between 1.2 and 4.0. Selection of N will depend on a number of factors, including economics, previous experience, the accuracy with which mechanical forces and material properties may be determined and most important, the consequences of failure in terms of loss of life or property damage.

Mechanical Properties Of Metals

Module - 4


1. Elastic deformation and Plastic deformation

2. Interpretation of tensile stress-strain curves

3. Yielding under multi-axial stress, Yield criteria,

Macroscopic aspects of plastic deformation and Property

variability & Design considerations

Contents


Mechanical Loads - Deformation

ObjectExternal load

translation rotation deformation

distortion – change in shape

dilatation – change in size


Temporary / recoverable Permanent

time independent – elastic

time dependent – anelastic (under load),

elastic aftereffect (after removal of load)

Deformation – Function Of Time?

time independent – plastic

time dependent –creep (under load),

combination of recoverable and permanent, but time dependent – visco-elastic


Engineering Stress – Engineering Strain

Load applied acts over an area.Parameter that characterizes the load effect is given as load divided by original area over which the load acts. It is called conventional stress or engineering stress or simply stress. It is denoted by s.Corresponding change in length of the object is characterized using parameter – given as per cent change in the length – known as strain. It is denoted by e.

As object changes its dimensions under applied load, engineering stress and strain are not be the true representatives.

0

0

0

,L

LLe

APs

−==


True Stress – True Strain

True or Natural stress and strain are defined to give true picture of the instantaneous conditions.

True strain:

True stress:

∑ +−

+−

+−

= ...2

23

1

12

0

01

LLL

LLL

LLL

ε0

ln0

LL

LdLL

L

== ∫ε

)1(0

0

+=== esAA

AP

APσ


Different Loads – Strains


Elastic Deformation - 1A material under goes elastic deformation first followed by plastic deformation. The transition is not sharp in many instances.For most of the engineering materials, complete elastic deformation is characterized by strain proportional to stress. Proportionality constant is called elastic modulus or Young’s modulus, E.

Non-linear stress-strain relation is applicable for materials. E.g.: rubber.

εσ ∝ εσ E=


For materials without linear stress-strain portion, either tangent or secant modulus is used in design calculations.

Elastic Deformation - 2

The tangent modulus is taken as the slope of stress-strain curve at some specified level.

Secant module represents the slope of secant drawn from the origin to some given point of the σ-ε curve.


Elastic Deformation - 3Theoretical basis for elastic deformation – reversible displacements of atoms from their equilibrium positions – stretching of atomic bonds.Elastic moduli measures stiffness of material. It can also be a measure of resistance to separation of adjacent atoms.Elastic modulus = fn (inter-atomic forces)

= fn (inter-atomic distance)= fn (crystal structure, orientation)

=> For single crystal elastic moduli are not isotropic.For a polycrystalline material, it is considered as isotropic.Elastic moduli slightly changes with temperature (decreases with increase in temperature).


Elastic Deformation - 4Linear strain is always accompanied by lateral strain, to maintain volume constant.The ratio of lateral to linear strain is called Poisson’s ratio (ν). Shear stresses and strains are related as τ = Gγ, where G is shear modulus or elastic modulus in shear.Bulk modulus or volumetric modulus of elasticity is defined as ratio between mean stress to volumetric strain. K = σm/∆All moduli are related through Poisson’s ratio.

)1(2 ν+=

EG)21(3 ν

σ−

=∆

=EK m


Plastic Deformation - 1Following the elastic deformation, material undergoes plastic deformation.Also characterized by relation between stress and strain at constant strain rate and temperature.Microscopically…it involves breaking atomic bonds, moving atoms, then restoration of bonds.Stress-Strain relation here is complex because of atomic plane movement, dislocation movement, and the obstacles they encounter.Crystalline solids deform by processes – slip and twinning in particular directions.Amorphous solids deform by viscous flow mechanism without any directionality.


Plastic Deformation - 2Because of the complexity involved, theory of plasticity neglects the following effects:- Anelastic strain, which is time dependent recoverable strain.- Hysteresis behavior resulting from loading and un-loading of material.- Bauschinger effect – dependence of yield stress on loading path and direction.Equations relating stress and strain are called constitutive equations.A true stress-strain curve is called flow curve as it gives the stress required to cause the material to flow plastically to certain strain.


Plastic Deformation - 3Because of the complexity involved, there have been many stress-strain relations proposed.

),,,( turemicrostrucTfn εεσ &=

nKεσ =

mKεσ &=

nK )( 0 εεσ +=

no Kεσσ +=

Strain hardening exponent, n = 0.1-0.5

Strain-rate sensitivity, m = 0.4-0.9

Yield strength – σ0

Strain from previous work – ε0


Tensile Stress-Strain Curve - 1

A – Starting point E– Tensile strengthE’ – Corresponding to E on flow curveF – Fracture point I – Fracture strain


Tensile Stress-Strain Curve - 2

A – Starting point B – Proportional limit C – Elastic limit D – Yield limitG – 0.2% offset strain H – Yield strain


Tensile Stress-Strain Curve - 3Apart from different strains and strength points, two other important parameters can be deduced from the curve are –resilience and toughness.Resilience (Ur) – ability to absorb energy under elastic deformationToughness (Ut) – ability to absorb energy under loading involving plastic deformation. Represents combination of both strength and ductility.

Es

Es

sesU r 221

21 2

00000 ===

fu

fut ess

esU2

0 +≈≈ fut esU32

≈

area ADH

area AEFI (for brittle materials)


Yielding Under Multi-Axial StressWith on-set of necking, uni-axial stress condition turns into tri-axial stress as geometry changes tales place. Thus flow curve need to be corrected from a point corresponding to tensile strength. Correction has been proposed by Bridgman.

[ ])2/1ln()/21()(

RaaRavgx

++=

σσ

where

(σx)avg measured stress in the axial direction,

a – smallest radius in the neck region,

R – radius of the curvature of neck


Yield Criteria - 1Von Mises or Distortion energy criterion:yielding occurs once second invariant of stress deviator (J2) reaches a critical value. In other terms, yield starts once the distortion energy reaches a critical value.

22 kJ = [ ]2

132

322

212 )()()(61 σσσσσσ −+−+−=J

Under uni-axial tension, σ1 = σ0, and σ2= σ3= 0

[ ] 212

132

322

210

022

020

)()()(2

1

3)(61

σσσσσσσ

σσσ

−+−+−=⇒

=⇒=+ kk

00 577.03

1 σσ ==k where k – yield stress under shear


Yield Criteria - 2Tresca or Maximum shear stress criterionyielding occurs once the maximum shear stress of the stress system equals shear stress under uni-axial stress.

231

maxσσ

τ−

=

Under uni-axial tension, σ1 = σ0, and σ2= σ3= 0

0310

031

max 22σσσ

στ

σστ =−⇒==

−=

031

21

2σ

σσ=

−=k

Under pure shear stress conditions (σ1 =- σ3 = k, σ2 = 0)


Macroscopic Aspects – Plastic Deformation - 1

As a result of plastic deformation (Dislocation generation,movement and (re-)arrangement ), following observations can be made at macroscopic level:dimensional changeschange in grain shapeformation of cell structure in a grain


Macroscopic Aspects – Plastic Deformation- 2


n

xx

n

ii∑

== 1

21

1

2

1

)(

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−=∑=

n

xxs

n

ii

Property VariabilityScatter in measured properties of engineering materials is inevitable because of number of factors such as:test methodspecimen fabrication procedureoperator biasapparatus calibration, etc.

Average value of x over nsamples.

Property variability measure –Standard deviation

Scatter limits:x - s, +sx


Design Consideration - 1To account for property variability and unexpected failure, designers need to consider tailored property values. Parameters for tailoring: safety factor (N) anddesign factor (N’). Both parameters take values greater than unity only.E.g.: Yield strength

σw = σy / N σd = N’σc

where σw – working stress

σy – yield strength

σd – design stress

σc – calculated stress


Design Consideration - 2Values for N ranges around: 1.2 to 4.0.Higher the value of N, lesser will the design efficiency i.e. either too much material or a material having a higher than necessary strength will be used.Selection of N will depend on a number of factors: Economics.Previous experienceThe accuracy with which mechanical forcesMaterial propertiesThe consequences of failure in terms of loss of life or property damage.

Material Science/Diffusion Lecture Notes


Chapter 5. Diffusion

5.1 Diffusion Mechanisms

Atom diffusion can occur by the motion of vacancies (vacancy diffusion) or impurities (impurity diffusion). The energy barrier is that due to nearby atoms which need to move to let the atoms go by. This is more easily achieved when the atoms vibrate strongly, that is, at high temperatures.

There is a difference between diffusion and net diffusion. In a homogeneous material, atoms also diffuse but this motion is hard to detect. This is because atoms move randomly and there will be an equal number of atoms moving in one direction than in another. In inhomogeneous materials, the effect of diffusion is readily seen by a change in concentration with time. In this case there is a net diffusion. Net diffusion occurs because, although all atoms are moving randomly, there are more atoms moving in regions where their concentration is higher.

5.2 Steady-State Diffusion

The flux of diffusing atoms, J, is expressed either in number of atoms per unit area and per unit time (e.g., atoms/m2-second) or in terms of mass flux (e.g., kg/m2-second).

Steady state diffusion means that J does not depend on time. In this case, Fick’s first law holds that the flux along direction x is:

J = – D dC/dx

Where dC/dx is the gradient of the concentration C, and D is the diffusion constant. The concentration gradient is often called the driving force in diffusion (but it is not a force in the mechanistic sense). The minus sign in the equation means that diffusion is down the concentration gradient.

5.3 Nonsteady-State Diffusion

This is the case when the diffusion flux depends on time, which means that a type of atoms accumulates in a region or that it is depleted from a region (which may cause them to accumulate in another region).

Material Science/Diffusion Lecture Notes


5.4 Factors that influence diffusion

As stated above, there is a barrier to diffusion created by neighboring atoms that need to move to let the diffusing atom pass. Thus, atomic vibrations created by temperature assist diffusion. Also, smaller atoms diffuse more readily than big ones, and diffusion is faster in open lattices or in open directions. Similar to the case of vacancy formation, the effect of temperature in diffusion is given by a Boltzmann factor: D = D0 × exp(–Qd/kT).

5.5 Non-equilibrium transformation and microstructure:

Non-equilibrium solidification

Conditions of equilibrium solidification and the development of microstructures are realized only for extremely slow cooling rates. The reason for that is that with changes in temperature, there must be readjustments in the compositions of liquids and solid phases in accordance with the phase diagram. These readjustments are accomplished by diffusional processes- that is, diffusion in both solid and liquid phases and also across the solid-liquid interface.

Non-equilibrium cooling

During cooling metastable equilibrium have been continuously maintained, that is sufficient time has been allowed to each new temperature for any necessary adjustment in phase compositions and relative amounts as predicted from iron-iron carbide phase diagram. In most situations these cooling rates are impractically slow and really unnecessary; in fact, on many occasions non-equilibrium conditions are desirable. Two non equilibrium effects of practical importance are (1) the occurrence of phase changes or transformations at temperatures other than those predicted by phase boundary lines on the phase diagram, and (2) the existence at room temperature of non-equilibrium phases that do not appear on the phase diagram.

Diffusion

Module 5


1. Diffusion mechanisms and steady-state & non-steady-state

diffusion

2. Factors that influence diffusion and non-equilibrium

transformation & microstructure

Contents


Diffusion Phenomenon

Definition – Diffusion is the process of mass flow in which atoms change their positions relative to neighbors in a given phase under the influence of thermal and a gradient.The gradient can be a compositional gradient, an electric or magnetic gradient, or stress gradient.Many reactions in solids and liquids are diffusion dependent.Diffusion is very important in many industrial and domestic applications.E.g.: Carburizing the steel, annealing homogenization after solidification, coffee mixing, etc.


Diffusion Mechanisms - 1From an atomic perceptive, diffusion is a step wise migration of atoms from one lattice position to another.Migration of atoms in metals/alloys can occur in many ways, and thus corresponding diffusion mechanism is defined.


Diffusion Mechanisms - 2Most energetically favorable diffusion mechanism is vacancy mechanism. Other important mechanism is interstitial mechanism by which hydrogen/nitrogen/oxygen diffuse into many metals.In ionic crystal, Schottky and Frankel defects assist the diffusion process.When Frenkel defects dominate in an ionic crystal, the cation interstitial of the Frenkel defect carries the diffusion flux. If Schottky defects dominate, the cation vacancy carries the diffusion flux.In thermal equilibrium, in addition to above defects, ionic crystal may have defects generated by impurities and by deviation from stochiometry.


Diffusion Mechanisms - 3

Diffusion that occurs over a region is volume diffusion.Diffusion can occur with aid of linear/surface defects, which are termed as short-circuit paths. These enhances the diffusivity.However, diffusion by short-circuit paths (E.g.:dislocaions, grain boundaries) is small because the effective cross-sectional area over which these are operative is small.Diffusion can occur even in pure metals that is not noticeable. Diffusion that occurs in alloys which is noticeable called net diffusion as there occurs a noticeable concentration gradient.


Diffusion – Time Function? - 1

Steady-state and Non-steady-state diffusion processes are distinguished by the parameter – diffusion flux, J.Flux is defined as number of atoms crossing a unit area perpendicular to a given direction per unit time.Thus flux has units of atoms/m2.sec or moles/m2.sec.If the flux is independent of time, then the diffusion process is called steady-state diffusion. On the other hand, for non-steady-state diffusion process, flux is dependent on time.


Diffusion – Time Function? - 2


Steady-State DiffusionSteady-state diffusion processes is characterized by Fick’s first law, which states that diffusion flux is proportional to concentration gradient.The proportionality constant, D, is called diffusion coefficient or diffusivity. It has units as m2/sec.For one-dimensional case, it can be written as

where D is the diffusion constant, dc/dx is the gradient of the concentration c, dn/dt is the number atoms crossing per unit time a cross-sectional plane of area A.E.g.: Hydrogen gas purification using palladium metal sheet.

dtdn

AdxdcDJ x

1=−= ),( txfJ x ≠


Non-Steady-State Diffusion 1 Most interesting industrial applications are non-steady-state diffusion in nature.Non-steady-state diffusion is characterized by Fick’s second law, which can be expressed as

where dc/dt is the time rate of change of concentration at a particular position, x.A meaningful solution can be obtained for the above second-order partial equation if proper boundary conditions can be defined.

⎟⎠⎞

⎜⎝⎛=−=

dxdcD

dxd

dxdJ

dtdc

2

2

dxcdD

dtdc

=


Non-Steady-State Diffusion 2One common set of boundary conditions and the solution is:For t = 0, C = C0 at For t > 0, C = Cs at x=0

C = C0 at The solution is

where Cx represents the concentration at depth x after time t.The term erf stands for Gaussian error function, whose values can be obtained from standard mathematical tables.

E.g.: Carburization and decarburization of steel, corrosionresistance of duralumin, doping of semi-conductors, etc.

∞=x

∞≤≤ x0

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−−

Dtxerf

CCCC

s

x

21

0

0


Influencing Factors For Diffusion 1Diffusing species: Interstitial atoms diffuse easily than substitution atoms. Again substitution atoms with small difference in atomic radius with parent atoms diffusewith ease than atoms with larger diameter.Temperature: It is the most influencing factor. Their relations can be given by the following Arrhenius equation

where D0 is a pre-exponential constant, Q is the activation energy for diffusion, R is gas constant (Boltzmann’s constant) and T is absolute temperature.

⎟⎠⎞

⎜⎝⎛−=

RTQDD exp0

Influencing Factors For Diffusion - 2From the temperature dependence of diffusivity, it is

experimentally possible to find the values of Q and D0.Lattice structure: Diffusivity is high for open lattice structure

and in open lattice directions.Presence of defects: The other important influencing factor of

diffusivity is presence of defects. Many atomic/volume diffusion processes are influenced by point defects like vacancies, interstitials.

Apart from these, dislocations and grain boundaries, i.e. short-circuit paths as they famously known, greatly enhances the diffusivity.

Non-Equilibrium Transformation & Microstructure 1

Non-equilibrium transformation occurs, usually, during many of the cooling processes like casting process.Equilibrium transformation requires extremely large time which is in most of the cases impractical and not necessary.Alloy solidification process involves diffusion in liquid phase, solid phase, and also across the interface between liquid and solid.As diffusion is very sluggish in solid, and time available for it is less, compositional gradients develop in cast components.These are two kinds: coring and segregation.


Coring: It is defined as gradual compositional changes across individual grains.Coring is predominantly observed in alloys having a marked difference between liquidus and solidus temperatures.It is often being removed by subsequent annealing and/or hot-working.It is exploited in zone-refining technique to produce high-purity metals.Segregation: It is defined as concentration of particular, usually impurity elements, along places like grain boundaries, and entrapments.Segregation is also useful in zone refining, and also in the production of rimming steel.


Micro-segregation is used to describe the differences in composition across a crystal or between neighboring crystals.Micro-segregation can often be removed by prolonged annealing or by hot-working.Macro-segregation is used to describe more massive heterogeneities which may result from entrapment of liquid pockets between growing solidifying zones.Macro-segregation persists through normal heating and working operations.Two non equilibrium effects of practical importance:(1) the occurrence of phase changes or transformations at temperatures other than those predicted by phase boundary lines on the phase diagram, and (2) the existence of non-equilibrium phases at room temperature that do not appear on the phase diagram.

Material Science/Dislocations and Strengthening Mechanisms Lecture Notes


Chapter 6. Dislocations and Strengthening Mechanisms

6.1 Basic Concept of dislocation

Dislocations can be edge dislocations, screw dislocations and exist in combination of the two. Their motion (slip) occurs by sequential bond breaking and bond reforming . The number of dislocations per unit volume is the dislocation density, in a plane they are measured per unit area.

Characteristics of Dislocations

There is strain around a dislocation which influences how they interact with other dislocations, impurities, etc. There is compression near the extra plane (higher atomic density) and tension following the dislocation line.

Dislocations interact among themselves. When they are in the same plane, they repel if they have the same sign and annihilate if they have opposite signs (leaving behind a perfect crystal). In general, when dislocations are close and their strain fields add to a larger value, they repel, because being close increases the potential energy (it takes energy to strain a region of the material).

The number of dislocations increases dramatically during plastic deformation. Dislocations spawn from existing dislocations, and from defects, grain boundaries and surface irregularities.

Plastic Deformation

Slip directions vary from crystal to crystal. When plastic deformation occurs in a grain, it will be constrained by its neighbors, which may be less favorably oriented. As a result, polycrystalline metals are stronger than single crystals (the exception is the perfect single crystal, as in whiskers.)

6.2 Mechanisms of Strengthening in Metals

General principles. Ability to deform plastically depends on ability of dislocations to move. Strengthening consists in hindering dislocation motion. We discuss the methods of grain-size reduction, solid-solution alloying and strain hardening. These are for single-phase metals. We discuss others when treating alloys. Ordinarily, strengthening reduces ductility.



Strengthening by Grain Size Reduction

This is based on the fact that it is difficult for a dislocation to pass into another grain, especially if it is very misaligned. Atomic disorder at the boundary causes discontinuity in slip planes. For high-angle grain boundaries, stress at end of slip plane may trigger new dislocations in adjacent grains. Small angle grain boundaries are not effective in blocking dislocations.

The finer the grains, the larger the area of grain boundaries that impedes dislocation motion. Grain-size reduction usually improves toughness as well. Usually, the yield strength varies with grain size d according to:

σy = σ0 + ky / d1/2

Grain size can be controlled by the rate of solidification and by plastic deformation.

Solid-Solution Strengthening

Adding another element that goes into interstitial or substitutional positions in a solution increases strength. The impurity atoms cause lattice strain (Figs. 7.17 and 7.18) which can "anchor" dislocations. This occurs when the strain caused by the alloying element compensates that of the dislocation, thus achieving a state of low potential energy. It costs strain energy for the dislocation to move away from this state (which is like a potential well). The scarcity of energy at low temperatures is why slip is hindered.

Pure metals are almost always softer than their alloys.

Strain Hardening

Ductile metals become stronger when they are deformed plastically at temperatures well below the melting point (cold working). (This is different from hot working is the shaping of materials at high temperatures where large deformation is possible.) Strain hardening (work hardening) is the reason for the elastic recovery discussed in Ch. 6.8.

The reason for strain hardening is that the dislocation density increases with plastic deformation (cold work) due to multiplication. The average distance between dislocations then decreases and dislocations start blocking the motion of each one.

The measure of strain hardening is the percent cold work (%CW), given by the relative reduction of the original area, A0 to the final value Ad :

%CW = 100 (A0–Ad)/A0



6.3 Recovery, recrystallization and Grain Growth

Plastic deformation causes 1) change in grain size, 2) strain hardening, 3) increase in the dislocation density. Restoration to the state before cold-work is done by heating through two processes: recovery and recrystallization. These may be followed by grain growth.

Recovery

Heating increased diffusion enhanced dislocation motion relieves internal strain energy and reduces the number of dislocation. The electrical and thermal conductivity are restored to the values existing before cold working.

Recrystallization

Strained grains of cold-worked metal are replaced, upon heating, by more regularly-spaced grains. This occurs through short-range diffusion enabled by the high temperature. Since recrystallization occurs by diffusion, the important parameters are both temperature and time.

Recrystallization temperature: is that at which the process is complete in one hour. It is typically 1/3 to 1/2 of the melting temperature. It falls as the %CW is increased. Below a "critical deformation", recrystallization does not occur.

Grain Growth

The growth of grain size with temperature can occur in all polycrystalline materials. It occurs by migration of atoms at grain boundaries by diffusion, thus grain growth is faster at higher temperatures. The "driving force" is the reduction of energy, which is proportional to the total area. Big grains grow at the expense of the small ones.

Dislocations And Strengthening Mechanisms

Module-6


1. Dislocations & Plastic deformation and Mechanisms of plastic

deformation in metals

2. Strengthening mechanisms in metals

3. Recovery, Recrystallization and Grain growth

Contents


Plastic Deformation – Dislocations

Permanent plastic deformation is due to shear process –atoms change their neighbors.Inter-atomic forces and crystal structure plays an important role during plastic deformation.Cumulative movement of dislocations leads to gross plastic deformation.Edge dislocation move by slip and climb, while screw dislocation move by slip and cross-slip.During their movement, dislocations tend to interact. The interaction is very complex because of number of dislocations moving over many slip systems in different directions.


Plastic Deformation – Dislocations

Dislocations moving on parallel planes may annihilate each other, resulting in either vacancies or interstitials.Dislocations moving on non-parallel planes hinder each other’s movement by producing sharp breaks – jog (break out of slip plane), kink (break in slip plane)Other hindrances to dislocation motion – interstitial and substitutional atoms, foreign particles, grain boundaries, external grain surface, and change in structure due to phase change.Material strength can be increased by arresting dislocation motion.


Plastic Deformation Mechanisms – Slip 1

Mainly two kinds: slip and twinning.Slip is prominent among the two. It involves sliding of blocks of crystal over other along slip planes.Slip occurs when shear stress applied exceeds a critical value.Slip occurs most readily in specific directions (slip directions) on certain crystallographic planes.Feasible combination of a slip plane together with a slip direction is considered as a slip system.During slip each atom usually moves same integral number of atomic distances along the slip plane.


Plastic Deformation Mechanisms – Slip 2

Extent of slip depends on many factors - external load and the corresponding value of shear stress produced by it, crystal structure, orientation of active slip planes with the direction of shearing stresses generated.Slip occurs when shear stress applied exceeds a critical value.For single crystal, Schmid defined critical shear stress as

λφ

λφσλφφλτ

coscos

coscoscoscoscoscos

=⇒

===

mAP

AP

R


Plastic Deformation Mechanisms - Slip3

In a polycrystalline aggregate, individual grains provide a mutual geometrical constraint on one other, and this precludes plastic deformation at low applied stresses.Slip in polycrystalline material involves generation, movement and (re-)arrangement of dislocations.During deformation, mechanical integrity and coherency are maintained along the grain boundaries.A minimum of five independent slip systems must be operative for a polycrystalline solid to exhibit ductility and maintain grain boundary integrity – von Mises.On the other hand, crystal deform by twinning.


<110>110NaCl

Close packed directions

Basal plane Prismatic & Pyramidal

planes

More common Less common

HCP

<111>110 112,123

More common Less common

BCC

<110>111FCC

Slip directions

Slip planesOccurrenceCrystal

Slip Systems


Plastic Deformation Mechanisms -Twinning

It results when a portion of crystal takes up an orientation that is related to the orientation of the rest of the untwined lattice in a definite, symmetrical way.The important role of twinning in plastic deformation is that it causes changes in plane orientation so that further slip can occur.Twinning also occurs in a definite direction on a specific plane for each crystal structure.

[¯1011](10¯12)Zn, Cd, Mg, TiHCP[111](112)α-Fe, TaBCC[112](111)Ag, Au, CuFCC

Twin direction

Twin planeExampleCrystal


Slip Vs. Twinning

On a particular plane for each crystal

On many slip systems simultaneouslyOccurrence

Micro secondsMilli secondsTime required

Every plane of region involvedWidely spread planesOccurs on

FractionsMultiplesSize (in terms of inter-atomic distance)

Differ across the twin plane

Same above and below the slip plane

Crystal orientation

during/in twinningduring/in slip


Strengthening MechanismsMaterial can be increased by hindering dislocation, which is responsible for plastic deformation.Different ways to hinder dislocation motion / Strengthening mechanisms:

in single-phase materials- Grain size reduction- Solid solution strengthening- Strain hardening

in multi-phase materials- Precipitation strengthening- Dispersion strengthening- Fiber strengthening- Martensite strengthening


Strengthening By Grain Size Reduction 1

It is based on the fact that dislocations will experience hindrances while trying to move from a grain into the next because of abrupt change in orientation of planes.Hindrances can be two types: forcible change of slip direction, and discontinuous slip plane.Smaller the grain size, often a dislocation encounters a hindrance. Yield strength of material will be increased.Yield strength is related to grain size (diameter, d) as Hall-Petch relation:

Grain size can be tailored by controlled cooling or by plastic deformation followed by appropriate heat treatment.

21−+= kdiy σσ


Strengthening By Grain Size Reduction 2

Grain size reduction improves not only strength, but also the toughness of many alloys.If d is average grain diameter, Sv is grain boundary area per unit volume, NL is mean number of intercepts of grain boundaries per unit length of test line, NA is number of grains per unit area on a polished surface:

Grain size can also be measured by comparing the grains at a fixed magnification with standard grain size charts.Other method: Use of ASTM grain size number (Z). It is related to grain diameter, D (in mm) as follows:

Lv NS 2=Lv NS

d2

33==

ANd

π6

=

12645

1001

−= GD


Solid Solution StrengtheningImpure foreign atoms in a single phase material produces lattice strains which can anchor the dislocations.Effectiveness of this strengthening depends on two factors – size difference and volume fraction of solute.Solute atoms interact with dislocations in many ways:

- elastic interaction- modulus interaction- stacking-fault interaction- electrical interaction- short-range order interaction- long-range order interaction

Elastic, modulus, and long-range order interactions are of long-range i.e. they are relatively insensitive to temperature and continue to act about 0.6 Tm.


Yield Point Phenomenon - 1

Localized, heterogeneous type of transition from elastic to plastic deformation marked by abrupt elastic-plastic transition – Yield point phenomenon.

It characterizes that material needs higher stress to initiate plastic flow than to continue it.


Yield Point Phenomenon - 2The bands are called Lüders bands / Hartmann lines / stretcher stains, and generally are approximately 45 to the tensile axis.Occurrence of yield point is associated with presence of small amounts of interstitial or substitutional impurities. It’s been found that either unlocking of dislocations by a high stress for the case of strong pinning or generation of new dislocations are the reasons for yield-point phenomenon.Magnitude of yield-point effect will depend on energy of interaction between solute atoms and dislocations and on the concentration of solute atoms at the dislocations.


Strain Hardening - 1Phenomenon where ductile metals become stronger and harder when they are deformed plastically is called strain hardening or work hardening.Increasing temperature lowers the rate of strain hardening. Hence materials are strain hardened at low temperatures, thus also called cold working.During plastic deformation, dislocation density increases. And thus their interaction with each other resulting in increase in yield stress.Dislocation density (ρ) and shear stress (τ) are related as follows:

ρττ A+= 0


Strain Hardening - 2During strain hardening, in addition to mechanical properties physical properties also changes:

- a small decrease in density- an appreciable decrease in electrical conductivity- small increase in thermal coefficient of expansion- increased chemical reactivity (decrease in corrosion resistance).

Deleterious effects of cold work can be removed by heating the material to suitable temperatures – Annealing. It restores the original properties into material. It consists of three stages –recovery, recrystallization and grain growth.In industry, alternate cycles of strain hardening and annealing are used to deform most metals to a very great extent.


Precipitation & Dispersion Hardening 1

Foreign particles can also obstructs movement of dislocations i.e. increases the strength of the material.Foreign particles can be introduced in two ways –precipitation and mixing-and-consolidation technique.Precipitation hardening is also called age hardening because strength increases with time.Requisite for precipitation hardening is that second phase must be soluble at an elevated temperature but precipitates upon quenching and aging at a lower temperature.E.g.: Al-alloys, Cu-Be alloys, Mg-Al alloys, Cu-Sn alloys If aging occurs at room temperature – Natural agingIf material need to be heated during aging – Artificial aging.


Precipitation & Dispersion Hardening2

In dispersion hardening, fine second particles are mixed with matrix powder, consolidated, and pressed in powder metallurgy techniques.For dispersion hardening, second phase need to have very low solubility at all temperatures.E.g.: oxides, carbides, nitrides, borides, etc.Dislocation moving through matrix embedded with foreign particles can either cut through the particles or bend around and bypass them.Cutting of particles is easier for small particles which can be considered as segregated solute atoms. Effective strengthening is achieved in the bending process, when the particles are submicroscopic in size.


Precipitation & Dispersion Hardening 3

Stress (τ) required to bend a dislocation is inversely proportional to the average interspacing (λ) of particles:

Interspacing (λ) of spherical particles:where r - particle radius, f - volume fraction

Optimum strengthening occurs during aging once the right interspacing of particles is achieved. - Smaller the particles, dislocations can cut through them at lower stresses- larger the particles they will be distributed at wider distances.

λτ Gb=

frf

3)1(4 −

=λ


Fiber Strengthening - 1Second phase can be introduced into matrix in fiber form too.Requisite for fiber strengthening:Fiber material – high strength and high modulusMatrix material – ductile and non-reactive with fiber materialE.g.: fiber material – Al2O3, boron, graphite, metal, glass, etc.

matrix material – metals, polymers.Mechanism of strengthening is different from other methods.Higher modulus fibers carry load, ductile matrix distributes load to fibers. Interface between matrix and fibers thus plays an important role.Strengthening analysis involves application of continuum, not dislocation concepts as in other methods of strengthening.


Fiber Strengthening - 2To achieve any benefit from presence of fibers, critical fiber volume which must be exceeded for fiber strengthening to occur:

where σmu – strength of strain hardened matrix, σ’m – flow stress of matrix at a strain equal to fiber breaking stress, σfu –ultimate tensile strength of the fiber.

Minimum volume fraction of fiber which must be exceeded to have real reinforcement:

'

'

mfu

mmucriticalf

σσσσ

−−

=

'

'

minmmufu

mmufσσσ

σσ−+

−=


Martensite Strengthening - 1This strengthening method is based on formation of martensitic phase from the retained high temperature phase at temperatures lower then the equilibrium invariant transformation temperature.Martensite forms as a result of shearing of lattices.Martensite platelets assumes characteristic lenticular shape that minimizes the elastic distortion in the matrix. These platelets divide and subdivide the grains of the parent phase. Always touching but never crossing one another.Martensite platelets grow at very high speeds (1/3rd of sound speed) i.e. activation energy for growth is less. Thus volume fraction of martensite exist is controlled by its nucleation rate.


Martensite Strengthening - 2Martensite platelets attain their shape by two successive shear displacements - first displacement is a homogeneous shear throughout the plate which occurs parallel to a specific plane in the parent phase known as the habit plane, seconddisplacement, the lesser of the two, can take place by one of two mechanisms: slip as in Fe-C Martensite or twinning as in Fe-Ni Martensite.Martensite formation occurs in many systems.E.g.: Fe-C, Fe-Ni, Fe-Ni-C, Cu-Zn, Au-Cd, and even in pure metals like Li, Zr and Co. However, only the alloys based on Fe and C show a pronounced strengthening effect.High strength of Martensite is attributed to its characteristic twin structure and to high dislocation density. In Fe-C system, carbon atoms are also involved in strengthening.


RecoveryAnnealing relieves the stresses from cold working – three stages: recovery, recrystallization and grain growth.Recovery involves annihilation of point defects.Driving force for recovery is decrease in stored energy from cold work.During recovery, physical properties of the cold-worked material are restored without any observable change in microstructure.Recovery is first stage of annealing which takes place at low temperatures of annealing.There is some reduction, though not substantial, in dislocation density as well apart from formation of dislocation configurations with low strain energies.


RecrystallizationThis follows recovery during annealing of cold worked material. Driving force is stored energy during cold work.It involves replacement of cold-worked structure by a new set of strain-free, approximately equi-axed grains to replace all the deformed crystals.This is process is characterized by recrystallization temperature which is defined as the temperature at which 50% of material recrystallizes in one hour time.The recrystallization temperature is strongly dependent on the purity of a material. Pure materials may recrystallizes around 0.3 Tm, while impure materials may recrystallizes around 0.5-0.7 Tm, where Tm is absolute melting temperature of the material.


Recrystallization LawsA minimum amount of deformation is needed to cause recrystallization (Rx).Smaller the degree of deformation, higher will be the Rx temperature.The finer is the initial grain size; lower will be the Rx temperature.The larger the initial grain size, the greater degree of deformation is required to produce an equivalent Rx temperature.Greater the degree of deformation and lower the annealing temperature, the smaller will be the recrystallized grain size.The higher is the temperature of cold working, the less is the strain energy stored and thus Rx temperature is correspondingly higher.The Rx rate increases exponentially with temperature.


Grain Growth

Grain growth follows complete crystallization if the material is left at elevated temperatures.Grain growth does not need to be preceded by recovery and recrystallization; it may occur in all polycrystalline materials.In contrary to recovery and recrystallization, driving force forthis process is reduction in grain boundary energy.Tendency for larger grains to grow at the expense of smaller grains is based on physics.In practical applications, grain growth is not desirable.Incorporation of impurity atoms and insoluble second phase particles are effective in retarding grain growth.Grain growth is very strongly dependent on temperature.

Material Science/Phase Diagrams Lecture Notes


Chapter 7. Phase Diagrams

7.1 Equilibrium Phase Diagrams

Give the relationship of composition of a solution as a function of temperatures and the quantities of phases in equilibrium. These diagrams do not indicate the dynamics when one phase transforms into another. Sometimes diagrams are given with pressure as one of the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at one atmosphere.

Binary Isomorphous Systems

This very simple case is one complete liquid and solid solubility, an isomorphous system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility occurs because both Cu and Ni have the same crystal structure (FCC), near the same radii, electronegativity and valence.

The liquidus line separates the liquid phase from solid or solid + liquid phases. That is, the solution is liquid above the liquidus line.

The solidus line is that below which the solution is completely solid (does not contain a liquid phase.)

Interpretation of phase diagrams

Concentrations: Tie-line method

a. locate composition and temperature in diagram b. In two phase region draw tie line or isotherm c. note intersection with phase boundaries. Read compositions.

Fractions: lever rule

a. construct tie line (isotherm) b. obtain ratios of line segments lengths.

Development of microstructure in isomorphous alloys

a) Equilibrium cooling

Solidification in the solid + liquid phase occurs gradually upon cooling from the liquidus line. The composition of the solid and the liquid change gradually during cooling (as can be determined by the tie-line method.) Nuclei of the solid phase form and they grow to consume all the liquid at the solidus line.



b) Non-equilibrium cooling

Solidification in the solid + liquid phase also occurs gradually. The composition of the liquid phase evolves by diffusion, following the equilibrium values that can be derived from the tie-line method. However, diffusion in the solid state is very slow. Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the invalidity of the tie-line method to determine the composition of the solid phase (it still works for the liquid phase, where diffusion is fast.)

Binary Eutectic Systems

Interpretation: Obtain phases present, concentration of phases and their fraction (%).

Solvus line: limit of solubility

Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the eutectic composition and the eutectic temperature.

Note:

• the melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek).

• At most two phases can be in equilibrium within a phase field.

• Single-phase regions are separated by 2-phase regions.

Development of microstructure in eutectic alloys

Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops when cooling below the eutectic temperature. Alloys which are to the left of the eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a proeutectic phase before reaching the eutectic temperature, while in the solid + liquid region. The eutectic structure then adds when the remaining liquid is solidified when cooling further. The eutectic microstructure is lamellar (layered) due to the reduced diffusion distances in the solid state.

To obtain the concentration of the eutectic microstructure in the final solid solution, one draws a vertical line at the eutectic concentration and applies the lever rule treating the eutectic as a separate phase .



Equilibrium Diagrams Having Intermediate Phases or Compounds

A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram. One that exists in the middle, separated from the extremes, is called an intermediate phase or solid solution.

An important phase is the intermetallic compound, that has a precise chemical compositions. When using the lever rules, intermetallic compounds are treated like any other phase, except they appear not as a wide region but as a vertical line.

Eutectoid and Peritectic Reactions

The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. It also shows as V on top of a horizontal line in the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid phase, eutectoid and proeutectoid microstructures.

Solid Phase 1 Solid Phase 2 + Solid Phase 3

The peritectic reaction also involves three solid in equilibrium, the transition is from a solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs when heating.

Solid Phase 1 + liquid Solid Phase 2

Congruent Phase Transformations

Another classification scheme. Congruent transformation is one where there is no change in composition, like allotropic transformations (e.g., α−Fe to γ-Fe) or melting transitions in pure solids.

7.2 Particle strengthening by precipitation

The strength and hardness of some metal and alloys may be enhanced by the formation of extremely small uniformly dispersed particles of a second phase within the original phase matrix; this must be accomplished by phase transformations that are induced by appropriate heat treatments. The process is called precipitation hardening because the small particles of the new phase are termed “precipitates”. Precipitation hardening and the treating of steel to form tempered matrensite are totally different phenomena, even though the heat treatment procedures are similar.

7.3 Precipitation reactions

A precipitation reaction is a reaction in which soluble ions in separate solutions are mixed together to form an insoluble compound that settles out of solution as a solid. That insoluble compound is called a precipitate



7.4 Kinetics of nucleation and growth

From a micro structural standpoint, the first process to accompany a phase transformation is nucleation- the formation of very small particles or nuclei, of the new phase which are capable of growing. The second stage is growth, in which the nuclei increase in size; during this process, some volume of the parent phase disappears. The transformation reaches completion if growth of these new phase particles is allowed to proceed until the equilibrium fraction is attained.

As would be expected, the time dependence of the transformations rate (which is often termed the kinetics of a transformation) is an important consideration in the heat treatment of materials. With many investigations, the fraction of reaction that has occurred is measured as a function of time, while the temperature is maintained constant. Transformation progress is usually ascertained by either microscopic examination or measurement of some physical property. Data are plotted as the fraction of transformed material versus the logarithm of time; an S-shaped curve, represents the typical kinetic behavior for most solid state reactions.



7.5 The Iron–Carbon Diagram

The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram

This is one of the most important alloys for structural applications. The diagram Fe—C is simplified at low carbon concentrations by assuming it is the Fe—Fe3C diagram. Concentrations are usually given in weight percent. The possible phases are:

• α-ferrite (BCC) Fe-C solution • γ-austenite (FCC) Fe-C solution • δ-ferrite (BCC) Fe-C solution • liquid Fe-C solution • Fe3C (iron carbide) or cementite. An intermetallic compound.

The maximum solubility of C in α- ferrite is 0.022 wt%. δ−ferrite is only stable at high temperatures. It is not important in practice. Austenite has a maximum C concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C) unless cooled rapidly (Chapter 10). Cementite is in reality metastable, decomposing into α-Fe and C when heated for several years between 650 and 770 C.

For their role in mechanical properties of the alloy, it is important to note that:

Ferrite is soft and ductile

Cementite is hard and brittle

Thus, combining these two phases in solution an alloy can be obtained with intermediate properties. (Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.)

Development of Microstructures in Iron—Carbon Alloys

The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms perlite, a lamellar or layered structure of two phases: α-ferrite and cementite (Fe3C).

Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite. Hypereutectoid alloys contain proeutectoid cementite plus perlite.

Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is not achieved by usual cooling from austenite. The new microstructures that form are discussed in Ch. 10.

The Influence of Other Alloying Elements



Alloying strengthens metals by hindering the motion of dislocations. Thus, the strength of Fe–C alloys increase with C content and also with the addition of other elements.



7.7 Transformation rate effects and TTT diagrams:

There are two main types of transformation diagram that are helpful in selecting the optimum steel and processing route to achieve a given set of properties. These are time-temperature transformation (TTT) and continuous cooling transformation (CCT) diagrams. CCT diagrams are generally more appropriate for engineering applications as components are cooled (air cooled, furnace cooled, quenched etc.) from a processing temperature as this is more economic than transferring to a separate furnace for an isothermal treatment. Time-temperature transformation (TTT) diagrams measure the rate of transformation at a constant temperature. In other words a sample is austenitised and then cooled rapidly to a lower temperature and held at that temperature whilst the rate of transformation is measured, for example by dilatometry. Obviously a large number of experiments is required to build up a complete TTT diagram. Continuous cooling transformation (CCT) diagrams measure the extent of transformation as a function of time for a continuously decreasing temperature. In other words a sample is austenitised and then cooled at a predetermined rate and the degree of transformation is measured, for example by dilatometry. Obviously a large number of experiments is required to build up a complete CCT diagram

• An increase in carbon content shifts the CCT and TTT curves to the right (this corresponds to an increase in hardenability as it increases the ease of forming martensite - i.e. the cooling rate required to attain martensite is less severe).

• An increase in carbon content decreases the martensite start temperature. • An increase in Mo content shifts the CCT and TTT curves to the right and also

separates the ferrite + pearlite region from the bainite region making the attainment of a bainitic structure more controllable.

7.8 Microstructure and Property Changes in Fe-C Alloys

Isothermal Transformation Diagrams

We use as an example the cooling of an eutectoid alloy (0.76 wt% C) from the austenite (γ- phase) to pearlite, that contains ferrite (α) plus cementite (Fe3C or iron carbide). When cooling proceeds below the eutectoid temperature (727 oC) nucleation of pearlite starts. The S-shaped curves (fraction of pearlite vs. log. time, fig. 10.3) are displaced to longer times at higher temperatures showing that the transformation is dominated by nucleation (the nucleation period is longer at higher temperatures) and not by diffusion (which occurs faster at higher temperatures).

The family of S-shaped curves at different temperatures can be used to construct the TTT (Time-Temperature-Transformation) diagrams (e.g., fig. 10.4.) For these diagrams to apply, one needs to cool the material quickly to a given temperature To before the transformation occurs, and keep it at that temperature over time. The horizontal line that indicates constant temperature To intercepts the TTT curves on the left (beginning of the transformation) and the right (end of the transformation); thus one can read from the



diagrams when the transformation occurs. The formation of pearlite shown in fig. 10.4 also indicates that the transformation occurs sooner at low temperatures, which is an indication that it is controlled by the rate of nucleation. At low temperatures, nucleation occurs fast and grain growth is reduced (since it occurs by diffusion, which is hindered at low temperatures). This reduced grain growth leads to fine-grained microstructure (fine pearlite). At higher temperatures, diffusion allows for larger grain growth, thus leading to coarse pearlite.

At lower temperatures nucleation starts to become slower, and a new phase is formed, bainite. Since diffusion is low at low temperatures, this phase has a very fine (microscopic) microstructure.

Spheroidite is a coarse phase that forms at temperatures close to the eutectoid temperature. The relatively high temperatures caused a slow nucleation but enhances the growth of the nuclei leading to large grains.

A very important structure is martensite, which forms when cooling austenite very fast (quenching) to below a maximum temperature that is required for the transformation. It forms nearly instantaneously when the required low temperature is reached; since no thermal activation is needed, this is called an athermal transformation. Martensite is a different phase, a body-centered tetragonal (BCT) structure with interstitial C atoms. Martensite is metastable and decomposes into ferrite and pearlite but this is extremely slow (and not noticeable) at room temperature.

In the examples, we used an eutectoid composition. For hypo- and hypereutectoid alloys, the analysis is the same, but the proeutectoid phase that forms before cooling through the eutectoid temperature is also part of the final microstructure.

Phase Diagrams

Module-07


1. Equilibrium phase diagrams, Particle strengthening by precipitation and precipitation reactions

2. Kinetics of nucleation and growth

3. The iron-carbon system, phase transformations

4. Transformation rate effects and TTT diagrams, Microstructure and property changes in iron-carbon system

Contents


Mixtures – Solutions – Phases - 1Almost all materials have more than one phase in them. Thus engineering materials attain their special properties.Macroscopic basic unit of a material is called component. It refers to a independent chemical species. The components of a system may be elements, ions or compounds. A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically homogeneous and mechanically separable portion of a system.A component can exist in many phases.E.g.: Water exists as ice, liquid water, and water vapor.Carbon exists as graphite and diamond.


Mixtures – Solutions – Phases - 2When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient.A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase.Solute (minor component of two in a solution) does not change the structural pattern of the solvent, and the composition of any solution can be varied. In mixtures, there are different phases, each with its own atomic arrangement. It is possible to have a mixture of two different solutions!


Gibbs Phase RuleIn a system under a set of conditions, number of phases (P) exist can be related to the number of components (C) and degrees of freedom (F) by Gibbs phase rule.Degrees of freedom refers to the number of independent variables (e.g.: pressure, temperature) that can be varied individually to effect changes in a system.Thermodynamically derived Gibbs phase rule:In practical conditions for metallurgical and materials systems, pressure can be treated as a constant (1 atm.). Thus Condensed Gibbs phase rule is written as:

2+=+ CFP 1+=+ CFP


Equilibrium Phase DiagramA diagram that depicts existence of different phases of a system under equilibrium is termed as phase diagram. It is actually a collection of solubility limit curves. It is also known as equilibrium or constitutional diagram.Equilibrium phase diagrams represent the relationships between temperature, compositions and the quantities of phases at equilibrium.These diagrams do not indicate the dynamics when one phase transforms into another.Useful terminology related to phase diagrams: liquidus, solidus, solvus, terminal solid solution, invariant reaction, intermediate solid solution, inter-metallic compound, etc.Phase diagrams are classified according to the number of component present in a particular system.


Phase Diagram – Useful Information

Important information, useful in materials development andselection, obtainable from a phase diagram:- It shows phases present at different compositions and temperatures under slow cooling (equilibrium) conditions.- It indicates equilibrium solid solubility of one element/compound in another.- It suggests temperature at which an alloy starts to solidify and the range of solidification.- It signals the temperature at which different phases start to melt.- Amount of each phase in a two-phase mixture can be obtained.


Unary Phase DiagramIf a system consists of just one component (e.g.: water), equilibrium of phases exist is depicted by unary phase diagram. The component may exist in different forms, thus variables here are – temperature and pressure.


Binary Phase DiagramIf a system consists of two components, equilibrium of phases exist is depicted by binary phase diagram. For most systems, pressure is constant, thus independently variable parameters are – temperature and composition.Two components can be either two metals (Cu and Ni), or a metal and a compound (Fe and Fe3C), or two compounds (Al2O3 and Si2O3), etc.Two component systems are classified based on extent of mutual solid solubility – (a) completely soluble in both liquid and solid phases (isomorphous system) and (b) completely soluble in liquid phase whereas solubility is limited in solid state.For isomorphous system - E.g.: Cu-Ni, Ag-Au, Ge-Si, Al2O3-Cr2O3.


Hume-Ruthery ConditionsExtent of solid solubility in a two element system can be predicted based on Hume-Ruthery conditions.If the system obeys these conditions, then complete solid solubility can be expected.Hume-Ruthery conditions:- Crystal structure of each element of solid solution must be the same.- Size of atoms of each two elements must not differ by more than 15%.- Elements should not form compounds with each other i.e. there should be no appreciable difference in the electro-negativities of the two elements.- Elements should have the same valence.


Isomorphous Binary SystemAn isomorphous system – phase diagram and corresponding microstructural changes.


Tie Line – Lever Rule - 1At a point in a phase diagram, phases present and their composition (tie-line method) along with relative fraction of phases (lever rule) can be computed.Procedure to find equilibrium concentrations of phases (refer to the figure in previous slide): - A tie-line or isotherm (UV) is drawn across two-phase region to intersect the boundaries of the region.- Perpendiculars are dropped from these intersections to the composition axis, represented by U’ and V’, from which each of each phase is read. U’ represents composition of liquid phase and V’ represents composition of solid phase as intersection U meets liquidus line and Vmeets solidus line.


Tie Line – Lever Rule - 2Procedure to find equilibrium relative amounts of phases (lever rule):- A tie-line is constructed across the two phase region at the temperature of the alloy to intersect the region boundaries.- The relative amount of a phase is computed by taking the length of tie line from overall composition to the phase boundary for the other phase, and dividing by the total tie-line length. In previous figure, relative amount of liquid and solid phases is given respectively by:

UVcVCL =

UVUcCS = 1=+ SL CC


Eutectic Binary SystemMany of the binary systems with limited solubility are of eutectic type – eutectic alloy of eutectic composition solidifies at the end of solidification at eutectic temperature.E.g.: Cu-Ag, Pb-Sn


EutecticSystem–Cooling Curve -Microstructure - 1


Eutectic System–Cooling Curve –Microstructure - 2


Eutectic system – Cooling curve –Microstructure - 3


Eutectic system – Cooling curve –Microstructure - 4


Invariant Reactions - 1

Observed triple point in unary phase diagram for water?How about eutectic point in binary phase diagram?These points are specific in the sense that they occur only at that particular conditions of concentration, temperature, pressure etc. Try changing any of the variable, it does not exist i.e. phases are not equilibrium any more!Hence they are known as invariant points, and represents invariant reactions.In binary systems, we will come across many number of invariant reactions!


Invariant Reactions - 2


Intermediate PhasesInvariant reactions result in different product phases –terminal phases and intermediate phases.Intermediate phases are either of varying composition (intermediate solid solution) or fixed composition (inter-metallic compound).Occurrence of intermediate phases cannot be readily predicted from the nature of the pure components!Inter-metallic compounds differ from other chemical compounds in that the bonding is primarily metallic rather than ionic or covalent.E.g.: Fe3C is metallic, whereas MgO is covalent.When using the lever rules, inter-metallic compounds are treated like any other phase.


Congruent, Incongruent Transformations

Phase transformations are two kinds – congruent and incongruent.Congruent transformation involves no compositional changes. It usually occurs at a temperature.E.g.: Allotropic transformations, melting of pure a substance.During incongruent transformations, at least one phase will undergo compositional change.E.g.: All invariant reactions, melting of isomorphous alloy.Intermediate phases are sometimes classified on the basis of whether they melt congruently or incongruently. E.g.: MgNi2, for example, melts congruently whereas Mg2Ni melts incongruently since it undergoes peritectic decomposition.


Precipitation – Strengthening – Reactions 1

A material can be strengthened by obstructing movement of dislocations. Second phase particles are effective.Second phase particles are introduced mainly by two means – direct mixing and consolidation, or by precipitation.Most important pre-requisite for precipitation strengthening: there must be a terminal solid solution which has a decreasing solid solubility as the temperature decreases.E.g.: Au-Cu in which maximum solid solubility of Cu in Al is 5.65% at 548 C that decreases with decreasing temperature.Three basic steps in precipitation strengthening: solutionizing, quenching and aging.



Solutionizing (solution heat treatment), where the alloy is heated to a temperature between solvus and solidus temperatures and kept there till a uniform solid-solution structure is produced.Quenching, where the sample is rapidly cooled to a lower temperature (room temperature). Resultant product –supersaturated solid solution.Aging is the last but critical step. During this heat treatment step finely dispersed precipitate particle will form. Aging the alloy at room temperature is called natural aging, whereas at elevated temperatures is called artificial aging. Most alloys require artificial aging, and aging temperature is usually between 15-25% of temperature difference between room temperature and solution heat treatment temperature.



Al-4%Cu alloy is used to explain the mechanism of precipitation strengthening.


Precipitation – Strengthening – Reactions 4 Al-4%Cu alloy when cooled slowly from solutionizing

temperature, produces coarse grains – moderate strengthening.For precipitation strengthening, it is quenched, and aged!Following sequential reactions takes place during aging:Supersaturated α → GP1 zones → GP2 zones (θ” phase) → θ’ phase → θ phase (CuAl2)


Nucleation And GrowthStructural changes / Phase transformations takes place by nucleation followed by growth.Temperature changes are important among variables (like pressure, composition) causing phase transformations as diffusion plays an important role.Two other factors that affect transformation rate along with temperature – 1. diffusion controlled rearrangement of atoms because of compositional and/or crystal structural differences; 2. difficulty encountered in nucleating small particles via change in surface energy associated with the interface.Just nucleated particle has to overcome the +ve energy associated with new interface formed to survive and grow further. It does by reaching a critical size.


Homogeneous Nucleation – Kinetics1

Homogeneous nucleation – nucleation occurs within parent phase. All sites are of equal probability for nucleation.It requires considerable under-cooling (cooling a material below the equilibrium temperature for a given transformation without the transformation occurring).Free energy change associated with formation of new particle

where r is the radius of the particle, ∆g is the Gibbs free energy change per unit volume and γ is the surface energy of the interface.

γππ 23 434 rgrf +∆=∆


Homogeneous Nucleation – Kinetics2

Critical value of particle size (which reduces with under-cooling) is given by

or

where Tm – freezing temperature (in K), ∆Hf – latent heat of fusion, ∆T – amount of under-cooling at which nucleus is formed.

gr

∆−=

γ2*TH

Tr

f

m

∆∆=

γ2*


Heterogeneous Nucleation – Kinetics1

In heterogeneous nucleation, the probability of nucleation occurring at certain preferred sites is much greater than that at other sites.E.g.: During solidification - inclusions of foreign particles (inoculants), walls of container holding the liquidIn solid-solid transformation - foreign inclusions, grain boundaries, interfaces, stacking faults and dislocations.Considering, force equilibrium during second phase formation:

βδαβαδ γθγγ += cos


Heterogeneous Nucleation – Kinetics 2

When product particle makes only a point contact with the foreign surface, i.e. θ = 180, the foreign particle does not play any role in the nucleation process →

If the product particle completely wets the foreign surface, i.e. θ = 0, there is no barrier for heterogeneous nucleation →

In intermediate conditions such as where the product particle attains hemispherical shape, θ = 0→

4coscos32)coscos32(

)(34 3

*hom

32

3* θθθθ

πγαβ +−∆=+−

∆=∆ f

gf het

*hom

* ff het ∆=∆

0* =∆ hetf

*hom

*

21 ff het ∆=∆


Growth Kinetics - 1After formation of stable nuclei, growth of it occurs until equilibrium phase is being formed.Growth occurs in two methods – thermal activated diffusion controlled individual atom movement, or athermal collective movement of atoms. First one is more common than the other.Temperature dependence of nucleation rate (U), growth rate (I) and overall transformation rate (dX/dt) that is a function of both nucleation rate and growth rate i.e. dX/dt= fn (U, I):


Growth Kinetics - 2Time required for a transformation to completion has a reciprocal relationship to the overall transformation rate, C-curve (time-temperature-transformation or TTT diagram).Transformation data are plotted as characteristic S-curve.At small degrees of supercooling, where slow nucleation and rapid growth prevail, relatively coarse particles appear; at larger degrees of supercooling, relatively fine particles result.


Martensitic Growth KineticsDiffusion-less, athermal collective movement of atoms can also result in growth – Martensitic transformation.Takes place at a rate approaching the speed of sound. It involves congruent transformation.E.g.: FCC structure of Co transforms into HCP-Co or FCC-austenite into BCT-Martensite.Because of its crystallographic nature, a martensitic transformation only occurs in the solid state.Consequently, Ms and Mf are presented as horizontal lines on a TTT diagram. Ms is temperature where transformation starts, and Mf is temperature where transformation completes.Martensitic transformations in Fe-C alloys and Ti are of great technological importance.


Fe-C Binary System – Phase Transformations - 1


Fe-C Binary System – Phase Transformations - 2

Fe-Fe3C phase diagram is characterized by five individual phases,: α–ferrite (BCC) Fe-C solid solution, γ-austenite (FCC) Fe-C solid solution, δ-ferrite (BCC) Fe-C solid solution, Fe3C (iron carbide) or cementite - an inter-metallic compound and liquid Fe-C solution and four invariant reactions:- peritectic reaction at 1495 C and 0.16%C, δ-ferrite + L↔ γ-iron (austenite)- monotectic reaction 1495 C and 0.51%C, L↔ L + γ-iron (austenite)- eutectic reaction at 1147 C and 4.3 %C, L ↔ γ-iron + Fe3C (cementite) [ledeburite]- eutectoid reaction at 723 C and 0.8%C, γ-iron ↔ α–ferrite + Fe3C (cementite) [pearlite]


Fe-C Alloy ClassificationFe-C alloys are classified according to wt.% C present in the alloy for technological convenience as follows:

Commercial pure irons % C < 0.008Low-carbon/mild steels 0.008 - %C - 0.3Medium carbon steels 0.3 - %C - 0.8High-carbon steels 0.8- %C - 2.11Cast irons 2.11 < %C

Cast irons that were slowly cooled to room temperature consists of cementite, look whitish – white cast iron. If it contains graphite, look grayish – gray cast iron. It is heat treated to have graphite in form of nodules – malleable cast iron. If inoculants are used in liquid state to have graphite nodules – spheroidal graphite (SG) cast iron.


TTT Diagram For Eutectoid Transformation In Fe-C System


Transformations Involving Austenite For Fe-C System


CCT Diagram For Fe-C System - 1TTT diagram though gives very useful information, they are of less practical importance since an alloy has to be cooled rapidly and then kept at a temperature to allow for respective transformation to take place.Usually materials are cooled continuously, thus Continuous Cooling Transformation diagrams are appropriate.For continuous cooling, the time required for a reaction to begin and end is delayed, thus the isothermal curves are shifted to longer times and lower temperatures.Main difference between TTT and CCT diagrams: no space for bainite in CCT diagram as continuous cooling always results in formation of pearlite.


CCT Diagram For Fe-C System - 2

Material Science/Failure Lecture Notes


Chapter 8. Failure

8.1 Fundamentals of Fracture

Fracture is a form of failure where the material separates in pieces due to stress, at temperatures below the melting point. The fracture is termed ductile or brittle depending on whether the elongation is large or small.

Steps in fracture (response to stress):

• Track formation • Track propagation

Ductile vs. brittle fracture

Ductile Brittle

Deformation Extensive Little

Track propagation Slow, needs stress Fast

Type of materials Most metals (not too cold) Ceramics, ice, cold metals

Warning Permanent elongation None

Strain energy Higher Lower

Fractured surface Rough Smoother

Necking Yes No

8.2 Ductile Fracture

Stages of ductile fracture

• Initial necking • Small cavity formation (microvoids) • Void growth (ellipsoid) by coalescence into a crack • Fast crack propagation around neck. Shear strain at

45o • Final shear fracture (cup and cone)



The interior surface is fibrous, irregular, which signify plastic deformation.

Brittle Fracture

There is no appreciable deformation, and crack propagation is very fast. In most brittle materials, crack propagation (by bond breaking) is along specific crystallographic planes (cleavage planes). This type of fracture is transgranular (through grains) producing grainy texture (or faceted texture) when cleavage direction changes from grain to grain. In some materials, fracture is intergranular.



8.3 Fracture Mechanics

Fracture occurs due to stress concentration at flaws, like surface scratches, voids, etc. If a is the length of the void and ρ the radius of curvature, the enhanced stress near the flaw is:

σm ≈ 2 σ0 (a/ρ)1/2

where σ0 is the applied macroscopic stress. Note that a is 1/2 the length of the flaw, not the full length for an internal flaw, but the full length for a surface flaw. The stress concentration factor is:

Kt = σm/σ0 ≈ 2 (a/ρ)1/2

Because of this enhancement, flaws with small radius of curvature are called stress raisers.



8.4 Impact Fracture:

Impact fractures can best be described as a flute or strip of material that was cleanly sheared from a projectile point. The most common type of impact fracture starts at the tip of a point and runs down one blade edge possibly reaching the shoulder of a point. Some points were reworked into a useable point after having been damaged by an impact fracture.

Normalized tests, like the Charpoy and Izod tests measure the impact energy required to fracture a notched specimen with a hammer mounted on a pendulum. The energy is measured by the change in potential energy (height) of the pendulum. This energy is called notch toughness.

8.5 Ductile brittle transition :

Ductile to brittle transition occurs in materials when the temperature is dropped below a transition temperature. Alloying usually increases the ductile-brittle transition temperature, for ceramics, this type of transition occurs at much higher temperatures than for metals.



8.6 Fatigue:

Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It can happen in bridges, airplanes, machine components, etc. The characteristics are:

• long period of cyclic strain • the most usual (90%) of metallic failures (happens

also in ceramics and polymers) • is brittle-like even in ductile metals, with little

plastic deformation • it occurs in stages involving the initiation and

propagation of cracks.

Cyclic Stresses

These are characterized by maximum, minimum and mean stress, the stress amplitude, and the stress ratio.

8.7 Crack Initiation and Propagation

Stages is fatigue failure:

I. crack initiation at high stress points (stress raisers)

II. propagation (incremental in each cycle)

III. final failure by fracture

Nfinal = Ninitiation + Npropagation

Stage I - propagation

• slow • along crystallographic planes of high shear stress • flat and featureless fatigue surface

Stage II - propagation

Crack propagates by repetitive plastic blunting and sharpening of the crack tip.



8.8 Crack propagation rate

Crack propagation life is computed based on a crack-growth model such as Paris, Forman, Walker, Elber or Collipriest, depending on the material and type of loading. The first two models are used for constant amplitude loading, while the latter three correspond to variable amplitude loading and include crack-growth retardation/ acceleration effects. Threshold cracks are also incorporated. K vs. relations are available for standard crack configurations. For other cases, values of K vs. a are generated from fracture analysis.

Crack growth is computed using either the cycle-by-cycle or segment-by-segment approach. While the first method is accurate, it requires considerable computational time. The latter approach provides a fast approximation. Accordingly, crack growth is divided into a finite number of segments and number of cycles required for each segment is obtained, which is then cumulated.



8.9 Creep

Creep is the time-varying plastic deformation of a material stressed at high temperatures. Examples: turbine blades, steam generators. Keys are the time dependence of the strain and the high temperature.

8.10 Generalized Creep Behavior

At a constant stress, the strain increases initially fast with time (primary or transient deformation), then increases more slowly in the secondary region at a steady rate (creep rate). Finally the strain increases fast and leads to failure in the tertiary region. Characteristics:

• Creep rate: dε/dt • Time to failure.

8.11 Stress and Temperature Effects:

Both temperature and the level of the applied stress influence the creep characteristics. The results of creep rupture tests are most commonly presented as the logarithm of stress versus the logarithm of rupture lifetime.

Creep becomes more pronounced at higher temperatures. There is essentially no creep at temperatures below 40% of the melting point.

Creep increases at higher applied stresses.

The behavior can be characterized by the following expression, where K, n and Qc are constants for a given material:

dε/dt = K σn exp(-Qc/RT)

Failure

Module-08


1. Fracture, ductile and brittle fracture

2. Fracture mechanics

3. Impact fracture, ductile-to-brittle transition

4. Fatigue, crack initiation and propagation, crack propagation rate

5. Creep, generalized creep behavior, stress and temperature effects

Contents


Failure – ClassificationFailure of a material component is the loss of ability to function normally or to perform the intended job!Three general ways failure: Excessive elastic deformation, E.g.: buckling. Controlled by design and elastic modulus of the material.Excessive plastic deformation, Controlled by yield strength of the material. E.g.: loss of shape, creep and/ or stress-rupture at elevated temperatures.Fracture, involves complete disruption of continuity of a component – under static load: brittle or ductile, under fluctuating/cyclic load: fatigue, mode in which most machine parts fail in service.


FractureFracture defined as the separation or fragmentation of a solid body into two or more parts under the action of stress.Fracture is classified based on several characteristic features:

Through grainsAlong grain boundariesCrack propagation

Granular and brightFibrous and grayAppearance

CleavageShearCrystallographic modeBrittleDuctileStrain to fracture

Terms UsedCharacteristic


Fracture ModesDuctile and Brittle are relative terms.Most of the fractures belong to one of the following modes: (a) rupture, (b) cup-&-cone and (c) brittle.


Ceramics, Glasses, Ice

Most metals (not too cold)Type of materials

Smooth and brightRough and dullFractured surfaceNoYesNeckingLittleExtensiveDeformationNonePlastic deformationWarning signFastSlowCrack propagation

ConstantIncreasingStress, during cracking

LowerHigherStrain energy required

Brittle fractureDuctile fractureParameter

Ductile Fracture Vs Brittle Fracture


Ductile Fracture - 1Ductile fracture in tension occurs after appreciable plastic deformation.It is usually preceded by necking. It exhibits three stages - (1) formation of cavities (2) growth of cavities (3) final failure involving rapid crack propagation at about 45 to the tensile axis.Fractography of ductile fracture reveals numerous spherical dimples separated by thin walls on the fractured surface.McClintock’s strain to ductile fracture, εf,

[ ])32()()1(sinh)2ln()1( 00

σσσε

baf n

bln+−

−=


Ductile Fracture - 2Stages of void nucleation, void growth, crack initiation and eventual fracture under ductile fracture mode:


Brittle FractureBrittle fracture intakes place with little or no preceding plastic deformation.It occurs, often at unpredictable levels of stress, by rapid crack propagation.Crack propagates nearly perpendicular to the direction of applied tensile stress, and hence called cleavage fracture.Most often brittle fracture occurs through grains i.e. transgranular.Three stages of brittle fracture - (1) plastic deformation that causes dislocation pile-ups at obstacles, (2) micro-crack nucleation as a result of build-up of shear stresses, (3) eventual crack propagation under applied stress aided by stored elastic energy.


Brittle Fracture – Griffith TheoryNominal fracture stress that causes brittle fracture in presence of cracks (length of interior crack=2c), the stress raisers,

Griffith’s criteria: a crack will propagate when the decrease in elastic energy is at least equal to the energy required to create the new crack surface. Thus for thin plates:

For thick plates:

When plastic energy is also taken into account (Orowan’s modification):

212⎟⎠⎞

⎜⎝⎛=

πγσ

cE

21

2 )1(2

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=πν

γσc

E

2121)(2⎟⎠⎞

⎜⎝⎛≈⎟

⎠⎞

⎜⎝⎛ +

=c

Epc

pEπγσ

21

4⎟⎠⎞

⎜⎝⎛≈

cE

fγσ


Fracture Mechanics - 1Relatively new field of mechanics, that deals with possibility whether a crack of given length in a material with known toughness is dangerous at a given stress level or not!Fracture resistance of a material in the presence of cracks, known as fracture toughness, is expressed in two forms.(1) Strain-energy release rate, G:

(2) Stress concentration factor, K:

Both parameters are related as:For plane stress conditions i.e. thin plates:For plane strain conditions i.e. thick plates:

EcG

2πσ=

πασ cK =

GEK =2

)1( 22 ν−= GEK


Fracture Mechanics - 2K depends on many factors, the most influential of which are temperature, strain rate, microstructure and orientation of fracture. The value of K decreases with increasing strain rate, grain size and/or decreasing temperature.Depending on the orientation of fracture, three modes of fracture are identified as shown in the figure:


Notch-Impact Testing - 1Ductile and Brittle are terms used to distinguish two extremes of fractures modes based on plastic deformation involved before fracture occurs.Three factors that aid transition from ductile to brittle-cleavage type of fracture are: 1. tri-axial state of stress 2. low temperature, and 3. rapid rate of loading.Since brittle fracture is most unpredictable, its been extend at a greater extent. Usually a notch will be introduced to simulate the conditions.A notch increases the tendency for brittle fracture by four means: a) by producing high local stresses, b) by introducing a tri-axial state of stress, c) by producing high local strain hardening and cracking, and d) by producing a local magnification to the strain rate.


Notch-Impact Testing - 2A material’s susceptibility to different kinds of fracture is measured using notched specimen subjected to impact load. Further study involves examining the fracture surfaces, and calculation of ductility.Two kind of specimen configurations & loading directions:


Ductile-To-Brittle TransitionEnergy absorbed during the notch-impact is plotted as a function of temperature to know at what temperature range (DBTT) material fracture in a particular mode.

In metals DBTT is around 0.1-0.2 Tm while in ceramics it is about 0.5-0.7 Tm, where Tm represents absolute melting temperature.


Fatigue Failure - 1Failure that occurs under fluctuating/cyclic loads – Fatigue.Fatigue occurs at stresses that considerable smaller than yield/tensile stress of the material.These failures are dangerous because they occur without any warning. Typical machine components subjected to fatigue are automobile crank-shaft, bridges, aircraft landing gear, etc. Fatigue failures occur in both metallic and non-metallic materials, and are responsible for a large number fraction of identifiable service failures of metals.Fatigue fracture surface is perpendicular to the direction of an applied stress.


Fatigue Failure - 2Fatigue failure can be recognized from the appearance of the fracture surface:

Any point with stress concentration such as sharp corner or notch or metallurgical inclusion can act as point of initiation of fatigue crack.


Fatigue Failure - 3Three basic requisites for occurrence of fatigue fracture are: a) a maximum tensile stress of sufficiently high value b) a large enough variation or fluctuation in the applied stress and c) a sufficiently large number of cycles of applied stress.Stress cycles that can cause fatigue failure are characterized using the following parameters:Range of stress, σr = σmax – σmin

Alternating stress, σa = σr/2 = (σmax – σmin)/2Mean stress, σm = (σmax + σmin)/2Stress ratio, R= σmin / σmax

Amplitude ratio, A= σa / σm = (1-R) / (1+R)


Fatigue Testing – Data PresentationFatigue test, usually, involves applying fluctuating load cyclically.A specimen of rotating beam type is often used because of its simplicity.Fatigue data is usually presented by plotting maximum stress (S) against number of cycles to fracture (N), using a logarithmic scale for the latter variable.

S-N curve can be represented by the Basquin equation:

CN pa =σ


Fatigue ParametersMaterial fails under fatigue mode at higher number of stress cycles if stress applied is lower.After a limiting stress, ferrous materials won’t fail for any number of stress cycles. This limiting stress is called –fatigue limit / endurance limit.For non-ferrous materials, there is no particular limiting stress i.e. as stress reduces, number of cycles to failure keep increasing. Hence stress corresponding to 107 cycles is considered as characteristic of material, and known as fatigue strength. Number of cycles is called fatigue life.Endurance ratio – ratio of fatigue stress to tensile stress of a material. For most materials it is in the range of 0.4-0.5.


The Goodman diagram presents the dependence of allowable stress ranges on mean stress for a material. Allowable stress range increases with increasing compressive mean stress i.e. compressive stress increases the fatigue limit.

Fatigue Data Presentation – Goodman Diagram - 1


An alternative method of presenting mean stress data is by using Heig-Soderberg diagram. The following equation summarizes the diagram:

x=1 for Goodman line, x=2 for the Gerber parabola.

Fatigue Data Presentation - 2

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

x

u

mea σ

σσσ 1


Fatigue failure consists of four stages:(a) crack initiation – includes the early development of fatigue damage that can be removed by suitable thermal anneal (b) slip-band crack growth – involves the deepening of initial crack on planes of high shear stress (stage-I crack growth) (c) crack growth on planes of high tensile stress – involves growth of crack in direction normal to maximum tensile stress (stage-II crack growth) (d) final ductile failure – occurs when the crack reaches a size so that the remaining cross-section cannot support the applied load.Stage-I is secondary to stage-II crack growth in importance because very low crack propagation rates involved during the stage.

Fatigue – Crack Initiation & Propagation


Not necessaryRequiredNecessity of diffusion

Very highLess Vacancy concentration

Some grainsAll grainsGrains involved

Extrusions & IntrusionsContour Deformation feature

1-101000Slip (nm)

Cyclic loadStatic loadFeature

Static Load Vs Cyclic Load - 1


Static Load Vs Cyclic Load - 2


Fatigue Crack Growth: Stage-I Vs Stage-II

StriationsFeature lessFeature

Multiple slip planesSingle slip planeSlip on

High (µm/cycle)Low (nm/cycle)Crack propagation rate

No Yes Crystallographic orientation

TensileShearStresses involved

Stage-IIStage-IParameter


Fatigue Crack Propagation Rate

nma aCafn

dNda σσ == ),(

pKAdNda )(∆=

Studies of fatigue crack propagation rate attained much importance because it can be used as fail-safe design consideration.

Paris law:

p= 3 for steels, 3-4 for Al alloys


Deformation that occurs under constant load/stress and elevated temperatures which is time-dependent is known as creep. Creep deformation (constant stress) is possible at all temperatures above absolute zero. However, it is extremely sensitive to temperature. Hence, creep in usually considered important at elevated temperatures (temperatures greater than 0.4 Tm, Tm is absolute melting temperature).Creep test data is presented as a plot between time and strain known as creep curve.The slope of the creep curve is designated as creep rate.

Creep Failure


Creep Curve - 1


Creep Curve - 2Creep curve is considered to be consists of three portions.After initial rapid elongation, ε0, the creep rate decreases continuously with time, and is known as primary or transient creep. Primary creep is followed by secondary or steady-state or viscous creep, which is characterized by constant creep rate. This stage of creep is often the longest duration of the three modes.Finally, a third stage of creep known as, tertiary creep occurs that is characterized by increase in creep rate.Andrade creep equation:

Garofalo creep equation:

ktet )1( 310 βεε +=

te srt

t εεεε &+−+= − )1(0


Creep In Different StagesFirst stage creep is associated with strain hardening of the sample.Constant creep rate during secondary creep is believed to be due to balance between the competing processes of strain hardening and recovery. Creep rate during the secondary creep is called the minimum creep rate.Third stage creep occurs in constant load tests at high stresses at high temperatures. This stage is greatly delayed in constant stress tests. Tertiary creep is believed to occur because of either reduction in cross-sectional area due to necking or internal void formation. Third stage is often associated with metallurgical changes such as coarsening of precipitate particles, recrystallization, or diffusional changes in the phases that are present.


Creep Rate – Stress & Temperature Effects

Two most important parameter that influence creep rate are: stress and temperature.With increase in either stress or temperature (a) instantaneous elastic strain increases (b) steady state creep rate increases and (c) rupture lifetime decreases.

RTQ

ns

c

eK−

= σε 2&

Material Science/Applications and Processing of Metals and Alloys Lecture Notes

Satish Kailash Vasu/IISc, Bangalore M9/L1/V1/feb2005/1

Chapter 9 Applications and Processing of Metals and Alloys

9.1 Types of metals and alloys:

Ferrous alloys:

Ferrous alloys are those in which iron is the prime constituent. They are especially important as engineering construction materials. The principal disadvantage of many ferrous alloys is their susceptibility to corrosion. Different alloys of iron are given below:

Alloys of iron

• Steel (carbon) o Stainless steel (chromium, nickel)

Surgical stainless steel (chromium, molybdenum, nickel) o Silicon steel (silicon) o Tool steel (tungsten or manganese)

• Cast iron (carbon) • Spiegeleisen (manganese, carbon, silicon)

Nonferrous alloys:

Alloys of cobalt

• Stellite (chromium, tungsten, carbon) o Talonite

Alloys of nickel

• Mu-metal (iron) • Monel metal (copper, iron, manganese) • Nichrome (chromium, iron)

Alloys of copper

• Brass (zinc) • Prince's metal (zinc) • Gilding metal (zinc) • Bronze (tin, aluminium or any other element)

o Phosphor bronze (tin and phosphorus) • Bell metal (tin) • Beryllium copper (beryllium) • Cupronickel (nickel)



• Nickel silver (nickel) • Billon (silver) • Nordic gold (aluminium, zinc, tin)

Alloys of silver

• Sterling silver (copper)

Alloys of tin

• Pewter (lead, copper) • Solder (lead)

Alloys of gold

• Electrum (silver, copper)

Alloys of mercury

• Amalgam

Alloys of lead • Solder • Type metal

Alloys of bismuth

• Wood's metal

9.2 Fabrication of Metals and Composite Materials:

The fabrication of metals and composite materials can be conducted on a variety of processing equipment. Alloys can be produced by arc melting or induction melting in a vacuum or in a controlled atmosphere, and can be shaped using a variety of equipment. The facility includes various sizes of rolling mills, draw benches, tubing reducers, welding equipment (including electron-beam), 1/2 in. steel capacity shear, swaging machines, straightening equipment, and hydraulic presses. Laboratory-sized extrusions can also be produced. Furnaces up to 24 in. x 24 in. x 72 in. in size and with temperatures up to 2400°C with controlled or vacuum atmospheres are available for heat treating. An area for cleaning and chemical etching with exhaust systems is also located at the facility. In addition, specialty equipment such as a hot isostatic press and a high-energy impact



mill are available. Complete metallographic facilities to study the microstructure of the materials processed are also located at the facility.

Forming operations

Forming operations are those in which the shape of a metal piece is changed by plastic deformation; for example, forging, rolling, extrusion and drawing are common forming techniques. When deformation is achived at a temperature above that at which recrystallization occurs, the process is termed hot working, otherwise it is cold working.

Forging

Forging is mechanically working or deforming a single piece of a normally hot metal; this may be accomplished by the application of successive blows or by continuous squeezing.

Rolling

Rolling, the most widely used deformation process consists of passing a piece of metal between two rolls, a reduction in thickness results from compressive stresses exerted by the rolls.

Extrusion

For extrusion, a bar of metal piece through a die orifice by a compressive force that is applied to a ram; the extruded piece that emerges has the desired shape and a reduced cross sectional area.

Drawing

Drawing is the pulling of a metal pice through a die having a tapered bore by means of a tensile force that is applied on the exit side. A reduction in cross section results, with a corresponding increase in length.

Casting:

Casting is a fabrication process whereby a totally molten metal is poured into a mold cavity having the desired shape; upon solidification, the metal assumes the shape of the mold but experiences some shrinkages. Different types of casting techniques which are commonly employed are: sand , die, investment and continuous casting.



Miscellaneous Techniques:

Powder Metallurgy

This is another fabrication technique which involoves the compaction of powdered metal, followed by a heat treatment to produce a more dense piece. Diffusional processes during the heat treatment are central to the development of these properties. This method is especially suitable for metals having low ductilities, since only small plastic deformation of the powder particles need occur.

Welding

In welding, two or more metal parts are joined to form a single piece when one part fabrication is expensive or inconvenient. Both similar and non similar metals can be joined by welding. The joining bond is metallurgical rather than juts mechanical. During arc and gas welding, the work pieces to be joined and the filler material are heated to a sufficiently high temperature to cause both to melt; upon solidification, the filler material forms a fusion joint between the work pieces.

9.3 Thermal Processing of metals

Annealing Processes Annealing is a heat treatment where the material is taken to a high temperature, kept there for some time and then cooled. High temperatures allow diffusion processes to occur fast. The time at the high temperature (soaking time) is long enough to allow the desired transformation to occur. Cooling is done slowly to avoid the distortion (warping) of the metal piece, or even cracking, caused by stresses induced by differential contraction due to thermal inhomogeneities. Benefits of annealing are:

• relieve stresses • increase softness, ductility and toughness • produce a specific microstructure



9.4 Heat Treatments

Precipitation hardening is achieved by:

a) solution heat treatment where all the solute atoms are dissolved to form a single-phase solution.

b) rapid cooling across the solvus line to exceed the solubility limit. This leads to a supersaturated solid solution that remains stable (metastable) due to the low temperatures, which prevent diffusion.

c) precipitation heat treatment where the supersaturated solution is heated to an intermediate temperature to induce precipitation and kept there for some time (aging).

If the process is continued for a very long time, eventually the hardness decreases. This is called overaging.

The requirements for precipitation hardening are:

• appreciable maximum solubility • solubility curve that falls fast with temperature • composition of the alloy that is less than the maximum solubility

9.5 Precipitation Hardening

Hardening can be enhanced by extremely small precipitates that hinder dislocation motion. The precipitates form when the solubility limit is exceeded. Precipitation hardening is also called age hardening because it involves the hardening of the material over a prolonged time.

Applications and Processing of Metals and Alloys

Module-09


1. Types of metals and alloys

2. Fabrication of metals

3. Thermal processing of metals

Contents


Materials – ClassificationMaterials are classified into three basic groups based on their mechanical and physical nature as – metals, ceramics and polymers.For an engineer, especially, metals are more important owing to ability to carry loads and ease of manufacturing.Metallic materials are again classified for ease of selection and/or based on their tonnage of usage broadly into two classes – ferrous and non-ferrous.Ferrous materials – chief constituent is iron (Fe). E.g.: steel, cast iron.Metallic materials those are not ferrous are termed as non-ferrous materials. E.g.: Brass, Silver, Aluminium, Titanium.


Ferrous Materials - IntroductionIn engineering applications, lion share is served by ferrous materials.Factors account for it are:- availability of abundant raw materials combined with economical extraction- ease of forming- their versatile mechanical and physical properties.There are some drawbacks about ferrous materials:- poor corrosion resistance- high density i.e. low specific strength- low thermal and electrical conductivities


Ferrous Materials - ClassificationThere are two classes – steels and cast irons – categorized based on carbon content.Steels: %C is up to 2.14%Cast irons: %C is above 2.14%Cast irons are called so because they are usually manufactured through casting technique owing to their brittle nature due to presence of iron carbide.Steels are serving major part of present engineering applications.However, cast irons mostly serve as structural components. E.g.: automobile motor casings, lathe bed, sliding guides in machinery.


Steels - 1In steels, C atoms occupies interstitial sites of Fe.Steels are classified based on their C content/alloying additions which in turn dictates their applications: plain carbon steels and alloying steels.Low-carbon steels: % wt of C < 0.3Medium carbon steels: 0.3 <% wt of C < 0.6High-carbon steels: % wt of C > 0.6Low carbon steels:- Carbon present is not enough to strengthen them by heat treatment, hence are strengthened by cold work.- They are easily weldable and machinable.- Typical applications: tin cans, automotive body components, structural shapes, etc.


Steels - 2Medium carbon steels:- They are less ductile and stronger than low carbon steels.- Heat treatable (austenitizing, quenching and tempering).- Hardenability is increased by adding Ni, Cr, Mo.- Used in various tempered conditions.- Typical applications: gears, railway tracks, machine parts.High carbon steels:- They are strongest and hardest of carbon steels.- Heat treatable. Used in tempered or hardened conditions.- Alloying additions – Cr, V, W, Mo- Typical applications: Knives, razors, hacksaw blades, etc where high wear resistance is the prime requirement.


HSLA And Stainless Steels - 1HSLA (high strength low alloy) steels:- They can be strengthened by heat treatment.- Ductile and formable.- Alloying addition – Cu, V, W, Ni, Cr, Mo, etc.- Typical applications: support columns, pressure vessels, bridge beams.Stainless steels:- They typical consists min.12% Cr along with other alloying elements, thus highly corrosion resistant owing to presence of chromium oxide.- Three kinds - ferritic & hardenable Cr steels, austenitic and precipitation hardenable (martensitic, semi-austenitic) – based on presence of prominent microstructural constituent.


Stainless Steels - 2Stainless steels:- Typical applications – cutlery, surgical knives, storage tanks, domestic items- Ferritic steels are principally Fe-Cr-C alloys with 12-14% Cr. And small additions of Mo, V, Nb, Ni.- Austenitic steels contain 18% Cr and 8% Ni plus minor alloying elements. Ni stabilizes the austenitic phase assisted by C and N. - For, martensitic steels Ms is made to be above the room temperature. These alloys are heat treatable. Major alloying elements are: Cr, Mn and Mo.- Ferritic and austenitic steels are hardened and strengthened by cold work because they are not heat treatable. - Austenitic steels are non-magnetic as against ferritic and martensitic steels, which are magnetic.


Cast Irons - 1Grey cast iron- Cementite decomposes during solidification to form carbon flakes. Thus they are brittle.- Fractured surface looks grey because of presence of graphite, hence the name.- Possess good damping properties. - Typical applications – base structures, machine bedsWhite cast iron- Cooled fast so that cementite does not decompose. - Fractures surface looks whitish because of cementite, hence the name. - They are brittle and extremely difficult to machine. - Used as source materials for producing malleable iron.


Cast Irons - 2Nodular cast iron- Alloying addition of Mg/Ce to grey cast iron melt results in graphite to form as modules.- They are stronger and ductile than grey cast iron.- Typical applications – pump bodies, crank shafts, automotive components, etc.Malleable cast iron- Formed by heat treating white cast iron. Heat treatment involves heating to 800-900C, keep it there for long hours, then cooling to room temperature.- Cementite decomposes to form graphite and ferrite.- Typical applications – railroad, connecting rods, marine and other heavy-duty services.


Non-Ferrous MaterialsTypical advantages of non-ferrous materials over ferrous materials:- high specific strength.- low density.- high electrical and thermal conductivities.- distinct properties thus used for specific purposes.- can be formed with ease.E.g.: Al-alloys

Cu-alloys (brass, bronze)Mg-alloysTi-alloysNoble metals (E.g.: Ag, Au, Pt, Pa)Refractory metals (E.g.: Nb, Mo, W and Ta)


Fabrication Of Metals And Alloys

Four basic manufacturing processes:Casting – to give a shape by pouring in liquid metal into a mold that holds the required shape, and letting harden the metal without external pressure.Forming – to give shape in solid state by applying pressure.Machining – in which material is removed in order to give it the required shape.Joining – where different parts are joined by various means.Other important technique is powder metallurgy.


Metal Casting – Metal FormingFour important casting techniques are:Sand castingDie castingInvestment castingContinuous castingFour important forming techniques are:ForgingRollingExtrusionDrawing


Metal Forming Techniques


Thermal ProcessingTwo main kinds of metal processing methods – mechanical and thermal.Thermal processing is also known as heat treatment.Purpose of heat treatment: - improvement in ductility- relieving internal stresses- grain size refinement- increase of strength- improvement in machinability and toughnessThermal processing factors – temperature up to which material is heated, length of time that the material is held at the elevated temperature, rate of cooling, and the surrounding atmosphere under the thermal treatment.


Thermal Processing MethodsTwo kinds heat treating methods are – annealing and quenching & tempering.These differ in the way material is cooled from an elevated temperature.Annealing involves cooling the material slowly, allowing phase changes.Quenching (also known as hardening) means cooling the material at a rapid rate to arrest the equilibrium phase transformations.During annealing, material is cooled in air and/or heating furnace itself.For quenching, material is immersed in water / oil quench bath.


Annealing TechniquesProcess annealing – applied to cold worked materials to negate effects of cold work. Commonly sandwiched between two cold work operations. Improves ductility.Stress relief – purpose of it is to remove stresses. Temperatures are low such that cold work effects are not affected.Full annealing – used for products that are to be machined later-on. Cooling is done in furnace itself. Hardness and strength are restored by additional heat treatments after machining.Normalizing – used to refine the grains and produce a more uniform and desirable size distribution. It involves heating the component to attain single phase (e.g.: austenite in steels), then cooling in open air atmosphere.


Quenching & TemperingQuenching operation is usually followed by tempering.Tempering involves heating martensitic steel at a temperature below the eutectoid transformation temperature to make it softer and more ductile. Here Martensite transforms to ferrite embedded with carbide particles.Martempering is used to minimize distortion and cracking. It involves cooling the austenized steel to temperature just above Ms temperature, holding it there until temperature is uniform, followed by cooling at a moderate rate to room temperature before austenite-to-bainite transformation begins. The final structure of martempered steel is tempered Martensite.Austempering involves austenite-to-bainite transformation. Thus, the final structure of austempered steel is bainite.

Material Science/Applications and Processing of Ceramics Lecture Notes


Chapter 10. Applications and Processing of Ceramics 10.1 Types and applications of ceramics:

Ceramics offer a high temperature range. However, ceramics are not very strong. To compensate for their lack of strength ceramics are usually combined with some other material to form a ceramic composite.

1) Glasses and glass ceramics- The glasses are a familiar group of ceramics; containers, windows, lenses and fiberglass represent typical applications. The properties of standard vitrified products are insufficient for architectural applications and structural building components, insulation or other specialized applications. Yet there is an effective way to improve these properties without major alterations to the process itself - the introduction of a controlled crystallization process through a subsequent heat treatment, i.e. by forming a glass-ceramic.

Production of Glass-Ceramics

Glass-ceramic articles may be produced by three routes:

· The heat treatment of solid glass (the traditional route)

· The controlled cooling of a molten glass, known as the petrurgic method

· The sintering and crystallisation of glass powders.

In the latter case, the powders are densified at relatively low temperatures by exploiting a viscous flow sintering mechanism. After densification, the material is subjected to a crystallisation heat-treatment to obtain the required glass-ceramic microstructure. Alternatively, both densification and crystallisation may take place during a single sintering step.

Along with the economic advantage of using relatively low processing temperatures, the powder technology route is suitable for the production of a range of advanced materials, including glass-ceramics with specified porosities and glass-ceramic matrix composites. Using the petrurgic method, the slow cooling from the molten state causes nucleation and growth of certain crystalline phases. Therefore, the final microstructure, and hence the properties, depends mainly on the composition and the cooling rate.

Glass-Ceramics Based on Coal Ash

The very high iron oxide content of coal ash, table 1, indicates the potential for developing magnetic phases using appropriate processing - this was the aim of our work. We calcined the as-received ash at 800°C for two hours to remove any volatile



compounds, including sulfur and carbon. The powder and petrurgic methods were explored, and gave us products with different phases and microstructures. For the sintering experiments, we mixed calcined ash powder with various amounts (10-50wt%) of borosilicate (Pyrex) glass. The powder mixtures were uniaxial cold pressed to a cylindrical shape and sintered in air at temperatures in the range of 1,000-1,500°C for periods of up to 15 hours. Using the petrurgic method, coal ash was mixed with soda-lime glass powder. The mixture was melted at 1,500°C and cooled to room temperature at rates of between 1-10°C per minute.

Glass-Ceramic Composites

Work to date has largely concentrated on composites with a matrix of the slag-based Silceram glass-ceramic (a glass-ceramic for floor and wall tiles and wear components). We have investigated both particulate- (SiC and TiC) and fibre-reinforcement (SiC). Properties measured include the fundamental mechanical properties but also more complex properties such as thermal shock resistance and erosion resistance. As mentioned previously, the thermal shock resistance of glass-ceramics is superior to the parent glasses, and the shock resistance is further improved by particulate reinforcement. For example, monolithic Silceram has a thermal shock critical temperature of 180°C, whereas a 20wt%SiC composite has a value of 270°C. Erosion resistance may also be improved by particulate reinforcement, e.g., for TiC reinforced Silceram - the larger the reinforcement particle size and the greater the volume fraction, the lower the erosion rate.

Results indicate a way for transforming vitrified silicate residues into useful products with broad application potential. The glass-ceramics obtained are candidate materials for applications in floors of industrial buildings and in construction, and for outside and inside facing walls. We are currently addressing issues associated with the effect of environmental influences on the chemical durability and toxic potential of the materials, which may be compromised by the presence of heavy metals incorporated in the glass or crystalline phases. Public acceptance of the use and exploitation of glass-ceramic-based materials in such applications will strongly depend on a satisfactory consideration of these issues.

2) Refractories -Refractories are materials needed for handling high temperature liquids, gases and solids, e.g., for industrial processing. Applications include solar furnaces, casting molds for molten materials, heat exchangers, and aerobraking heat shields.

Industrial refractory needs can be satisfied by sintered calcia (CaO), silica (SiO2), magnesia (MgO), alumina (Al2O3) and titania (TiO2), with the desired porosity. Of course, these stable materials are commonly used on Earth for the same purposes, due to their great resistance to heat, oxidation (they are already fully oxidized), corrosion and abrasion. Minerals such as olivine [(MgFe)2SiO4] and anorthite (CaAl2Si2O8) are also useful for making refractory bricks and ceramics. Some refractories and their ceramics have low expansion due to heat and are attractive for space environments where a wide range of temperatures are experienced.



Production of ceramics and refractories in space from lunar materials has been discussed in a number of papers, including Poisl and Fabes, as well as Shirley et al., and Mackenzie and Claridge, among others.

One particular application of refractories is in transportation for returning cargoes to low Earth orbit by aerobraking with the upper atmosphere, and perhaps slowing down some incoming asteroid payloads by aerobraking. Of course, this is the method used by spacecraft to return to Earth, including the reusable Space Shuttle. The Space Shuttle's tiles are made from silica (SiO2) (with a thin borosilicate coating to provide a smooth, aerodynamic surface for a smooth landing).

Aerobraking tiles are produced from amorphous silica fibers which are pressed and sintered, with the resulting tile having as much as 93% porosity (i.e., very lightweight) and low thermal expansion, low thermal conductivity, and good thermal shock properties. This process can be readily performed in space when we can produce silica of the required purity.

Cheaper materials besides silica fibers can be used. Silica fibers are used on the Space Shuttle in order to keep its weight down, thereby increasing cargo weight capacity. For resources already in space, we don't have this economic need. A number of other materials can be used for heat shields, e.g., alumina (Al2O3) or anorthite (CaAl2Si2O8).

3) Abrasives- Abrasive cements are used to wear, grind or cut away other material, which necessarily is softer. Therefor, the prime requisite for this group of materials is hardness or wear resistancr; in addition, a hig degree of toughness is essential to ensure that the abrasive particles do not easily fracture. Furthermore, high temperatures may be produced from abrasive frictional forces, so some refractoriness is also desirable. Diamonds, both natural and synthetic, are utilized as abrasives; however, they are relatively expensive. The more common ceramic abrasives include silicon carbide, tungsten carbide(WC), aluminium oxide and silica sand. Abrasives are used in several forms-bonded to grinding wheels, as coated abrasives and as loose grains. Coated abrasives are those in which an abrasive powder is coated on some type of paper or cloth material; sandpaper is probably the mostly familiar example. Wood, metals, ceramics and plastics are all frequently ground and polished using this form of abrasive.Grinding, lapping and polishing wheels often employ loose abrasive grains that are delivered in some type of oil or water based vehicle. Diamonds, corundum,silicon carbide and rouge are used in loose form over a variety of grain size ranges.

4) Cements:

Several familiar ceramic materials are classified as inorganic cements:cements, plaster of paris, and lime, which as a group are produced in extremely large quantities. The characteristic feature of these materials is that when mixed with water, they form a paste that subsequently sets and hardens. This trait is especially useful in that solid and rigid structures having just about any shape may be expeditiously formed.



Portland Cement

Portland cement is a closely controlled chemical combination of calcium, silicon, aluminum, iron and small amounts of other compounds, to which gypsum is added in the final grinding process to regulate the setting time of the concrete. Some of the raw materials used to manufacture cement are limestone, shells, and chalk or marl, combined with shale, clay, slate or blast furnace slag, silica sand, and iron ore. Lime and silica make up approximately 85 percent of the mass (1).

The term "Portland" in Portland cement originated in 1824 when an English mason obtained a patent for his product, which he named Portland Cement. This was because his cement blend produced concrete that resembled the color of the natural limestone quarried on the Isle of Portland in the English Channel.

Different types of Portland cement are manufactured to meet different physical and chemical requirements for specific purposes. The American Society for Testing and Materials (ASTM) Designation C 150 provides for eight types of Portland cement: (reference).Portland Cement is a type of cement, not a brand name. Many cement manufacturers make Portland Cement. Variuos types of Portland cements are:

Type 1 normal portland cement. Type 1 is a general use cement.

Type 2 is used for structures in water or soil containing moderate amounts of sulfate, or when heat build-up is a concern.

Type 3 high early strength. Used when high strength are desired at very early periods.

Type 4 low heat portland cement. Used where the amount and rate of heat generation must be kept to a minimum.

Type 5 Sulfate resistant portland cement. Used where the water or soil is high in alkali.

Types IA, IIA and IIIA are cements used to make air-entrained concrete. They have the same properties as types I, II, and III, except that they have small quantities of air-entrained materials combined with them.

These are very short descriptions of the basic types of cement. There are other types for various purposes such as architectural concrete and masonry cements, just to name two examples



5) Advanced Ceramics:

Advanced Cerametrics Inc. (ACI) has evolved over its 56 year history from a small, family owned manufacturer of ceramic wear parts for the textile industry, to a prominent, high-tech company developing and manufacturing advanced materials. In recent years ACI has been the recipient of numerous R & D grants from the Defense Department, NASA and the Department of Energy.

ACI serves the aerospace, military, industrial, medical, textile, consumer, electronic, and automotive industries with three main product lines — traditional ceramics, including thread guides, insulators and thermally resistant parts; an advanced line of thick walled and complex injection molded ceramics; and ceramic fiber. Visit the pages below for further information on services and products.

ACI Products - photographs and technical details of ceramic components, finishes, capabilities, and processes. Includes a material selection and property chart.

ACI Technology - information on applications of ACI materials, and current research and development projects.

Contact Advanced Cerametrics for product details, new materials research information, and all other inquiries.

Ceramic Fiber

ACI has developed a line of piezoelectric fiber materials using its patented VSSP manufacturing process to make actively controlled structures. This fiber technology has been incorporated in the newest generation of active, smart sporting goods. Head Sport introduced their new line of Intellifiber and Intellichip active fiber composite tennis rackets and skis with energy harvesting actuators made from ACI's patented PZT fiber. These self-powered products actively dampen the vibration created during a ball strike or edge chatter from a ski turn and use the energy to create electrical force to control the shape of the ski or racket, using ACI’s PZT fiber's electrical and mechanical properties to counteract the forces. This active structural control adds up to 15% more power to a ball hit and about 6% more functional edge on a ski. This technology has opened the doors to many new sporting goods

ACI's fiber works extremely well as an acoustic transducer. As an integral component for the ultrasonic equipment market, the ability of a transducer to provide clear signals directly impacts the quality of the images produced. Using ACI's fiber transducers to replace the bulk



ceramic transducers, which are currently used in commercial ultrasound testing equipment, has yielded excellent results with no lateral wave interference. Acoustic applications include ultrasound imaging for medical and non-destructive testing, hearing aids, music, voice reproduction, recreational and commercial fish finders, and military systems.

Other products using this fiber include smart, actively controlled automotive suspensions, vibration damping in military and industrial systems and energy harvesting footwear.

Energy Harvesting: ACI's PZT materials have demonstrated the capability for use as a renewable energy source by incorporating it's patented PZT technology into flexible, motion sensitive (vibration, compression or flexure), active fiber composite shapes that can be placed in shoes, boots, and clothing or any location where there is a source of waste energy or mechanical deflexion. These flexible composites generate power from the scavenged energy and harness it using microprocessor controls developed specifically for this purpose. Projects currently under development with major manufacturers include self-heated boots for hiking, skiing, and military applications (also for battery charging

Industry of Ceramic Segments

Industry Segment Common Examples

Structural clay products Brick, sewer pipe, roofing tile, clay floor and wall tile (i.e., quarry tile), flue linings

Whitewares Dinnerware, floor and wall tile, sanitaryware, electrical porcelain, decorative ceramics

Refractories Brick and monolithic products are used in iron and steel, non-ferrous metals, glass, cements, ceramics, energy conversion, petroleum, and chemicals industries

Glasses Flat glass (windows), container glass (bottles), pressed and blown glass (dinnerware), glass fibers (home insulation), and advanced/specialty glass (optical fibers)

Abrasives Natural (garnet, diamond, etc.) and synthetic (silicon carbide, diamond, fused alumina, etc.) abrasives are used for grinding, cutting,



polishing, lapping, or pressure blasting of materials

Cements Used to produce concrete roads, bridges, buildings, dams, and the like

Advanced ceramics

Structural Wear parts, bioceramics, cutting tools, and engine components

Electrical Capacitors, insulators, substrates, integrated circuit packages, piezoelectrics, magnets and superconductors

Coatings Engine components, cutting tools, and industrial wear parts

Chemical and environmental

Filters, membranes, catalysts, and catalyst supports

10.2 Fabrication and processing of ceramics: Ceramic Synthesis: Our expertise and capabilities in synthesizing ceramics are based on chemical solution techniques. Chemical solution or sol-gel approaches have been developed to fabricate powders, films, and porous bodies. Materials of interest range from silica to complex, multicomponent electronic ceramics. The complexity inherent in fabricating materials with structured nanoporosity or complex chemistries requires a fundamental understanding of these chemical solution approaches. Fabrication of unique precursors for complex oxides is being done with novel metal alkoxide chemistry to produce powders and thin-film materials with carefully controlled properties. Our ability to synthesize materials with complex structures, chemistries, or both, is at the heart of numerous research and development efforts at Sandia. Ceramic Processing: Sandia's fabrication of ceramic components and devices is based on a strong ceramic-processing capability. We recently have demonstrated the ability to characterize and model the powder-compaction process in detail, and to address and control density gradients in powder compacts that cause shape distortion and differential shrinkage. Proprietary 3D, finite-element code packing and compaction models, and process-control tools are now available to improve the production of ceramic components. Sandia has capabilities in the areas of hydrostatic and triaxial compaction testing to characterize materials properties, and x-ray radiography, ultrasound, and computed tomography for density characterization. In addition, expertise in slurry



processing has enabled the development of direct-fabrication processes. Furthermore, we are developing phenomenological sintering models to enhance both ceramic component design and manufacturing capability.

Ceramic Synthesis and Processing Research Briefs:

Constrained Sintering of Multi-Material Systems

Development of A Predictive Model for Ceramic Powder Compaction

ESP (Engineered Stress Profile) Glass - Unique Opportunities for Performance and Reliability

Molecular Dynamics Simulations of Reactive Wetting in Ceramic-Metal Systems

PZT 95/5 Material Development for Neuron Generator Applications

Precursor's Structure Effects on Thin-Film Densification of TiO2

Relationship between Interfacial Interactions and Fracture Stress for Adhesive Joints in Mode II Loading

Robocasting : Layered Manufacturing by Slurry Extrusion

Synthesis and Processing of Composites by Reactive Metal Penetration

10.3 Electrical conduction in ionic ceramics and in polymers:

This requires creation of electron [e'] and hole [h⋅] pairs in ionic solid according to the symbolic chemical reaction, which describes creation of carriers due to thermal activation (this process results in intrinsic conductivity):

nil ⇔ e' + h⋅ K = [e'] + [h⋅ ] = n . p = exp (- ∆G0/RT) = exp (∆S0/R) exp (-Eg /RT)

Accordingly, a supply of "band gap" energy Eg is necessary, hence the strong dependence of conductivity on temperature. The equilibrium constant of the above reaction can be approximately expressed as: n.p ≈ 1019exp(Eg/kT), or, the carrier concentration (assuming the same concentration of holes p and electrons e), c ≈ 109.5exp(Eg/2kT).



The magnitude of the band gap Eg determines ability of a material to conduct. For Eg > 6 eV, materials are considered as insulators . This wide energy gap is typical for the ionic oxides of metals having a single stable oxidation state: groups IA, IIA, IIIA. The electrical resistivity of most stable insulators correlates with the ionic character of their bond: the larger difference of electronegativity, the larger % of ionic bond, and the larger energy gap Eg. The band gap magnitude correlates also with the ionic bond energy, i.e. the most stable ionic ceramic are also the best insulators. For example, the bond energy of alumina is ~6eV/equivalent (1/3 Al2O3) and Eg = ~7eV; the bond energy of one equivalent of cadmium oxide (CdO) is ~4 eV/equivalent and Eg = ~2eV. The oxides of metals able to have multiple oxidation states (such as transition elements, with partially filled "d" orbitals) have narrower band gaps of the order of 2-5eV, resulting in intrinsic semiconducting properties. The presence of point defects in ionic solids (such as solutes, vacancies, interstistials) can dramatically decrease the energy required for the creation of electron/hole pairs. This is because these defects are typically located “within” the energy gap, either close to the valence band (acceptors) or conduction band (donors). An example is KCl containing VK', VCl•, CaK• , or MgO containing VMg'', VO•,VMg', VC0, AlMg•. The point defects are the key feature of extrinsic semiconductors, the basic components of modern electronics.

Mixed and Ionic Ceramic Conductors The variety of point defects present in ceramics gives frequently a mixed ionic and electronic type of electrical conduction. To some extent, every ionic crystal is a mixed conductor, but the share of electronic conductivity, expressed through the charge transference number for electrons, can be negligible. If Ohm’s law is expressed in terms of current density J [A/m2], material conductivity σ [A/Vm] and electric field Ee, [V/m] following relationship results:

J = - σ.Ee



where, for mixed a conductor, σ = Σσi, the sum of conductvities due to the various charge-carrying species, i.e. ions, holes and electrons. The transference number ti of a given species is then defined as: tj = σj/Σσi For ionic conductors, the aim is to maximize the charge transference due to the movement of ions and minimize the transference due to electrons and holes movement. That is, tion ≈ 1 , te,h ≈ 0 . This is principle behind the operation of solid electrolytes. The sub-class of solid electrolytes useful for solid-state electrochemical devices (batteries, sensors) can be defined as "fast ionic conductors" as long as: 1. The activation energy Ed for diffusion is LOW, less than ~0.1 eV/atom, or 2.5 kcal/mole, or 10 kJ/mole, or ~10% of the energy needed to form a point defect in a close packed ionic solid.

2. The corresponding D0 value (diffusion coefficient D = D0exp[-Ed/kT], so

D = D0 at T = ∞) is HIGH (D0 >10-4 cm2/s) and therefore the corresponding σ0 value (ionic conductivity σ=σ0exp[-E/kT]) is HIGH, σ0 > 0.1 1/Ω.cm. If the above conditions are fulfilled, the diffusivity at room temperature will be D > 10-6 cm2/s, and room temperature ionic conductivity will be σ > 0.01 1/Ωcm, or resistivity ρ = 100 Ωcm . This magnitude of conductivity allows the use of solid state ionic conductors in devices like batteries, sensors and fuel cells. The resistivity of ionic conductor is the primary factor that determines internal resistance of the cell, and thus maximum current that can be drawn from the cell. As resistance R = ρ L/A (L being electrolyte thickness, typically 0.1-1 cm, and A area, typically 10-1000 cm2), then the internal resistance of such battery is typically 1 Ω .

Applications and Processing of Ceramics

Module-10


1. Types and applications of ceramics

2. Fabrication and processing of ceramics

Contents


Introduction – Ceramics The word ‘ceramic’ is originated from greek word keromikos, which means ‘burnt stuff’.Ceramics are compounds of metallic and non-metallic elements.Characteristics of ceramics are:- high temperature stability- high hardness- brittleness- high mechanical strength- low elongation under application of stress- low thermal and electrical conductivities


Classification – Ceramics - 1

Ceramics are classified in many ways. It is due to divergence in composition, properties and applications.Based on their composition, ceramics are:- Oxides- Carbides- Nitrides- Sulfides- Fluorides etc.



Based on their specific applications, ceramics are classified as:- Glasses- Clay products- Refractories- Abrasives- Cements- Advanced ceramics for special applications



Based on their engineering applications, ceramics are classified into two groups as: traditional and engineering ceramics.Traditional ceramics – most made-up of clay, silica and feldspar.Engineering ceramics – these consist of highly purified aluminium oxide (Al2O3), silicon carbide (SiC) and silicon nitiride (Si3N4)


Introduction – Processing Ceramics

The very specific character of ceramics – high temperature stability – makes conventional fabrication routes unsuitable for ceramic processing.Inorganic glasses, though, make use of lower melting temperatures. Most other ceramic products are manufactured through powder processing.Typical ceramic processing route: powder synthesis –green component (casting, extrusion, compaction) –sintering / firing.


Processing Ceramics – GlassesMost of them are silica-soda-lime variety. Raw materials are heated to an elevated temperature where melting occurs.Glass melt is processed by different route to form different products:Pressing – to form shapes like plates and dishesBlowing – used to produce objects like jars, bottles, light bulbs.Drawing – to form lengthier objects like tubes, rods, whiskers, etc.


Ceramic Powder Processing

Ceramic powder processing route: synthesis of powder, followed by fabrication of green product which is then consolidated to obtain the final product.Synthesis of powder involves crushing, grinding, separating impurities, blending different powders.Green component can be manufactured in different ways: tape casting, slip casting, extrusion, injection molding and cold-/hot- compaction.Green component is then fired/sintered to get final product.


Ceramic Powder Processing - Casting

Slurry of ceramic powder is processed via casting routes –tape casting, and slip casting.Tape casting – also known as doctor blade process – used for making thin ceramic tapes. In this slurry of ceramic powder + binders + plasticizers is spread over plastic substrate. Tape is then dried using hot air. Later tape is subjected to binder burnout and sintering.Slip casting – here aqueous slurry of ceramic powder is poured into plaster of Paris mold. As water begins to move out due to capillary action, thick mass builds along mold wall. It is possible to form solid piece by pouring more slurry.


Ceramic Powder Processing –Extrusion & Injection Molding

Extrusion – viscous mixture of ceramic particles, binder and other additives is fed through an extruder where continuous shape of green ceramic is produced. Then the product is dried and sintered.Injection molding – it is similar to the process used for polymer processing. Mixture of ceramic powder, plasticizer, thermoplastic polymer, and additives is injected into die with use of a extruder. Then polymer is burnt off, before sintering rest of the ceramic shape. It is suitable for producing complex shapes.Extrusion and Injection molding are used to make ceramic tubes, bricks, and tiles.


Ceramic Powder Processing –Compaction

Ceramic powder is compacted to form green shapes of sufficient strength to handle and to machine.Basis for compaction – application of external pressure from all directions.In cold iso-static pressing (CIP), pressure is applied using oil/fluid, then green product is subjected to sintering.In hot iso-static pressing (HIP), pressure is applied at high temperatures thus compaction and sintering occurs simultaneously. Its is expensive, but have certain advantages.


Ceramic Powder Processing –Compaction, HIP

HIP is used- when during CIP not enough strength is gained- almost nil porosity is the requirement- for Refractories and covalently bonded ceramics.Sintering – process of subjecting the green ceramic to elevated temperatures with the purpose of gaining mechanical integrity.Driving force for sintering – reduction in total surface area and thus energy.Diffusion (atomic- and bluk-) is responsible for growth of bonds at contact points of particles (necks). This lead to coalescence of particles, and eventual mechanical integrity.

Material Science/Applications and Processing of Polymers Lecture Notes


Chapter 11. Applications and Processing of Polymers

11.1 Mechanical behavior of polymers

The description of stress-strain behavior is similar to that of metals, but a very important consideration for polymers is that the mechanical properties depend on the strain rate, temperature, and environmental conditions.

The stress-strain behavior can be brittle, plastic and highly elastic (elastomeric or rubber-like). Tensile modulus (modulus) and tensile strengths are orders of magnitude smaller than those of metals, but elongation can be up to 1000 % in some cases. The tensile strength is defined at the fracture point and can be lower than the yield strength.

Mechanical properties change dramatically with temperature, going from glass-like brittle behavior at low temperatures (like in the liquid-nitrogen demonstration) to a rubber-like behavior at high temperatures .

In general, decreasing the strain rate has the same influence on the strain-strength characteristics as increasing the temperature: the material becomes softer and more ductile.

11.2 Deformation of Polymers

Many semicrystalline polymers have the spherulitic structure and deform in the following steps :

• elongation of amorphous tie chains • tilting of lamellar chain folds towards the tensile direction • separation of crystalline block segments • orientation of segments and tie chains in the tensile direction

The macroscopic deformation involves an upper and lower yield point and necking. Unlike the case of metals, the neck gets stronger since the deformation aligns the chains so increasing the tensile stress leads to the growth of the neck. (Fig. 16.5).

Factors that Influence the Mechanical Properties of Polymers

The tensile modulus decreases with increasing temperature or diminishing strain rate.

Obstacles to the steps mentioned in strengthen the polymer. Examples are cross-linking (aligned chains have more van der Waals inter-chain bonds) and a large mass (longer molecules have more inter-chain bonds). Crystallinity increases strength as the secondary bonding is enhanced when the molecular chains are closely packed and parallel. Pre-deformation by drawing, analogous to strain hardening in metals, increases strength by orienting the molecular chains. For undrawn polymers, heating increases the tensile



modulus and yield strength, and reduces the ductility - opposite of what happens in metals.

.



11.3 Crystallization, Melting, and Glass Transition Phenomena

Crystallization rates are governed by the same type of S-curves we saw in the case of metals (Fig. 16.7). Nucleation becomes slower at higher temperatures.

The melting behavior of semicrystalline polymers is intermediate between that of crystalline materials (sharp density change at a melting temperature) and that of a pure amorphous material (slight change in slope of density at the glass-transition temperature). The glass transition temperature is between 0.5 and 0.8 of the melting temperature.

The melting temperature increases with the rate of heating, thickness of the lamellae, and depends on the temperature at which the polymer was crystallized.

Melting involves breaking of the inter-chain bonds, so the glass and melting temperatures depend on:

• chain stiffness (e.g., single vs. double bonds) • size, shape of side groups • size of molecule • side branches, defects • cross-linking

Rigid chains have higher melting temperatures.

11.4 Types of Polymers:

Thermoplastic and Thermosetting Polymers

Thermoplastic polymers (thermoplasts) soften reversibly when heated (harden when cooled back)

Thermosetting polymers (thermosets) harden permanently when heated, as cross-linking hinder bending and rotations. Thermosets are harder, more dimensionally stable, and more brittle than thermoplasts.

11.5 Polymer synthesis and processing:

The large macromolecules of the commercially useful polymers must be synthesized from substances having smaller molecules in a process termed polymerization. Furthermore, the properties of a polymer may be modified and enhanced by the inclusion of additive materials.

Polymerization



The synthesis of the large molecular weight polymers is termed polymerization; it is simply the process by which monomer units are joined over, to generate each of the constituent giant molecules. The reactions by which polymerization occurs are grouped into two general classification- addition and condensation, according to the reaction mechanisms.

Addition polymerization is a process by which bifuncational monomer units are attached one at a time in chainlike fashion to form a linear macromolecules; the composition of the resultant products molecule is an exact multiple for that of the original reactant monomer. Three distinct stages- initiation, propagation and termination are involved in addition polymerization.

Condensation polymerization is the formation of polymers by stepwise intermolecular chemical reactions that normally involve more than one monomer species; there is usually a small molecular weight by producer such as water, which is eliminated. No reactant species has the chemical formula of the mer repeat unit, and the intermolecular reaction occurs every time a mer repeat unit is formed

Applications and Processing of Polymers

Module-11


1. Polymer types and polymer synthesis and processing

2. Crystallization, melting and glass transition

3. Mechanical behavior of polymers

4. Mechanisms of deformation and strengthening of polymers

Contents


Introduction – PolymersThe word ‘polymer’ is originated from Greek word meros, which means ‘a part’.Polymers are primarily organic compounds, however few polymers are made of inorganic compounds.Characteristics of ceramics are:- low temperature stability- low hardness- low mechanical strength- high elongation under application of stress- low thermal and electrical conductivities- high sensitivity of properties to their morphology


Classification – Polymers

Ceramics are classified in many ways. The prime classification based on their industrial usage is: plastics and elastomers.Plastic polymers are again classified based on their temperature dependence of their structure as follows:- thermoplasts and- thermosets


Thermoplasts

Plastics which softens up on heating and hardens up on cooling where the softening and hardening are totally reversible processes. Hence thermoplasts can be recycled.They consist of linear molecular chains bonded together by weak secondary bonds or by inter-winding.Cross-linking between molecular chains is absent in theromplasts. E.g.: Acrylics, PVC, Nylons, Perspex glass, etc.


Thermosets

Plastics which are ‘set’ under the application of heat and/or pressure. This process is not reversible, hence thermosets can not be recycled.They consist of 3-D network structures based on strong covalent bonds to form rigid solids. linear molecular chains bonded together by weak secondary bonds or by inter-winding.Characterized by high modulus / rigidity / dimensional stability when compared with thermoplasts.E.g.: Epoxies, Amino resins, some polyester resins, etc.


Elastomers

These polymers are known for their high elongations, which are reversible upon release of applied loads.They consist of coil-like molecular chains, which straightens up on application of load.Characterized by low modulus / rigidity / strength, but high toughness.E.g.: natural and synthetic rubber.


Polymer Synthesis - 1

Processing of polymers primarily limits to synthesis followed by forming.Polymers are synthesized by process known as polymerization.Polymerization is process in which multi-functional monomers are attached to form linear/3-D macro molecular chains.When polymerization process involves single kind of monomers i.e. in Additional polymerization, resultant macro-molecule’s composition is an exact multiplication of composition of individual monomer.


Additional polymerization process involves three stages namely initiation, propagation and termination.Initiation process will be started by an initiator (e.g. benzoyl peroxide) which forms an reactive site where carbon atom of another monomer is attracted, upon which reaction site transfers to different place leading to molecular chain growth.As molecular chain grows longer, reaction rate decreases. However the growth process is terminated either by the combination or disproportionation process.



Condensation polymerization process involves more then one monomer species. This process is also known as step growth polymerization.In condensation polymerization, smaller macro-molecule by-product such as water is eliminated.No resultant product has the chemical formula of mere one monomer.Repeat unit in condensation process itself is product of polymerization involving basic constituents.Reaction times for condensation polymerization is usually longer than those for additional polymerization.



Degree Of Polymerization

Extant of polymerization is characterized in terms of ‘degree of polymerization’.It si defined as number of mer units in molecular chain or ration of average molecular weight of polymer to molecular weight of repeat unit.Average molecular weight is defined in two ways: Weight average molecular weight (based on weight fraction) and Number average molecular weight (based on the number fraction).Number average molecular weight is is always smaller than the weight average molecular weight.


Polymer FormingThermoplasts usually formed above their glass transition temperatures under application of pressure which ensures detailed product shape.Thermosets are formed in two stages – making liquid polymer and then molding it.Different molding techniques are employed to mold polymers –

compression moldingtransfer molding

injection moldingblow molding

extrusion


Polymer Forming Mechanics - 1Polymer forming involves melting, cooling upon which crystallization takes place. In addition, glass transition occurs in polymers.Crystallization rate depends on temperature and molecular weight. It decrease with increase in molecular weight.Polymer melting is different from that of metals as it takes place over a temperature range.Glass transition occurs in amorphous and semi-crystalline polymers. Upon cooling, this transformation corresponds to gradual change of liquid to rubbery material, and then rigid solid.


Polymer Forming Mechanics - 2

Polymer melting and glass transition is heavily dependent on polymer morphology.Following factors has marked effect on these:chain stiffness (e.g., single vs. double bonds)

size, shape of side groups size of molecule side branches, defects cross-linking


Mechanical Behavior Of Polymers - 1

To an large extant, mechanical behavior of polymers is similar to metals and ceramics.However, polymers are distinct in the sense that parameters namely temperature, strain rate, and morphology of polymers has strong influence on mechanical behavior of polymers.Mechanical properties of polymers change dramatically with temperature, going from glass-like brittle behavior at low temperatures to a rubber-like behavior at high temperatures.


Mechanical Behavior Of Polymers - 2

Highly crystalline polymers behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation.Due to unique structures of cross-linked polymers, recoverable deformations up to very high strains / point of rupture are also observed with polymers (elastomers).Tensile modulus (modulus) and tensile strengths are orders of magnitude smaller than those of metals, but elongation can be up to 1000 % in some cases.


Mechanical Behavior Of Polymers - 3Typical stress-strain diagram for polymers:


Mechanisms Of Deformation In Polymers

Elastic deformation – bending and stretching of covalent bonds and slight adjustments of secondary vander Waals forces.Plastic deformation – NOT by dislocation movement, but either rotation, stretching, sliding or disentanglement of molecular chains, which may occurs in several stages.Elastomers – simple uncoiling, and straightening of molecular chains that are highly twisted, kinked, and coiled in unstressed state. When an elastomer is stretched, causing decrease in entropy, in-turn causes the modulus of elasticity to increase with increasing temperature, which is opposite to the behavior of other materials.


Strengthening Polymers

Polymers’ resistance to deformation – strength – is influenced by many parameters.For thermoplasts: average molecular mass, degree of crystallization, presence of side groups, presence of polar and other specific atoms, presence of phenyl rings in main chains and addition of reinforcements.For thermosets, its reinforcement methods.Every parameter that influence the strength can be used as means of strengthening the polymers.


Reinforcements For PolymersReinforcement strengthening in polymers is an important mechanisms, applicable to both thermoplasts and thermosets.Fibers used as reinforcements are made of either glass, carbon or aramid.Glass fibers are two verities – E-glass and S-glass. The later variety is costlier but offers more strength than former.Aramid (aromatic polyamide) fibers – also known as Kevlar – are commercially highly successful fibers. They are used with plastics in many application including protection from ballasts, ropes, aerospace, marine, and many other industrial applications.

Material Science/Composites Lecture Notes


Chapter 12. COMPOSITES

12.1 Particle-reinforced composites

These are the cheapest and most widely used. They fall in two categories depending on the size of the particles:

• large-particle composites, which act by restraining the movement of the matrix, if well bonded.

• dispersion-strengthened composites, containing 10-100 nm particles, similar to what was discussed under precipitation hardening. The matrix bears the major portion of the applied load and the small particles hinder dislocation motion, limiting plastic deformation.

12.2 Large-Particle Composites

Properties are a combination of those of the components. The rule of mixtures predicts that an upper limit of the elastic modulus of the composite is given in terms of the elastic moduli of the matrix (Em) and the particulate (Ep) phases by:

Ec = EmVm + EpVp

where Vm and Vp are the volume fraction of the two phases. A lower bound is given by:

Ec = EmEp / (EpVm + EmVp)

Concrete

The most common large-particle composite is concrete, made of a cement matrix that bonds particles of different size (gravel and sand.) Cement was already known to the Egyptians and the Greek. Romans made cement by mixing lime (CaO) with volcanic ice.

In its general from, cement is a fine mixture of lime, alumina, silica, and water. Portland cement is a fine powder of chalk, clay and lime-bearing minerals fired to 1500o C (calcinated). It forms a paste when dissolved in water. It sets into a solid in minutes and hardens slowly (takes 4 months for full strength). Properties depend on how well it is mixed, and the amount of water: too little - incomplete bonding, too much - excessive porosity.

The advantage of cement is that it can be poured in place, it hardens at room temperature and even under water, and it is very cheap. The disadvantages are that it is weak and brittle, and that water in the pores can produce crack when it freezes in cold weather.

Concrete is cement strengthened by adding particulates. The use of different size (stone and sand) allows better packing factor than when using particles of similar size.



Concrete is improved by making the pores smaller (using finer powder, adding polymeric lubricants, and applying pressure during hardening.

Reinforced concrete is obtained by adding steel rods, wires, mesh. Steel has the advantage of a similar thermal expansion coefficient, so there is reduced danger of cracking due to thermal stresses. Pre-stressed concrete is obtained by applying tensile stress to the steel rods while the cement is setting and hardening. When the tensile stress is removed, the concrete is left under compressive stress, enabling it to sustain tensile loads without fracturing. Pre-stressed concrete shapes are usually prefabricated. A common use is in railroad or highway bridges.

Cermets

are composites of ceramic particles (strong, brittle) in a metal matrix (soft, ductile) that enhances toughness. For instance, tungsten carbide or titanium carbide ceramics in Co or Ni. They are used for cutting tools for hardened steels.

Reinforced rubber

is obtained by strengthening with 20-50 nm carbon-black particles. Used in auto tires.

Dispersion-Strengthened Composites

Use of very hard, small particles to strengthen metals and metal alloys. The effect is like precipitation hardening but not so strong. Particles like oxides do not react so the strengthening action is retained at high temperatures.

12.3 Fiber-reinforced composites

In many applications, like in aircraft parts, there is a need for high strength per unit weight (specific strength). This can be achieved by composites consisting of a low-density (and soft) matrix reinforced with stiff fibers.

The strength depends on the fiber length and its orientation with respect to the stress direction.

The efficiency of load transfer between matrix and fiber depends on the interfacial bond.

12.4 Structural Composites

Largest and most diverse use of composites due to ease of fabrication, low cost and good properties.

Glass-fiber reinforced composites (GFRC) are strong, corrosion resistant and lightweight, but not very stiff and cannot be used at high temperatures. Applications include auto and boat bodies, aircraft components.



Carbon-fiber reinforced composites (CFRC) use carbon fibers, which have the highest specific module (module divided by weight). CFRC are strong, inert, allow high temperature use. Applications include fishing rods, golf clubs, aircraft components.

Kevlar, and aremid-fiber composite can be used as textile fibers. Applications include bullet-proof vests, tires, brake and clutch linings.

Wood

This is one of the oldest and the most widely used structural material. It is a composite of strong and flexible cellulose fibers (linear polymer) surrounded and held together by a matrix of lignin and other polymers. The properties are anisotropic and vary widely among types of wood. Wood is ten times stronger in the axial direction than in the radial or tangential directions.

Material Science/Corrosion and Degradation of Materials Lecture Notes


Chapter 13. Corrosion and Degradation of Materials

13.1 Corrosion of Metals

The corrosion resistance of metals and alloys is a basic property related to the easiness with which these materials react with a given environment. Corrosion is a natural process that seeks to reduce the binding energy in metals. The end result of corrosion involves a metal atom being oxidized, whereby it loses one or more electrons and leaves the bulk metal. The lost electrons are conducted through the bulk metal to another site where they are reduced. In corrosion parlance, the site where metal atoms lose electrons is called the anode, and the site where electrons are transferred to the reducing species is called the cathode.

The following links will lead to interesting information concerning specific metals and indexes to relevant pages of the Corrosion Doctors site:

Aluminum Cadmium Chromium Cobalt Copper Gold Iron Lead Magnesium Molybdenum Nickel Silver Tin Titanium Zinc

Pure metals are used in many applications. Copper, for example, is used to make the wire which goes inside electrical cables. Copper was chosen because it can be drawn into long thin wires very easily (it is ductile) and because it is a good conductor of electricity. Pure aluminum can also be used in wiring. It is also used as a cladding material for aluminum alloy substrates.

Currently there are 86 known metals. Before the 19th century only 24 of these metals had been discovered and, of these 24 metals, 12 were discovered in the 18th century. Therefore, from the discovery of the first metals, gold and copper, until the end of the 17th century, some 7700 years, only 12 metals were known. Four of these metals, arsenic, antimony , zinc and bismuth , were discovered in the thirteenth and fourteenth centuries, while platinum was discovered in the 16th century. The other seven metals, known as the Metals of Antiquity, were the metals upon which civilization was based. These seven metals are Gold, Copper, Silver, Lead, Tin, Iron,Mercury.



13.2 Corrosion of Ceramics: It is often said that one of the biggest advantages which ceramics have over other materials is their corrosion resistance, that is, their chemical inertness in corrosive environments. Is this always true? Corrosion is generally understood as property degradation due to environmental attack. As it will be shown in this section, there are a number of environments in which ceramics can degrade at a rapid rate. There exists a tremendous need for reliable and corrosion resistant structural ceramic or partly ceramic materials which can be used in aggressive environments such as: - high energy battery systems (such as sodium-sulphur): beta-alumina is being investigated - gas turbines: silicon nitride and/or carbide are being investigated - heat exchangers: SiC, composites are being investigated Ceramics are indeed much more environmentally stable, as compared to any other group of engineering materials, e.g. metals or plastics. Still, the potential for ceramics as corrosion resistant engineering structural materials are far from being fully realized, because of: • mechanical nonreliability of structural ceramic components • difficult design with brittle materials • a shortage of information and standardization of ceramics • human reluctance to use non-ductile materials Issues of particular importance when considering corrosion of ceramics: • The resistance of many ceramics to wetting by a corrosive liquid is a valuable property. Little corrosion is expected if a liquid does not wet a ceramic. This is why, for example, born nitride (BN) and graphite are useful in handling melts and including the extremely corrosive melts of silicate glasses. BN and graphite are not wetted by these liquids.



• The solubility of the reaction product in the corrosive environment (liquid) is critical to the extent of corrosion. Reaction barriers can form and prevent corrosion. Some examples are silica on silicon carbide or nitride, and alumina on Al. On the other hand, continuous dissolution of the reaction product can occur and sustain corrosion even for small chemical driving force, for instance Al2O3 in molten KOH. • Even if a major component of the ceramic is resistant to a given corrosive environment, a minor phase (especially a grain boundary phase, in particular under stress) could be corroded (leached), leading to the general failure of the component. Some examples include: - Alumina in water, where preferential attack of the grain boundary glassy (silicate) phases occurs. - The preferential attack of free Si in reaction bonded SiC, by alkalis or molten metals. - The oxide grain boundary phases in nonoxides (B2O3 in BN, silicates in Si3N4 and SiC) are sensitive to water. Severe corrosion takes place if the ceramic is in contact with a substance which can combine with it and form low-melting liquids (i.e. with eutectic point below ambient temperature). The example of above situation is the system composed of metallurgical slag in contact with refractories. If the reaction is thermodynamically possible, the corrosion will proceed at a dramatic rate if the refractory is wetted by the slag. Degradation of polymers:

While the plastics industry searches for solutions to the problem of plastics waste, there is, surprisingly, a growing band of people trying to save plastics.Although the manufacturers of early ‘plastics’ such as horn buttons, Bois Durci paperweights or celluloid collars would be astonished to see how well many of their goods have survived, many other plastics have begun to show disturbing signs of instability. Every collection of plastics worldwide, from the Science Museum and Tate Gallery to the Comb & Plastics Museum in Oyonnax, has already lost or is losing unique and beautiful pieces through degradation.

Plastics, Not as Long-Lasting as Once Thought



The crucial fact is that plastics are organic and have been described as a time bomb ticking away since cellulose nitrate based plastics were invented around 130 years ago. It can of course be argued that manufacturers’ foremost intentions have never been to make beautiful objects for museums. However, museums have a duty to preserve their acquisitions.

Recognition of Polymer Degradation

It was not until the late 1980s that attention was paid to the fact that plastics artefacts had been physically changing, showing signs of acid vapour, tackiness, warping, embrittlement and crazing. Cellulose nitrate and cellulose acetate were particularly affected. By 1991 John Morgan of the Plastics Historical Society had collected enough data to write Conservation of Plastics -An Introduction, a joint PHS /Conservation Unit publication, and the Conservation Unit launched a survey to identify objects at risk with the aim of setting up a research programme. The survey included everything from radios and cables to textiles and sculptures.

Deterioration of Acrylic Paintings and Pieces of Art

By 1992 acrylic based paintings worth millions of pounds by leading artists of the 1960s including David Hockney and Jackson Pollock had begun to suffer discolouration, cracking and greyness due to the absorption of dust and atmospheric pollutants. These paints seemed particularly vulnerable. At room temperature they are relatively soft and attract dirt which becomes embedded. However, to date no method has been found of cleaning them.

Impact on the Photographic Film Industry

The photographic film industry was also badly hit when irreplaceable archive nitrate stock started to decompose. Today, the National Film Archive transfers cellulose nitrate and cellulose triacetate onto more stable polyester at the rate of a million metres a year.

Preserving Plastics Pieces in Museums

The PHS/CU survey unearthed some interesting facts. For example, 40% of museums surveyed contain plastics objects manufactured and collected since 1980, and modem plastics are also showing symptoms of decay. Polyurethane foam appears to be one of the worst victims, and many early video and audio tapes on magnetic media are already unplayable. The curator who has to supervise a collection of high-tech, mixed material products such as space suits is confronted with a conservation dilemma: which material deserves priority treatment when each separate plastic has different requirements?

Factors Affecting Polymer Degradation

The degradation of plastics can be said to begin as soon as the polymer is synthesised, and is increased by residual stresses left by moulding processes. This can be followed by



exposure to light (especially UV), humidity, oxygen, heat, bacteria and stress. Plastics can also be contaminated by other materials, including other plastics. A polystyrene camera body, for example, can be attacked by plasticiser migrating from a PVC strap. Ideally the conservator needs information about the history of an object before prescribing treatment, but even before this, the plastics ‘doctor’ must jump another hurdle. Specific conservation action cannot be taken until the polymer has been identified, and this is a technical area full of pitfalls. A 1920s black brooch could be made of at least six different plastics materials, or simply painted as was common practice in the 19th century. Even a patent number, one of the few ‘hallmarks’ found on plastics and an obvious aid to identification, may refer to a fixing mechanism and not to the moulding.

Preserving Plastics

Derek Pullen, a conservator at the Tate Gallery, explains, ‘Plastics are giant molecules held together by forces which can be broken by attacking energy forces such as light. All the conservator can do is to keep mouldings in a very stable, low energy environment (the burial chambers of the Pyramids were ideal)’.

Types of Polymer Degradation

There are two main types of plastics degradation being researched at present: physical and chemical, and both are closely inter-connected. Physical degradation can involve environmental stress cracking and plasticiser migration and loss. Chemical reactions include oxidation and hydrolysis, and are a problem particularly affecting the cellulose esters (cellulose nitrate and cellulose acetate), which emit acidic degradation products. If not removed, these catalyse further reactions and eventually cause serious crazing and total destruction of the object. If degrading cellulose esters are not isolated, the acidic fumes will infect similar objects stored close by and initiate degradation there.

Solutions to Polymer Degradation

As the recognition of polymer degradation improves, conservation guidelines are beginning to emerge. High-tech solutions which could help in theory are prohibitively expensive, but tailor made scavengers such as activated charcoal or Ageless help to create a low oxygen environment. Ageless is a reactive powdered iron and is normally used to prolong the shelf-life of dry foods by absorbing oxygen. Epoxidised soyabean oil (ESBO), has also been tested with encouraging results as an acid absorbing coating on degrading cellulose nitrate.



Conclusion

Compared to traditional materials with long established technologies such as metals and glass, the complex chemical nature of plastics is providing conservators with possibly their most formidable challenge yet.

Material Science/Electrical Properties Lecture Notes


Chapter 14. Electrical Properties

14.1 Electrical Conduction

Ohm’s Law

When an electric potential V is applied across a material, a current of magnitude I flows. In most metals, at low values of V, the current is proportional to V, according to Ohm's law:

I = V/R

where R is the electrical resistance. R depends on the intrinsic resistivity ρ of the material and on the geometry (length l and area A through which the current passes).

R = ρl/A

Electrical Conductivity

The electrical conductivity is the inverse of the resistivity: σ = 1/ρ.

The electric field in the material is E=V/l, Ohm's law can then be expressed in terms of the current density j = I/A as:

j = σ E

The conductivity is one of the properties of materials that varies most widely, from 107 (Ω-m) typical of metals to 10-20 (Ω-m) for good electrical insulators. Semiconductors have conductivities in the range 10-6 to 104 (Ω-m).

Electronic and Ionic Conduction

In metals, the current is carried by electrons, and hence the name electronic conduction. In ionic crystals, the charge carriers are ions, thus the name ionic conduction.

Energy Band Structures in Solids

When atoms come together to form a solid, their valence electrons interact due to Coulomb forces, and they also feel the electric field produced by their own nucleus and that of the other atoms. In addition, two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion. The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same property (which include



the energy). As a result of all these effects, the valence electrons of atoms form wide valence bands when they form a solid. The bands are separated by gaps, where electrons cannot exist. The precise location of the bands and band gaps depends on the type of atom (e.g., Si vs. Al), the distance between atoms in the solid, and the atomic arrangement (e.g., carbon vs. diamond).

In semiconductors and insulators, the valence band is filled, and no more electrons can be added, following Pauli's principle. Electrical conduction requires that electrons be able to gain energy in an electric field; this is not possible in these materials because that would imply that the electrons are promoted into the forbidden band gap.

In metals, the electrons occupy states up to the Fermi level. Conduction occurs by promoting electrons into the conduction band, that starts at the Fermi level, separated by the valence band by an infinitesimal amount.

Electrical Resistivity of Metals

The resistivity then depends on collisions. Quantum mechanics tells us that electrons behave like waves. One of the effects of this is that electrons do not scatter from a perfect lattice. They scatter by defects, which can be:

o atoms displaced by lattice vibrations o vacancies and interstitials o dislocations, grain boundaries o impurities

One can express the total resistivity ρtot by the Matthiessen rule, as a sum of resistivities due to thermal vibrations, impurities and dislocations. Fig. 19.8 illustrates how the resistivity increases with temperature, with deformation, and with alloying..

14.2 Semiconductivity:

Intrinsic Semiconduction

Semiconductors can be intrinsic or extrinsic. Intrinsic means that electrical conductivity does not depend on impurities, thus intrinsic means pure. In extrinsic semiconductors the conductivity depends on the concentration of impurities.

Conduction is by electrons and holes. In an electric field, electrons and holes move in opposite direction because they have opposite charges. The conductivity of an intrinsic semiconductor is:

σ = n |e| µe + p |e| µh



where p is the hole concentration and µh the hole mobility. One finds that electrons move much faster than holes:

µe > µh

In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the conduction band. Thus:

n = p

Thus, σ = 2 n |e| (µe + µh) (only for intrinsic semiconductors).

Extrinsic Semiconduction

Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called p-type if p>n and n-type if n>p. They are made by doping, the addition of a very small concentration of impurity atoms. Two common methods of doping are diffusion and ion implantation.

Excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix. For instance phosphorous, with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Thus, elements in columns V and VI of the periodic table are donors for semiconductors in the IV column, Si and Ge. The energy level of the donor state is close to the conduction band, so that the electron is promoted (ionized) easily at room temperature, leaving a hole (the ionized donor) behind. Since this hole is unlike a hole in the matrix, it does not move easily by capturing electrons from adjacent atoms. This means that the conduction occurs mainly by the donated electrons (thus n-type).

Excess holes are produced by substitutional impurities that have fewer valence electrons per atom than the matrix. This is the case of elements of group II and III in column IV semiconductors, like B in Si. The bond with the neighbors is incomplete and so they can capture or accept electrons from adjacent silicon atoms. They are called acceptors. The energy level of the acceptor is close to the valence band, so that an electron may easily hop from the valence band to complete the bond leaving a hole behind. This means that conduction occurs mainly by the holes (thus p-type).

The Temperature Variation of Conductivity and Carrier Concentration

Temperature causes electrons to be promoted to the conduction band and from donor levels, or holes to acceptor levels. The dependence of conductivity on temperature is like other thermally activated processes:

σ = A exp(–Eg/2kT)



where A is a constant (the mobility varies much more slowly with temperature). Plotting ln σ vs. 1/T produces a straight line of slope Eg/2k from which the band gap energy can be determined. Extrinsic semiconductors have, in addition to this dependence, one due to the thermal promotion of electrons from donor levels or holes from acceptor levels. The dependence on temperature is also exponential but it eventually saturates at high temperatures where all the donors are emptied or all the acceptors are filled.

This means that at low temperatures, extrinsic semiconductors have larger conductivity than intrinsic semiconductors. At high temperatures, both the impurity levels and valence electrons are ionized, but since the impurities are very low in number and they are exhausted, eventually the behavior is dominated by the intrinsic type of conductivity.

Semiconductor Devices

A semiconductor diode is made by the intimate junction of a p-type and an n-type semiconductor (an n-p junction). Unlike a metal, the intensity of the electrical current that passes through the material depends on the polarity of the applied voltage. If the positive side of a battery is connected to the p-side, a situation called forward bias, a large amount of current can flow since holes and electrons are pushed into the junction region, where they recombine (annihilate). If the polarity of the voltage is flipped, the diode operates under reverse bias. Holes and electrons are removed from the region of the junction, which therefore becomes depleted of carriers and behaves like an insulator. For this reason, the current is very small under reverse bias. The asymmetric current-voltage characteristics of diodes is used to convert alternating current into direct current. This is called rectification.

A p-n-p junction transistor contains two diodes back-to-back. The central region is very thin and is called the base. A small voltage applied to the base has a large effect on the current passing through the transistor, and this can be used to amplify electrical signals (Fig. 19.22). Another common device is the MOSFET transistor where a gate serves the function of the base in a junction transistor. Control of the current through the transistor is by means of the electric field induced by the gate, which is isolated electrically by an oxide layer.

Conduction in Ionic Materials

In ionic materials, the band gap is too large for thermal electron promotion. Cation vacancies allow ionic motion in the direction of an applied electric field, this is referred to as ionic conduction. High temperatures produce more vacancies and higher ionic conductivity.

At low temperatures, electrical conduction in insulators is usually along the surface, due to the deposition of moisture that contains impurity ions.



14.3 Superconductivity:

Superconductivity is the ability of certain materials to conduct electrical current with no resistance and extremely low losses. This ability to carry large amounts of current can be applied to electric power devices such as motors and generators, and to electricity transmission in power lines. For example, superconductors can carry as much as 100 times the amount of electricity of ordinary copper or aluminum wires of the same size.

Scientists had been intrigued with the concept of superconductivity since its discovery in the early 1900s, but the extreme low temperatures the phenomenon required was a barrier to practical and low-cost applications. This all changed in 1986, when a new class of ceramic superconductors was discovered that "superconducted" at higher temperatures. The science of high-temperature superconductivity (HTS) was born, and along with it came the prospect for an elegant technology that promises to "supercharge" the way energy is generated, delivered, and used.

14.5 Dielectric Behavior

A dielectric is an electrical insulator that can be made to exhibit an electric dipole structure (displace the negative and positive charge so that their center of gravity is different).

Capacitance

When two parallel plates of area A, separated by a small distance l, are charged by +Q, –Q, an electric field develops between the plates

E = D/εε0

where D = Q/A. ε0 is called the vacuum permittivity and ε the relative permittivity, or dielectric constant (ε = 1 for vacuum). In terms of the voltage between the plates, V = E l,

V = Dl/εε0 = Q l/Aεε0 = Q / C

The constant C= Aεε0/l is called the capacitance of the plates.

Field Vectors and Polarization

The dipole moment of a pair of positive and negative charges (+q and –q) separated at a distance d is p = qd. If an electric field is applied, the dipole tends to align so that the positive charge points in the field direction. Dipoles between the plates of a capacitor will produce an electric field that opposes the applied field. For a given applied voltage V, there will be an increase in the charge in the plates by an amount Q' so that the total



charge becomes Q = Q' + Q0, where Q0 is the charge of a vacuum capacitor with the same V. With Q' = PA, the charge density becomes D = D0 E + P, where the polarization P = ε0 (ε–1) E .

Types of Polarization

Three types of polarization can be caused by an electric field:

• Electronic polarization: the electrons in atoms are displaced relative to the nucleus.

• Ionic polarization: cations and anions in an ionic crystal are displaced with respect to each other.

• Orientation polarization: permanent dipoles (like H2O) are aligned.

Frequency Dependence of the Dielectric Constant

Electrons have much smaller mass than ions, so they respond more rapidly to a changing electric field. For electric field that oscillates at very high frequencies (such as light) only electronic polarization can occur. At smaller frequencies, the relative displacement of positive and negative ions can occur. Orientation of permanent dipoles, which require the rotation of a molecule can occur only if the oscillation is relatively slow (MHz range or slower). The time needed by the specific polarization to occur is called the relaxation time.

Dielectric Strength

Very high electric fields (>108 V/m) can free electrons from atoms, and accelerate them to such high energies that they can, in turn, free other electrons, in an avalanche process (or electrical discharge). This is called dielectric breakdown, and the field necessary to start the is called the dielectric strength or breakdown strength.

Dielectric Materials

Capacitors require dielectrics of high ε that can function at high frequencies (small relaxation times). Many of the ceramics have these properties, like mica, glass, and porcelain). Polymers usually have lower ε.

14.6 Ferroelectricity

Ferroelectric materials are ceramics that exhibit permanent polarization in the absence of an electric field. This is due to the asymmetric location of positive and negative charges within the unit cell. Two possible arrangements of this asymmetry results in two distinct polarizations, which can be used to code "0" and "1" in ferroelectric memories. A typical ferroelectric is barium titanate, BaTiO3, where the Ti4+ is in the center of the unit cell and four O2- in the central plane can be displaced to one side or the other of this central ion .



14.7 Piezoelectricity

In a piezolectric material, like quartz, an applied mechanical stress causes electric polarization by the relative displacement of anions and cations.

Material Science/Thermal Properties Lecture Notes


Chapter 15. Thermal Properties 15.1 Heat Capacity: Heat Capacity is a property that is indicative of a materials ability to absorb heat from external surroundings; it represnts tha amount of energy required to produce a unit temperature rise.In mathematical terms, the heat capacity C is expressed as follows: C=dQ/dT Where dQ is the energy required to produce a dT temperature change. Unit of heat capacity is J/kg-K. 15.2 Thermal expansion: Most solid materials expand upon heating and contract when cooled. The change in length with temperature for a solid material may be expressed as follows:

Over small temperature ranges, the linear nature of thermal expansion leads to expansion relationships for length, area, and volume in terms of the linear expansion coefficient.

The coefficient of thermal expansion is generally defined as the fractional increase in length per unit rise in temperature. The exact definition varies, depending on whether it is specified at a precise temperature (true coefficient of thermal expansion) or over a temperature range (mean coefficient of thermal expansion). The former is related to the slope of the tangent to the length – temperature plot, while the latter is governed by the slope of the chord between two points on this curve. Considerable variation in the value of the CTE can occur according to the definition employed.

For metallic materials values in the range 10 x 10-6 to 30 x 10-6 K-1 are common, and the thermal expansion of pure metals up to their melting points has been well characterised. However data for engineering alloys at very high temperatures is often limited. This is significant since there is generally a variation (usually an increase) in CTE with temperature.

15.3 Thermal Conductivity:

The thermal conductivity of a material is equivalent to the quantity of heat that passes in unit time through unit area of a plate, when its opposite faces are subject to unit temperature gradient (e.g. one degree temperature difference across a thickness of one unit).

Thermal conductivity = Heat flow rate ÷ (Area × Temperature gradient)

In the SI system of units, thermal conductivity is measured in watts per metre-kelvin, (W·m-1·K-1) where a

• watt is the unit of power • metre is the unit of distance

Material Science/Thermal Properties Lecture Notes


• kelvin is the unit of temperature

15.4 Thermal Stress

Thermal stresses are stresses induced in a body as a result of changes in temperature. There are various types of thermal deformation.

Completely Constrained Thermal Deformation:

The thermal stress which develops if a structure or member is completely constrained (not allowed to move at all) is the product of the coefficient of linear expansion and the temperature change and Young's modulus for the material.

Partially Constrained Thermal Deformation: A more normal situation in a structure, rather than completely constrained or completely free thermal deformation, is a partially constrained thermal deformation. This means a member may expand (or contract) but not as much as it would if unconstrained.

Stresses resulting from temperature gradients:

When a solid body is heated or cooled, the internal temperature distribution will depend on its size and shape, the thermal conductivity pf the material and the rate of temperature change. Thermal stresses may be established as a result of temperature gradients across a body, which are frequently caused by rapid heating or cooling, in that the outside changes temperature more rapidly than the interior.

Material Science/Magnetic Properties Lecture Notes


Chapter 16. Magnetic Properties 16.1 Diamagnetism and Para magnetism: Diamagnetism is a very weak form of magnetism that is nonpermanent and persists only while an external field is being applied. It is induced by a change in the orbital motion of electrons due to an applied magnetic field. The magnitude of the induced magnetic moment is extremely small and in a direction opposite to that of the applied field.

paramagnetic material is one whose atoms do have permanent dipole moments, but the magic of ferromagnetism is not active. If a magnetic field is applied to such a material, the dipole moments try to line up with the magnetic field, but are prevented from becoming perfectly aligned by their random thermal motion. Because the dipoles try to line up with the applied field, the susceptibilities of such materials are positive, but in the absence of the strong ferromagnetic effect, the susceptibilities are rather small, say in the range to . When a paramagnetic material is placed in a strong magnetic field, it becomes a magnet, and as long as the strong magnetic field is present, it will attract and repel other magnets in the usual way. But when the strong magnetic field is removed, the net magnetic alignment is lost as the dipoles relax back to their normal random motion.

16.2 Ferromagnetism: Certain metallic materials possess a permanent magnetic moment in the absence of an external field, and manifest very large and permanent magnetizations. These are the characteristics of ferromagnetism, and they are displayed by the transition metals iron, cobalt, nickel, and some of the rare earth metals. Permanent magnetic moments in ferromagnetic materials result from atomic magnetic moments due to electron spin-uncancelled electron spins as a consequence of the electron structure. There is also an orbital magnetic moments contribution that is small in comparison to the spin moment. Furthermore, in a ferromagnetic material, coupling interactions cause net spin magnetic moments of adjacent atoms to align with one another, even in the absence of an external field. The maximum possible magnetization or saturation magnetization Ms of a ferromagnetic material represents the magnetization that results when all the magnetic diploes in a solid piece are mutually aligned with the external field; there is also a corresponding saturation flux density Bs. 16.3 Antiferromagnetism: This phenomenon of magnetic moment coupling between adjacent atoms or ions occurs in materials other than those that are ferromagnetic. In one such group, this coupling results in an antiparallel alignment; the alignment of the spin moments of neighbouring atoms or ions in exactly opposite directions is termed antiferromagentism. Manganese oxide(MnO) is one such material that displays this behavior. Manganese oxide is a ceramic material that is ionic in character, having both Mn and O ions.No net magnetic moment is associated with O ions, since there is a total cancellation of both spin and orbital moments. However, the Mn ions possesses s nrt magnetic moment that is

Material Science/Magnetic Properties Lecture Notes


predominantly of spin origin.These Mn ions are arrayed in the crystal structure such that the moments of adjacent ions are antiparallel. Obvioulsy, the opposing magnetic moments cancel one another and as a consequence, the solid as a whole possesses no net magnetic moment.

Ferrimagnetism Some ceramics also exhibit a permanent magnetizations termed ferrimagentism. The macroscopic magnetic characteristics of ferromagnets and ferrimagents are similar; the distinction lies in the source of the net magnetic moments. The net ferrimagentic moment arises from the incomplete cancellation of spin moments.

16.4 Influence of temperature on magnetic behavior: Temperature can also influence the magnetic characteristics of materials. The atomic magnetic moments are free to rotate, hence with rising temperature, the increased thermal motion of the atoms tends to randomize the directions of any moments that may be aligned. For ferromagnetic, antiferromagentic and ferrimagentic materials, the atomic thermal motions counteract the coupling forces between the adjacent atomic dipole moments, causing some dipole misalignment, regardless of whether an external field is present. The result is a decrease in the saturation magnetization for both ferro and ferrimagnets. The saturation magnetization is a maximum at ) K, at which temperature the thermal vibrations are a minimum. With increasing temperature, the saturation magnetization diminishes gradually and then abruptly drops to zero at what is called the curie temperature Tc. The magnitude of the curie temparature varies from material to material; for example, for iron, cobalt, nickel., the respective values are 768,1120,335 and 585 degree Celsius. Antiferromagnetism is also affected by temperature; this behavior vanishes at what is called the Neel temperature. At temperatures above this point, antiferromagnteic materials also become paramagnetic.

16.5 Domains and Hysteresis: Any ferromagnetic or ferromagnetic material that is at a temperature below Tc is composed of small-volume regions in which there is a mutual alignment in the same direction of all magnetic dipole moments. Such a region is called a domain, and each one is magnetized to its saturation magnetization. Adjacent domains are separated by domain boundaries or walls across which the direction of magnetization gradually changes. Normally, domains are microscopic in size and for a polycrystalline specimen, each grain may consist of a single domain. Thus, in a microscopic piece of material, there will be large number of domains and all may have different magnetization orientations.

Material Science/Optical Properties Lecture Notes


Chapter 17. Optical Properties 17.1 Basic concepts: Electromagnetic Radiation- In the classical sense, electromagnetic radiation is considered to be wave-like, consisiting of electric and magnetic field components that are perpendicular to each other and also to the direction of propagation. Light, heat, radio waves, radar and x-rays are all forms of electromagnetic radiation. Each is characterized primarily by a specific range of wavelengths, and also according to the technique by which it is generated. The electromagnetic spectrum of radiation spans the wide range from gamma rays having wavelengths on the order of 10-12, through x-rays, ultraviolet, visible, infrared and finally radio waves with wavelengths as long as 1015 All electromagnetic radiation traverses a vacuum at the same velocity, that of light. This velocity,c, is related to the electric permittivity of a vacuum and the magnetic permeability of a vacuum through . Thus there is an association between the electromagnetic constant c and these electrical and magnetic constants. Furthermore, the frequency ν and wavelength λ of the electromagnetic radiation are a function of velocity according to: C= ν/λ Frequency is expressed in terms of hertz(Hz), and 1 Hz=1 cycle per second. Ranges of frequency for the various forms of electromagnetic radiation are also included in the spectrum. The electromagnetic spectrum covers a wide range of wavelengths and photon energies. Light used to "see" an object must have a wavelength about the same size as or smaller than the object. The ALS generates light in the far ultraviolet and soft x-ray regions, which span the wavelengths suited to studying molecules and atoms. 17.2 Optical properties of metals: Consider the electron energy band schemes for metals; in both cases a high-energy band is only partially filled with electrons. Metals are opaque because the incident radiation having frequencies within the visible range excites electrons into unoccupied energy states above the Fermi energy. All frequencies of visible light are absorbed by metals because of the continuously available empty electron states, which permit electron transitions. In fact, metals are opaque to all electromagnetic radiation on the low end of the frequency spectrum, from radio waves, through infrared, the visible and into about the middle of the ultraviolet radiation. Metals are transparent to high frequency radiation. Most of the absorbed radiation is reemitted from the surface in the form of visible light of the same wavelength, which appears as reflected light. Since metals are opaque and highly reflective the perceived color is determined by the wavelength distribution of the radiation that is reflected and not absorbed. A bright silvery appearance when exposed to white light indicates that the metal is highly reflected beam; the composition of these reemitted photons, in terms of frequency and number is approximately the same as for the incident beam. Aluminum and silver are the two metals that exhibit this reflective behavior. Copper and gold appear red orange and yellow, respectively, because some of



the energy associated with light photons having short wavelengths is not reemitted as visible light. 17.3 Optical properties of non metals: By virtue of their electron energy band structures, nonmetallic materials may be transparent to visible light. Therefore, in addition to reflection and absorption, refraction and transmission phenomena also need to be considered. Refraction: Light that is transmitted into the interior of transparent materials experiences decrease in velocity and as result is bent at the interface; this phenomenon is termed refraction. The index of refraction n of a material is defined as the ratio of the velocity in vacuum c to the velocity in the medium ν , or n=c/ν The magnitude of n will depend on the wavelength of the light. This effect is graphically demonstrated by the familiar dispersion or separation of a beam of white light into its component colors by a class prism. Each color is deflected by a different amount as it passes into and out of the glass, which results in the separation of colors. Not only does the index of refraction affect the optical path of light, but also it influences the fraction of incident light that is reflected at the surface. The phenomenon of refraction is related to electronic polarization at the relatively high frequencies for visible light; thus the electronic component of the dielectric constant may be determined from index of refraction measurements. Since the retardation of electromagnetic radiation in a medium results from electronic polarization, the size of the constituent atoms or ions has a considerable influence on the magnitude of this effect-generally, the larger an atom or ion, the greater will be the electronic polarization, the slower the velocity and greater the index of refraction. Reflection: When light radiation passes from one medium into another having a different index of refraction, some of the light is scattered at the interface between the two media even if both are transparent. The reflectivity R represents the fraction of the incident light that is reflected at the interface. R=Ir/Io Where Io and Ir are the intensities of the incident and reflected beams, respectively.Just as the index of refraction of a solid depends on the wavelength of the incident light, so does the reflectivity vary with wavelength. Absorption: Nonmetallic materials may be opaque or transparent to visible light; and, if transparent, they often appear colored. In principle, light radiation is absorbed in this group of materials by two basic mechanisms, which also influence the transmission characteristics of these nonmetals. Absorption by electronic polarization is important only at light frequencies in the vicinity of the relaxation frequency of the constituent atoms. The other mechanism involves valence band-conduction band electron transitions, which depends on the electron energy band structure of the material.



Transmission: The phenomena of absorption, reflection and transmission may be applied to the passage of light through a transparent solid. The fraction of incident light that is transmitted through a transparent material depends on the losses that are incurred by absorption and reflection. The sum of reflectivity R, absorptivity A and transmittivity T, is unity. Also, each of of the variables R, A and T depends on light wavelength. 17.4 Applications of optical phenomena Luminescence Some materials are capable of absorbing energy and then reemitting visible light in a phenomenon called luminescence. Photons of emitted light are generated from electron transitions in the solid. Energy is absorbed when an electron is promoted to an excited energy; visible light is emitted when it false back to a lower energy state. The absorbed energy may be applied as higher energy electrons or by heat, mechanical or chemical energy. Furthermore, luminescence is classified according to the magnitude of the delay time between absorption and reemission events.

Luminescence is "cold light", light from other sources of energy, which can take place at normal and lower temperatures. In luminescence, some energy source kicks an electron of an atom out of its "ground" (lowest-energy) state into an "excited" (higher-energy) state; then the electron gives back the energy in the form of light so it can fall back to its "ground" state.

There are several varieties of luminescence, each named according to what the source of energy is, or what the trigger for the luminescence is.

Fluorescence and Photoluminescence are luminescence where the energy is supplied by electromagnetic radiation (rays such as light, which will be discussed later); photoluminescence is generally taken to mean luminance from any electromagnetic radiation, while fluorescence is often used only for luminescence caused by ultraviolet, although it may be used for other photoluminescences also. Fluorescence is seen in fluorescent lights, amusement park and movie special effects, the redness of rubies in sunlight, "day-glo" or "neon" colors, and in emission nebulae seen with telescopes in the night sky. Bleaches enhance their whitening power with a white fluorescent material.

Photoluminescence should not be confused with reflection, refraction, or scattering of light, which cause most of the colors you see in daylight or bright artificial lighting. Photoluminescence is distinguished in that the light is absorbed for a significant time, and generally produces light of a frequency that is lower than, but otherwise independent of, the frequency of the absorbed light.

Electroluminescence is luminescence caused by electric current. Cathodoluminescence is electroluminescence caused by electron beams; this is how television pictures are formed. Other examples of electroluminescence are neon lights, the auroras, and lightning flashes. This should not be mistaken for what occurs with the ordinary incandescent



electric lights, in which the electricity is used to produce heat, and it is the heat that in turn produces light.

Radioluminescence is luminescence caused by nuclear radiation. Older glow-in-the-dark clock dials often used a paint with a radioactive material (typically a radium compound) and a radioluminescent material. The term may be used to refer to luminescence caused by X-rays, also called photoluminescence

Photoconductivity

Photoconductivity is an optical and electrical phenomenon in which a material becomes more conductive when subjected to ultraviolet or gamma radiation. See photoconductor.

Photoconductivity is the tendency of a substance to conduct electricity to an extent that depends on the intensity of light-radiant energy (usually infrared transmission or visible light) striking the surface of a sample. Most semiconductor materials have this property.

When there is no illumination, a photoconductive sample has a conductance that depends on its dimensions, on the specific material(s) from which it is made, and on the temperature. In most cases, the greater the radiant energy of a specific wavelength that strikes the surface, the higher the conductance of the sample becomes, up to a certain maximum. When the maximum conductance is reached for a particular sample, further increases in irradiation produce no change in the conductance. Photoconductive materials are used in the manufacture of photoelectric devices. Typical photoconductive substances consist of germanium, gallium, selenium, or silicon with impurities, also known as dopants, added. Other common materials include metal oxides and sulfides.

Lasers

All the radioactive electron transitions are spontaneous; that is, an electron falls from a high energy state to a lower one without any external provocation. These transition events occur independently of one another and at random times, producing radiation that is incoherent; that is, the light waves are out of phase with one another. With lasers,however,coherent light is generated by electron transitions initiated by an external stimulus;in fact,”laser” is just the acronym for light amplification by stimulated emission of radiation.

Applications of Lasers

The light beam produced by most lasers is pencil-sized, and maintains its size and direction over very large distances; this sharply focused beam of coherent light is suitable for a wide variety of applications. Lasers have been used in industry for cutting and boring metals and other materials, and for inspecting optical equipment. In medicine, they have been used in surgical operations. Lasers have been used in several kinds of



scientific research. The field of holography is based on the fact that actual wave-front patterns, captured in a photographic image of an object illuminated with laser light, can be reconstructed to produce a three-dimensional image of the object.

Lasers have opened a new field of scientific research, nonlinear optics, which is concerned with the study of such phenomena as the frequency doubling of coherent light by certain crystals. One important result of laser research is the development of lasers that can be tuned to emit light over a range of frequencies, instead of producing light of only a single frequency. Work is being done to develop lasers for communication; in a manner similar to radio transmission, the transmitted light beam is modulated with a signal and is received and demodulated some distance away. Lasers have also been used in plasma physics and chemistry.

For years after its invention, the laser was spoken of as a solution without a problem. That reputation soon disappeared as lasers found uses in a variety of industries. But now several new lasers, particularly solid state instruments that operate at ultraviolet wavelengths and those based on nonlinear materials, are finding uses in emerging areas. Computing, telecommunications, and, in particular, medicine, stand to benefit from the unique qualities of these new or improved systems.

Optical fibers in communications:

Our current "age of technology" is the result of many brilliant inventions and discoveries, but it is our ability to transmit information, and the media we use to do it, that is perhaps most responsible for its evolution . Progressing from the copper wire of a century ago to today’s fiber optic cable, our increasing ability to transmit more information, more quickly and over longer distances has expanded the boundaries of our technological development in all areas. Today’s low-loss glass fiber optic cable offers almost unlimited bandwidth and unique advantages over all previously developed transmission media. The basic point-to-point fiber optic transmission system consists of three basic elements: the optical transmitter, the fiber optic cable and the optical receiver.

The Optical Transmitter: The transmitter converts an electrical analog or digital signal into a corresponding optical signal. The source of the optical signal can be either a light



emitting diode, or a solid state laser diode. The most popular wavelengths of operation for optical transmitters are 850, 1300, or 1550 nanometers.

The Fiber Optic Cable: The cable consists of one or more glass fibers, which act as waveguides for the optical signal. Fiber optic cable is similar to electrical cable in its construction, but provides special protection for the optical fiber within. For systems requiring transmission over distances of many kilometers, or where two or more fiber optic cables must be joined together, an optical splice is commonly used.

The Optical Receiver: The receiver converts the optical signal back into a replica of the original electrical signal. The detector of the optical signal is either a PIN-type photodiode or avalanche-type photodiode.

Advantages of Fiber Optic Systems Fiber optic transmission systems – a fiber optic transmitter and receiver, connected by fiber optic cable – offer a wide range of benefits not offered by traditional copper wire or coaxial cable. These include:

1. The ability to carry much more information and deliver it with greater fidelity than either copper wire or coaxial cable.

2. Fiber optic cable can support much higher data rates, and at greater distances, than coaxial cable, making it ideal for transmission of serial digital data.

3. The fiber is totally immune to virtually all kinds of interference, including lightning, and will not conduct electricity. It can therefore come in direct contact with high voltage electrical equipment and power lines. It will also not create ground loops of any kind.

4. As the basic fiber is made of glass, it will not corrode and is unaffected by most chemicals. It can be buried directly in most kinds of soil or exposed to most corrosive atmospheres in chemical plants without significant concern.

5. Since the only carrier in the fiber is light, there is no possibility of a spark from a broken fiber. Even in the most explosive of atmospheres, there is no fire hazard, and no danger of electrical shock to personnel repairing broken fibers.

6. Fiber optic cables are virtually unaffected by outdoor atmospheric conditions, allowing them to be lashed directly to telephone poles or existing electrical cables without concern for extraneous signal pickup.

7. A fiber optic cable, even one that contains many fibers, is usually much smaller and lighter in weight than a wire or coaxial cable with similar information carrying capacity. It is easier to handle and install, and uses less duct space. (It can frequently be installed without ducts.)



8. Fiber optic cable is ideal for secure communications systems because it is very difficult to tap but very easy to monitor. In addition, there is absolutely no electrical radiation from a fiber.

How are fiber optic cables able to provide all of these advantages? This guide will provide an overview of fiber optic technology – with sections devoted to each of the three system components – transmitters, receivers, and the fiber cable itself. An appreciation of the underlying technology will provide a useful framework for understanding the reasons behind its many benefits.

Material Science/Economic, Environmental, and Social Issues of Material Usage Lecture Notes


Chapter 18. Economic, Environmental, and Social Issues of Material Usage 18.1 Economic Considerations: It is essential for the engineer to know about and understand economic issues simply because the company/institution for which he or she works must realize a profit from the products it manufactures. Materials engineering decisions have economic consequences with regard to both material and production cost 18.2 Environmental and Social considerations:

Issues of environmental protection and sustainable development are gaining an increasing importance in everyday life, and nowhere is this more so than in the field of Materials Science and Engineering. Almost every aspect of materials usage, from extraction and production, through product design and ultimately disposal issues, is now subject to environmental considerations. Furthermore there are many cases where the developments of novel ‘environmentally-friendly’ materials are providing new challenges for materials scientists and engineers.

The growing awareness of environmental issues has increased the attention focused on the materials industry. There is a danger that this could give a negative picture, highlighting examples where materials production and use has led to environmental problems. In many of these cases, materials, additives and production methods were used for very good materials engineering reasons before environmental concerns were established. The more positive image of materials engineering that can be portrayed is one where the industry is at the forefront of technical advances - not only to 'deal with past mistakes', but also to drive sustainable and safe use of materials for the future.

The topic of 'Environmental Materials' is broad and can touch on some relatively in-depth aspects of materials structure, chemical and physical properties, processing and design as well as more general areas such as legislative, economic and social aspects. Interesting topics within this area can be presented at a range of levels: for instance the sustainable use of materials in the IT sector can be discussed by 11 year olds with as much enthusiasm as by post-graduate students - although the latter would be expected to grasp the chemical details of identifying brominated flame-retardants, whereas the former would consider much simpler aspects, that are nonetheless important.

18.3 Recycling issues:

It could easily be argued that steel is a very sustainable material; it is abundant, takes relatively little energy to extract and is easy to recycle, however people living near a steelworks would argue against this. It is probably sensible to define such materials as those that have distinct differences that achieve environmental benefit compared to conventional materials. With this definition, the list would include:



1. Materials of a significantly plant-based nature, including wood, natural fibre composites, natural polymers.

2. Materials produced using a large proportion of waste material, including recycled polymers, composites made from waste mineral powders, and arguably also much steel and aluminum.

The most exciting developments in Materials Science are in the realm of functional materials, and many of these serve an environmentally-beneficial purpose, particularly in the production of green energy. These include:

o Solar-cell materials o Fuel-cell technology o Catalytic pollution control

The figure below schematically shows how the disparate areas under the heading of 'environmental materials' can be linked via a life cycle analysis approach.



18.4 Life Cycle Analysis and its use in design:

Life Cycle Analysis is essentially a method of considering the entire environmental impact, energy and resource usage of a material or product. It is often known as a 'cradle-to-grave' analysis and can encompass the entire lifetime from extraction to end-of-life disposal. Life cycle analysis can be an extremely effective way of linking many different aspects of the environmental impacts of materials usage. The scope of a life cycle analysis can be adjusted to suit a particular case. For instance it could cover the environmental impact of the global aluminium industry or simply that of one single plastic injection moulding machine. In order to gain most learning benefit from this area, students would be expected to have a good grasp of the necessary underlying technical areas, which could be quite complex and so this ideally suits more advanced degree level students. The most conventional way of approaching a life cycle analysis is to follow a particular material or product through its lifetime. Therefore the first consideration would be the impact of materials extraction, and then production and manufacture, product use and finally end-of-life considerations. This approach is followed below. Various aspects, such as energy usage, economic and legislative issues occur throughout the cycle.

material science

Documents

modern materials module

microstructure module

degradation of polymers

structural composites

properties of polymers

properties of ceramics

atomic vibrations module

processing of polymers