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REAL CRYSTALS- REAL CRYSTALS- IMPERFECTIONS, ANIZOTROPY IMPERFECTIONS, ANIZOTROPY AND MATERIALS ALLOTROPYAND MATERIALS ALLOTROPY

COURSE COURSE 22

Materials Science

Prof.dr.ing. Brânduşa GHIBAN

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A. A. REAL REAL CRISTALCRISTALS S – – CRYSTALLINE CRYSTALLINE IMPERFECIMPERFECTIONSTIONS

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“Crystals are like people, have flaws (DEFECTC), making them more attractive and interesting! ”

Scheme of a polycrystalline material with many defects

Real crystals Real crystals are never are never

perfect, they perfect, they always always contain contain

defectsdefects ! !

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3These faults (defects) have a significant impact These faults (defects) have a significant impact on the macroscopic properties materials.on the macroscopic properties materials.

Atomic bondAtomic bond

StructurStructuree

DefectsDefects

PROPPROPEERTIRTIESES

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MATERIALS PROCESSING MAY MATERIALS PROCESSING MAY DETERMINE DEFECTS FORMATIONDETERMINE DEFECTS FORMATION

Thermo-Thermo-mechanical mechanical processing processing

MicrostructuMicrostructurree

IntroducIntroducttiion andon and directing the defectsdirecting the defects

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CRYSTALLINE IMPERFECTIONS IN REAL CRYSTALS CRYSTALLINE IMPERFECTIONS IN REAL CRYSTALS From the point of view of its location in the crystal, crystalline imperfections are classified :

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1. Point 1. Point defectdefectss

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Vacancy

Interstitial foreign atom

Interstitial atom

Foreign substitution atom

simplesimple

complexcomplex

Point defects are characterized by measures of about the size of an Point defects are characterized by measures of about the size of an interatomic distanceinteratomic distance. .

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DEFECTDEFECTSS IN IONIC IN IONIC CRISTALCRISTALS S

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Schottky Defect Schottky Defect (the absence of ion pairs(the absence of ion pairs)) Frenkel Defect Frenkel Defect

(cathion in an interstitial space)(cathion in an interstitial space)

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Linear imperfections are strings (lines) of atoms, straight or curved, of limited length that are "deployed" in the particular ideal crystal, for which they are called dislocations. To explain the formation and location of dislocations in real crystals resort to a mechanical model based on the possibility that their crystallographic planes to slide over each other along a slip plane imaginary planes parallel to the plane crystallographic centers of two neighboring cathions (common tangent plane of the two atomic planes.)

2. Linear 2. Linear ImperfectiImperfectionsons - Disloca - Dislocattiionsons

8Building an edge dislocations with Burgers vector perpendicular to the dislocation line.

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9Building a screw dislocations with Burgers vector parallel to the dislocation.

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Dislocations Properties Dislocations Properties

alinterstiti T

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latticeperfect 11 vacance

T1

1

tionpoligoniza

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Have a great mobility, either by sliding or by climbing, allowing the plastic deformation of metals,

Have a specific material density, depending on its condition, i.e. 104 105 cm-2 in semiconductors,

106 108 cm-2 in annealed materials, 1011 1012cm-2 in plastic formed materials,

Up to 1012 cm-2 for materials during fracture.

Dislocations may interact between them, Dislocations may be multiply-

mechanism “Frank Read Source”

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3. 3. Plane Plane ImperfecImperfections- Interfacial tions- Interfacial Defects Defects

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Plane imperfections have a single size of the same order as the interatomic distance, and the other two higher. They are areas within the body of material separating the portions that differ in some respect: after the crystalline structure after crystallographic orientation as the orientation of spontaneous magnetization, etc..

External SurfacesExternal Surfaces

Grain BoundariesGrain Boundaries

Twin BoundariesTwin Boundaries

Stacking faultsStacking faults

Phase BoundariesPhase Boundaries

Interfacial Interfacial defects defects includeinclude

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3.1 EXTERNAL SURFACES3.1 EXTERNAL SURFACES

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One of the most obvious boundaries One of the most obvious boundaries is the external surface, along which is the external surface, along which the crystal structure terminates. the crystal structure terminates. Surface atoms are not bonded to the Surface atoms are not bonded to the maximum number of nearest maximum number of nearest positions. The bonds of these surface positions. The bonds of these surface atoms that are not satisfied give rise atoms that are not satisfied give rise to a surface energy, expressed in to a surface energy, expressed in units of energy per unit area (J/munits of energy per unit area (J/m2 2 or or erg/cmerg/cm22). To reduce this energy, ). To reduce this energy, materials tend to minimize, if at all materials tend to minimize, if at all possible, the total surface area. For possible, the total surface area. For example, liquids assume a shape example, liquids assume a shape having a minimum area, the droplets having a minimum area, the droplets become spherical. Of course, this is become spherical. Of course, this is not possible with solids which are not possible with solids which are mechanically rigid.mechanically rigid.

Liquid dropletLiquid droplet

Metal dropletMetal droplet

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3.2 GRAINS BOUNDARIES

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Represents separations of two small grains or crystals having different crystallographic orientation in polycrystalline materials. Various degrees of crystallographic misalignment between adjacent grains are possible. When the orientation mismatch is slight, on the order of a few degrees, then the term small (or low) angle grain boundary is used.

Schematic diagram showing small and high-angle Schematic diagram showing small and high-angle grain boundaries and the adjacent atom positionsgrain boundaries and the adjacent atom positions

Demonstration of how a tilt boundary Demonstration of how a tilt boundary having an angle of misorientation having an angle of misorientation results results

from an alignment of edge dislocationsfrom an alignment of edge dislocations

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3.3 TWIN BOUNDARIES3.3 TWIN BOUNDARIES

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Twin boundary is a special type of grain boundary, across which there is a specific mirror lattice symmetry; that is, atoms on one side of the boundary are located in mirror-image positions of the atoms on the other side. The region of materials between these boundaries is appropriately termed twin. Twins result from atomic displacements that are produced from applied mechanical shear forces (mechanical twins), and also during annealing heat treatments following deformation (annealing twins). Twinning occurs on a definite crystallographic plane and in a specific direction, both of which depend on the crystal structure. Annealing twins are typically found in metals that have FCC crystal structure, while mechanical twins are observed in BCC and HCP metals.

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3.4 PHASE BOUNDARIES3.4 PHASE BOUNDARIES

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Incoherent boundary interface between phases

Coherent boundary interface between phases

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CLOSE –PACKED CRYSTAL STRUCTURES

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Close-packed plane stacking sequence for hexagonal close-packed

The real distinction between FCC and HCP lies in where the third close-packed layer is positioned. For HCP, the centers of this layer are aligned directly above the original A positions. This stacking sequence, ABABAB…, is repeated over and over. Also, ACACAC… arrangement would be equivalent.

A second close-packed plane may be positioned with the centers of its atoms over either B or C sites; at this point both are equivalent. Suppose that B positions are arbitrarily chosen; the stacking sequence is termed AB.

If we note all the atoms of a close packed plane with A, and the following plane with atom in close packed situation with B, the remaining depressions are those with the down vertices, which are marked C.

A portion of a close-packed plane of A, B, and C atoms

The AB stacking sequence for close-packed atomic planeThe AB stacking sequence for close-packed atomic plane

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3.5 Stacking faults and twining 3.5 Stacking faults and twining

Stacking faults and twinning in FCC Stacking faults and twinning in FCC metals. (100) plane is parallel with metals. (100) plane is parallel with

(111) twin boundary(111) twin boundary. .

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Stacking faults occur in a number of crystal Stacking faults occur in a number of crystal structures, but the common example is in close-structures, but the common example is in close-packed structures. Face-centered cubic (fcc) packed structures. Face-centered cubic (fcc) structures differ from hexagonal close packed (hcp) structures differ from hexagonal close packed (hcp) structures only in stacking order: both structures structures only in stacking order: both structures have close packed atomic planes with sixfold have close packed atomic planes with sixfold symmetry—the atoms form equilateral triangles. symmetry—the atoms form equilateral triangles. When stacking one of these layers on top of When stacking one of these layers on top of another, the atoms are not directly on top of one another, the atoms are not directly on top of one another—the first two layers are identical for hcp another—the first two layers are identical for hcp and fcc, and labelled AB. If the third layer is placed and fcc, and labelled AB. If the third layer is placed so that its atoms are directly above those of the so that its atoms are directly above those of the first layer, the stacking will be ABA—this is the hcp first layer, the stacking will be ABA—this is the hcp structure, and it continues ABABABAB. However, structure, and it continues ABABABAB. However, there is another possible location for the third layer, there is another possible location for the third layer, such that its atoms are not above the first layer. such that its atoms are not above the first layer. Instead, it is the atoms in the fourth layer that are Instead, it is the atoms in the fourth layer that are directly above the first layer. This produces the directly above the first layer. This produces the stacking ABCABCABC, and is actually a cubic stacking ABCABCABC, and is actually a cubic arrangement of the atoms. A stacking fault is a one arrangement of the atoms. A stacking fault is a one or two layer interruption in the stacking sequence, or two layer interruption in the stacking sequence, for example, if the sequence ABCABABCAB were for example, if the sequence ABCABABCAB were found in an fcc structure.found in an fcc structure.

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4. Bulk or volume defects4. Bulk or volume defectsIn real metals may appear imperfections which may be extended in small or even big volumes, often called defects of compactity.

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PoresPores - can greatly affect optical, - can greatly affect optical, thermal, mechanical propertiesthermal, mechanical properties

CracksCracks - can greatly affect - can greatly affect mechanical propertiesmechanical properties

Foreign inclusionsForeign inclusions - can greatly - can greatly affect electrical, mechanical, affect electrical, mechanical, optical properties.optical properties.

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Due to the geometric distribution of atoms

arranged in crystalline bodies, the matter will

be found unevenly distributed according to different directions. Therefore her behavior

towards physical action determined to be different from one direction to another

The consequences of atomic The consequences of atomic arrangementsarrangements

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B. AniB. Anissotropotropy of materials y of materials

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Crystals anisotropy throughout the whole elastic and plastic properties :

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Anisotropic behaviorAnisotropic behavior Generally, the properties of materials are the same in all direction,

which is called isotropy. For example, the electrical conductivity for materials having a cubic lattice structure is completely isotropic.

Because of differences in atomic arrangement in the planes and direction within a crystal, the properties may vary with the direction. A material is anisotropic if its properties depend on the crystallographic directions along with the property is measured.

Anisotropy in natural materialsAnisotropy in natural materials

Wood is a good example of an anisotropic material. In a tree, the cells are arranged parallel to the trunk (axially). Consequently the strength is different along different directions (axial, radial). This is because the tree is commonly loaded in the direction of the trunk e.g. by wind.

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These graphs illustrate the effect of direction on two important mechanical These graphs illustrate the effect of direction on two important mechanical properties: the properties: the Young modulusYoung modulus and the and the compressive strengthcompressive strength. Note that for . Note that for dense woods such as oak, the directional effect is less pronounced, whereas dense woods such as oak, the directional effect is less pronounced, whereas 'light' woods such as balsa are extremely anisotropic - the Young modulus is 'light' woods such as balsa are extremely anisotropic - the Young modulus is about 100 times higher in the axial direction than the transverse. about 100 times higher in the axial direction than the transverse.

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STRUCTURAL ANISOTROPY OF MAN-MADE COMPOSITES (1)STRUCTURAL ANISOTROPY OF MAN-MADE COMPOSITES (1) Ceramic fibres have a higher strength than metals. By combining two phases (ceramic fibre and metal matrix), a mixture of both properties is obtained.If the fracture strain of metal and ceramics are of the same magnitude the following formula holds:

σσLL =  = VVff σ σfbfb + (1 −  + (1 − VVff)σ)σmbmbσL =fracture stress in longitudinal directionσfb=fracture stress of the ceramic fibreσmb=fracture stress of the metalV f =volume fraction of the ceramic fibres

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STRUCTURAL ANISOTROPY OF MAN-MADE COMPOSITES (2) STRUCTURAL ANISOTROPY OF MAN-MADE COMPOSITES (2) If the fibres are not all oriented in the same direction (i.e. short-fibre-reinforced composites) the properties depend on the distribution of their orientations. If the fibres are distributed randomly (mean orientation = 45°), the composite is isotropic. With increasing orientation in loading direction the strength increases parallel to the loading direction but decreases in the transverse direction.

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  ANISOTROPY IN ALUMINIUMANISOTROPY IN ALUMINIUM Compared to wood and fibre-reinforced composites, aluminium and its alloys

tend to possess less pronounced anisotropic mechanical properties. Nevertheless, the properties of aluminium are never completely isotropic - some

degree of anisotropy is always present. This can have very important consequences on both the processing/production of

aluminium, and on the in-service performance of an aluminium structure or component. Sometimes this anisotropy can be beneficial, at other times problematic.

Anisotropy in the mechanical properties can cause 'earing' in the can body. The ears must be cut off, leading to wastage.

The following graph shows the anisotropic nature of the Young modulus of a single crystal of aluminium (as calculated by Nye). As the cube axis is rotated from 0°/90° to 45° to the tensile axis, the modulus increases from 63 to 72 GPa, or about 15%.

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ANISOTROPY IN ALUMINUMSTRESS-STRAIN BEHAVIOUR

The stress-strain curve clearly illustrates the anisotropic nature of two important mechanical properties: namely strength (UTS) and elongation to failure.The highest strength is obtained for the sample cut parallel to the rolling direction, while the curves for samples cut at 45° and 90° to the rolling direction are lower and almost identical.The anisotropy of the elongation to failure very pronounced, with the 45° sample having an elongation nearly 25% (in relative terms) greater than the longitudinal (0°) sample.

Uniaxial stress-strain curve for recrystallised alloy 5754-O.

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C. POLYMORPHIC AND ALLOTROPIC MATERIALSC. POLYMORPHIC AND ALLOTROPIC MATERIALSSome materials have different crystal structures at lower temperatures than at higher temperatures. (The inherent energy of a crystal structure is temperature-dependent.) Materials that undergo a transformation from one crystal structure to another are called polymorphicpolymorphic or, when referring to elements, allotropicallotropic. A well-known example is the allotropic transformation of room temperature, ductile, tetragonal, white, -tin to its low-temperature, brittle, diamond cubic, gray, modification. The transformation occurs slowly at 286.2 K and causes a 27% expansion and thus a disintegration into powder (tin plague, tin pest or tin leprosy). As a consequence of this transformation, old organ pipes made of tin (or tin alloys) may disintegrate in severe winter temperatures. A similar breakdown has been reported for the tin-based coat buttons of Napoleon’s army in a harsh Russian winter. Another example is the temperature-dependent FCC to BCC allotropic transformation of pure iron at 912°C. The prevailing crystal structure also may depend on the external pressure. As an example, graphite is stable at ambient conditions whereas diamond is the high pressure modification of carbon.

Diamond and graphite are two allotropes of carbon: pure forms of the same element that differ in structure.

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Some allotropes of carbon:

a) diamond;

b) graphite;

c) lonsdaleite;

d) –f) fullerenes (C60, C540, C70);

g) amorphous carbon;

h) carbon nanotube.

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EXAMPLES OF ALLOTROPESEXAMPLES OF ALLOTROPESelements Allotropes

Carbon diamond - an extremely hard, transparent crystal, with the carbon atoms arranged in a tetrahedral lattice. A poor electrical conductor. An excellent thermal conductor. lonsdaleite - also called hexagonal diamond. graphite - a soft, black, flaky solid, a moderate electrical conductor. The C atoms are bonded in flat hexagonal lattices (graphene), which are then layered in sheets. amorphous carbon fullerenes, including "buckyballs", such as C60. carbon nanotubes - allotropes of carbon with a cylindrical nanostructure.

Phosphorus White phosphorus - crystalline solid P4 Red phosphorus - polymeric solid Scarlet phosphorus Violet phosphorus Black phosphorus - semiconductor, analogous to graphite Diphosphorus

Oxygen dioxygen, O2 - colorless ozone, O3 - blue tetraoxygen, O4 - metastable octaoxygen, O8 - red

Nitrogen dinitrogen tetranitrogen trinitrogen two solid forms: one hexagonal close-packed and the other alpha cubic

elements Allotropes

Sulfur Plastic (amorphous) sulfur - polymeric solid Rhombic sulfur - large crystals composed of S8 molecules Monoclinic sulfur - fine needle-like crystals Other ring molecules such as S7 and S12

Selenium Red selenium," cyclo-Se8 Gray selenium, polymeric Se Black selenium

Boron amorphous boron - brown powder crystalline boron - black, hard (9.3 on Mohs'scale), and a weak conductor at room temperature.

Germanium α-germanium - β-germanium - at high pressures

Silicon amorphous silicon - brown powder crystalline silicon - has a metallic luster and a grayish color. Single crystals of crystalline silicon can be grown with a process known as the Czochralski process

Arsenic Yellow arsenic - molecular non-metallic As4 Gray arsenic, polymeric As (metalloid) Black arsenic (metalloid) and several similar other ones.

Antimony •blue-white antimony - the stable form (metalloid) •yellow antimony (non-metallic) •black antimony (non-metallic) •(a fourth one too)

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EXAMPLES OF METALS WITH ALLOTROPIC PROPERTIES EXAMPLES OF METALS WITH ALLOTROPIC PROPERTIES

425425

912912

885885

865865

450450