ELE 362 Materials Science: Intro., Structure, and Bonding

James V. Masi, Ph.D.

Work together

Helping Hand

Materials Cycle

The evolution of materials

Unit 1, Frame 1.2

Materials, process and shape

Metals, ceramics, glassesMATERIALS

polymerscomposites...

Flat and dished sheet

SHAPESprismatic,

3-D

Casting , moulding

PROCESSESpowder methods,

machining...

The world of materials

PE, PP, PCPA (Nylon)

Polymers,elastomers

Butyl rubberNeoprene

Polymer foamsMetal foams

FoamsCeramic foams

Glass foams

Woods

Naturalmaterials

Natural fibres:Hemp, Flax,

Cotton

GFRPCFRP

CompositesKFRP

Plywood

AluminaSi-Carbide

Ceramics,glasses

Soda-glassPyrex

SteelsCast ironsAl-alloys

MetalsCu-alloysNi-alloysTi-alloys

Unit 1, Frame 1.4

Basic material properties

GeneralWeight: Density ρ, Mg/m3

Expense: Cost/kg Cm, $/kg

MechanicalStiffness: Young’s modulus E, GPaStrength: Elastic limit σy , MPa Fracture strength: Tensile strength σts , MPa Brittleness: Fracture toughness Kic , MPa.m1/2

ThermalExpansion: Expansion coeff. α, 1/KConduction: Thermal conductivity λ, W/m.K

ElectricalConductor? Insulator?

Young’s modulus, E

Elastic limit, yσ

Strain ε

Stre

ss σ

Ductile materials

Brittle materials

Young’s modulus, E

Tensile (fracture) strength, tsσ

Strain ε

Stre

ss σ

∗

∗

Thermal expansion

oll

Expansion coefficient, α

Temperature, T

Ther

mal

stra

in ε

T1 To

Q joules/sec

x

Area A

Thermal conduction

Mechanical properties

Thermal conductivity, λ

(T1 -T0)/x

Hea

t flu

x, Q

/A

Materials information for design

The goal of design:“To create products that perform their function effectively, safely, at acceptable cost”What do we need to know about materials to do this? More than just test data.

Test Test data

Data capture

Statisticalanalysis

Design data

Mechanical Properties

Bulk Modulus 4.1 - 4.6 GPaCompressive Strength 55 - 60 MPaDuctility 0.06 - 0.07Elastic Limit 40 - 45 MPaEndurance Limit 24 - 27 MPaFracture Toughness 2.3 - 2.6 MPa.m1/2

Hardness 100 - 140 MPaLoss Coefficient 0.009- 0.026Modulus of Rupture 50 - 55 MPaPoisson's Ratio 0.38 - 0.42Shear Modulus 0.85 - 0.95 GPaTensile Strength 45 - 48 MPaYoung's Modulus 2.5 - 2.8 GPa

Successfulapplications

$

Economic analysisand business case

Selection ofmaterial and process

Potential applications

Characterization Selection and implementation

Material property- charts: Modulus - Density

0.1

10

1

100

Metals

Polymers

Elastomers

Ceramics

Woods

Composites

Foams

0.01

1000

1000.1 1 10Density (Mg/m3)

You

ng’s

mod

ulus

E,

(GP

a)

Modulus –Density

Unit 1, Frame 1.17

Commercial Material's Linkshttp://www-engr.sjsu.edu/WofMatE/Metals&Alloys.htm

Metals and AlloysCeramicsGlassesPolymersCompositesSemiconductorsBiomaterialsMaterials Characterization Concept of StructureFailure Analysis

Periodic Tables1. pearl1.lanl.gov/periodic2. www.webelements.com/webelements/scholar3. www.chemicalelements.com4. www.csrri.iit.edu/periodic-table.html5. environmentalchemistry.com/yogi/periodic

HTML Periodic Table

Electron VoltsA convenient energyunit, particularly for atomic and nuclearprocesses, is the energy given to an electron by accelerating it through 1 volt of electric potential difference. The work done on the charge is given by the charge times the voltage difference, which in this case is:

The abbreviation for electron volt is eV.

νλ

hhcEphoton == ,In Joules

phEparticle = ,in Joules,

where p = mvPlanck’s constant, h = 6.63x10-34 J-s

Energies in Electron VoltsRoom temperature thermal energy of a molecule..................................0.03 eV

Visible light photons....................................................................................1.5-3.5 eV

Energy for the dissociation of an NaCl molecule into Na+ and Cl- ions:......4.2 eV

Ionization energy of atomic hydrogen ........................................................13.6 eV

Approximate energy of an electron striking a color television screen.....20,000 eV

High energy diagnostic medical x-ray photons...............................200,000 eV (=0.2 MeV)

Typical energies from nuclear decay:(1) gamma..................................................................................................0-3 MeV(2) beta.......................................................................................................0-3 MeV(3) alpha....................................................................................................2-10 MeV

Cosmic ray energies ........................................................................1 MeV - 1000 TeV

Planetary model of H-atom

Quantized Energy StatesThe electrons in free atoms can will be found in only certain discrete energy states. These sharp energy states are associated with the orbits or shells of electrons in an atom, e.g., a hydrogen atom. One of the implications of thesequantized energy states is that only certain photon energies are allowed when electrons jump down from higher levels to lower levels, producing the hydrogen spectrum. The Bohr model successfully predicted the energies for the hydrogen atom, but had significant failures that were corrected by solving

the Schrodinger equation for the hydrogen atom.

The Bohr Atom:ionization potential

Bohr found that the energy levels which give rise to the Hydrogen spectrum correspond to electron orbits of radius r and momentum psuch that the expression

has one of the values n=1, n=2, n=3, ....Only works for circular orbits (H, He, s….)

Energy (eV) W = 13.6 Z2/n2

Z = atomic #

Ionization Level

The Bohr Atom:ionization potential

Bohr's Hydrogen atom has an electron which runs like a train on isolated circular tracks. Photons are emitted or absorbed when the electron jumps from one track to another.

O.K only for circular orbits!

Bohr's model started to fail for atoms with more than one electron. Attempts to generalize the rules were only partly successful.

Shell model of the atom

Quantum Mechanical Selection rulesNAME SELECTION RULE

principal quantum number n = 1, 2, 3, ....angular momentum quantum no. 1 = 0, 1, 2, ...., (n-1)magnetic quantum number m = 1, (1-1), ...., -(1-1), -1spin quantum number ms = +/- 1/2NOTE: The spin quantum number results from Pauli's exclusion principle, which states that "a given quantum state determined by n, 1, m , can be occupied by not more than two electrons" (one spin-up and one spin-down). Let us also recall that 1 = 0, 1, 2, 3, ...., is nothing more than a numerical statement of the old spectroscopic notation, namely,

1 = 0 is "s" or sharp1 = 1 is "p" or principal1 = 2 is "d" or diffuse1 = 3 is "f" or fundamental, etc.n = 1 is K shelln = 2 is L shelln = 3 is M shelln = 4 is N shell, etc.

Pauli exclusion principle

Orbitals: electron density/path

Shell GameFor example, let us look at the L shell (n=-2)

n 1 m ms2 0 0 +/- 1/22 1 1 +/- 1/22 1 0 +/- 1/22 1 -1 +/- 1/2

, or 2x4 = 8, electrons for the L shell 1) The principal quantum number "n" is the major factor in determining energy, n=1,2,3,....Corresponding shells are sometimes called K, L, M...

2) "1" determines the way in which the orbital angular momentum is quantized, 1=0 to (n-1). Sometimes called s, p, d, f, ....

3) m is the magnetic quantum number that describes the orientation of angular momentum in space -1 ≤ m ≤ +1.

4) ms is the spin quantum number, that describes the two possible components of angular momentum, up or down (+/- ½).

NOTE: See the table of electron configurations described in the periodic table.

Q.N. and Orbitals

Filling order of subshells

Maximum possible number of electrons in the shells and subshellsof an atom.

Subshelll = 0 1 2 3

s p d fn Shell----------------------------------------------------------------------------------1 K 22 L 2 63 M 2 6 104 N 2 6 10 14------------------------------------------------------------------------------------------------

Band structure of Magnesium

Probability: It’s in there somewhere

Energy is “Discreet” in the atom

Force and Potential Energy

Bonds and vibrations

FA + FR = FN

At equil. FA + FR = 0

Bonding energy

Average separation and expansion with temperature

∫∞

•=r

N drFE

∫∫∫∞∞∞

•+•=•=r

R

r

A

r

NN drFdrFdrFE

Types of Atomic & Molecular BondsPrimary Atomic BondsIonic BondsCovalent BondsMetallic Bonds

Secondary Atomic & Molecular BondsPermanent Dipole BondsFluctuating Dipole Bonds

Covalent CrystalsCrystals in this class are hard, have a high melting point, and a low electrical conductivity. They are usually near one another in the periodic chart. Unlike the ionic crystals, they have high electron density in the directions of the tetrahedron corners and hereby possess directional; bonds. Some examples of covalently bonded crystals are Diamond, Si, Ge, SiC, CH4, etc.M.P. ~ 100 to 4000KB.E. x.xx eV/mol, at, ion

Covalent bonding

Large interatomic forces are created by the sharing of electrons to form directional bonds.The atoms have small differences inelectronegativity & close to each other in the periodic table.The atoms share their outer s and pelectrons so that each atom attains the noble-gas electron configuration.

Covalent bond for H2

Covalent bond

Covalentdiamond carbon

CovalentBondEnergies

Metallic CrystalsCrystals in this class are, in general, opaque, deformable, and have high electrical and thermal conductivity. The bonding electrons are essentially free. The bonds are non-directional for the metals with filled inner shells, eg. Mg, Cu, Ag, etc.The bonds are directional for the transition metals such as Ti, W, Fe, etc.M.P. ~500 to 400KB.E. x.xx eV/at, mol, ion

Metallic BondingLarge interatomic forces are created by the sharing of electrons in a delocalizedmanner to form strongnondirectionalnondirectional bonding.

[Note the schematic representation of copper atoms arranged in a FCC crystal at the left, and the representation of the cloud of electrons surrounding the positively charged cores.]

Metallic Bonding

Ionic CrystalsCrystals in this class have low electrical conductivity, they are transparent, brittle, and have a high melting point. They are made up of strong electropositive (metal) ions bonded to strong electronegative (non-metal) ions. They have spherical symmetry, implying that there is no preferred bond direction. Charge neutrality is preserved and every negative charge is balanced by equal and opposite positive charge. Ionic crystals have packing sequence consistent with the size of the ions involved. Some examples of these crystals are:NaCl, MgF2, CsCl, etc.M.P. ~ 800 to 300KB.E. x.xx eV/at, mol, ion

Ionic BondingLarge interatomic forces are created by the “coulombic” effect produced by positively and negatively charged ions. Ionic bonds are “nondirectionalnondirectional”.The “cation” has a + charge & the “anion” has the -charge.The cation is much smaller than the anion.

Ionic bond Ionic dissociation

Because the ionic bond isnondirectional the ions pack together in a solid in ways which are governed by their relative sizes. Another important factor is that the ions must be arranged so that their is local charge neutrality. [Note the structure of NaCl.]

Typical Solids

BondEnergyeV/atom

Melt. Temp.(°C)

Elastic Modulus(GPa)

Density(g cm -3)

Typical Properties

Ionic NaCl,(rock salt)MgO, (magnesia)

3.210

8012852

40250

2.173.58

Generally electrical insulators. May become conductive at high temperatures.High elastic modulus. Hard and brittle but cleavable. Thermal conductivity less than metals.

Metallic CuMg

3.11.1

1083650

12044

8.961.74

Electrical conductor.Good thermal conduction.High elastic modulus.Generally ductile. Can be shaped.

Covalent SiC (diamond)

47.4

14103550

190827

2.333.52

Large elastic modulus. Hard and brittle. Dia mond is the hardest material.Good electrical insulator.Moderate thermal conduction, though diamond has exceptionally high thermal conductivity.

van der Waals: Hydrogenbonding

PVC, (polymer)H2O, (ice)

0.70.52

2120

49.1

1.30.917

Low elastic modulus. Some ductility.Electrical insulator. Poor thermal conductivity.Large thermal expansion coefficient.

van der Waals:Induced dipole

CrystallineArgon

0.09 −189 8 1.8 Low elastic modulus.Electrical insulator. Poor thermal conductivity.Large thermal expansion coefficient.

-

Comparison of bond types and typical properties (general trends

Potential energy vs distance:NaCl

F = q1q2/(4πε0r2)

Force

Potential Energy

P.E. = q1q2/(4πε0r)

q1q2 = charges of Na and Clε0 = permittivity of space

(1/36π) x 10−9 F/m

REMEMBER:

Dipolar molecules:van der Waals bond; H-bond

Van der Waals CrystalsCrystals in this class possess weak attractive forces. The interactions are dipole-dipole, dipole-quadruple, etc. Some members of this class are He, Ne, Ar, CH4, etc.M.P. ~ 100 to 200KB.E. 0.xx eV/at, mol, ion

Secondary Atomic & Molecular Bonds [Van der Waals Bonds]

Permanent Dipole BondsWeak intermolecular bonds are formed between molecules which possess permanent dipoles.A dipole exists in a molecule if there is asymmetry in its electron density distribution.

Fluctuating Dipole BondsWeak electric dipole bonding can take place among atoms due to an instantaneous asymmetrical distribution of electron densities around their nuclei.This type of bonding is termed fluctuation since the electron density is continuously changing.

Hydrogen Bonded Crystals

These crystals have higher bond energies and therefore higher melting points than the van der Waals crystals.

They tend to form groups of molecules, for instance, HF, H20, etc.M.P. ~ 160 to above 300KB.E. 0.xx eV/at, mol, ion

Induced dipole interactions

Mixed Bonding

Metallic-Covalent Mixed Bonding: The Transition Metals are an example where dspbonding orbitals lead to high melting points.Ionic-Covalent Mixed Bonding: Many oxides and nitrides are examples of this kind of bonding.

Forces for metalsIt is convenient for many purposes to regard an atom in a metal as having a definite size, which may be defined by the distance between its center and that of its neighbor.This distance is that at which the various forces acting on the atom are in equilibrium.In a metal, the forces can be considered as

•(a) the attractive forces between electrons & positive ions, •(b) the repulsion between the complete electron shells of the positive ions, & •(c) the repulsion between the positive ions as a result of theirsimilar positive charges.

Stability of states

Activation Energy

R = R0 exp (-Qa/kT) = R0 exp (-qV/kT)

Rate Equation: R-rate, Qa- activation energy, q – electronic charge, V - voltage

The Hard Sphere ModelThis approach can be called the "hard sphere" model of an atom, however the radius of an atom (or ion) determined for a particular crystal structure is not a real characteristic of that atom, because when the same atom appears in different crystal structure it displays different radii. The radius of an atom (or ion) can be determined for a particular metal by using the dimensions of the unit cell of the crystal structure it forms. Remember, where q is the charge and r is

the separation20

21

4 rqqF

πε=

Butterfly Wing400 X Magnification.A 2 inch butterfly would be over 60 feet long.

Boron Nitride Layer onMagnesium Oxide

7,200,000 X Magnification.

PencilWood from a broken pencil.200 x Magnification.A pencil would be over 4 feet wide.

Eye of a FlyEye of a house fly.300 x Magnification.A fly would be over 25 feet long.