MSE-227Materials Engineering Fall 2014

Riccardo DeSalvo

Quizzes Four absentsOr ~ empty sheet

Recap

Youngs modulus definitionSlope of the linear (elastic) region

E

Stiffness Youngs ModulusElastic modulus depends on atomic structureTightly bound atoms => stiffLoosely bound atoms => softCorrelated with melting temperature

Typical stress strainElastic (linear) region

Yield point

Maximum stress

Break

Plasticity, fragility depend on types of bondsRigid bonds=>brittleness=>fragilityEasy to slide bonds => ductility=> plasticity=> malleability

What is behind all of material science?Atomic structure of materials:Bonding type/structures Rigidity/plasticityBonding energiesMelting pointsAtomic sizespackingOrder/disorderCrystals/glassesDefectsPlasticity, hardness, . . . .

Types of atomic bondsbondsIonicCovalentMetallicVander WaalsHydrogenCharacterMaterialRigidSalts, CrystalsRigidDiamond, SiliconNot rigidMetalsNot rigidCl2, Ar, PolymersNot rigidH2O, NH3, WettingStrengthMelting temperature

Brief summary of chemistryAtoms are made of a positively charged nucleus with electrons orbiting around

Same number of protons and electrons

Atomic shell structureAtoms are built with electrons in concentric shells

Each shell carry growing number of electrons

Periodic table of elements reflects the shell structure of the atom

* Why? Valence (outer) shell usually not filled completely. Most elements: Electron configuration not stable.SURVEY OF ELEMENTSAdapted from Table 2.2, Callister & Rethwisch 4e.

*Electronic Configurationsex: Fe - atomic # =26Adapted from Fig. 2.4, Callister & Rethwisch 4e.

Atomic shell structureComplete shells are stableNoble gases Only make van der Waals bonds

Ionic bondsSome Atoms have a single electron in valence shellSome Atoms have a missing electrons in valence shell

Ionic bondsSome Atoms have a single electron in valence shellSome Atoms have a missing electrons in valence shell

Gain stability in transferring one electron from Sodium to ChlorineForm two complete shellsForm two ions of opposite sign !AttractionAtomic shell structure

Rigid crystalStrong attraction forces between different chargesRepulsion between same chargesRigid and compact structure

*Ionic BondingEnergy minimum energy most stableEnergy balance of attractive and repulsive termsAdapted from Fig. 2.8(b), Callister & Rethwisch 4e.

Covalent bondsOne Two or more electrons missing in large atom to complete a shellFixed angular positionsRigidity

Orbital shapesOrbitals have rigid shapes

Covalent bondDiamondExtreme rigidity & strength

Metallic Shells with one or two extra electronsForm a crystal where free electrons take the place of large negative ions

Note the difference

Metallic The absence of large negative ions eliminate the rigidityA fluid of free electrons act as a glue between positive charges

MalleabilityElectrical conductivityThermal conductivity

Metal bondingOrbitals are much less important because the electrons are shared in a common cloudRigidity of diamond and salts does not apply

*Arises from interaction between dipoles Permanent dipoles-molecule induced Fluctuating dipoles-general case:-ex: liquid HCl-ex: polymerAdapted from Fig. 2.13, Callister & Rethwisch 4e.Adapted from Fig. 2.14, Callister & Rethwisch 4e.SECONDARY BONDINGsecondary bondingsecondary bondingsecondary bonding

Van Der WaalsAct between sheets of strongly bound atoms

Hydrogen bondsAct between lines of strongly bound atoms PolymersDNA

bonding

ExercisesWhat is the predominant type of bonding for titanium (Ti)?A. IonicB. HydrogenC. CovalentD. van der WaalsE. Metallic

*TypeIonicCovalentMetallicSecondaryBond EnergyLarge!Variablelarge-Diamondsmall-BismuthVariablelarge-Tungstensmall-MercurysmallestCommentsNondirectional (ceramics)Directional(semiconductors, ceramicspolymer chains)Nondirectional (metals)Directionalinter-chain (polymer)inter-molecularSummary: Bonding

Todays AimsWhat is the difference in atomic arrangement between crystalline and noncrystalline solids? What features of a metals/ceramics atomic structure determine its density?How do the crystal structures of ceramic materials differ from those for metals?Under what circumstances does a material property vary with the measurement direction?

materials organize into gases, liquids or solidsWe have seen various kinds of crystals

Crystals vs. liquid

Glasses are solid liquids (amorphous)

How do we know crystals exist?Some are visibleBreaking (cleavage) of crystals can be obvious

How do we know crystals exist?X-ray scattering reveals the structure of crystals (grains) and allows their study

Study crystals from unit cellMinimum repeating structureExample face centered cubic

One exerciseFor a K+Cl ion pair, attractive and repulsive energies EA and ER, respectively, depend on the distance between the ions r, according to

For these expressions, energies are expressed in electron volts per K+Cl pair, and r is the distance in nanometers. The net energy EN is just the sum of the two expressions above.(a) Superimpose on a single plot EN, ER, and EA versus r up to 1.0 nm.(b) On the basis of this plot, determine (i) the equilibrium spacing r0 between the K+ and Cl ions, and (ii) the magnitude of the bonding energy E0 between the two ions.

Create table

Create functions Coulomb attraction from + & - ions

Atomic repulsion from filled shells

Graph Coulomb attractionScale EVSoft curve

Graph shell repulsionScale KeVStiff curveZoom in

Graph shell repulsionScale KeVStiff curveRadius of ions

Overlap two curvesWhere did Coulomb attraction go?

Zoom in again

Overlap two curvesWowCoulomb force is so small ?

Zoom in more

Overlap two curvesCoulomb dominates over 0.35 nm

Shell repulsion dominated below 0.25 nmEquilibrium pointBonding energy

Conclusions?Atoms can be seen as hard ballsFilled shells give size to atomsAtoms are kept together by electrostatic forces

We are now ready to discuss crystal structures

How do atoms choose a crystalline structure?By size and bonding type.Some dictated by bonding orientation Example in diamondShells are as rigid as they are tough!In metals mostly by size (and mixing)Electrons bond any metal atom to any other

Pure Metal packing structuresFor metals

Essentially 3 (4) options only:Face Centered Cubic FCCBody Centered Cubic BCCHexagonal Close Packed HCPCubic

FCC Packing densityCell size a = 2R2Number of atoms/cell 6/2 + 8/8 = 4Atomic packing fraction 0.74Coordination number 12 neighbors

2R8x6xa

BCC Packing densityCell size a = 4R/3Number of atoms/cell 1 + 8/8 = 2Atomic packing fraction 0.68Coordination number 8 neighbors

2R8x1x

HCP Packing densityCell size a = R c = ~ 1.63 RNumber of atoms/cell 3 + 2/2 + 12/6 = 6Atomic packing fraction 0.74Coordination number 12 neighbors

2R = a1x8xc

Similarities of FCC and HCPDiffer in appearanceSameAtomic packing fraction 0.74SameCoordination number 12 neighborsSame surface structureDifferent layering

Same surface structure

A little more on packingClose pack on a plane

Another close pack plane can go in either B or C

A little more on packingThe next plane can go in either A or CIt is different

On ASequence is A B A B A BClose Packed HexagonalCPH

On CSequence is A B C A B CBody Centered CubicBCC

CPH and BCCSame densitySame atomic spacing

Very different Bragg scattering

FCC packing fractionCalculate:Cell volumeAtom volumeNumber of atomsPacking fraction

Density

r = n A / Vc NA

N = number of atoms in cellA = Atomic weight Vc = Cells VolumeNA = Avogadros Number

Weight per moleVolume of a mole of cells

DensityCopper has FCC structureR = 0.128Atomic weight 63.5 g/mole

Calculate density

Few words of Ionic compoundsImportant featuresRelative size of anion and cationCharge of anion or cationDetermine choice of varied crystal shapes

Crystalline structures of compoundsVariations of FCC, BCC, HCP and more complex structures

Orbital geometryOrbital geometry also affects crystalline structure

SiO2

Carbon

Crystals and glassesWhat is the difference

Between this

And this?

Crystals and glassesLinesAnglesPlanesOrderPackingCells

Questions How do you define a direction?

How do you define a plane?

Exercise coordinatesWhat are the coordinates of:An atom at the center of the front faceThe origin atomThe opposite atomAn atom at the center of the cell

Exercise What is this structure?List position of atoms in this cell,List fraction of atoms in cellHow many atomsin this cell?

Exercise What is this structure?List position of atoms in this cell,List fraction of atoms in cellHow many atomsin this cell?

How do we study crystals?X-ray scattering reveals the structure of crystals (grains) and allows their study

When do x-ray scatter?.

Understanding scattering IncorrectArgument!

Only for understanding

Understanding scattering

Changed wavelength

Wave amplitude and power amplitudeA property of waves is that wave power is proportional to the square its height!Two coherent scatters adding in phase double its amplitude

11

4

Wave amplitude and power amplitudeA property of waves is that wave power is proportional to the square its height!Two coherent scatters adding in phase double its amplitude

11

422

161010

400

Wave amplitude and power amplitudeA property of waves is that wave power is proportional to the square its height!Two coherent scatters adding in phase double its amplitudeIf many atoms line up perfectly reflection ismany2

Understanding scattering 9x at perfect angleNothing at other angles

Understanding scattering How many in this case?

Count the dots

When do x-ray scatter?Scattering happens reflecting on planesScattering happens only when reflections are in phase

Full Bragg scattering

Simplified Bragg scatteringUse powders of crystalsMany not alignedEach crystal scatter at a fixed Bragg angleInstead of angles one gets cones

How do we identify planes? Perpendicular vector identify the planesAll parallel planes are equivalentRule:Take plane away from originFind intercepts with axis(parallel = infinite)Invert all three values

Plane vectorsThese vectors identify the planes on which Bragg scattering occurs.

Bragg scattering occurs only at the angles that produce coherent scattering

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