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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