2Defects in solids All solid materials… Solidification process… contain large # of defects.Solidification process…classificationabove TmDefects…imperfection in structures of solid materialscrystal structure due to irregular/disordered atomicarrangement.amorphous structure due to molecular chains error.- classify in terms of geometry (dimension) & size.normally, formed during solidification process.zero dimensionone dimensiontwo dimensionthree dimensionliquidnucleiSolidification process…result of primary materials forming/working.i.e: for metals, casting process.2 steps:1. Nuclei form – formation of stable nuclei.2. Nuclei grow to form crystals – formation of grainstructure.start with a molten (all liquid) material & grains (crystals) grow until they meet each other.point defectsLinear/dislocation defectsarea/planar/surface defectsvolume defects (i.e: crack)crystals growingcrystal growing- Grains structure can be:1. equiaxed grains (roughly same size in all directions).2. columnar grains (elongated grains).room temp.grain structureColumnar grains in area with less undercoolingMoldEquiaxed grainsdue to rapid cooling (greater T) near wallCasting process
3Defects in solids classification Point defects in ceramics 1. Vacancies- vacancies exist in ceramics for bothcations and anions.2. Interstitials- exist for cations only.- interstitials are not normally observed foranions because anions are large relativeto the interstitial sites.3. Frenkel defect- a cation vacancy-cation interstitial pair.4. Schottky defect- a paired set of cation and anion vacancies.CationInterstitialVacancyAnionDefects in solidsclassificationzero dimensionpoint defectsSchottkydefectFrenkelmetalsceramicspolymersPoint defects in metals2. Vacancies1. Self-Interstitialsvacant atomic sites exist in a structure.form due to a missing atom.form (one in 10,000 atoms) duringcrystallization, mobility of atoms orrapid cooling.- "extra" atoms positioned between atomicsites.- cause structural distortion.self-interstitialdistortionof planesVacancydistortionof planesinterstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurityself-interstitial & vacancy (metals)interstitial & substitutional (metal alloys)Chain packing errorPoint defects in polymersDefects due in part to chain packing errors andimpurities such as chain ends and side chains.i.e: thin platelets10 nmAdapted from Fig. 4.12, Callister & Rethwisch 3e.
4Measuring Activation Energy… Equilibrium concentration: Point defectsMeasuring Activation Energy…Defects in solids• We can get Qv from an experiment.classificationequilibrium # of point defects (vacancies) forsolids depends on & increase with temperature.apply the formula:• Measure this...Nvzero dimension# of vacancy sites, NvVacancy concentration=total # of atomic sites, Npoint defectsexponentialæöNQdependence!v=çvexpçèøNkTTDefect vacancy) concentrationNv = # of defects (vacancies site)N = total # of atomic sites• Replot it...T = temperature1/TNvln-Q/kslopemetalsceramicspolymersQv = activation energyk = Boltzmann's constant(1.38 x J/atom-K)(8.62 x 10-5 eV/atom-K)- each lattice/atom site is potential vacancy site.Example:Answer:interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity8.62 x 10-5eV/atom-K0.9 eV/atom1273 Kç÷Nv=exp-QkTæèöø= 2.7 x 10-4self-interstitial & vacancy (pure metals)interstitial & substitutional (metals alloy)Chain packing error(a)In 1 m3 of Cu at 1000C, calculate:(a) vacancy concentration, Nv/N.(b) equilibrium # of vacancies, Nv.Given that,r= 8.4 g/cm3(b) = N ACuVCu NAQv= 0.9 eV/atomACu= 63.5 g/molFor 1 m3, N =NACurx1 m3= 8.0 x 1028 atom sitesNA= 6.02 x 1023atoms/molNv=(2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies
5Defects in solids classification General concept… Impurities in ceramicsDefects in solidsElectroneutrality (charge balance) must bemaintained when impurities are present.2. Substitutional anion impurityclassificationO2-i.e: NaClNa+Cl-zero dimensioncation--point defects1. Substitutional cation impurityClClvacancywithout impurityO2-Ca2+impurity+Naanion vacancyNa+Ca2+without impurityCa2+impuritywith impuritymetalsceramicspolymerswith impurityImpurities in metalsMetal alloys are used in mostengineering applications.Metal alloy is a mixture of two ormore metals and nonmetals.Solid solution is a simple type ofmetal alloy in which elements aredispersed in a single phase.General concept…Two outcomes if impurity (B) added to host (A):1. Small amount of B added to Ainterstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurityself-interstitial & vacancy (metals)interstitial & substitutional (metal alloys)Chain packing errorSubstitutional solid soln.(e.g., Cu in Ni)Interstitial solid soln.(e.g., C in Fe)2. Large amount of B added to A plus particles of anew phaseSecond phase particle- different composition.- often different structure.
6Electro-negativity difference Impurities in metalsThe solubility of solids is greater if:r (atomic radius difference) < 15%.Proximity in periodic table-- i.e, similar electronegativities.Same crystal structure for pure metals.Valency-- all else being equal, a metal willhave a greater tendency to dissolveanother metal of higher valency thanone of lower valency.Conditions for solid solubility- apply W. Hume – Rothery rule.have 4 conditions which is applied forsubstitutional solid solution.Specification of compositiondetermine the composition for a 2element in alloy system.specify in weight percent, wtatom percent, at %.weight percent, wt%atom percent, at%C2 = 100 – C1C’2 = 100 – C’1C1 = m1 x 100m1+ m2C’1 = nm1 x 100nm1+ nm2m1 & m2 = mass of component 1 & 2C1 & C2 = composition (in wt%) of component 1 & 2nm1 = m1/A1nm2 = m2/A2nm1 & nm2 = number of moles of component 1 & 2A1 & A2 = at. weight of component 1 & 2C’1 & C’2 = composition (in at%) of component 1 & 2Defects in solidsElement Atomic Crystal Electro- Valence Radius (nm) Structure negativityCu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCPWould you predict more Al or Ag to dissolve in Zn?2. More Zn or Al in Cu?Example 1:classificationzero dimensionpoint defectsmetalsceramicspolymersExample 2:SystemAtomic radiusdifferenceElectro-negativity differenceSolidsolubilityCu-Zn3.9%0.338.3%Cu-Pb36.7%0.20.17%Cu-Ni2.3%0.1100%interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurityself-interstitial & vacancy (metals)interstitial & substitutional (metal alloys)Chain packing errorLower solid solubility (interstitial S.S)Higher solid solubility (subs. S.S)Example 3:A hypothetical alloy consist of 120 g element A & 80 g element B. Determine the composition (in wt%) for each element?
7Defects in solids classification Linear defects in materials SEM micrograph shows dislocation as a dark linesalso known as dislocations.defects around which atoms are misalignedin a lattice distortions are centeredaround a line.slip between crystal planes result when disl.moves.formed during permanentdeformation.classificationDislocations in Zinc (HCP)one dimensionlinear defectsslip stepsType of dislocations…SEM micrograph1. Edge dislocation:- extra half-plane of atoms inserted in acrystal structure.- b perpendicular to dislocation line.All materialsinitialafter tensile elongation2. Screw dislocation:spiral planar ramp resulting from sheardeformation.- b parallel to dislocation line.edge dislocationscrew dislocationmixed dislocation3. Mixed dislocation:- most crystal have components of bothedge and screw dislocation.Edge dislocationEdgeScrewMixedScrew DislocationBurgers vector bDislocationline(a)b(b)Mixed dislocationScrew dislocation
8Dislocations & Crystal Structures • Structure: close-packedplanes & directionsare preferred.view onto twoclose-packedplanes.close-packed directionsclose-packed plane (bottom)close-packed plane (top)• Comparison among crystal structures:FCC: many close-packed planes/directions;HCP: only one plane, 3 directions;BCC: none• Specimens thatwere tensiletested.Mg (HCP)tensile directionHigher solid solubility (subs. S.S)Al (FCC)8
9planar/surface defects Planar defects in materialsDefects in solidsDefects due to formation of grains structure.classification1. Grain boundaries- region between grains (crystallites).- formed due to simultaneously growingcrystals meeting each other.- slightly disordered.- restrict plastic flow and prevent dislocationmovement (control crystal slip).- low density in grain boundaries-- high mobility.-- high diffusivity.-- high chemical reactivity.two dimensionplanar/surface defectsAll materialsGrain boundariesin 1018 steel2. Twin boundaries- essentially a reflection of atom positionsacross the twin plane.- a region in which mirror image of structureexists across a boundary.- formed during plastic deformation andrecrystallization.- strengthens the metal.grain boundariestwin boundariesstacking faults3. Stacking faults- piling up faults during recrystallization due tocollapsing.- for FCC metals an error in ABCABC packingsequence, i.e: ABCABABC.TwinTwin plane
10Catalysts and Surface Defects Catalyst is a substance in solid form.A catalyst increases the rate of a chemical reaction without being consumed.Reactant molecules in a liquid phase (CO, NOx & O2) are absorbed onto catalyst surface.Reduce the emission of exhaust gas pollutants.Adsorption/active sites on catalysts are normally surface defects.Fig. 5.15, Callister & Rethwisch 3e.Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converterFig. 5.16, Callister & Rethwisch 3e.10
11Defects in solids microscopic examination Microscopic examination Process flow…1. mount2. grind3. polish4. clean5. etch6. observe7. analyze0.75mmDefects in solidssuch microscope used to observe & analyzedefects of materials.i.e: OM, IM, SEM, TEM, STM, AFM etc.microscopic examinationGrain boundaries observationused metallographic techniques.the metal sample must be first mounted for easyhandling.- then the sample should be ground and polished-- with different grades of abrasive paper andabrasive solution.-- removes surface features (e.g., scratches).the surface is then etched chemically.-- tiny groves are produced at grain boundaries.-- groves do not intensely reflect light.-- may be revealed as dark lines.- hence observed by optical microscope.Fe-Cr alloygrain boundarysurface groovepolished surfaceOptical Microscope (OM)Inverted Microscope (IM)Scanning Electron Microscope (SEM)Transmission Electron Microscope (TEM)Scanning Tunneling Microscope (STM)Atomic Force Microscope (AFM)metallographic techniquesEffect of etching…UnetchedSteel200 XEtchedBrassobserve grain structure & boundariesanalyze grain sizeexamine topographical map (surface features)SEM micrographSTM topographic
12Defects in solids microscopic examination Size of grains… - affects the mechanical properties of the material.the smaller the grain size, more are the grainboundaries.more grain boundaries means higher resistance toslip (plastic deformation occurs due to slip).more grains means more uniform the mechanicalproperties are.Defects in solidsHow to measure grain size?use the formula:N = 2n -1microscopic examinationn = ASTM grain size number.N = number of grains per square inchof a polished & etched specimenat 100x magnification.ASTM grain size number ‘n’ is ameasure of grain size.Measuring average grain diameterAverage grain diameter, d more directlyrepresents grain size.Random line of known length is drawn onphotomicrograph.- Number of grains intersected is counted.Ratio of number of grains intersected to length ofline, nL is determined.d = C/nL(M) C = 1.5 & M = magnificationn < 3 – Coarse grained4 < n < 6 – Medium grained7 < n < 9 – Fine grainedn > 10 – ultrafine grainedOptical Microscope (OM)Inverted Microscope (IM)Scanning Electron Microscope (SEM)Transmission Electron Microscope (TEM)Scanning Tunneling Microscope (STM)Atomic Force Microscope (AFM)- If ASTM grain size #, n increase,-- size of grains decrease.-- # of grains/in2, N increase.metallographic techniques3 inches 5 grains1045 cold rolled steel, n=8observe grain structure & boundariesanalyze grain sizeexamine topographical map (surface features)Example:1018 cold rolled steel, n=10Determine the ASTM grain size number of a metal specimen if 45 grains per square inch are measured at a magnification of 100x.log N = (n-1) log 2n = log N+ 1log 2n = log 45+ 1log 2n = 6.5
13Summary • Point, Line, and Area defects exist in solids. • The number and type of defects can be variedand controlled (e.g., T controls vacancy conc.)• Defects affect material properties (e.g., grainboundaries control crystal slip).• Defects may be desirable or undesirable(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)13