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Chapter 5Defects in solidsDefects in solidsSolidification processclassificationzero dimensionDefects imperfection in structures of solid materials crystal structure due to irregular/disordered atomic arrangement. amorphous structure due to molecular chains error. - classify in terms of geometry (dimension) & size. normally, formed during solidification process.one dimensiontwo dimensionthree dimensionpoint defectsLinear/dislocation defectsarea/planar/surface defectsvolume defects (i.e: crack) 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 grain structure. start with a molten (all liquid) material & grains (crystals) grow until they meet each other.

nucleiliquid

grain structureAll solid materials contain large # of defects.Solidification processcrystal growing- Grains structure can be: 1. equiaxed grains (roughly same size in all directions). 2. columnar grains (elongated grains).

Columnar grains in area with less undercoolingEquiaxed grains due to rapid cooling (greater T) near wallabove Tmroom temp.

Moldcrystals growingCasting processDefects in solidsclassificationzero dimensionpoint defectsmetalsself-interstitial & vacancy (metals) ceramicsinterstitial & substitutional (metal alloys)interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impuritypolymersChain packing errorCation InterstitialCation Vacancy

Anion VacancyPoint defects in ceramics1. Vacancies - vacancies exist in ceramics for both cations and anions. 2. Interstitials - exist for cations only. - interstitials are not normally observed for anions because anions are large relative to the interstitial sites.3. Frenkel defect - a cation vacancy-cation interstitial pair.4. Schottky defect - a paired set of cation and anion vacancies.

Schottky defectFrenkel defectPoint defects in metals1. Self-Interstitials- "extra" atoms positioned between atomic sites.- cause structural distortion.

self-interstitialdistortion of planes2. Vacancies vacant atomic sites exist in a structure. form due to a missing atom. form (one in 10,000 atoms) during crystallization, mobility of atoms or rapid cooling.

Vacancydistortion of planesPoint defects in polymers

10 nmAdapted from Fig. 4.12, Callister & Rethwisch 3e. Defects due in part to chain packing errors and impurities such as chain ends and side chains. i.e: thin plateletsDefects in solidsclassificationzero dimensionpoint defectsmetalsself-interstitial & vacancy (pure metals) ceramicsinterstitial & substitutional (metals alloy)polymersChain packing errorinterstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurityEquilibrium concentration: Point defectsk = Boltzmann's constant(1.38 x 10-23 J/atom-K)(8.62 x 10-5 eV/atom-K)Nv = # of defects (vacancies site)Qv = activation energyT = temperature- each lattice/atom site is potential vacancy site. equilibrium # of point defects (vacancies) for solids depends on & increase with temperature. apply the formula: NvN=expQvkT N = total # of atomic sites We can get Qv from an experiment. Measure this...NvNTexponential dependence!Defect (@ vacancy) concentration Replot it...1/TNNvln-Qv/kslopeMeasuring Activation EnergyExample:In 1 m3 of Cu at 1000C, calculate:(a) vacancy concentration, Nv/N.(b) equilibrium # of vacancies, Nv.Given that, ACu = 63.5 g/molr = 8.4 g/cm3Qv = 0.9 eV/atomNA = 6.02 x 1023atoms/mol8.62 x 10-5eV/atom-K0.9 eV/atom1273 K NvN=exp-QvkT = 2.7 x 10-4Answer:(a)(b) = N ACuVCu NAFor 1 m3, N =NAACur xx 1 m3= 8.0 x 1028 atom sitesNv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacanciesVacancy concentration# of vacancy sites, Nvtotal # of atomic sites, N=Defects in solidsclassificationzero dimensionpoint defectsmetalsself-interstitial & vacancy (metals) ceramicsinterstitial & substitutional (metal alloys)interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impuritypolymersChain packing errorImpurities in ceramics Electroneutrality (charge balance) must be maintained when impurities are present. i.e: NaClNa+Cl- 1. Substitutional cation impuritywithout impurityCa2+ impurity with impurityCa2+Na+Na+Ca2+cation vacancy2. Substitutional anion impuritywithout impurity O2- impurityO2-Cl-anion vacancyCl- with impurityImpurities in metalsTwo outcomes if impurity (B) added to host (A):1. Small amount of B added to A

Substitutional 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 a new phase

Second phase particle- different composition.- often different structure. Metal alloys are used in most engineering applications.

Metal alloy is a mixture of two or more metals and nonmetals.

Solid solution is a simple type of metal alloy in which elements are dispersed in a single phase. General conceptDefects in solidsclassificationzero dimensionpoint defectsmetalsself-interstitial & vacancy (metals) ceramicsinterstitial & substitutional (metal alloys)interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impuritypolymersChain packing error SystemAtomic radiusdifferenceElectro-negativity differenceSolidsolubility Cu-Zn 3.9% 0.3 38.3% Cu-Pb 36.7% 0.2 0.17% Cu-Ni 2.3% 0.1 100%Example 2:Element Atomic CrystalElectro-Valence Radius (nm) Structure negativity Cu 0.1278 FCC1.9+2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC1.9+1 Al 0.1431 FCC1.5+3 Co 0.1253 HCP1.8+2 Cr 0.1249 BCC1.6+3 Fe 0.1241 BCC1.8+2 Ni 0.1246 FCC1.8+2 Pd 0.1376 FCC2.2+2 Zn 0.1332 HCP1.6+2Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu?Example 1:Example 3:A hypothetical alloy consist of 120 g element A & 80 g element B. Determine the composition (in wt%) for each element?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 will have a greater tendency to dissolve another metal of higher valency than one of lower valency.Conditions for solid solubility- apply W. Hume Rothery rule.have 4 conditions which is applied for substitutional solid solution.Specification of composition determine the composition for a 2 element in alloy system. specify in weight percent, wt % @ atom percent, at %. weight percent, wt%atom percent, at%C2 = 100 C1C2 = 100 C1C1 = m1 x 100 m1+ m2C1 = nm1 x 100 nm1+ 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 & 2C1 & C2 = composition (in at%) of component 1 & 2Higher solid solubility (subs. S.S)Lower solid solubility (interstitial S.S)Defects in solidsclassificationone dimensionlinear defectsAll materialsedge dislocationLinear defects in materials also known as dislocations. defects around which atoms are misaligned in a line @ lattice distortions are centered around a line. slip between crystal planes result when disl. moves. formed during solidification @ permanent deformation.

screw dislocationmixed dislocation1. Edge dislocation: - extra half-plane of atoms inserted in a crystal structure. - b perpendicular to dislocation line.2. Screw dislocation: spiral planar ramp resulting from shear deformation.- b parallel to dislocation line.

Screw Dislocation

Burgers vector bDislocationline(a)

b(b)

EdgeScrewMixed 3. Mixed dislocation: - most crystal have components of both edge and screw dislocation. SEM micrograph shows dislocation as a dark lines Screw dislocationEdge dislocationMixed dislocationType of dislocationsSEM micrographslip stepsafter tensile elongationinitialDislocations in Zinc (HCP)

Dislocations & Crystal Structures Structure: close-packed planes & directions are preferred.view onto twoclose-packedplanes.close-packed plane (bottom)close-packed plane (top)close-packed directions Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none Specimens that were tensile tested.

Mg (HCP)Al (FCC)tensile directionHigher solid solubility (subs. S.S)8

Defects in solidsclassificationtwo dimensionplanar/surface defectsAll materialsgrain boundariesPlanar defects in materials Defects due to formation of grains structure.stacking faultstwin boundaries1. Grain boundaries - region between grains (crystallites). - formed due to simultaneously growing crystals meeting each other. - slightly disordered. - restrict plastic flow and prevent dislocation movement (control crystal slip). - low density in grain boundaries -- high mobility. -- high diffusivity. -- high chemical reactivity.

Grain boundariesin 1018 steel2. Twin boundaries - essentially a reflection of atom positions across the twin plane. - a region in which mirror image of structure exists across a boundary. - formed during plastic deformation and recrystallization. - strengthens the metal.

TwinTwin plane3. Stacking faults - piling up faults during recrystallization due to collapsing. - for FCC metals an error in ABCABC packing sequence, i.e: ABCABABC.Catalysts and Surface DefectsCatalyst is a substance in solid form.A catalyst increases the rate of a chemical reaction without being consumed.Reactant molecules in a gas @ 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.Fig. 5.16, Callister & Rethwisch 3e.Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converter

10Defects in solidsmicroscopic examinationGrain boundaries observation used metallographic techniques. the metal sample must be first mounted for easy handling.- then the sample should be ground and polished -- with different grades of abrasive paper and abrasive 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.

0.75mm

Fe-Cr alloy

grain boundarysurface groove polished surface

Unetched Steel200 XEtched Steel200 XUnetched Brass200 XEtched Brass200 X

Effect of etchingMicroscopic examination such microscope used to observe & analyze structures @ defects of materials. i.e: OM, IM, SEM, TEM, STM, AFM etc.Optical Microscope (OM)Scanning Electron Microscope (SEM)Inverted Microscope (IM)Scanning Tunneling Microscope (STM)Atomic Force Microscope (AFM)Transmission Electron Microscope (TEM)observe grain structure & boundariesanalyze grain sizeProcess flow1. mount2. grind3. polish4. clean5. etch6. observe7. analyzeexamine topographical map (surface features)metallographic techniques

SEM micrographSTM topographicMeasuring average grain diameterSize of grains- affects the mechanical properties of the material. the smaller the grain size, more are the grain boundaries. more grain boundaries means higher resistance to slip (plastic deformation occurs due to slip). more grains means more uniform the mechanical properties are. Defects in solidsmicroscopic examinationOptical Microscope (OM)Scanning Electron Microscope (SEM)Inverted Microscope (IM)Scanning Tunneling Microscope (STM)Atomic Force Microscope (AFM)Transmission Electron Microscope (TEM)observe grain structure & boundariesanalyze grain sizeexamine topographical map (surface features)metallographic techniquesn < 3 Coarse grained4 < n < 6 Medium grained7 < n < 9 Fine grainedn > 10 ultrafine grainedN = number of grains per square inch of a polished & etched specimen at 100x magnification.n = ASTM grain size number.

1018 cold rolled steel, n=10

1045 cold rolled steel, n=8How to measure grain size? ASTM grain size number n is a measure of grain size. use the formula: N = 2n -1- If ASTM grain size #, n increase, -- size of grains decrease. -- # of grains/in2, N increase. Average grain diameter, d more directly represents grain size. Random line of known length is drawn on photomicrograph.- Number of grains intersected is counted. Ratio of number of grains intersected to length of line, nL is determined. d = C/nL(M) C = 1.5 & M = magnification

3 inches 5 grainsExample:Determine 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 log 2+ 1n = log 45 log 2+ 1n = 6.5 Point, Line, and Area defects exist in solids. The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.) Defects affect material properties (e.g., grain boundaries control crystal slip). Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.)Summary13