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Chapter 5 Defects in solids

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1 Chapter 5 Defects in solids

2 Defects in solids All solid materials… Solidification process…
contain large # of defects. Solidification process… classification above Tm Defects… 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. zero dimension one dimension two dimension three dimension liquid nuclei Solidification 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 grain structure. start with a molten (all liquid) material & grains (crystals) grow until they meet each other. point defects Linear/dislocation defects area/planar/surface defects volume defects (i.e: crack) crystals growing crystal growing - Grains structure can be: 1. equiaxed grains (roughly same size in all directions). 2. columnar grains (elongated grains). room temp. grain structure Columnar grains in area with less undercooling Mold Equiaxed grains due to rapid cooling (greater T) near wall Casting process

3 Defects in solids classification Point defects in ceramics
1. 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. Cation Interstitial Vacancy Anion Defects in solids classification zero dimension point defects Schottky defect Frenkel metals ceramics polymers Point defects in metals 2. Vacancies 1. Self-Interstitials 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. - "extra" atoms positioned between atomic sites. - cause structural distortion. self-interstitial distortion of planes Vacancy distortion of planes interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity self-interstitial & vacancy (metals) interstitial & substitutional (metal alloys) Chain packing error Point defects in polymers Defects due in part to chain packing errors and impurities such as chain ends and side chains. i.e: thin platelets 10 nm Adapted from Fig. 4.12, Callister & Rethwisch 3e.

4 Measuring Activation Energy…
Equilibrium concentration: Point defects Measuring Activation Energy… Defects in solids • We can get Qv from an experiment. classification equilibrium # of point defects (vacancies) for solids depends on & increase with temperature. apply the formula: • Measure this... N v zero dimension # of vacancy sites, Nv Vacancy concentration = total # of atomic sites, N point defects exponential æ ö N Q dependence! v = ç v exp ç è ø N k T T Defect vacancy) concentration Nv = # of defects (vacancies site) N = total # of atomic sites • Replot it... T = temperature 1/ T N v ln - Q /k slope metals ceramics polymers Qv = activation energy k = 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 impurity 8.62 x 10-5 eV/atom-K 0.9 eV/atom 1273 K ç ÷ N v = exp - Q k T æ è ö ø = 2.7 x 10-4 self-interstitial & vacancy (pure metals) interstitial & substitutional (metals alloy) Chain packing error (a) In 1 m3 of Cu at 1000C, calculate: (a) vacancy concentration, Nv/N. (b) equilibrium # of vacancies, Nv. Given that, r = 8.4 g / cm3 (b)  = N ACu VCu NA Qv = 0.9 eV/atom ACu = 63.5 g/mol For 1 m3 , N = N A Cu r x 1 m3 = 8.0 x 1028 atom sites NA = 6.02 x 1023 atoms/mol N v = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies

5 Defects in solids classification General concept…
Impurities in ceramics Defects in solids Electroneutrality (charge balance) must be maintained when impurities are present. 2. Substitutional anion impurity classification O 2- i.e: NaCl Na + Cl - zero dimension cation - - point defects 1. Substitutional cation impurity Cl Cl vacancy without impurity O 2- Ca 2+ impurity + Na an ion vacancy Na + Ca 2+ without impurity Ca 2+ impurity with impurity metals ceramics polymers with impurity Impurities in metals 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 concept… Two outcomes if impurity (B) added to host (A): 1. Small amount of B added to A interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity self-interstitial & vacancy (metals) interstitial & substitutional (metal alloys) Chain packing error 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.

6 Electro-negativity difference
Impurities in metals The 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 – C1 C’2 = 100 – C’1 C1 = m1 x 100 m1+ m2 C’1 = nm1 x 100 nm1+ nm2 m1 & m2 = mass of component 1 & 2 C1 & C2 = composition (in wt%) of component 1 & 2 nm1 = m1/A1 nm2 = m2/A2 nm1 & nm2 = number of moles of component 1 & 2 A1 & A2 = at. weight of component 1 & 2 C’1 & C’2 = composition (in at%) of component 1 & 2 Defects in solids Element Atomic Crystal Electro- Valence Radius (nm) Structure negativity Cu FCC C H O Ag FCC Al FCC Co HCP Cr BCC Fe BCC Ni FCC Pd FCC Zn HCP Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? Example 1: classification zero dimension point defects metals ceramics polymers Example 2: System Atomic radius difference Electro-negativity difference Solid solubility Cu-Zn 3.9% 0.3 38.3% Cu-Pb 36.7% 0.2 0.17% Cu-Ni 2.3% 0.1 100% interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity self-interstitial & vacancy (metals) interstitial & substitutional (metal alloys) Chain packing error Lower 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?

7 Defects in solids classification Linear defects in materials
SEM micrograph shows dislocation as a dark lines also known as dislocations. defects around which atoms are misaligned in a lattice distortions are centered around a line. slip between crystal planes result when disl. moves. formed during permanent deformation. classification Dislocations in Zinc (HCP) one dimension linear defects slip steps Type of dislocations… SEM micrograph 1. Edge dislocation: - extra half-plane of atoms inserted in a crystal structure. - b perpendicular to dislocation line. All materials initial after tensile elongation 2. Screw dislocation: spiral planar ramp resulting from shear deformation. - b parallel to dislocation line. edge dislocation screw dislocation mixed dislocation 3. Mixed dislocation: - most crystal have components of both edge and screw dislocation. Edge dislocation Edge Screw Mixed Screw Dislocation Burgers vector b Dislocation line (a) b (b) Mixed dislocation Screw dislocation

8 Dislocations & Crystal Structures
• Structure: close-packed planes & directions are preferred. view onto two close-packed planes. close-packed directions close-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 that were tensile tested. Mg (HCP) tensile direction Higher solid solubility (subs. S.S) Al (FCC) 8

9 planar/surface defects
Planar defects in materials Defects in solids Defects due to formation of grains structure. classification 1. 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. two dimension planar/surface defects All materials Grain boundaries in 1018 steel 2. 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. grain boundaries twin boundaries stacking faults 3. Stacking faults - piling up faults during recrystallization due to collapsing. - for FCC metals an error in ABCABC packing sequence, i.e: ABCABABC. Twin Twin plane

10 Catalysts 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 converter Fig. 5.16, Callister & Rethwisch 3e. 10

11 Defects in solids microscopic examination Microscopic examination
Process flow… 1. mount 2. grind 3. polish 4. clean 5. etch 6. observe 7. analyze 0.75mm Defects in solids such microscope used to observe & analyze defects of materials. i.e: OM, IM, SEM, TEM, STM, AFM etc. microscopic examination Grain 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. Fe-Cr alloy grain boundary surface groove polished surface Optical Microscope (OM) Inverted Microscope (IM) Scanning Electron Microscope (SEM) Transmission Electron Microscope (TEM) Scanning Tunneling Microscope (STM) Atomic Force Microscope (AFM) metallographic techniques Effect of etching… Unetched Steel 200 X Etched Brass observe grain structure & boundaries analyze grain size examine topographical map (surface features) SEM micrograph STM topographic

12 Defects in solids microscopic examination Size 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 solids How to measure grain size? use the formula: N = 2n -1 microscopic examination n = ASTM grain size number. N = number of grains per square inch of a polished & etched specimen at 100x magnification. ASTM grain size number ‘n’ is a measure of grain size. Measuring average grain diameter 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 n < 3 – Coarse grained 4 < n < 6 – Medium grained 7 < n < 9 – Fine grained n > 10 – ultrafine grained Optical 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 techniques 3 inches 5 grains 1045 cold rolled steel, n=8 observe grain structure & boundaries analyze grain size examine topographical map (surface features) Example: 1018 cold rolled steel, n=10 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 2 n = log N + 1 log 2 n = log 45 + 1 log 2 n = 6.5

13 Summary • 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.) 13

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