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Chapter 5 Defects in solids. Defects in solids Solidification process… classification zero dimension Defects… - imperfection in structures of solid materials.

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Presentation on theme: "Chapter 5 Defects in solids. Defects in solids Solidification process… classification zero dimension Defects… - imperfection in structures of solid materials."— Presentation transcript:

1 Chapter 5 Defects in solids

2 Defects in solids Solidification process… classification zero dimension 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. one dimension two dimension three dimension point 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. nuclei liquid grain structure All solid materials… - contain large # of defects. Solidification process… crystal 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 undercooling Equiaxed grains due to rapid cooling (greater  T) near wall above T m room temp. Mold crystals growing Casting process

3 Defects in solids classification zero dimension point defects metals self-interstitial & vacancy (metals) ceramics interstitial & substitutional (metal alloys)interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity polymers Chain packing error Cation Interstitial Cation Vacancy Anion Vacancy 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. Schottky defect Frenkel defect Point defects in metals 1. Self-Interstitials - "extra" atoms positioned between atomic sites. - cause structural distortion. self-interstitial distortion of planes 2. 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. Vacancy distortion of planes Point defects in polymers 10 nm Adapted 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 platelets

4 Defects in solids classification zero dimension point defects metals self-interstitial & vacancy (pure metals) ceramics interstitial & substitutional (metals alloy) polymers Chain packing errorinterstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity Equilibrium concentration: Point defects k = Boltzmann's constant (1.38 x J/atom-K) (8.62 x eV/atom-K) N v = # of defects (vacancies site) Q v = activation energy T = temperature - each lattice/atom site is potential vacancy site. - equilibrium # of point defects (vacancies) for solids depends on & increase with temperature. - apply the formula:  N v N  exp  Q v kT      N = total # of atomic sites We can get Q v from an experiment. Measure this... N v N T exponential dependence! Defect vacancy) concentration Replot it... 1/T N N v ln - Q v /k/k slope Measuring Activation Energy… Example: In 1 m 3 of Cu at 1000  C, calculate: (a) vacancy concentration, N v /N. (b) equilibrium # of vacancies, N v. Given that, A Cu = 63.5 g/mol  = 8.4 g/cm 3 QvQv = 0.9 eV/atom NANA = 6.02 x atoms/mol 8.62 x eV/atom-K 0.9 eV/atom 1273 K  N v N  exp  Q v kT       = 2.7 x Answer: (a) (b)  = N A Cu V Cu N A For 1 m 3, N = N A A Cu  x x1 m 3 = 8.0 x atom sites N v =(2.7 x )(8.0 x ) sites = 2.2 x vacancies Vacancy concentration # of vacancy sites, N v total # of atomic sites, N =

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

6 Defects in solids classification zero dimension point defects metals self-interstitial & vacancy (metals) ceramics interstitial & substitutional (metal alloys)interstitial, vacancy, Frenkel & Schottky, substitutional anion & cation impurity polymers Chain packing error System Atomic radius difference Electro- negativity difference Solid solubility Cu-Zn 3.9% % Cu-Pb 36.7% % Cu-Ni 2.3% % Example 2: Element Atomic CrystalElectro-Valence Radius (nm) Structure negativity Cu FCC1.9+2 C H O Ag FCC1.9+1 Al FCC1.5+3 Co HCP1.8+2 Cr BCC1.6+3 Fe BCC1.8+2 Ni FCC1.8+2 Pd FCC2.2+2 Zn HCP Would 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 metals The solubility of solids is greater if: 1.  r (atomic radius difference) < 15%. 2.Proximity in periodic table -- i.e, similar electronegativities. 3.Same crystal structure for pure metals. 4.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% C 2 = 100 – C 1 C’ 2 = 100 – C’ 1 C 1 = m 1 x 100 m 1 + m 2 C’ 1 = n m1 x 100 n m1 + n m2 m 1 & m 2 = mass of component 1 & 2 C 1 & C 2 = composition (in wt%) of component 1 & 2 n m1 = m 1 /A 1 n m2 = m 2 /A 2 n m1 & n m2 = number of moles of component 1 & 2 A 1 & A 2 = at. weight of component 1 & 2 C’ 1 & C’ 2 = composition (in at%) of component 1 & 2 Higher solid solubility (subs. S.S) Lower solid solubility (interstitial S.S)

7 Defects in solids classification one dimension linear defects All materials edge dislocation Linear defects in materials - 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. screw dislocationmixed dislocation 1. 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 b Dislocation line (a) b (b) Edge Screw Mixed 3. Mixed dislocation: - most crystal have components of both edge and screw dislocation. SEM micrograph shows dislocation as a dark lines Screw dislocation Edge dislocation Mixed dislocation Type of dislocations… SEM micrograph slip steps after tensile elongation initial Dislocations in Zinc (HCP)

8 Dislocations & Crystal Structures Structure: close-packed planes & directions are preferred. view onto two close-packed planes. 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 direction Higher solid solubility (subs. S.S)

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

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, NO x & O 2 ) 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 (Ce 0.5 Zr 0.5 )O 2 used in an automotive catalytic converter

11 Defects in solids 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. 0.75mm Fe-Cr alloy grain boundary surface groove polished surface Unetched Steel 200 X Etched Steel 200 X Unetched Brass 200 X Etched Brass 200 X Effect of etching… Microscopic examination - such microscope used to observe & analyze 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 size Process flow… 1. mount 2. grind 3. polish 4. clean 5. etch 6. observe 7. analyze examine topographicalmap (surface features) metallographic techniques SEM micrograph STM topographic

12 Measuring average grain diameter 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 microscopic examination 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 sizeexamine topographicalmap (surface features) metallographic techniques n < 3 – Coarse grained 4 < n < 6 – Medium grained 7 < n < 9 – Fine grained n > 10 – ultrafine grained N = number of grains per square inch of a polished & etched specimen at 100x magnification. n = ASTM grain size number cold rolled steel, n= cold rolled steel, n=8 How to measure grain size? - ASTM grain size number ‘n’ is a measure of grain size. - use the formula: N = 2 n -1 - If ASTM grain size #, n increase, -- size of grains decrease. -- # of grains/in 2, 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, n L is determined. d = C/n L (M) C = 1.5 & M = magnification 3 inches 5 grains Example: 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 log n = log 45 log n = 6.5

13 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.) Summary


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