Materials Cribsheet

# Materials Cribsheet - Materials Crib Sheet Chapter 3 Crystal Structures Atomic Structures Atomic packing factor(APF = Vatoms in unit cell Vunit

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M a t e r i a l s C r i b S h e e t Mike Bebjak Chapter 3 – Crystal Structures Constants & Conversions giga G 10 9 milli m 10 -3 mega M 10 6 micro µ 10 -6 kilo k 10 3 nano n 10 -9 centi c 10 -2 pico p 10 -12 k = 1.38×10 -23 J/atom K = 8.62×10 -5 eV/atom K R = 8.314 J/mol K N A = 6.023×10 23 atoms/mol e = 1.602×10 -19 C m e = 9.11×10 -31 kg h = 6.63×10 -34 J s Atomic Structures Atomic packing factor (APF) = atoms in unit cell unit cell / VV CN = number of atoms that each given atom touches in a unit cell FCC – close packed ABCABC sequence 22 aR = APF = 0.74 CN = 12 4 atoms/cell BCC – not close packed 4 3 = APF = 0.68 CN = 8 2 atoms/cell HCP – close packed ABABAB sequence = APF = 0.74 CN = 12 Braggs’ Law: 2s i n nd λ θ = , Density: ii cA nA nA VN ρ == , Planar spacing: 222 2sin na d hkl + + . Miller Indices : Steps – lines: 1. Start at any cell corner; 2. Find coordinates of vectors, subtract; 3. Multiply by common factor, planes: 1. Find intercepts in a, b, c; 2. Find reciprocals 1/a, 1/b, 1/c; 3. Multiply to make integer. Notations – lines: [u v w], planes: (h k l), families of planes: {1 1 1} family includes (1 1 1), (1 1 1) , etc. uu =− Chapter 4 - Imperfections Point Defects - Vacancies: Q V RT V NN e = (N is the total # of atomic sites, Q the energy required to form a vacancy) Thermodynamics: perfect crystal S=0, add n vacancies to N atoms n S G (G = H - T S). Will create vacancies until G is a minimum. Impurities – Substitutional: replace an atom; Interstitial: lie between atoms; Q sol kT sol Xe = . Linear Defects – Dislocations: edge (extra plane of atoms), screw (shear distortion of lattice) dislocations = S thermodynamically unstable. Planar Defects – Grain boundaries: 1 2 n N = (N – avg. # of grains/sq. inch, n – grain size #). Solidification Process : 1. Nucleation; 2. Growth; 3. Impingement grain boundaries form. Metals have more vacancies than self-interstitials. Conditions: 32 0 J/m 0 J/m VS GG ∆< G V RT r Pe = (probability of getting a critical radius r * ), 1/ tp 4 4 3 Ts o l s Gr π γ ∆= + , * 2 V r G = ' 11 1 '' 1 12 2 2 mC A C mm CA CA + + , ' 2 1 21 m n CA C nn C AC A ++ , ' 1 1 C C CC = + , 100 avg ρρ + + + , 100 100 avg A AA + + (C-wt%, C’-at%, C’’-conc.) Chapter 5 - Diffusion Types Interdiffusion : atoms of one metal diffuse into another, Self-diffusion : atoms of metal exchange positions Mechanisms Vacancy Diffusion : substitutional atoms diffuse into vacancies (used by interdiffusion & self-diffusion). Interstitial Diffusion : atoms move into interstitials locations (gases, much faster than vacancy). Steady-state Diffusion

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## This note was uploaded on 02/04/2011 for the course ENGINEERIN 1m03 taught by Professor Porove during the Spring '10 term at McMaster University.

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Materials Cribsheet - Materials Crib Sheet Chapter 3 Crystal Structures Atomic Structures Atomic packing factor(APF = Vatoms in unit cell Vunit

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