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Materials Cribsheet - BEST ONE - M a t e r ia ls Cr ib Sh e...

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Materials Crib Sheet 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 / V V CN = number of atoms that each given atom touches in a unit cell FCC – close packed ABCABC sequence 2 2 a R = APF = 0.74 CN = 12 4 atoms/ cell BCC – not close packed 4 3 a R = APF = 0.68 CN = 8 2 atoms/ cell HCP – close packed ABABAB sequence 2 2 a R = APF = 0.74 CN = 12 Braggs’ Law: 2 sin n d λ θ = , Density: i i c A c A n A nA V N V N ρ = = , Planar spacing: 2 2 2 2sin n a d h k l λ θ = = + + . 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. u u = − Chapter 4 - I m perfections Point Defects - Vacancies: Q V RT V N Ne = (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 X e = . 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: 3 2 0 J/m 0 J/m V S G G < < G V RT r P e = (probability of getting a critical radius r * ), 1 / t p 3 2 4 4 3 T sol s G r G r π π γ = + , * 2 V r G γ = ' 1 1 1 ' ' 1 1 2 1 1 2 2 m C A C m m C A C A = = + + , ' 1 1 2 1 1 2 2 1 1 2 m m m n C A C n n C A C A = = + + , '' 1 1 1 2 1 2 C C C C ρ ρ = + , ' ' 1 1 2 2 ' ' 1 2 1 1 2 2 1 2 1 2 100 avg C A C A C C C A C A ρ ρ ρ ρ ρ + = = + + , ' ' 1 1 2 2 1 2 1 2 100 100 avg C A C A A C C A A + = = + (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 – diffusion flux doesn’t change with time: 1 M dM J At A dt = = , Fick’s 1 st Law: dC J D dx = − (D – diffusion coefficient), (q – amount diffusing), q JA = 0 Q RT D D e = Chapter 6 – Mechanical Properties of Metals Types of stresses : Tensile, Compressive, Shear, Biaxial Tension Compression, Hydrostatic Stress: 0 F A σ = , Strain: 0 l l ε = , Shear stress: 0 F
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