COMPUTATIONAL MATERIALS ENGINEERING Episode 5 pot

... basic cellular automata. 110 COMPUTATIONAL MATERIALS ENGINEERING Particle Dimple Boundary Grain B Grain A r ρ y o θ γ BP γ AP (a) 55 50 45 40 35 30 25 10 15 20 25 30 40 35 X Z Hellman and Hillert ... [2] Static Monte Carlo θ θ = 45 (b) Boundary Detaches 1 .5 0 .5 -0 .5 -1 .5 1 -1 -2 0 Force/πγY -0 .5 0 .5 1 .5 2 .51 20-1 s/r (c) Theory kT′ = 1 kT′ = 2 kT′ = 3 FIGURE...

Ngày tải lên: 13/08/2014, 08:21

... each sublattice we have  i y s i =1 (2.94) and 0 ≤ y s i ≤ 1 (2. 95) 34 COMPUTATIONAL MATERIALS ENGINEERING Equations (2.94) and (2. 95) can be viewed as constraints of the thermodynamic model, namely, ... have E  AA = 1 2 ZN A · X A ·  AA E  BB = 1 2 ZN B · X B ·  BB (2 .55 ) E  AB = ZN · X A X B ·  AB 22 COMPUTATIONAL MATERIALS ENGINEERING is reversible. In the following...

Ngày tải lên: 13/08/2014, 08:21

... kT s =0. 75, the isotropic case, (b) R A = R B =1 .5, kT s =0. 75, (c) R A >R B ,R A =1,R B =0.67, kT s =0. 75, (d) R A = R B =0 .5, kT s =0, (e) R A >R B ,R A =1 .5, R B =1, kT s =0. 75, (f) R A = ... function, and kT s =0. 75. 74 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 3-21 Potts model simulation carried out on a square lattice, using Glauber dynamics and kT s =0. 75. The s...

Ngày tải lên: 13/08/2014, 08:21

... vector. As a 286 COMPUTATIONAL MATERIALS ENGINEERING and for the stress field, σ 13 = − b 3 2π  C 44 C 55 − C 2 45  1/2  C 45 x 1 − C 55 x 2 C 44 x 2 1 − 2 C 45 x 1 x 2 + C 55 x 2 2  σ 23 = ... C 55 x 2 C 44 x 2 1 − 2 C 45 x 1 x 2 + C 55 x 2 2  σ 23 = − b 3 2π  C 44 C 55 − C 2 45  1/2  C 44 x 1 − C 45 x 2 C 44 x 2 1 − 2 C 45 x 1 x 2 + C 55 x 2 2  (8.1...

Ngày tải lên: 13/08/2014, 08:21

... and Mobilities 92 3 .5. 4 Validating the Energy and Mobility Implementations 93 3 .5. 5 Anisotropic Grain Growth 95 3 .5. 6 Abnormal Grain Growth 98 3 .5. 7 Recrystallization 102 3 .5. 8 Zener Pinning 103 3.6 ... Conditions 51 3.2 .5 The Vanilla Algorithm 53 3.2.6 Motion by Curvature 54 3.2.7 The Dynamics of Kinks and Ledges 57 3.2.8 Temperature 61 3.2.9 Boundary Anisotropy 62 3.2.1...

Ngày tải lên: 13/08/2014, 08:21

... ln(β m +1)·  τ 5 10 + τ − 15 3 15 + τ − 25 150 0   51 8 11 25 + 11692 159 75  1 p − 1  (2.100) and for τ<1,wehave mo G m = RT ln(β m +1)  1 −  79τ −1 140p + 474 497  1 p − 1  τ 3 6 + τ 9 1 35 + τ 15 600   51 8 11 25 + 11692 159 75  1 p − ... 1  τ 3 6 + τ 9 1 35 + τ 15 600   51 8 11 25 + 11692 159 75  1 p − 1  (2.101) The parameter p is 0.2...

Ngày tải lên: 13/08/2014, 08:21

... grid 200 CA simulations 250 ´ 250 grid 200 CA simulations 250 ´ 250 grid 100 CA simulations 250 ´ 250 grid 10 CA simulations 250 ´ 250 grid 1 CA simulation FIGURE 4- 15 Application of ... neighborhood and state transformation function. 120 COMPUTATIONAL MATERIALS ENGINEERING 0 250 50 0 750 1000 1 1000 CA Increment Number of Grains 0 5 10 15 20 Normal...

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... species. Fick published his result in 1 855 [Fic 55] and accordingly, for the one-dimensional case with the spatial coordinate r,wehave J = −D ∂c ∂r (5. 15) Equation (5. 15) is known as Fick’s first law. ... (10 3 K -1 ) T (C) -32 -28 -24 -20 -16 -12 -8 -4 0 0 0 .5 1 .5 2.0 3.0 3 .51 .0 2 .5 Al Mo W Ni Fe Cu 1000 300 200 10 050 03000 Log( ) X eq Va FIGURE 5- 2 Equilibrium vacancy concen...

Ngày tải lên: 13/08/2014, 08:21

... semi-infinite boundary, that is, c(0,t)=c 0 (5. 35) x (Length) 0 0 .5 1.0 1 .5 2.0 -3 -2 -1 01 3 2 0.0 25 0. 05 0.1 0. 25 1 c(x)/M (Length −1 ) Dt = 0 FIGURE 5- 7 Solutions to Fick’s second law for a point ... of equations (5. 51) and (5. 54) shows that the thermodynamic factor φ in a binary system and in terms of mole fraction variables X i is φ A = X A RT  ∂µ A ∂X A − ∂µ A ∂X B  (...

Ngày tải lên: 13/08/2014, 08:21

... 0.3 0 .5 0.7 0.9 1.1 1.3 1 .5 1.7 1.9 0.0 0 .5 1.0 1 .5 2.0 2 .5 Normalized Precipitate Radius Normalized Number Density 3.0 C 0.1 0.3 0 .5 0.7 0.9 1.1 1.3 1 .5 1.7 1.9 0.0 0 .5 1.0 1 .5 2.0 2 .5 Normalized ... =  ρ 2 0 +4K 2 Dt (6 .57 ) where K can unfortunately only be given in implicit form as 2K 2 ·  1 − √ πKe K 2 erfc(K)  = S (6 .58 ) With the additional substitution Φ=2K 2...

Ngày tải lên: 13/08/2014, 08:21