COMPUTATIONAL MATERIALS ENGINEERING Episode 6 pdf

... of squares or cubes. Other types of grids are possible, as illustrated in Figure 4 -6. 1 16 COMPUTATIONAL MATERIALS ENGINEERING If one performs a simulation with an algorithm like Algorithm 4-3, the ... A 00000 00000 01110 01111 11111 FIGURE 4- 16 A method for direct approximation of local curvature at a grain boundary. See text for more details. 124 COMPUTATIONAL MATERIALS ENGI...

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... self-ordering behavior. Figure 3- 16 shows the evolution of such a system simulated using the Potts model. Instead of bubbles we have domains 64 COMPUTATIONAL MATERIALS ENGINEERING will each do so using ... show no obvious faceting, nor is it shown in the migration of boundaries in general. 62 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 3-19 The effect of anisotropic boundary en...

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... simulation Y N Y N FIGURE 3-30 The parallel algorithm for the Potts model. 86 COMPUTATIONAL MATERIALS ENGINEERING 0.05 0 −0.05 0 2000 4000 60 00 8000 1 × 10 4 Time (MCS) dp/dt Simulation Theory FIGURE ... boundaries during grain growth. Materials Science and Technology, 19 :68 3 68 7, 2003. [Hil65] M. Hillert. On the theory of normal and abnormal grain growth. Acta Metall., 13:...

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... case of an infinitesimally small 1 36 COMPUTATIONAL MATERIALS ENGINEERING C _ C 0 _ C 0 + C 1 Dt 1 2 1 0.8 0 .6 0.4 0.4 0.2 0.2 0.4 0 .6 0.8 1 0.2 0.005 FIGURE 4- 26 Comparison of theory (lines) ... 52: 265 3– 266 4, 2004. [Raa04b] D. Raabe. Overview of the lattice Boltzmann method for nano- and microscale fluid dynamics in materials science and engineering. Model. Simul. Mate...

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... “ref” φ i = X i RT  ∂µ i ∂X i − ∂µ i ∂X ref  (5. 56) 166 COMPUTATIONAL MATERIALS ENGINEERING The total extended volume, which is created by all nucleation events, can be obtained by integration of equation (6. 3), which, for ... (Length) c(x)/c 0 0 2 468 10 sqrt(4 Dt) = 100 2 1 0.5 0 0.2 0.4 0 .6 1.0 0.8 5 20 FIGURE 5-8 Solutions to Fick’s second law for semi-inifinite sample. 16...

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... vacancies. 1 86 COMPUTATIONAL MATERIALS ENGINEERING Block 1 Block 2 Block 3 Block 4 AA A ABB B B FIGURE 6- 7 Calculation of interfacial energies. Interface Matrix Precipitate FIGURE 6- 8 Two-dimensional ... equation (6. 14) with respect to ρ to zero, that is, ∂∆G ∂ρ =4πρ 2 ∆G 0 bulk +8πργ =0 (6. 15) The critical nucleation radius ρ ∗ follows with ρ ∗ = − 2γ ∆G 0 bulk = 2γ D (6. 16)...

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... simulation code. 234 COMPUTATIONAL MATERIALS ENGINEERING Substitution of equation (6. 66) into (6. 67) and integration yields Q 2 = m  k=1 n  i=1 4πRTρ 5 k 45c ki D ki ˙c 2 ki (6. 68) The third contribution ... equations (6. 62), (6. 65), (6. 68), and (6. 71), the following set of equations has to be evaluated: ∂G ∂ρ k = − 1 2 ∂Q ∂ ˙ρ k (k =1, ,m) (6. 73) ∂G ∂c ki = − 1 2 ∂Q ∂ ˙c ki...

Ngày tải lên: 13/08/2014, 08:21