COMPUTATIONAL MATERIALS ENGINEERING Episode 7 doc

... of recrystal- lization and grain growth. Model. Simul. Mater. Sci., 11(2):1 57 171 , 2003. 148 COMPUTATIONAL MATERIALS ENGINEERING [XL01] Q. Y. Xu and B. C. Liu. Modeling of as-cast microstructure ... interatomic potentials. 152 COMPUTATIONAL MATERIALS ENGINEERING Hop Scatter FIGURE 4-28 Hexagonal LGCA. The example of an LGCA on a square grid was first published by Hardy et al. [HP...

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... ! FUNCTION GFEM23C6 2.98150E+02 +7. 6666 67* GFECEM# -1.6666 67* GHSERCC#+66920-40*T; 6.00000E+03 N ! FUNCTION GCRM7C3 2.98150E+02 -201690+1103.128*T -190. 177 *T*LN(T) 0 578 2 07* T**2; 6.00000E+03 N ! Each ... -205342+141.66 67* T; 6.00000E+03 N ! PARAMETER G(M23C6,CR,FE:FE:C;0) 2.98150E+02 -205342+141.66 67* T; 6.00000E+03 N ! PHASE M7C3 \% 2 7 3 ! CONSTITUENT M7C3 :CR%,FE:C: ! PARAMETER...

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... of vacancies, which can be calculated from J Va = − n  j=1 J i (5 .77 ) and v = J Va V m (5 .78 ) 172 COMPUTATIONAL MATERIALS ENGINEERING volume concept. The second section of this chapter deals ... discretization intervals as well; however, the expressions become more involved then. 174 COMPUTATIONAL MATERIALS ENGINEERING Distance x (au) Concentration c ii+1i-1 D xD x D x FI...

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... Transformation 1 97 0.1 0.3 0.5 0 .7 0.9 1.1 1.3 1.5 1 .7 1.9 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Precipitate Radius Normalized Number Density 1.2 A 0.1 0.3 0.5 0 .7 0.9 1.1 1.3 1.5 1 .7 1.9 0.0 0.2 0.4 0.6 0.8 1.0 Normalized ... Density B 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 Precipitate Radius Normalized Number Density 3.0 C 0.1 0.3 0.5 0 .7 0.9...

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... 15 .70 4.20 2.9 87 0.46 Cr bcc 35.00 5 .78 10.10 0.691 0.14 Cu fcc 16.84 12.14 7. 54 3.209 0.42 Fe bcc 24.20 14.65 11.20 2.346 0.38 Li bcc 1.48 1.25 1.08 9.391 0.46 278 COMPUTATIONAL MATERIALS ENGINEERING where ... σ 1 σ 2 σ 3 =       σ 11 σ 12 σ 13 σ 12 σ 22 σ 23 σ 13 σ 23 σ 33       (8.16) 272 COMPUTATIONAL MATERIALS ENGINEERING Cr Ni Cu Ni 60 Cu 24 Cr 16 Ni 60 C...

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... part Displacement gradient tensor, 272 T Taylor expansion, 273 Taylor, R. L., 321 Tensor Displacement gradient, 272 Invariants, 273 Strain, 272 Stress, 273 Stress deviator, 273 Ternary alloy, 253 Texture, ... variable, 9, 322, 323 Static equilibrium, 273 , 274 Stationary, 320 Diffusion equation, 320 Heat equation, 320 Process, 319, 329 Stefan, J., 179 Stored energy, 77 Strain Field,...

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... 229 7. 3.3 Boundary Values 231 7. 3.4 Stability Condition 232 7. 3.5 Structure of the Code 232 7. 3.6 Main Computation 233 7. 3 .7 Parameter File 236 7. 3.8 MatLab Visualization 2 37 7.3.9 Examples 238 7. 4 ... Substances 222 7. 2.1 Anisotropy Formulation 224 7. 2.2 Material and Model Parameters 226 7. 2.3 Application to Dendritic Growth 226 7. 3 Case Study 228 7. 3.1 Phase-Fiel...

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... 0.6 1 0.8 −0.8 −0 .7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 X A ln X A + X B ln X B FIGURE 2-3 Configurational entropy contribution in a binary A–B alloy. 20 COMPUTATIONAL MATERIALS ENGINEERING 2.2.1 ... X α B = X α B X β B − X α B · 2γV β m RT · 1 ρ (2. 87) or X α,P B = X α B ·  1+ 2γV β m (X β B − X α B ) · RT · 1 ρ  (2.88) 32 COMPUTATIONAL MATERIALS ENGINEERING In the limiting...

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... 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 second phase has ... 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 =...

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... recrys- tallization nuclei. Acta Mater., 51: 270 1– 271 6, 2003. [HMR 07] Y. Hu, M. A. Miodownik, and V. Randle. Materials Science and Technology, 20 07. In Press. [HSC93] E. A. Holm, D. J. Srolovitz, ... Phys., 27: 900–904, 1956. [RM 97] A. D. Rollett and W. W. Mullins. Scripta Mater., 36: 975 , 19 97. [RR01] A. D. Rollett and D. Raabe. A hybrid model for mesoscopic simulation recrystalli...

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