COMPUTATIONAL MATERIALS ENGINEERING Episode 14 pptx

... for applications in computational materials science. For instance, parabolic large-scale bulk diffusion or heat transport problems can be solved by 320 COMPUTATIONAL MATERIALS ENGINEERING Equation ... 13:1097, 1965. [LK87] J. L ´ epinoux and L. P. Kubin. Scr. Metall., 21:833, 1987. 314 COMPUTATIONAL MATERIALS ENGINEERING ... differential equation 4 A (ˆx 1 , ˆx 2 ) C (ˆx 1 , ˆ...

Ngày tải lên: 13/08/2014, 08:21

... write  dS =  dQ T =0 (2 .14) 10 COMPUTATIONAL MATERIALS ENGINEERING This page intentionally left blank 1 Introduction —Koen Janssens The book in front of you is an introduction to computational microstructure ... multitude of elements, leading to the saying that materials science is the physics of dirt” [Cah02]—but that is another story 2 COMPUTATIONAL MATERIALS ENGINEERING...

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... obtain B = − RT Ω X β B  ln eq X 0 B X 0 B  = −RTc β B ln eq c 0 B c 0 B (6.87) 214 COMPUTATIONAL MATERIALS ENGINEERING φ n+1 i,j = φ n i,j + δt τ  2γ  φ n i+1,j − 2φ n i,j + φ n i−1,j δx 2 + φ n i,j+1 − ... [HSAF99] —crystallographic direction 226 COMPUTATIONAL MATERIALS ENGINEERING Boundary 1 0 0 0.5 0.5 0.25 0.25 Dirichlet φ 0,0 φ 1,1 φ 0, Ny φ Nx, 0 φ Nx, Ny φ Nx−1, Ny−1...

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... entropy production dS ip in differential form reads dS ip =dQ · T b − T a T a T b (2.32) 14 COMPUTATIONAL MATERIALS ENGINEERING 2.2 Solution Thermodynamics More than 100 years ago, in a single two-part ... (ln X A − ln(1 − X A )) ∂ 2 ∆G ∂X A 2 = −Z ·ω + RT ·  1 X A + 1 1 − X A  (2.60) 24 COMPUTATIONAL MATERIALS ENGINEERING heat Q 1 =∆S · T a is transferred into the cooler heat...

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... Comprehensive Guide. Pergamon Materials Series, Pergamon, Oxford, 1998. [Wag52] C. Wagner. Thermodynamics of Alloys. Addison-Wesley Press, Reading, MA, 1952. 46 COMPUTATIONAL MATERIALS ENGINEERING corresponding ... 2.22; 6.00000E+03 N ! PARAMETER TC(BCC_A2,CR:C;0) 2.98150E+02 -311.5; 6.00000E+03 N ! 38 COMPUTATIONAL MATERIALS ENGINEERING FUNCTION 3-1: Basic Glauber Dynamics Usin...

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... quantitatively compare the speed-up algorithms with the vanilla code. 80 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 3 -14 Snapshot of circle shrinking under curvature on a 2D triangular lattice, ... dynamics, Metropolis transition probability function, and kT s =0.75. 76 COMPUTATIONAL MATERIALS ENGINEERING PROBLEM 3 -14: Self-Ordering Behavior Perform 2D Potts model simulations w...

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... starting configuration for an isotropic grain growth simulation using the Potts model. 90 COMPUTATIONAL MATERIALS ENGINEERING Grain B D/2 DD/2 Grain A Grain C Grain B q 1 q 1 q 1 q 2 q 2 g 1 g 1 g 2 f 12 FIGURE ... cannot be resolved. That is, at some point, the last step is removed, the boundary 94 COMPUTATIONAL MATERIALS ENGINEERING = 500 ; Map1; Step = 3 ; Grid501 × 98 FIGURE 3...

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... tabulated function. 114 COMPUTATIONAL MATERIALS ENGINEERING 4.4 +2D CA Modeling of Grain Growth One could argue that precise modeling of grain boundary surfaces, that is, making sure the computational ... that for each 128 COMPUTATIONAL MATERIALS ENGINEERING κ =15−  k ∈ 1st nn k ∈ 2nd nn φ k ε k (4 .14) which returns 0 for a locally flat grain boundary. Combining equation (4...

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... recrystal- lization and grain growth. Model. Simul. Mater. Sci., 11(2):157–171, 2003. 148 COMPUTATIONAL MATERIALS ENGINEERING [XL01] Q. Y. Xu and B. C. Liu. Modeling of as-cast microstructure of Al ... state transformation State Change Neighborhood FIGURE 4-30 Network cellular automata. 144 COMPUTATIONAL MATERIALS ENGINEERING Cell State Network Connection B AA A A B A B B State...

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... lattice frame of reference, a convenient measure when operating on the atomic scale. 170 COMPUTATIONAL MATERIALS ENGINEERING The solution to equation (5.24) with the constraint (5.32) is closely related ... movement of the markers is related to the difference in the diffusion coefficients. 168 COMPUTATIONAL MATERIALS ENGINEERING Equation (5.48) shows that the macroscopic diffusion coeffi...

Ngày tải lên: 13/08/2014, 08:21