Computational materials engineering

... Modeling 4 .10 Further Reading 12 4 12 8 12 9 13 1 13 5 13 6 13 6 13 7 14 0 14 0 14 2 14 4 14 4 14 5 14 7 Modeling Solid-State Diffusion 5 .1 Diffusion Mechanisms in Crystalline Solids 5.2 Microscopic Diffusion 5.2 .1 The ... Diffusion Equation 15 1 15 1 15 4 15 4 15 5 15 7 16 0 16 0 16 2 16 4 16 8 17 1 17 4 Modeling Precipitation as a Sharp-Interface Phase Transform...

Ngày tải lên: 13/08/2014, 08:21

... XB XB ∂XB (2. 86) With this approximation and equation (2. 82) , we finally have α,P α XB − XB = α XB β α XB − XB · β 2 Vm · RT ρ (2. 87) or α,P α XB = XB · 32 COMPUTATIONAL MATERIALS ENGINEERING ... NB NA NB − = NA + NB (NA + NB )2 = ωXB 2 ·ω (2. 64) and the chemical potential of a regular solution can be expressed as RS µA = µA + RT ln XA + ωXB 2 (2. 65) 2. 2.4 General Solution...

Ngày tải lên: 13/08/2014, 08:21

... of a sphere is, V = 4 /3 R3 , so equation (3. 8) becomes: V 2 /3 2 /3 Vo =1− αv t (3. 9) Vo 2 /3 2 /3 where αv = (4 /3 )2 /3 γM Figure 3- 8 shows the plot of V 2 /3 /Vo versus t/Vo 2 /3 for the sphere The ... +.00189 435 *T**2-1.47721E-06*T* *3+ 139 250*T**(-1); 2.18000E+ 03 Y -34 869 .34 4 +34 4.18*T-50*T*LN(T)-2.88526E +32 *T**(-9); 6.00000E+ 03 N ! FUNCTION GHSERFE 2.98140E+02 +1...

Ngày tải lên: 13/08/2014, 08:21

... such a system simulated using the Potts model Instead of bubbles we have domains 64 COMPUTATIONAL MATERIALS ENGINEERING (a) (b) FIGURE 3-15 (a) A soap froth—the structure is self-ordering, (b) ... lattice, Glauber dynamics, Metropolis transition probability function, and kTs = 0.75 74 COMPUTATIONAL MATERIALS ENGINEERING is obvious from the form of probability transition function...

Ngày tải lên: 13/08/2014, 08:21

... Carlo Potts Model 1 05 Grain A Particle r θ yo Boundary Dimple γAP γBP ρ Grain B (a) 55 Hellman and Hillert [2] Static Monte Carlo 50 θ Z 45 40 θ = 45 35 30 25 10 15 20 25 X (b) 30 35 40 1 .5 Force/πγY ... 25 10 15 20 25 X (b) 30 35 40 1 .5 Force/πγY 0 .5 Boundary Detaches -0 .5 kT′ = kT′ = kT′ = Theory -1 -1 .5 -2 -1 -0 .5 0 .5 s/r 1 .5 2 .5 (c) FIGURE 3- 45 (a) A sche...

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... or cubes Other types of grids are possible, as illustrated in Figure 4 -6 1 16 COMPUTATIONAL MATERIALS ENGINEERING FIGURE 4 -6 Types of periodical cellular automaton grids in two and three dimensions ... continued 0.97174 0.5454 06 Corrected (Probabilistic) Moore FIGURE 4-12 A corrected Moore-type neighborhood and state transformation function 120 COMPUTATIONAL MATERIALS ENGINE...

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... Sci., 11(2):1 57 171 , 2003 148 COMPUTATIONAL MATERIALS ENGINEERING [JB85] R Jullien and R Botet Scaling properties of the surface of the eden model in d=2, 3, J Phys A, 18:2 279 –22 87, 1985 [JHF04] ... Forum, 3 17: 113–115, 1993 J Hardy, Y Pomeau, and O de Pazzis Time evolution of a two-dimensional model system i Invariant states and time correlation functions J Math Phys., 14(12): 17...

Ngày tải lên: 13/08/2014, 08:21

... resistance 1.0 sqrt(4 Dt) = 100 0 .8 20 c(x)/c0 0.6 0.4 0.2 0.5 0 x (Length) FIGURE 5 -8 Solutions to Fick’s second law for semi-inifinite sample 164 COMPUTATIONAL MATERIALS ENGINEERING 10 against movement ... 2.2 .8) Other software that can be used is the package MatCalc (http://matcalc.tugraz.at) Bibliography [AHJA90] [Cra75] [Dar 48] [Ein05] [Fic55] [Gli00] [Kir42] [KTU39] [KY87] [P...

Ngày tải lên: 13/08/2014, 08:21

... approximation, equation (6. 29) can deliver reasonable first estimates of interfacial energies even for general matrix–precipitate interfaces 196 COMPUTATIONAL MATERIALS ENGINEERING 6.3 Diffusion-Controlled ... practical evaluation of the composition with highest driving force, see Section 2.2.6 192 COMPUTATIONAL MATERIALS ENGINEERING dfm (J/mol) a 1e + 004 b c d e f 5000 0 0.2 0.8...

Ngày tải lên: 13/08/2014, 08:21