COMPUTATIONAL MATERIALS ENGINEERING Episode 1 pptx

... thermodynamics. 8 COMPUTATIONAL MATERIALS ENGINEERING Table of Contents Preface xiii 1 Introduction 1 1 .1 Microstructures Defined 1 1.2 Microstructure Evolution 2 1. 3 Why Simulate Microstructure Evolution? 4 1. 4 ... 8 2 .1. 1 The First Law of Thermodynamics 8 2 .1. 2 The Gibbs Energy 11 2 .1. 3 Molar Quantities and the Chemical Potential 11 2 .1. 4 Entropy Production and...

Ngày tải lên: 13/08/2014, 08:21

... σ 0 T M /(∆HT Q ) =1. 659 × 10 10 m, the averaged kinetic coefficient β 0 =(µ 1 100 + µ 1 110 )/ 2T Q 5.3 × 10 −3 s/m, and the strength of the kinetic anisotropy  k =(µ 10 0 − µ 11 0 )/(µ 10 0 − µ 11 0 )=0 .13 . 7.2.3 ... model. Figure 6 -18 compares the different growth rates as a function of the supersaturation S. The 10 -4 10 -3 10 -2 10 -1 1 Dimensionless Supersatur...

Ngày tải lên: 13/08/2014, 08:21

... used: K 1 (ζ,{)= 1 2 (1 + ζ) (1+ {) K 2 (ζ,{)= 1 2 (1 + ζ) (1 {) K 3 (ζ,{)= 1 2 (1 −ζ) (1+ {) K 4 (ζ,{)= 1 2 (1 −ζ) (1 {) (9 .10 ) The variables ζ and { lie within the the range 1 ≤ ζ,{ ≤ +1. The values ... =         K 1, 1 00 K i ,1 00 K n ,1 00 0 K 1, 2 0 0 K i,2 0 0 K n,2 0 00K 1, 3 00K i,3 00K n,3 K 1, 2 K 1, 1 0 K i,2 K i ,1 0 K n,2 K n ,1 0 0 K 1,...

Ngày tải lên: 13/08/2014, 08:21

... 2 818 2 610 326 2 60Nd 2 818 2 610 426 2 61Pm 2 818 2 610 526 2 62Sm 2 818 2 610 626 2 63Eu 2 818 2 610 726 2 64Gd 2 818 2 610 72 612 65Tb 2 818 2 610 926 2 66Dy 2 818 2 610 1026 2 67Ho 2 818 2 610 112 6 ... 818 2 610 1226 2 69Tm2 818 2 610 1326 2 70Yb 2 818 2 610 1426 2 71Lu 2 818 2 610 142 612 72Hf 2 818 2 610 142622 n D 12 3 45 6 7 l D ———— 01 23 012 0 73 Ta 2 8 18 32 2 6 3 2 74W 2 81...

Ngày tải lên: 11/08/2014, 16:22

... obtain ∆G = 1 2 X A (1 − X A )Z · ω − RT · (X A ln X A + (1 X A ) ln (1 − X A )) ∂∆G ∂X A = 1 2 (1 − 2X A )Z · ω − RT · (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 ... Transformations 19 Site Fraction X i Gibbs Energy G 1 2 3 4 5 k = 0 0 0.2 0.4 0.6 0.8 1 −0 .1 0 0 .1 0.2 0.3 FIGURE 2 -11 Shape of Redlich–Kister polynomials f...

Ngày tải lên: 13/08/2014, 08:21

... temperature τ> ;1, wehave mo G m = −RT ln(β m +1) ·  τ −5 10 + τ 15 315 + τ −25 15 00   518 11 25 + 11 692 15 975  1 p − 1  (2 .10 0) and for τ< ;1, wehave mo G m = RT ln(β m +1)  1 −  79τ 1 140p + 474 497  1 p − ... 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 13 5 + τ 15 600   518 1...

Ngày tải lên: 13/08/2014, 08:21

... the 2D square lattice, kink motion occurs easily along the [10 ] directions but not along [11 ] directions, for example, M [10 ] /M [11 ] ≈ 25 at kT s =0.2 [MSGS02]. Given this inherent anisotropy ... algorithm. Quantify the efficiency gain for grain growth for various lattice sizes, 10 × 10 and 10 0 × 10 0 and 10 00 × 10 00. 3.4.3 Parallel Algorithm The Potts algorithm does not readily...

Ngày tải lên: 13/08/2014, 08:21

... γ(θ 2 ). Simulation Read-Shockley Misorientation (θ 2 ) (a) 10 5 10 4 10 00 10 0 10 1 1 10 10 0 10 00 10 4 10 5 Measured µ 1 Nominal µ 1 (b) 0 0 0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 12 14 16 Normalised Effective Driving Force (γ 2 / γ max ) FIGURE ... systems. initial 800-2 Sample (d) (a) (b) 800-5 Area Proportion(%) 60 50 40 30 20 10 0 11 1 11 0 10 0 initial 800-2...

Ngày tải lên: 13/08/2014, 08:21

... resulting 5 × 5 matrix (adding up to 12 in the example in Figure 4 -16 ) returns a number which can be scaled to an approximation of the curvature: 11 111 1 1 11 1 11 111 11 111 11 111 Kink Template Applied to ... A 00000 00000 011 10 011 11 111 11 FIGURE 4 -16 A method for direct approximation of local curvature at a grain boundary. See text for more details. 12 4 COMPUTATIONA...

Ngày tải lên: 13/08/2014, 08:21

... 1 1 − 1+ 1 1 1 1+ 1− 1 1 1 +1 − 1 − 1 1 1 1 − 1 − 1 −3 9 4 +1+ 1 +1+ 1 +4 16 [ (1/ 16) · 64] 1/ 2 +1 − 1+ 1 +1 +2 4 = (4) 1/ 2 +1+ 1− 1+ 1 +2 4 +1+ 1 +1 1+ 2 4 +1 − 1 − 1+ 1 0 0 +1 − 1+ 1− 10 0 +1+ 1− 1 − 10 ... Sequence (λ)(λ 2 )(  1/ k  λ 2 ) 1 +1 +1 1 [ (1/ 2) · 2] 1/ 2 1 1 1 = (1) 1/ 2 2 +1+ 1 +2 4 [ (1/ 4) · 8] 1/ 2 1+ 1 0 0 =...

Ngày tải lên: 13/08/2014, 08:21