COMPUTATIONAL MATERIALS ENGINEERING Episode 8 doc
COMPUTATIONAL MATERIALS ENGINEERING Episode 8 doc
... (Length)
c(x)/c
0
0
24 681 0
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.
164 COMPUTATIONAL MATERIALS ENGINEERING
c
i,t+∆t
= ... the markers is related to the difference in the diffusion coefficients.
1 68 COMPUTATIONAL MATERIALS ENGINEERING
Equation (5. 48) shows that the macroscopic diffusion coefficient...
COMPUTATIONAL MATERIALS ENGINEERING Episode 3 doc
... -173 68. 441+170.73*T-24.3*T*LN(T)
-4.723E-04*T**2+2562600*T**(-1)-2.643E+ 08* T**(-2)+1.2E+10*T**(-3);
6.00000E+03 N !
FUNCTION GHSERCR 2. 981 40E+02 -88 56.94+157. 48* T-26.9 08* T*LN(T)
+.00 189 435*T**2-1.47721E-06*T**3+139250*T**(-1); 2. 180 00E+03 Y
-3 486 9.344+344. 18* T-50*T*LN(T)-2 .88 526E+32*T**(-9);
6.00000E+03 ... G(CEMENTITE,CR:C;0) 2. 981 50E+02 +3*GHSERCR#+GHSERCC#
- 480 00-9...
COMPUTATIONAL MATERIALS ENGINEERING Episode 7 doc
... limiting case of an infinitesimally small
136 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 ... of a random walker [equation (5.5)] and using the spatial
coordinate
r leads to
1 58 COMPUTATIONAL MATERIALS ENGINEERING
Literature in Journals
Here is a list of articles in whic...
COMPUTATIONAL MATERIALS ENGINEERING Episode 9 doc
... to, for example, the textbook by Khashchiev [Kha00] or the review
by Russell [Rus80].
188 COMPUTATIONAL MATERIALS ENGINEERING
Concentration of B
Temperature
b
a + b
a
A
B
c
b
c
ab
FIGURE 6-11 Binary ... vacancies.
186 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
FIGUR...
COMPUTATIONAL MATERIALS ENGINEERING Episode 12 doc
... 10 .82 6.13 2 .85 1.215 0.36
Au fcc 18. 60 15.70 4.20 2. 987 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 ... the use of the Airy stress function, equations
(8. 86)–( 8. 88) . By using the substitution
(σ
11
+ σ
22
)=∇φ (8. 91)
the biharmonic equation (8. 88) can be transformed into the ha...
COMPUTATIONAL MATERIALS ENGINEERING Episode 15 docx
... statics, 284 – 288
2D, 285 , 286 , 287 , 289
Anisotropic, 287
Isotropic, 285
3D
Anisotropic, 292
Field equation, 289
Field equations, 292
Isotropic, 289
Infinite dislocation, 285 , 286 , 287
Isotropic, 289
Dislocation–dislocation ... 67, 87 , 88 , 253
Grain structure, 220
Green’s function, 2 68, 280 , 281 , 283
Tensor, 281
Time-dependent, 281
Time-independent, 281
Green–Lagrange...
COMPUTATIONAL MATERIALS ENGINEERING Episode 1 pptx
... Green’s Tensor Function in Elasticity Theory 280
8. 2 .8 The Airy Stress Function in Elasticity Theory 283
8. 3 Dislocation Statics 284
8. 3.1 Introduction 284
8. 3.2 Two-Dimensional Field Equations for ... Acknowledgments 265
8 Introduction to Discrete Dislocations Statics and Dynamics 267
8. 1 Basics of Discrete Plasticity Models 267
8. 2 Linear Elasticity Theory for Plasticity 2 6...
COMPUTATIONAL MATERIALS ENGINEERING Episode 2 pot
... solution limit.
28 COMPUTATIONAL MATERIALS ENGINEERING
Mole Fraction Mo
Activity a
0
1
0
0.2
0
.4 0.6 0.
81
Fe
Mo
Liquid
Mole Fraction Mo
Mo
Fe
Solid (bcc)
0
0.
2
0.4 0.6
0 .8
1
FIGURE 2-6 Activity ... 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 case of a dilu...
COMPUTATIONAL MATERIALS ENGINEERING Episode 4 potx
... very easy to 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 ... this occurs then when the two processors attempt to calculate
∆E for a spin flip, they
84 COMPUTATIONAL MATERIALS ENGINEERING
(b)(a)
FIGURE 3-15 (a) A soap froth—the structure is s...
COMPUTATIONAL MATERIALS ENGINEERING Episode 5 pot
... nonlinear transient at the beginning and end of the
simulations. Why do these occur?
88 COMPUTATIONAL MATERIALS ENGINEERING
PROBLEM 3-32: Comparing the Effect of Boundary Conditions
Use your imported ... 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 6000 80 00 1
×
10
4
Time (MCS)
dp...
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