COMPUTATIONAL MATERIALS ENGINEERING Episode 14 pptx
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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 1 pptx
... write
dS =
dQ
T
=0
(2 .14)
10 COMPUTATIONAL MATERIALS ENGINEERING
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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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 10 pptx
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 2 pot
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 3 doc
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 4 potx
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 5 pot
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 6 pdf
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 7 doc
... 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...
COMPUTATIONAL MATERIALS ENGINEERING Episode 8 doc
... 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...
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