Pandat软件培训ppt

Liquid
-14000
0.0
0.2
0.4
0.6
0.8
1.0
Cc
mol. fracn. B
Dd
88
Gibbs Energy (J/mol. atom)
Temperature (K)
1600
1400
Liquid
1200
α
β
1000
800
0.0
0.2
0.4
0.6
0.8
1.0
Cc
Dd
10000
5000
0
Liquid
+
yiI
y
II A
yBII
(
y
II A
−
yBII )v Lvi:A,B
j = A,B
v
i= A,B
v
+
y
I A
yBI
y
II A
yBII
LA,
B:
A,
B
13 13
Simple Binary A-B
4000
3800
L
3600
3400
L+bcc
3200
bcc
3000
2800 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
44
The Calphad Approach
55
Y. A. Chang, et al., Progress in Materials Science 49 (2004) 313-345
Experimental thermodynamic data and “first principles” calculated values at 0K and phase equilibrium data
-5000
α
-10000 0.0
Cc
0.2
0.4
0.6
mol. fracn. B
β
0.8
1.0
Dd
Phase Diagram Calculations
99
Temperature (K)
1600 1400
Liquid
1200
α
β
1000
800
0.0
0.2
0.4
0.6
0.8
1.0
Cc
Dd
Disordered Solution Phases
MA o
x
WB
disordered solution phase with BCC structure
14 14
Simple Binary A-B
4000
3800
L
G = xA ⋅ GAo,ϕ + xB ⋅ GBo,ϕ + RT ⋅ (xA ln xA + xB ln xB ) + Gex
3600
n
T − − − Temperature.
G ex
=
xA
⋅ xB
n
⋅ ∑ λi
⋅(xA
−
xB )i
i=0
xA, xB : mole fractions of component A and B.
GAo,ϕ , GBo,ϕ : Gibbs energy of pure A, and B with ϕ structure.
T(K)
4000
L
3600
3200
bcc
2800
2400
2000
bcc’+bcc’’
1600
1200
800
400 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
A
x
B
Gex (L) = 0 Gex (bcc) = 2000x(1− x)
Gex (L) = 64000x(1− x) Gex (bcc) = 50000x(1− x)
bcc’+bcc’’
800
400 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
A
x
B
Gex (L) = 0 Gex (bcc) = 2000x(1− x)
Gex (L) = 0 Gex (bcc) = 50000x(1− x)
18 18
Simple Binary A-B: Monotectic
Ordered Intermetallic Phases
12 12
II I
• A prefers sublattice I,
B prefers sublattice II.
• Use yPi to describe
the state of order
∑ yPi = 1
(
y
I A
+
y
I B
= 1)
P= A,B
¾ Real Example: developing Al-Zn database ¾ Application to Commercial Alloys
11
A Materials Scientist’s Dream
It is a demanding world!
¾New alloys (multicomponent): with desired properties; ¾Exiting alloys: improve their properties and life span;
λis − Model parameters,obtained by optimization using available experimental data
Regular solution model : Gex = λ0 ⋅ xA ⋅ xB
10 10
Stoichiometric Phases
Reproduce experimental diagrams and thermodynamic properties of the binaries and ternaries
More importantly – extrapolate the Gibbs energies of lower order phases to those of higher order phases
A
x
B
Gex (L) = 0 Gex (bcc) = 2000x(1− x)
Gex (L) = 0 Gex (bcc) = 20000x(1− x)
17 17
3
Simple Binary A-B: Eutectic
T(K)
4000
L
3600
3200
2800
L+bcc
2400
2000
bcc
1600
1200
• No preference on site • Composition varied in the
whole composition range
G = xA ⋅ GAo,ϕ + xB ⋅ GBo,ϕ +
RT ⋅ (xA ln xA + xB ln xB ) + Gex
R − − − Gas constant.
Select thermodynamic models for each phase Optimize model parameters
Obtain Gibbs energies for each phase in a binary or a ternary system (Thermodynamic description)
G = G(x, y,T , parameters)
∑ ∑ ∑ ∑ Gmϕ
=
yiI
y
II j
Giϕ: j
i= A,B j= A,B
+
RT [
p
p +
q
yiI
i= A,B
ln
yiI
+
p
q +
q
i=
yiII
A, B
ln
yiII
]
∑ ∑ ∑ ∑ +
y
I A
yBI
y
II j
(
y
I A
−
yBI )v LvA,B: j
Disordered solution phases: Liquid, bcc, hcp, fcc Stoichiometric phases: TiAl2, Ti2Al5
• Perfectly ordered • Composition fixed (AB)
A
B
G = xAGAo,φ + xBGBo,φ + ΔGf ΔGf = a +b⋅T +c⋅T ⋅lnT +⋅⋅⋅ a,b,c,⋅⋅⋅: parameters
11 11
2
Ordered Intermetallic Phases
Gex = xA ⋅ xB ⋅ ∑ λi ⋅ (xA − xB )i
3400
i=0
L+bcc
3200
Gex (L) = 0
3000
bcc
Gex (bcc) = 2000xw (1− xw )
2800 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
MA o
x
WB
19 19
Complicated Binary System: Ti-Al
Temperature (K)