材料热力学讲义-6

x 2 P xlP
Modified from Ju Li
32
16
TM1 G L L TP


1 2
x1P x 2 P xlP
TM2
T TM2
x
Modified from Ju Li
33
T TM1
1
2
1
x1E
x
x lE
x 2 E
x1E
x
x lE
x 2 E
Modified from Ju Li
28
14
TM1 L G TE TM2
L
2
1
2
1
x1E
x
x
x lE
x 2 E
Modified from Ju Li
29

G L
TM1

TE
L
TM2
x
Modified from Ju Li

L1 + L2 ↔ s
A
B
15
Do you know where to find phase diagrams?
• Go to • Go to Students or Faculty Tab • Click on Libraries • Under Links, click Research Databases List • Type “ASM Phase Diagram” into “Find a database” field • Perform the search • Click on ASM Alloy Phase Diagrams Center • Select S l t “Explore” “E l ” or “S “Search” h” ( (which hi h works k b best tf for t ternaries) i ) • Select the systems of interest.
10
T TM1
G L
TM2 TM1 L G


L
T
T* Tc
2
1
x
x
x
Modified from Ju Li
21
TC T T *
L
T T*
L TM1 L G G
TM2


T
T* Tc
2
x
x
*
1
x
x
22
Modified from Ju Li
11
T Tc
L TM1 L G T T* Tc TM2
Gm T , P , x i


with fitting parameters
Optimize model parameters
No Gm T , P , x i Calculate phase diagrams and thermodynamic values & compare with experimental data Yes Accept the model parameters, extrapolate to higher-order system & build databases
Thermodynamic parameters
5
CALPHAD Optimization
Thermodynamic parameters for Ni-Al:
CALPHAD Assessment / Optimization
Gm T , P , x i


Huang & Chang & other phases
16
8
Schematic Gibbs free energy vs composition curves
T Ta TM2
T TM2
G
Ta L L+s T
TM2
G s L x
s L
TM1
s
x
x
Modified from Ju Li
17
T TM1
T TM1
L L+s
TM2
G L s
L1 + L2 ↔ s
12
6
Definition of Invariant Reactions
L1 + L2 ↔ s
13
Definition of Invariant Reactions
L1 + L2 ↔ s
14
7
Definition of Invariant Reactions
T

L L1 L2
Sublattice models
• Non-stoichiometric compound: (A,B)a(C,D)b
ideal xs G( A, B ) a (C , D ) b G o Gmix G mix
I II o I II o I II o I II o Go yA yC G A :C y A y D G A:D y B yC GB:C y B y D GB:D
xlE
x E
xlE
x E
30
15
Peritectic
G
T TM1
G
TM1
L l
1 2
x1P x 2 P xlP
TM2

L
TP

L x x
Modified from Ju Li
31
G
L

L G

TM1 TP
L l
1 2
x1P x 2 P xlP
TM2

x
x1P
x




xs I I II k I I k II k I I k Gmix i y A y B yC L A, B:C ( y A y B ) y D L A, B:D ( y A y B ) k 0 k 0 II II I k II II k I k II II k yD y A LA:C ,D ( yC LB:C ,D ( yC yC yD ) yB yD ) k 0 k 0 I I II II y A y B yC y D I A,B:C ,D
8
4
Gibbs Phase Rule
f=c–p+2
f = degrees g of freedom c = number of components/elements p = number of phases When pressure is constant
f=c–p+1
9
At constant pressure
Degrees of freedom: f = p(1+c) – (p – 1)(c +2) = c – p + 2
7
Gibbs Phase Rule
f=c–p+2
f = degrees of freedom g c = number of components/elements p = number of phases



Ab Initio Calculation
Apply to materials design & others
CALPHAD = CALculation of PHAse Diagrams
3
Thermodynamic Models Sublattice models
• • • • Interstitial solutions: i.e., (Fe,Cr)a(Va,C)b Ordering: g i.e., (Ni,Al)0.75(Al,Ni)0.25 Compositional point defects: i.e., (Al,Ni)1(Ni,Va)1 Site preference: i.e., (Al,Ge,Ni)1(Ni,Va)1
Thermodynamic parameters
2
1
Introduction to the CALPHAD Approach
Obtain/select experimental data on phase diagrams & thermodynamic quantities
Cp H
Obtain other data
• Crystal structures • Point defects • Site preferences • Ordering transitions • Curie temperatures • Magnetic moments • ……
i
S l t/d l models Select/develop d l for f each h phase h
Lecture 6
Thermodynamics of Phase Diagrams
1
Thermodynamic Models
• Pure elements (set by SGTE)
G H SER a bT cT ln(T ) d iT i
SER: Standard Element Reference
f=c–p+1
Eutectic reaction: L ↔ solid-phase 1 + solid phase 2 L ↔ s1 + s2
10
5
Peritectic reaction: L + solid phase 1 ↔ solid phase 2 L + s1 ↔ s2