Chapter 8 Phase equilibria and potential phase diagrams
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Transcript of Chapter 8 Phase equilibria and potential phase diagrams
Chapter 8
Phase equilibria andpotential phase diagrams
as mentioned in Chapter 1- a particular state of equil identified by giving the values to state
variables c+2 variables must be given the rest are dependent- equil state of system : represented by a point in a c+2 dim diagram,
all pts in such a diagram represent possible states state diagram (but, giving no information)
- thus, by sectioning at constant values of c+1 variables and plotting a dependent variable as another axis property diagram
Fig. 1.1
- the line itself represents the property of the system property diagram
• fundamental property diagram:
the relation of c+2 intensive var is plotted in c+2 dim space
relation of G-D eq results in a surface or a if c > 1 representing thermo properties of the sys such a diagram, with the surface included
regarded as property diagram of special interest, because it is composed of
a complete set of (T, P, i)
fundamental property diagram potential diagram
ex) T-P diagram for one comp A, with one phase SdT-VdP+∑Nidi=0 (G-D eq) becoming
SdT-VdP+NAdA=0
μA
T
-P
• the equil state completely determined by giving values to T, P (by giving a pt in T-P diagram) → state diagram
• μA can be calculated from G-D and plotted as a surface above the T-P state diagram → yielding a 3D diagram → property diagram
• μA=Gm=Gm(T, P) : equation of state
→ fundamental property diagram
• in unary sys, G =∑μiNi = μANA ∴ μA = G/NA
=Gm
• for a higher-order system, 1= 1(T, P, 2, 3, …)
- for A, possible two phases (,
ateach G-D surface
- considering a possible transition from phase β to phase α at fixed T, P
- evaluation of the integrated driving force of
dU = TdS - PdV + ΣμidNi - Ddξ
= TdS - PdV + μAdNA - Ddξ
(U = TS - PV + μANA )
(dU = TdS + SdT - PdV - VdP + μAdNA + NAdμA)
∴ Ddξ= - SdT + VdP - NAdμA )()(
AAAAAAAA NNdNDd
okey ,0:
okey ,0: ,
Dd
Dd
AA
AA즉
∴ the phase with the lower A will be more
(at constant T, P)
• μAμA
equil, D=0 - in Fig. 8.3, the line of intersection of two surfaces
must be a line of - projection of fundamental property diagram onto T-P
state diagram removal of both dμAdμA
potential phase diagram
T
-P
(potential) Phase Diagram
in Germany, phase diagram
state diagram
in Japan, 狀態圖
1. Property diagram for unary system with one phase: properties of this phase are represented by a surface
2. Property diagram for unary system with two phases; is driving force for β→α AA
3. Construction of a phase diagram by projecting a property diagram; two phases can exist at line of intersection of their property surfaces
4. Simple phase diagram obtained by construction shown in Fig. 3
5. Unary phase diagram with three phases; broken lines are metastable extrapolations of two phase equilibria