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