Chapter 8 Phase equilibria and potential 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 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+∑N i d  i =0 (G-D eq) becoming SdT-VdP+N A d  A =0 μAμA T -P the equil state completely determined by giving values to T, P (by giving a pt in T-P diagram) → state diagram μ A can be calculated from G-D and plotted as a surface above the T-P state diagram → yielding a 3D diagram → property diagram μ A =G m =G m (T, P) : equation of state → fundamental property diagram in unary sys, G =∑μ i N i = μ A N A ∴ μ A = G/N A =G m for a higher-order system,  1 =  1 (T, P,  2,  3, …)

- for A, possible two phases ( ,          at  each 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 + Σ μ i dN i - Ddξ = TdS - PdV + μ A dN A - Ddξ (U = TS - PV + μ A N A ) (dU = TdS + SdT - PdV - VdP + μ A dN A + N A d μ A ) ∴ Ddξ= - SdT + VdP - N A d μ A ∴ the phase with the lower  A will be more (at constant T, P)

μ A   μ A   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 dμ A   dμ A   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 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 Unary phase diagram with three phases; broken lines are metastable extrapolations of two phase equilibria