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Chapter 8 Phase equilibria and potential phase diagrams

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

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Chapter 8 Phase equilibria and potential phase diagrams

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  1. Chapter 8 Phase equilibria andpotential phase diagrams

  2. 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

  3. 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

  4. ex) T-P diagram for one comp A, with one phase a SdT-VdP+∑Nidi=0 (G-D eq) becoming SdT-VdP+NAdA=0 • 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, …) μA T -P

  5. - for A, possible two phases (a, b)  mAa, mAbateach G-D surface - considering a possible transition from phase βto phase α at fixed T, P - evaluation of the integrated driving force ofb  a dU = TdS - PdV + ΣμidNi - Ddξ = TdS - PdV + μAdNA - Ddξ (U = TS - PV + μANA ) (dU = TdS + SdT - PdV - VdP + μAdNA + NAdμA) ∴ Ddξ= - SdT + VdP - NAdμA (at constant T, P) ∴ the phase with the lowerA will be more

  6. T b a + b a -P • μAa = μAb  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 dμAa , dμAb  potential phase diagram (potential) Phase Diagram in Germany, phase diagram  state diagram in Japan, 狀態圖

  7. 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 5. Unary phase diagram with three phases; broken lines are metastable extrapolations of two phase equilibria 4. Simple phase diagram obtained by construction shown in Fig. 3

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