For a ternary A–B–C system, there exist three binary intermetallic phases, AB, BC, and AC. The standard Gibbs energies of formation of these three compounds at 1000 K are A 0.5 B 0.5 (−10), A 0.5 C...

For a ternary A–B–C system, there exist three binary intermetallic phases, AB, BC, and AC.

The standard Gibbs energies of formation of these three compounds at 1000 K are A_0.5B_0.5
(−10), A_0.5C_0.5
(−20), and B_0.5C_0.5
(−5), all expressed in terms of kilojoules per mole of atoms.

(a) Calculate the 1000-K isotherm assuming there are mutual solubilities in pure A, B, and C and the three binary compounds are negligible.

(b) Calculate and plot an isothermal field–density phase diagram using μC/RT as a function of x_B/(x_B
+ xA) at 1000 K. Assume that there are no mutual solubilities between any of the phases. Draw another (schematic) diagram where finite solubilities between these phases is assumed.