Phase Equilibrium and Critical Behavior in a Two-Component Bethe-Lattice Gas or Three-Component Bethe-Lattice Solution

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Abstract
The complete coexistence surface is found for a symmetric case of a two‐component Bethe‐lattice gas or three‐component Bethe‐lattice solution. It is shown to agree with previously obtained results in the limit of a two‐component lattice solution and in the limit of the Bragg–Williams approximation to a three‐component solution. The coexistence surface is found to be parabolic in the neighborhood of the plait point in this approximation, and the isothermal coexistence curve remains inside the composition triangle even at absolute zero of temperature. The behavior of fluctuations in concentration, density, and energy in the vicinity of the plait‐point curve is investigated, and the density fluctuations are found to have the interesting property that they approach a finite constant at the plait point, the value of which depends upon the path of approach to the plait point. The problem is similar, but not equivalent, to that of the randomly dilute ferromagnet. A proof is given that the quasichemical approximation holds exactly for a Bethe‐lattice gas of any number of components.

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