STOCHASTIC THEORY OF NON-IDEAL BEHAVIOR .4. THERMAL RELAXATION

An approximate theory is proposed for the thermal relaxation of condensed binary [A, B] systems. During the relaxation the composition varies, or is kept constant. (The former case corresponds to an Ising lattice, the latter to a binary alloy, for example.) A variation of the composition is described with the help of a stochastic exchange A⇌B (as in the Glauber Model), but the microscopic transition probabilities are replaced by smoothed probabilities which depend on the system's composition and interna] energy, as proposed in Part I. The variation of the internal energy is estimated with the help of a dynamic counterpart of the quasi-chemical approximation. The equations can be integrated numerically, describing the time dependence of the system's composition (if varying), internal energy, entropy and of intensive parameters corresponding to transient ‘quasi-equilibria’. The theory is applied to an Ising lattice undergoing heating or cooling through the critical temperature and compared with Monte Carlo simulation of identical processes. The agreement is judged to be very good, especially since it involves no parameter fitting. The relaxation of an [A, B] system of fixed composition, undergoing cooling to inside the co-existence curve is also studied. Three alternative lines for the evolution of internal energy are estimated: (i) unstable, with no decomposition into two phases; (ii) metastable, with spinodal decomposition and (iii) stable, with binodal decomposition. Comparison with a computer simulation of the process indicates that the initial relaxation (up to order of 100 trial exchanges per particle, depending on the system’s size) fits the metastable line, the initial stage being followed by an extremely slow crossover to the stable line. © 1979 Taylor & Francis Ltd.