Synergetics of macrostructure evolution of a new phase

Abstract

The status of the theory of nucleation of a new phase is reviewed. Special attention is devoted to the relation between the micro- and macroscopic levels. A systematic exposition is given of the methods developed by Cahn, Cook, Langer, and Mazenko for describing the spatiotemporal correlation of the order-parameter field for the continuous (spinodal) mechanism of formation of a new phase. The time dependence of the characteristic size L(t) is found for the cases of nonconserved and conserved order parameters as well as for the coalescence process. It is shown that in the case of the intermittent (binodal) formation mechanism a critical nucleus of a new phase can be represented as the soliton solution of the field equation. It is found that the appearance of sharp interphase boundaries results in a transition from spinodal to heterophase kinetics, represented as a loss of ergodicity. The nonergodicity parameter is determined as a function of the interatomic interaction and anharmonicity within the Ginzburg-Landau scheme. Coalescence in the presence of intense external noise is investigated for systems with a conserved order parameter. A stochastic equation is derived for the size distribution function of precipitates of the new phase and the effect of intensity fluctuations and supersaturation of the limiting component on the solution of this equation is investigated.