Phase Separation of Dilute ⁴He Impurities in Solid ³He

Abstract

Time evolution of the phase separation is investigated. It consists of two stages: nucleation of stable clusters of ⁴He impurities and succeeding growth of the clusters through quantum diffusion. Master equation for impurity cluster concentration and diffusion equation are analyzed to obtain time variation or the impurity concentration by making use of steady state solutions. Time scale of the separation is determined by the magnitude of diffusion constant and nucleation rate in the steady state, both of which depend strongly on molar volume in the same manner. In contrast with this, the form of time evolution changes as a result of either time lag in the nucleation or density dependence of the diffusion constant.