The Clausius—Clapeyron equations for phase transitions of the first kind in a thermoelastic material

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Abstract A model of the quasi-stationary isothermal phase transitions of thermoelastic solids is considered. Some problems connected with the specification of the kinematic characteristic of the phase transition are discussed. Relations on the surface of a strong discontinuity separating the phases of the material are formulated. Unlike the classical case of the equilibrium of liquid (gas) phases, the proposed relations take into account the irreversible nature of the transition in solids, the tensor character of the chemical potential and the important dependence on the type of anisotropy of the material of the phases. The Clausius—Clapeyron equations are formulated for a thermoelastic medium with arbitrary symmetry; these determine expressions for the derivatives of the phase-transition temperature with respect to the initial strain and orientation of the surface. These equations enable the the investigation of the neighbourhood of the jump in the space of initial parameters to be investigated. For the case of an initially isotropic material it is shown that the normal to the interface, which coincides with one of the principal axes of the tensor of finite deformation of the initial phase, yields an extremum of the phase transition temperature for a fixed strain of the initial phase. The phase transition of the first kind in a linear initially isotropic thermoelastic material is investigated in detail. It is shown that the smallness of the deformations of each of the phases implies smallness of the jump, which experiences rotation of the material particle on the phase boundary. A class of materials for which, when there is a change in the deformation of the initial phase, the type of the phase transition inevitably changes, i.e. a transition occurs from a normal phase transition to an anomalous transition, is discussed.