Non-hydrostatic thermodynamics of chemical systems

Abstract

This paper considers a multi-phase chemical system which includes solid substances, which can sustain non-hydrostatic stresses. The correct mechanical coordinates are introduced for a phase, which give the correct work done whether the dimensions of the phase are altered by deformation, phase transformations, or by chemical actions such as solution or crystallization at the surface of the phase. These coordinates are integrals over the surface of the phase, which are properties of affine transformations of points in the reference state of the phase. For coherent processes, during which atoms or molecules which are initially neighbours remain neighbours, the affine transformations are such that points of the reference space transform to remain coincident with the structural entities, such as idealized atoms etc, of the solid. Thus the ‘deformations’ of the space coincide with that of the solid. Such coherent processes are, for example, deformations, coherent transitions such as the α-β quartz transitions, diffusion of a mobile chemical component into the solid. Processes which involve surface changes such as solution or deposition of the basic material of the solid are incoherent, and in these cases, since chemical bonds are broken, it is assumed that the pressure must be normal. By making use of this latter fact, the change per mole of the coordinates resulting from such surface incoherent effects is determinable. However, while the coordinates V αβ are extensive if processes are limited to be either coherent or incoherent, it is shown that the molar change depends on the process. This property is reflected into the Gibbs function, through the terms containing the V αβ . However, the Gibbs function may be easily and conveniently used to obtain the conditions of equilibrium for all the above processes. Comparison with experiments on quartz is given. The empirical maximal energy principle of Thomas & Wooster for de-twinning (Dauphiné) of quartz is rigorously justified. It is shown that for a stressed solid in contact with a solution of the solid, the condition of equilibrium obtained by Gibbs is equivalent to the fact that μ — T s + P n v is a change per mole in the Gibbs function of the solid phase, for the processes of solution and crystallisation at the fluid/solid interface where the normal pressure P n is that of the fluid, u , s , v being the molar energy, entropy, volume of the solid. The equilibrium conditions for coherent phase transitions, and diffusion into a solid are also obtained. The mechanical coordinates V αβ are shown to be additive for a multi-phase system . It is also shown that the theory, which is described for simplicity first using infinitesimal deformation theory, is easily extended to finite deformations.