The Interactions of Composition and Stress in Crystalline Solids

Abstract

The thermodynamics of stressed crystals that can change phase and composition is examined with particular attention to hypotheses used and approximations made, Bulk and surface conditions are obtained and for each of them practical expressions are given in terms of experimentally measurable quantities. The concept of open-system elastic constants leads to the reformulation of internal elastochemical equilibrium problems into purely elastic problems, whose solutions are then used to compute the composition distribution. The atmosphere around a dislocation in a cubic crystal is one of several examples that are completely worked out. The effects of vacancies and their equilibrium within a solid and near surfaces are critically examined, and previous formulas are found to be first order approximations. Consequences of the boundary equations that govern phase changes are studied with several examples. Finally, problems connected with diffusional kinetics and diffusional creep are discussed.

Interaction between diffusion and chemical stresses

“…Defining the hydrostatic stress as σ = σ 11 + σ 22 + σ 33 3 (8) and using Eq. (2), the relation between the volumetric strain and the hydrostatic stress can be expressed as…”

“…composite materials. Larch and Cahn [7,8] investigated the stresses arising from inhomogeneities in materials. Recently, Yang and Li [9] considered the effect of chemical stresses on the bending of beam/plate structure.…”

“…Based on the concept of thermodynamic factor, Alefeld et al [15] solved the problem of diffusion when subjected to applied stress. Larch and Cahn [7,8] analyzed the effect of stresses on local diffusion in a solid, where the coupling between diffusion and chemical stresses was addressed. The effect of chemical stresses on diffusion was discussed by Chu and Lee [16] using Li's solution [2], while they did not consider the coupling effect.…”

Solubility of Hydrogen

“…Since these early fairly specific treatments, Larché and Cahn [17][18][19][20] systematically set about formulating a very general thermodynamic theory capable of rigorously accounting for the constraints imposed by a crystalline lattice (which they referred to as the lattice constraint) in a multicomponent coherent system. The thermodynamic equilibrium relationships were formulated in such a way that they were applied regardless of the operative diffusion mechanism.…”

Influence of chemical stresses in the permeation, one-side and two-side charging processes

“…On the other hand, stresses play a certain role in a diffusion process, which has also attracted many researchers. For example, Larche and Cahn 19,20 investigated the stress dependence of local diffusion flux in a solid. Chemical stresses are generated during diffusion, which, in turn, affect the diffusion process by affecting the diffusion coefficient.…”