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.

The Role of Interlayer Chemistry in Li‐Metal Growth through a Garnet‐Type Solid Electrolyte

“…Another possible factor that may affect the interfacial energy is the crystal structure of the final alloy state of the interlayer and its compatibility with crystalline lithium metal, which may create elastic strain energy. [60][61][62][63][64][65] Ichitsubo et al demonstrated that the strain accommodated by the aluminum matrix during lithium insertion significantly retards lithiation kinetics. [62] While determining the structure of the crystallographic interface between the lithium precipitate and the matrix alloy, as well as the corresponding strain field is not trivial, the strain energy is greatly influenced by the structure of the material; it is therefore likely that changes in the crystal structure of the alloy matrix change the precipitation energy barrier.…”

Modelling the chemo-mechanical responses of solid solutions far from equilibrium under heterogeneous stresses

“…As suggested in Gurtin et al (2010); Dal & Miehe (2015); Miehe et al (2016); Tsagrakis & Aifantis (2017), three primary fields govern the coupled chemo-mechanical responses of a solidspecies solution: the deformation field, the species concentrations, and the chemical po-tentials. Our description of a solid-species solution builds on the Larché-Cahn model of solids (Larché & Cahn, 1973, 1978a, 1984, 1978b. This model defines the relative chemical potential as a result of the Larché-Cahn derivative (Gurtin et al, 2010;Larché & Cahn, 1973).…”

“…When a new species grows and nucleates the solid network must accounts for the lattice misalignment between the phases. According to Larché & Cahn (1973, 1978a, 1984, 1978b, the growth and nucleation of new phases require describing non-coherent phase transitions by defining a crystalline structure and proper orientations of the mechanical properties for each phase. In our framework, the mass transport and the nucleation and growth of new species induced by chemical reactions generate elastic strains.…”

“…The thermodynamic pressure is defined as the negative variation of the Helmholtz free-energy with respect to the volumetric variations, that is, p th = −∂Ψ/∂v. In general at steady state, this thermodynamic pressure may be spatially inhomogeneous which implies that the system reaches equilibrium under non-hydrostatic stresses (Larché & Cahn, 1973, 1978a, 1984, 1978b.…”

Shot-Peening of Pre-Oxidized Plates of Zirconium: Influence of Residual Stress on Oxidation

“…Experimental findings have been widely documented. A first theoretical base for the coupling between stress and diffusion based on thermodynamics was proposed by Larché and Cahn [2,3] and includes the influence of the stress gradient on the interstitial diffusion. More recently [4][5][6][7][8][9][10][11][12], studies have developed the thermodynamic model and have completed the dependence of the diffusion with respect to the stress gradient and stress values.…”