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.

#2Perry H. Leo(UMN: University of Minnesota)H-Index: 24

We consider the loss of lattice coherence at a planar interface between a thin film and substrate. Coherence is determined locally at the interface by a relative deformation gradient at the interface. We construct an interfacial free energy density fxs such that a fully coherent interface is a global minimizer fxs, and there are symmetry related local minima of fxs corresponding to line defects at the interface. By considering both the interfacial energy and the elastic energy of the film, we ca...

A front-tracking, finite difference approach has been used to examine the influence of misfit strain and applied stress on interdiffusion in binary, coherent, two-phase planar diffusion couples assuming local thermodynamic equilibrium at the interface. The phases are cubic; possess different lattice parameters, elastic constants, and diffusivities; and can be oriented in either the [001] or [111] direction. Interface compositions, which are time independent in the stress-free case, become time d...

Abstract The effects of elastic stress on the spatial distribution and morphology of misfitting particles during coarsening in an elastically anisotropic system are examined. No assumptions are made on the morphology of the particles; they evolve in a manner consistent with the diffusion and elastic fields in the system. Through these calculations we have identified the microstructural signature of elastic-stress induced particle migration. In addition, we find that elastic stress leads not only...

Abstract We develop a general thermodynamical description of an evolving interface appropriate to situations far from equilibrium. The theory represents a broad departure from theories based on classical nonequilibrium thermodynamics, as we do not assume a linear relationship between fluxes and forces, and we do not limit our theory to small departures from equilibrium. Further, we allow for diffusion in the bulk material; we allow the composition of material transferred across the interface to ...

We develop the thermodynamic theory for the decomposition of a ``coherent`` two-phase open system consisting of an interstitial solid solution in equilibrium with a gas reservoir of solute atoms. It is shown that, contrary to what is expected for incoherent systems, the phase rule is inapplicable and the ``plateau`` on the pressure-composition isotherm does not correspond to two coexisting phases. The coherency strain introduces an unsurmountable macroscopic energy barrier between the transformi...

#2Julia Slutsker(UMD: University of Maryland, College Park)H-Index: 17

A crystal which can be in two possible phase states is considered. During tensile extension the crystal is deformed elastically. After a certain amount of elastic strain a phase transformation begins. For each fixed level of strain an equilibrium mesostructure is established, which corresponds to a minimum in the free energy of the crystal. The equilibrium mesostructure consists of plane, parallel layers of a product phase separated by layers of an initial phase. The product phase itself consist...

#1Zi Kui Liu(KTH: Royal Institute of Technology)H-Index: 79

#2John Ågren(KTH: Royal Institute of Technology)H-Index: 61

The two types of phase equilibria, the normal unconstrained one and the constrained one, and their thermodynamics are discussed. The concepts of potential and phase rule, which have recently been discussed in the literature, are reconsidered, and their formal definitions are analyzed in some detail. It is realized that in the unconstrained equilibrium system, the properly defined chemical potentials of all components must be constant across the phase interface in both the hydrostatically and non...

The conditions for thermodynamic equilibrium in two-phase, multicomponent, elastically stressed ionic crystals are derived within the realm of phenomenological thermodynamics using a Gibbsian variational approach. Equilibria between a stressed ionic crystal and a fluid and between two elastically stressed crystals possessing a coherent interface are examined, and an expression for the dependence of the electrochemical potential on stress is derived. The equilibrium conditions are used to calcula...

Abstract Recent investigations on coherent equilibria have shed much light on the nature of phase stability. For example, equilibrium phase concentrations are shown to depend on the alloy composition, and two-phase coexistence can terminate at a critical coherency strain, termed a Williams point. This work, however, presents that when lattice parameter, hence coherency strain, is taken to be a function of phase composition, Williams point can disappear, i.e. the two-phase termination occurs only...

#1Perry H. Leo(UMN: University of Minnesota)H-Index: 24

#2Herng Jeng Jou(UMN: University of Minnesota)H-Index: 1

Abstract The diffusional growth of a precipitate transforming under applied stress is analyzed to determine the shape evolution of the precipitate. The analysis is based on linearizing the precipitate shape about a circle. Because of applied stresses, a circle is a stable shape only when the shear moduli of the precipitate and the surrounding matrix are identical. Otherwise, one finds a non-circular base shape that depends on the applied stress and the elastic constants of both phases. For small...

#2S. Esmizadeh(UI: University of Isfahan)H-Index: 2

Abstract null null Although continuum frameworks have been developed in the past for studying how material defects behave in solid solutions, recent studies have demonstrated that the self-stress field of the solutes which enter the chemical potential in the prevalent continuum models must be excluded, and instead the image stresses included, in a correct treatment. Here, working within the framework of Gibbs canonical ensemble of statistical mechanics, and accounting for the image stresses of t...

Abstract Nanomaterials are now well established as a distinct class of materials. Among them, the nanoparticles of metals and alloys constitute an important subclass that has attracted wide attention from the point of view of scientific understanding and wide domain of potential applications. The present review primarily deals with alloy nanoparticles or nanoalloys containing more than one element having single or multiphase microstructure. Both free, as well as embedded alloy nanoparticles, wil...

The complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells are discussed in more detail. They are formulated from restrictions i...

Last. Robert J. Kee(Colorado School of Mines)H-Index: 60

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This paper reports an extended Nernst-Planck computational model that couples charged-defect transport and stress in tubular electrochemical cell with a ceramic proton-conducting membrane. The model is particularly concerned with coupled chemo-mechanical behaviors, including how electrochemical phenomena affect internal stresses and vice versa. The computational model predicts transient and steady-state defect concentrations, fluxes, stresses within a thin BaZr0.8Y0.2O3-δ (BZY20) membrane. Depen...

In this paper, we discuss a theoretical approach to morphological instability analysis of the coherent interphase boundaries in strained heterostructures. Taking into account the fact that, under certain conditions, the atomic arrangement of solid–solid interfaces is thermodynamically unstable, the evolution equation describing the kinetics of the relief formation is obtained. The considered process is controlled by interface diffusion activated by the nonuniform stress field which occurs due to...

Last. Congkang Xu(STU: Shantou University)H-Index: 2

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Based on the network model and the regular solution model, the equilibrium surface and interface segregations are investigated for the Ni(111)2 at%(Au) nano-films under diffusion-induced stress and intrinsic stress. The size effect with respect to the film thickness, the interlayer interactions and the heteroepitaxial strain in the film are taken into account. The equilibrium layer concentration in the film with the lowest Gibbs free energy of the system is obtained according to the coordinate d...

Abstract Phase separation arises in many materials systems as a result of solute intercalation. It is in particular known that the mechanical stresses resulting from phase separation in lithium-ion batteries can be large enough to cause formation of a variety of defects and degradation of the host electrode upon cycling. Fracture mechanics models have been previously developed for identifying the critical conditions which lead to the growth of a pre-existing crack in two-phase electrode particle...