Thermochemical equilibrium of multiphase solids under stress

Lärché, F.; Cahn, John W.

doi:10.1016/0001-6160(78)90067-6

Cited by 228 publications

(154 citation statements)

References 7 publications

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“…In other words, a coherent grain boundary is capable of supporting a static shear stress parallel to its plane. 13,14,18 The condition preventing grain boundary migration now reads…”

Section: Equilibrium Conditionsmentioning

confidence: 99%

Sharp interface model of creep deformation in crystalline solids

2015

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We present a rigorous irreversible thermodynamics treatment of creep deformation of solid materials with interfaces described as geometric surfaces capable of vacancy generation and absorption and moving under the influence of local thermodynamic forces. The free energy dissipation rate derived in this work permits clear identification of thermodynamic driving forces for all stages of the creep process and formulation of kinetic equations of creep deformation and microstructure evolution. The theory incorporates capillary effects and reveals the different roles played by the interface free energy and interface stress. To describe the interaction of grain boundaries with stresses, we classify grain boundaries into coherent, incoherent and semi-coherent, depending on their mechanical response to the stress. To prepare for future applications, we specialize the general equations to a particular case of a linear-elastic solid with a small concentration of vacancies.The proposed theory creates a thermodynamic framework for addressing more complex cases, such as creep in multi-component alloys and cross-effects among vacancy generation/absorption and grain boundary motion and sliding.

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“…In other words, a coherent grain boundary is capable of supporting a static shear stress parallel to its plane. 13,14,18 The condition preventing grain boundary migration now reads…”

Section: Equilibrium Conditionsmentioning

confidence: 99%

Sharp interface model of creep deformation in crystalline solids

2015

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“…As discussed in Section II B (see also Part I), 3 the product γA appearing in the adsorption equations (6) and (10) is the total free energy of a GB patch within a selected region containing a fixed set of lattice sites. During the lateral deformations described by the strain tensor de ij , those lattice sites are conserved and are only stretched and/or sheared elastically parallel to the GB plane.…”

Section: The Lagrangian and Physical Forms Of The Adsorption Equationmentioning

confidence: 99%

“…The lateral dimensions of the system are also varied due to the compositional strain. 6,7,34 For this path, the integrated form of Eq. (6) is…”

Section: B Pure Cu At Finite Temperaturesmentioning

confidence: 99%

Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

Frolov

Mishin

2012

Phys. Rev. B

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The thermodynamic theory of coherent interfaces developed in Part I of this work is applied to grain boundaries (GBs) subject to non-hydrostatic elastic deformations. We derive expressions for the GB free energy as the reversible work of GB formation under stress. We also present a generalized adsorption equation whose differential coefficients define the GB segregation, GB stress tensor, GB excess volume, and GB excess shear. The generalized adsorption equation generates a set of Maxwell relations describing cross-effects between different GB properties. The theory is applied to atomistic simulations of a symmetrical tilt GB in Cu and Cu-Ag alloys.Using a combination of molecular dynamics and Monte Carlo methods, we compute a number of GB excess quantities and their dependencies on the applied stresses, temperature and chemical composition in the grains.We also test several Maxwell relations and obtain excellent agreement between the theory and simulations.

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“…Hillert avoids the difficulty by requiring only the solute chemical potential to be continuous, but in order to treat alloys of arbitrary composition one would like to have a theory that treats both species of atom in the same way. In the present theory, there is no liquid layer and no phase equilibrium, and so neither chemical potential need be continuous; what does have to be continuous is the diffusion potential of Larché and Cahn [12][13][14]. For interstitial alloys, the diffusion potential is equal to the solute chemical potential so that our continuity condition is equivalent to the one used by Hillert, but for substitutional alloys the diffusion potential is equal to the difference between the chemical potentials of the two species of atom.…”

Section: Introductionmentioning

confidence: 93%

“…where Y + is the value of Y in front of the grain boundary, defined by using the elastic constants for the shrinking grain in (13).…”

Section: µ(C(vt − 0)) = µ(C(vtmentioning

confidence: 99%

On the elastic driving force in diffusion-induced grain boundary motion

Penrose

2004

Acta Materialia

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In 1983 Hillert obtained the formula Y η 2 (c + −c − ) 2 for the driving force per unit area of grain boundary arising from elastic misfit in an isotropic alloy, where the mole fractions c + and c − on the two sides of the grain boundary are small, η is a measure of the elastic misfit and Y = E/(1 − ν) where E is Young's modulus and ν is Poisson's ratio. It is shown here that the formula is still valid (with suitably defined Y, η) when c + , c − are not small. The formula for Y in a general anisotropic solid is given. The physical origin of the elastic force on the grain boundary is considered, with help from the 'energy-momentum tensor' devised by Eshelby to quantify the forces on other crystal imperfections such as dislocations. The theory also makes a prediction about the direction of motion of an initially stationary grain boundary.

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Thermochemical equilibrium of multiphase solids under stress

Cited by 228 publications

References 7 publications

Sharp interface model of creep deformation in crystalline solids

Sharp interface model of creep deformation in crystalline solids

Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

On the elastic driving force in diffusion-induced grain boundary motion

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