arXiv subjects

Y. Mishin

Publications and source records attributed to Y. Mishin.

25 records · Page 2Linked to original sources

arXiv2015

Thermodynamic theory of equilibrium fluctuations

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.

cond-mat.stat-mech↗

arXiv2013

Calculation of the gamma/gamma' interface free energy in the Ni-Al system by the capillary fluctuation method

Monte Carlo computer simulations with an embedded-atom potential are applied to study coherent gamma/gamma' interfaces in the Ni-Al system. The (100) interface free energy has been extracted from the power spectrum of equilibrium shape fluctuations (capillary waves) and found to decrease with temperature from about 20 mJ/m2 at 550 K to about 10 mJ/m2 at 1200 K. These numbers are in reasonable agreement with existing experimental data. Strengths and disadvantages of the capillary wave method are discussed.

cond-mat.mtrl-sci↗

arXiv2013

Irreversible thermodynamics of creep in crystalline solids

We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-hydrostatically stressed multi-component solid medium with non-conserved lattice sites and inhomogeneities handled by employing gradient thermodynamics. Phase fields describe microstructure evolution which gives rise to redistribution of vacancy sinks and sources in the material during the creep process. We derive a general expression for the entropy production rate and use it to identify of the relevant fluxes and driving forces and to formulate phenomenological relations among them taking into account symmetry properties of the material. As a simple application, we analyze a one-dimensional model of a bicrystal in which the grain boundary acts as a sink and source of vacancies. The kinetic equations of the model describe a creep deformation process accompanied by grain boundary migration and relative rigid translations of the grains. They also demonstrate the effect of grain boundary migration induced by a vacancy concentration gradient across the boundary.

cond-mat.mtrl-sci↗

arXiv2013

Effect of interface phase transformations on diffusion and segregation in high-angle grain boundaries

Recent experimental measurements of Ag impurity diffusion in the Σ5 (310) grain boundary (GB) in Cu revealed an unusual non-Arrhenius behavior suggestive of a possible structural transformation [Divinski et al., Phys. Rev. B 85, 144104 (2012)]. On the other hand, atomistic computer simulations have recently discovered phase transformations in high-angle GBs in metals [Frolov et al., arXiv:1211.1756v2 (2013)]. In this paper we report on atomistic simulations of Ag diffusion and segregation in two different structural phases of the Cu Σ5 (310) GB which transform to each other with temperature. The obtained excellent agreement with the experimental data validates the hypothesis that the unusual diffusion behavior seen in the experiment was caused by a phase transformation. The simulations also predict that the low-temperature GB phase exhibits a monolayer segregation pattern while the high-temperature phase features a bilayer segregation. Together, the simulations and experiment provide the first convincing evidence for the existence of structural phase transformations in high- angle metallic GBs and demonstrate the possibility of their detection by GB diffusion measurements and atomistic simulations.

cond-mat.mtrl-sci↗

arXiv2013

Thermodynamics of coherent interfaces under mechanical stresses. I. Theory

We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using chemical potentials and diffusion potentials, respectively. All interface excess quantities are derived using Cahns (1979) generalized excess method without resorting to geometric dividing surfaces. We present expressions for the interface free energy as an excess quantity and derive a generalized adsorption equation and an interface Gibbs-Helmholtz equation that does not contain the interface entropy. The interface stress tensor emerges naturally from the generalized adsorption equation as an appropriate excess over bulk stresses and is shown to be generally nonunique. Another interface property emerging from the generalized adsorption equation is the interface excess shear. This property is specific to coherent interfaces and represents the thermodynamic variable conjugate to the shear stress applied parallel to the interface. The theory reveals a number of Maxwell relations describing cross effects between thermal, chemical, and mechanical responses of coherent interfaces. In Part II of this work, this theory will be applied to atomistic computer simulations of grain boundaries.

cond-mat.mtrl-sci↗

arXiv2012

Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulations

Previous simulation and experimental studies have shown that some grain boundaries (GBs) can couple to applied shear stresses and be moved by them, producing shear deformation of the lattice traversed by their motion. While this coupling effect has been well confirmed for symmetrical tilt GBs, little is known about the coupling ability of asymmetrical boundaries. In this work we apply a combination of molecular dynamics and phase field crystal simulations to investigate stress-driven motion of asymmetrical GBs between cubic crystals over the entire range of inclination angles. Our main findings are that the coupling effect exists for most of the asymmetrical GBs and that the coupling factor exhibits a non-trivial dependence on both the misorientation and inclination angles. This dependence is characterized by a discontinuous change of sign of the coupling factor, which reflects a transition between two different coupling modes over a narrow range of angles. Importantly, the magnitude of the coupling factor becomes large or divergent within this transition region, thereby giving rise to a sliding-like behavior. Our results are interpreted in terms of a diagram presenting the domains of existence of the two coupling modes and the transition region between them in the plane of misorientation and inclination angles. The simulations reveal some of the dislocation mechanisms responsible for the motion of asymmetrical tilt GBs. The results of this study compare favorably with existing experimental measurements and provide a theoretical ground for the design of future experiments.

cond-mat.mtrl-sci↗

arXiv2003

Interatomic potentials for atomistic simulations of the Ti-Al system

Semi-empirical interatomic potentials have been developed for Al, alpha-Ti, and gamma-TiAl within the embedded atomic method (EAM) by fitting to a large database of experimental as well as ab-initio data. The ab-initio calculations were performed by the linear augmented plane wave (LAPW) method within the density functional theory to obtain the equations of state for a number of crystal structures of the Ti-Al system. Some of the calculated LAPW energies were used for fitting the potentials while others for examining their quality. The potentials correctly predict the equilibrium crystal structures of the phases and accurately reproduce their basic lattice properties. The potentials are applied to calculate the energies of point defects, surfaces, planar faults in the equilibrium structures. Unlike earlier EAM potentials for the Ti-Al system, the proposed potentials provide reasonable description of the lattice thermal expansion, demonstrating their usefulness in the molecular dynamics or Monte Carlo studies at high temperatures. The energy along the tetragonal deformation path (Bain transformation) in gamma-TiAl calculated with the EAM potential is in a fairly good agreement with LAPW calculations. Equilibrium point defect concentrations in gamma-TiAl are studied using the EAM potential. It is found that antisite defects strongly dominate over vacancies at all compositions around stoichiometry, indicating that gamm-TiAl is an antisite disorder compound in agreement with experimental data.

cond-mat.mtrl-sci↗