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

Molecular Dynamics Study of Self-Diffusion in Zr

We employed a recently developed semi-empirical Zr potential to determine the diffusivities in the hcp and bcc Zr via molecular dynamics simulation. The point defect concentration was determined directly from MD simulation rather than from theoretical methods using T=0 calculations. We found that the diffusion proceeds via the interstitial mechanism in the hcp Zr and both the vacancy and interstitial mechanisms give contribution in diffusivity in the bcc Zr. The agreement with the experimental data is excellent for the hcp Zr and for the bcc Zr it is rather good at high temperatures but there is a considerable disagreement at low temperatures

A stochastic model and kinetic Monte Carlo simulation of solute interactions with stationary and moving grain boundaries. II. Application to 2D systems

In Part I of this work, we proposed a stochastic model describing solute interactions with stationary and moving grain boundaries (GBs) and applied it to planar GBs in 1D systems. The model reproduces nonlinear GB dynamics, solute saturation in the segregation atmosphere, and all basic features of the solute drag effect. Part II of this work extends the model to 2D GBs represented by solid-on-solid interfaces. The model predicts a GB roughening transition in stationary GBs and reversible dynamic roughening in moving GBs. The impacts of the GB roughening on GB migration mechanisms, GB mobility, and the solute drag are studied in detail. The threshold effect in GB dynamics is explained by the dynamic roughening transition, which is amplified in the presence of solute segregation. The simulation results are compared with the classical models by Cahn and L\"ucke-St\"uwe and previous computer simulations.Comment: Submitted to Physical Review Material

A stochastic model and kinetic Monte Carlo simulation of solute interactions with stationary and moving grain boundaries. I. Model formulation and application to 1D systems

A simple stochastic model of solute drag by moving grain boundaries (GBs) is presented. Using a small number of parameters, the model describes solute interactions with GBs and captures nonlinear GB dynamics, solute saturation in the segregation atmosphere, and the breakaway from the atmosphere. The model is solved by kinetic Monte-Carlo (KMC) simulations with time-dependent transition barriers. The non-Markovian nature of the KMC process is discussed. In Part I of this work, the model is applied to planar GBs driven by an external force. The model reproduces all basic features of the solute drag effect, including the maximum of the drag force at a critical GB velocity. The force-velocity functions obtained depart from the scaling predicted by the classical models by Cahn and L\"ucke-St\"uwe, which are based on more restrictive assumptions. The paper sets the stage for Part II, in which the GB will be treated as a 2D solid-on-solid interface.Comment: Submitted to Physical Review Material

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