Related papers: A discrete nonlinear mass transfer equation with a…
We study a nonlinear kinetic model of mass exchange between interacting grains. The transition rates follow the Arrhenius equation with an activation energy that depends on the grain mass. We show that the activation parameter can be…
Non-Arrhenius grain growth has been observed in a range of polycrystalline materials; however, its fundamental mechanisms, particularly whether the process is thermally activated or exhibits anti-thermally activation, remain controversial.…
A formula of grain growth rate, based on a nonlinear capillarity-driven relation, is derived to predict and interpret realistic growth processes in polycrystalline systems. The derived formula reveals how the growth and stagnation of grains…
We determine the non-equilibrium grain size distribution during the crystallization of a solid in $d$ dimensions at fixed thermodynamic conditions, for the random nucleation and growth model, and in absence of grain coalescence. Two…
The size distribution of grains is a fundamental characteristic of polycrystalline solids. In the absence of deformation, the grain-size distribution is controlled by normal grain growth. The canonical model of normal grain growth,…
Sintering is a pivotal technology for processing ceramic and metallic powders into solid objects. A profound understanding of microstructure evolution during sintering is essential for manufacturing products with tailored properties. While…
We study the time dependence of the grain size distribution N(r,t) during crystallization of a d-dimensional solid. A partial differential equation including a source term for nuclei and a growth law for grains is solved analytically for…
The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under…
Volume shrinkage, grain growth, and their interaction are major events occurring during free sintering of ceramics. A high temperature sintering dilatometry curve is influenced by these both phenomena. It is shown that the continuum theory…
The dynamical mechanisms underlying the grain evolution and growth are of fundamental importance in controlling the structural properties of large-scale polycrystalline materials, but the effects of lattice ordering and distinct atomic…
This paper investigates the statistical behavior of two-dimensional grain microstructures during grain growth under anisotropic grain boundary characters. We employ the threshold-dynamics method, which allows for unparalleled computational…
A continuum grain boundary model is developed that uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a 1-D grain array. The model uses a continuum…
Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its…
Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth…
Particle coarsening and grain growth take place to minimize the total interfacial energy. The classical mean-field treatments by Lifshitz, Slyozov, [1] Wagner [2] and Hillert [3] predicted cubic growth law under bulk-diffusion controlled…
We revisit the evolution model of grain size distribution in a galaxy for the ultimate purpose of implementing it in hydrodynamical simulations. We simplify the previous model in such a way that some model-dependent assumptions are replaced…
We present several numerical results on granular mixtures. In particular, we examine the efficiency of diffusion as a mixing mechanism in these systems. The collisions are inelastic and to compensate the energy loss, we thermalize the…
We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of…
The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general…
We investigated the effective influence of grain structures on the heat transfer between a fluid and solid domain using mathematical homogenization. The presented model consists of heat equations inside the different domains, coupled…