A discrete nonlinear mass transfer equation with applications in solid-state sintering of ceramic materials

TL;DR

This paper introduces a nonlinear discrete mass transfer model for grain growth in materials, emphasizing the role of activation energy influenced by amorphization, validated through numerical simulations relevant to solid-state sintering.

Contribution

It presents a novel phenomenological model linking grain size evolution to amorphization-dependent activation energy, advancing understanding of sintering processes.

Findings

Activation energy impacts final grain size distribution

Numerical simulations confirm the model's predictions

Model captures complex grain growth dynamics

Abstract

The evolution of grain structures in materials is a complex and multiscale process that determines the material's final properties. Understanding the dynamics of grain growth is a key factor for controlling this process. We propose a phenomenological approach, based on a nonlinear, discrete mass transfer equation for the evolution of an arbitrary initial grain size distribution. Transition rates for mass transfer across grains are assumed to follow the Arrhenius law, but the activation energy depends on the degree of amorphization of each grain. We argue that the magnitude of the activation energy controls the final (sintered) grain size distribution, and we verify this prediction by numerical simulation of mass transfer in a one-dimensional grain aggregate.