A discrete nonlinear mass transfer equation with applications in solid-state sintering of ceramic materials
Department of Mineral Resources Engineering Technical, University of Crete, Chania, 73100, Greece
Revised: 24 November 2005
Published online: 8 February 2006
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.
PACS: 81.07.Bc – Nanocrystalline materials / 81.10.Aj – Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation / 81.20.Ev – Powder processing: powder metallurgy, compaction, sintering, mechanical alloying, and granulation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006