Sintering behavior of two roughened crystals just after contact

TL;DR

This paper models the initial sintering process of two roughened spherical crystals by deriving new scaling laws for neck growth over time, considering both bulk and surface diffusion limited kinetics.

Contribution

It introduces a novel geometric approximation and analytical solutions for the early-stage sintering of roughened crystals, providing new scaling laws for neck growth.

Findings

Neck size scales as t^{1/4} in bulk diffusion limited sintering.

Neck size scales as t^{1/3} in surface diffusion limited sintering.

Post-contact geometry can be approximated by a two-dimensional slot-shaped cavity.

Abstract

We consider two spherical, roughened crystals with approximately isotropic surface free energy which are brought into contact and begin to sinter. We argue that the geometry immediately post-contact is two dimensional and Cartesian and can be approximated by the evolution of a slot-shaped cavity. On this basis, we construct travelling wave solutions for the crystal shape in the limits of bulk diffusion limited and surface diffusion limited kinetics. These solutions are then used to calculate novel scalings for the neck size as a function of time $t$ after contact: We predict that neck size is proportional to $t^{1/4}$ for the bulk diffusion limited case and (following a single pinch-off event) approximately proportional to $t^{1/3}$ for the surface diffusion limited case.