A Mathematical Model for Flash Sintering

TL;DR

This paper develops a mathematical model for flash sintering in ceramics, focusing on Joule heating and temperature-dependent conductivity, to understand conditions leading to rapid sintering via thermal runaway.

Contribution

It introduces a simplified mathematical framework to analyze how electrical and thermal factors cause flash sintering, highlighting the role of thermal runaway conditions.

Findings

Thermal runaway is necessary for flash sintering.

Different reaction terms influence stability and runaway.

Conditions for incipient thermal runaway are identified.

Abstract

A mathematical model is presented for the Joule heating that occurs in a ceramic powder compact during the process of flash sintering. The ceramic is assumed to have an electrical conductivity that increases with temperature, and this leads to the possibility of runaway heating that could facilitate and explain the rapid sintering seen in experiments. We consider reduced models that are sufficiently simple to enable concrete conclusions to be drawn about the mathematical nature of their solutions. In particular we discuss how different local and non-local reaction terms, which arise from specified experimental conditions of fixed voltage and current, lead to thermal runaway or to stable conditions. We identify incipient thermal runaway as a necessary condition for the flash event, and hence identify the conditions under which this is likely to occur.