# Effect of shear-coupled grain boundary motion on coherent precipitation

## TL;DR

This paper investigates how shear-coupled grain boundary motion influences the interaction with coherent precipitates, affecting elastic energy and solubility limits, with analytical and numerical methods applied to the Fe-C system.

## Contribution

It provides a new analytical framework for understanding the elastic energy interactions between shear-coupled grain boundaries and precipitates.

## Key findings

- Elastic energy interactions can reduce total energy near grain boundaries.
- Grain boundary shape and solubility limits are affected by precipitate interactions.
- Application to Fe-C system predicts changes in cementite solubility near boundaries.

## Abstract

We examine the interaction between precipitates and grain boundaries, which undergo shear-coupled motion. The elastic problem, emerging from grain boundary perturbations and an elastic mismatch strain induced by the precipitates, is analysed. The resulting free elastic energy contains interaction terms, which are derived numerically via the integration of the elastic energy density. The interaction of the shear-coupled grain boundary and the coherent precipitates leads to potential elastic energy reductions. Such a decrease of the elastic energy has implications on the grain boundary shape and also on the solubility limit near the grain boundary. By energy minimisation we are able to derive the grain boundary shape change analytically. We apply the results to the Fe-C system to predict the solubility limit change of cementite near an $\alpha$-iron grain boundary.