# Ab Initio Investigation Of Phosphorus And Hydrogen Co-segregation And Embrittlement In {\alpha}-fe Twin Boundaries

## TL;DR

This paper introduces a new statistical physics model to analyze how phosphorus and hydrogen co-segregate at grain boundaries in alpha-iron and how this affects embrittlement, using atomistic calculations for parameters.

## Contribution

The study develops a general, efficient model for solute segregation at grain boundaries that incorporates multiple species, sites, and entropy, applied specifically to P-H co-segregation in alpha-Fe.

## Key findings

- P-H interactions increase phosphorus segregation at grain boundaries.
- Co-segregation of P and H leads to greater embrittlement than individual segregation.
- The model accurately predicts segregation behavior using parameters from density-functional theory.

## Abstract

We propose a new statistical physics model to study equilibrium solute segregation at grain boundaries and the resulting embrittlement effect. This low-temperature expansion model is general and efficient, and its parameters can be obtained from atomistic calculations. It is possible to take into account multiple species, multiple segregation sites with different segregation free energies, account for configurational entropy, grain radius and site competition between solutes. As an example, the model is then applied to the study of phosphorus and hydrogen co-segregation at $\Sigma3$ $109.5\deg[0\bar{1}1]\{111\}$ twin boundaries in $\alpha$-Fe, using energetic parameters from density-functional theory calculations. We show that P--H interactions may lead to increased P segregation at grain boundaries and cause additional embrittlement compared to the case where P and H are considered separately.