# Predicting Superhard Materials via a Machine Learning Informed Evolutionary Structure Search

## TL;DR

This paper introduces a machine learning-guided evolutionary search method to predict and discover new superhard materials, successfully identifying 43 novel phases in the carbon system with potential hardness exceeding diamond.

## Contribution

It combines ML-based hardness estimation with evolutionary algorithms to efficiently discover stable superhard materials, advancing materials discovery techniques.

## Key findings

- Identified 43 new superhard carbon phases.
- Validated ML hardness predictions with experimental data.
- Discovered phases with hardness comparable to or exceeding diamond.

## Abstract

Good agreement was found between experimental Vickers hardnesses, $H_\text{v}$, of a wide range of materials and those calculated by three macroscopic hardness models that employ the shear and/or bulk moduli obtained from: (i) first principles via AFLOW-AEL (AFLOW Automatic Elastic Library), and (ii) a machine learning (ML) model trained on materials within the AFLOW repository. Because $H_\text{v}^\text{ML} $ values can be quickly estimated, they can be used in conjunction with an evolutionary search to predict stable, superhard materials. This methodology is implemented in the XtalOpt evolutionary algorithm. Each crystal is minimized to the nearest local minimum, and its Vickers hardness is computed via a linear relationship with the shear modulus discovered by Teter. Both the energy/enthalpy and $H_\text{v, Teter}^{\text{ML}}$ are employed to determine a structure's fitness. This implementation is applied towards the carbon system, and 43 new superhard phases are found. A topological analysis reveals that phases estimated to be slightly harder than diamond contain a substantial fraction of diamond and/or lonsdaleite.