# Mechanical stability and thermodynamic properties of GeP and [image] as battery anode materials from first principles

## TL;DR

This study compares different forms of germanium phosphide as potential battery anode materials, finding that GeP3 offers the best balance of mechanical and electronic properties for long-term battery performance.

## Contribution

The paper introduces a first-principles analysis of multiple GeP polymorphs and GeP3, revealing their mechanical and electronic properties for battery applications.

## Key findings

- GeP-cubic is mechanically unstable and unsuitable for practical use.
- GeP3 shows optimal mechanical stiffness and low elastic anisotropy, making it a promising anode material.
- GeP-tetragonal exhibits high stiffness but brittleness, which may limit its cycling durability.

## Abstract

The demand for high-capacity anode materials beyond conventional graphite has intensified research into alternative candidates for next-generation lithium-ion and sodium-ion batteries. Germanium phosphides emerge as promising materials, combining germanium’s high theoretical capacity with phosphorus’s structural versatility and potential for improved cycling stability. We employ first-principles density functional theory calculations to systematically investigate the mechanical, electronic, and thermodynamic properties of three GeP polymorphs (monoclinic, tetragonal, cubic) and rhombohedral \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {GeP}_{3}$$\end{document} as potential anode materials. Our comprehensive analysis reveals that polymorphism critically influences anode performance through distinct mechanical and electronic characteristics. GeP-cubic exhibits mechanical instability, rendering it unsuitable for practical applications. GeP-tetragonal shows the highest stiffness (bulk modulus 79.4 GPa, Young’s modulus 170.7 GPa) but pronounced brittleness (Pugh’s ratio K/G = 1.06), potentially limiting cycling durability. GeP-monoclinic offers greater mechanical compliance (bulk modulus 32.1 GPa) but suffers from extreme elastic anisotropy (universal anisotropy index A\documentclass[12pt]{minimal}
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\begin{document}$$_U$$\end{document} = 7.90), which may lead to non-uniform stress distribution and structural degradation during cycling. In contrast, \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {GeP}_{3}$$\end{document} demonstrates an optimal balance of properties with intermediate mechanical stiffness (bulk modulus 61.0 GPa, Young’s modulus 121.6 GPa), low elastic anisotropy (A\documentclass[12pt]{minimal}
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\begin{document}$$_U$$\end{document} = 0.77). Electronic structure calculations reveal metallic conductivity for GeP-tetragonal, GeP-cubic, and \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {GeP}_{3}$$\end{document}, ensuring efficient charge transport during battery operation. These findings establish \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {GeP}_{3}$$\end{document} as the most promising candidate among the studied materials, offering balanced mechanical resilience, thermal robustness, and isotropic properties essential for stable long-term cycling performance in practical battery applications.