Mechanical stability and thermodynamic properties of GeP and $$\hbox {GeP}_{3}$$ as battery anode materials from first principles

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 [Formula: see text] 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[Formula: see text] = 7.90), which may lead to non-uniform stress distribution and structural degradation during cycling. In contrast, [Formula: see text] 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[Formula: see text] = 0.77). Electronic structure calculations reveal metallic conductivity for GeP-tetragonal, GeP-cubic, and [Formula: see text], ensuring efficient charge transport during battery operation. These findings establish [Formula: see text] 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.