Unveiling the role of high-order anharmonicity in thermal expansion: A first-principles perspective

Thermal expansion is crucial for various industrial processes and is increasingly the focus of research endeavors aimed at improving material performance. However, it is the continuous advancements in first-principles calculations that have enabled researchers to understand the microscopic origins of thermal expansion. In this study, we propose a coefficient of thermal expansion (CTE) calculation scheme based on self-consistent phonon theory, incorporating the fourth-order anharmonicity. We selected four structures (Si, CaZrF₆, SrTiO₃, NaBr) to investigate high-order anharmonicity’s impact on their CTEs, based on bonding types. The results indicate that our method goes beyond the second-order quasi-harmonic approximation and the third-order perturbation theory, aligning closely with experimental data. Furthermore, we observed that an increase in the ionicity of the structures leads to a more pronounced influence of high-order anharmonicity on CTE, with this effect primarily manifesting in variations of the Grüneisen parameter. Our research provides a theoretical foundation for accurately predicting and regulating the thermal expansion behavior of materials.