Quantitative descriptor of lattice anharmonicity in crystal

<sec>Anharmonic effect is often one of the physical root causes of some special material properties, such as soft mode phase transition, negative thermal expansion, multiferroicity, and ultra-low thermal conductivity. However, the existing methods of quantifying the anharmonicity of material do not give a clear and accurate anharmonicity descriptor. The calculation of the anharmonic effect requires extremely time-consuming molecular dynamics simulation, the calculation process is complex and costly. Therefore, a quantitative descriptor is urgently needed, which can be used to implement quick calculation so as to understand, evaluate, design, and screen functional materials with strong anharmonicity.</sec><sec>In this paper, we propose a method to quantify the anharmonicity of materials by only phonon spectrum and static self-consistent calculation through calculating and analyzing the material composed of germanium and its surrounding elements. In this method, the lattice anharmonicity is decomposed into the anharmonic contribution of independent phonon vibration modes, and the quantitative anharmonicity descriptor <inline-formula><tex-math id="M3">\begin{document}$ {\sigma }_{\boldsymbol{q},j}^{A} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M3.png"/></alternatives></inline-formula> of phonons is proposed. Combining it with the Bose-Einstein distribution, the quantitative descriptor <inline-formula><tex-math id="M4">\begin{document}$ {A}_{{\mathrm{p}}{\mathrm{h}}}\left(T\right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M4.png"/></alternatives></inline-formula> of temperature-dependent material anharmonicity is proposed. We calculate the bulk moduli and lattice thermal conductivities at 300 K of nine widely representative materials. There is a clear linear trend between them and our proposed quantitative descriptor <inline-formula><tex-math id="M5">\begin{document}$ {A}_{{\mathrm{p}}{\mathrm{h}}}\left(T\right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231428_M5.png"/></alternatives></inline-formula>, which verifies the accuracy of our proposed descriptor. The results show that the descriptor has the following functions. i) It can systematically and quantitatively classify materials as the strength of anharmonicity; ii) it intuitively shows the distribution of the anharmonic effect of the material on the phonon spectrum, and realizes the separate analysis of the phonon anharmonicity that affects the specific properties of the material; iii) it is cost-effective in first-principles molecular dynamics calculations and lays a foundation for screening and designing materials based on anharmonicity.</sec><sec>This study provides an example for the high-throughput study of functional materials driven by anharmonic effect in the future, and opens up new possibilities for material design and application. In addition, for strongly anharmonic materials such as CsPbI₃, the equilibrium position of the atoms is not fixed at high temperatures, resulting in a decrease in the accuracy of quantifying anharmonicity using our proposed descriptor. In order to get rid of this limitation, our future research will focus on the distribution of atomic equilibrium positions in strongly anharmonic materials at high temperatures, so as to propose a more accurate theoretical method to quantify the anharmonicity in strongly anharmonic materials.</sec>