Structural chemistry based analytical model for mechanical, acoustic, and thermal property predictions

Opposites attract and likes repel is a universal law in nature, with electromagnetic interactions being the most ingrained in our minds, such as the interaction between positive and negative poles, and the North and South Poles... In the microscopic world of atoms and molecules, electromagnetic forces provide a stable mechanical system for the interactions between a series of fundamental units such as elementary particles, molecules, and proteins. These basic units combine in different structures to form matter, exhibiting a variety of physical and chemical properties, thereby constructing a rich diversity of functionalities.

The geometric method based on point groups and space groups is one of the important methodologies in material development, and now nearly a million structural data have been collected in the ICSD and CCDC databases. However, the understanding of the functionality of these structures is far behind (for example, only 5,000 thermal conductivity data have been collected), mainly because: the algebraic method based on classical mechanics and quantum mechanics gives an overly complex energy expression, making first-principles calculations require a lot of computing power, and machine learning requires a large amount of (accurate) experimental samples. This greatly increases the difficulty of developing functional materials.

In response to this issue, the research team of Tongji University, starting from electrostatic interactions and based on the structural chemical information of materials to simplify the potential energy expression, proposed an analytical model for predicting the mechanical, acoustic, and thermal properties of crystal materials. The relevant research was published in the National Science Review (the full text link is https://doi.org/10.1093/nsr/nwae269). This study is led by Dr. Zhiwei Chen (School of Materials Science and Engineering, Tongji University) and Dr. Yanzhong Pei (School of Materials Science and Engineering, Tongji University.

To obtain the analytical expression, the model involves the following approximations and steps: 1. According to the difference and average value of the electronegativity of elements/groups, one chemical bond is decomposed into ionic, covalent, and metallic components; 2. Under the adiabatic approximation, the ionic core is a stationary point charge, and the potential energy between ionic cores is the Coulomb potential; 3. Learning from the hydrogen molecule ion, the Coulomb/exchange/overlap integrals are replaced with analytical functions E± with similar mathematical forms; 4. Based on the equilibrium conditions, the structural factor β is obtained from the known average bond length; 5. The net charge of the ionic core is obtained according to the composition elements and their coordination environment. Finally, the analytical form of the interaction potential energy for a specific material is confirmed.

Taking the first, second, and third derivatives of the potential energy (U) with respect to the interatomic distance (r) can respectively obtain the mechanical, acoustic, and thermal properties. For example, the relationship between force and atomic distance corresponds to the macroscopic stress-strain curve, reflecting the elastic modulus and theoretical maximum fracture strength. The Grüneisen parameter is the ratio of the third derivative to the second derivative. Combined with the Boltzmann transport equation, the lattice thermal conductivity can be obtained. Performance prediction results show that the properties of dozens of materials can be well predicted. The above predictions can be quickly solved by Excel.

This model can further be used to analyze the impact of structural chemical factors on mechanical, acoustic, and thermal properties. Taking the nature of chemical bonds as an example, the competition between ionicity and covalency makes an additional contribution to bond strength, leading to a minimum value of elastic modulus; pressure increases the overlap of valence electron orbits and the covalency of chemical bonds, significantly improving sound speed; ionicity in chemical bonds promotes long-range electrostatic interactions, enhancing the anharmonicity of the crystal.

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