基于物理模型的BaZrO_(3)钙钛矿机器学习力场

Investigation of a physical model-based machine-learning force field for BaZrO_(3)perovskite

钙钛矿已经作为高性能航空发动机热障涂层陶瓷的备选材料之一。其在高温、高压和辐照等复杂环境中原子间的相互作用往往非常复杂。经验力场仅考虑了原子间的两体、三体或四体等相互作用,物理假设过于简单,对于复杂环境的势能面往往难以精确描述。机器学习力场能获得远比经验力场准确的势能面。本文采用机器学习方法,针对最常见的钙钛矿氧化物锆酸钡(BaZrO_(3)),提出了基于物理模型的机器学习力场,用来描述BaZrO_(3)这种典型钙钛矿的静态性质、相稳定性和力学性质。使用密度泛函理论数据库训练了基于物理模型的机器学习力场,计算了静态性质、相稳定性和力学性质。对于静态性质,使用纯机器学习力场和基于物理模型的机器学习力场计算了弹性常数C11、C12和C44,模拟结果与DFT相比,前者的误差为0.34%、8.75%和10.71%,后者的误差为0.34%、2.5%和7.14%,远优于经验力场。对于相稳定性,发现基于物理模型的机器学习力场继承了经验力场在维持相稳定性方面的优势,优于纯机器学习力场。对于力学性能,计算了BaZrO_(3)的四个不同晶向的杨氏模量,发现机器学习力场和基于物理模型的机器学习力场的计算结果与试验值的误差分别为9.22%和1.6%,远低于经验力场的结果。可见,将物理模型融入机器学习力场开发是提升原子模拟精准度的重要途径。

Interatomic potential is a key component of large-scale atomic simulation of materials.For scientific problems in complex environments such as high temperature,high pressure and irradiation,the interactions between atoms are often very complex.The empirical force field only considers two-body,three-body or four-body interactions between atoms.The physical assumption is simple,and it is often difficult to accurately describe the potential energy surface of complex environment.Machine learning force fields can obtain potential energy surfaces that are more accurate than empirical force fields.In this paper,a machine learning force field based on physical model is proposed for BaZrO_(3),the most common perovskite system,to describe the static properties,phase stability and mechanical properties of BaZrO_(3).The density functional theory database is used to train the machine learning force field based on physical model,and the static properties,phase stability and mechanical properties are calculated.For the static properties,the elastic constants C11,C12 and C44 were computed using both a pure machine-learning force field and a machine-learning force field based on a physical model,and the simulation results were much better than the empirical force field when compared to the DFT with errors of 0.34%,8.75%and 10.71%for the former,and 0.34%,2.5%and 7.14%for the latter.As for the phase stability,it is found that the machine learning force field based on physical model inherits the advantage of the empirical force field in maintaining the phase stability,which is better than the pure machine learning force field.For mechanical properties,Young's modulus of four different crystal directions of BaZrO_(3)are calculated.It was found that the errors between the calculated and experimental values for the machine learning force field and the machine learning force field based on the physical model were 9.22%and 1.6%,which were much lower than the results of the empirical force field.It can be seen that integrating physical models into the development of machine learning force field is an important way to improve the accuracy of atomic simulations.