创新铁电材料：数据驱动模拟

铁电材料具有可与外加电场自由切换的自发电极化特性。作为一种典型的铁电材料，钛酸钡(BaTiO₃)的自发极化被认为是钛原子在封闭的氧八面体内偏离中心的结果，但其铁电跃迁的详细微观性质一直是各种实验和理论激烈研究的主题。铁电跃迁的两种描述模型—位移模型和有序–无序模型捕捉了一些实验表征BaTiO₃的现象，而第一性原理模拟可以提供对相变本质的宝贵微观理解。

计算机模拟材料的铁电相变需要三个关键成分：描述原子和结构扭曲的能量响应的势能面模型，在相关的有限温度热力学条件下采样的自由能面，以及通过对样本的平均来确定宏观极化的单个配置极化。

Fig. 2 Spatial correlations of the unit-cell dipoles computed on a 5 × 5 × 5 supercell simulated at 250 K.

密度泛函理论(DFT)在探索BaTiO₃的势能面及软声子等方面取得了成功，但有效的模型依赖于哈密顿量的显示参数化。因此，为了对热力学做出第一性原理的准确预测，最好使用一种无偏的、不可知的方法，而不以势能面的形式进行任何先验假设。

来自瑞士洛桑联邦理工学院材料研究所计算科学与模拟实验室的Lorenzo Gigli等，开发了一个现代的、通用的机器学习(ML)框架，来描述钙钛矿铁电体的有限温度和功能性质(介电响应)，并将其具体应用于BaTiO₃。

该框架在进行分子动力学时不需要在模拟规模和尺度间进行妥协。该框架基于原子间ML势和极化矢量ML模型的组合，可同时预测铁电材料的总能量、原子力和极化，以探索其复杂的、随温度变化的相图，并预测其功能特性。

Fig. 5 Phases of BaTiO3 in CV space.

他们的方法可计算宏观的可观测量，如化学势和介电磁化率，其精度相当于基础DFT计算的理论水平，但计算成本要小得多。它适用于任何钙钛矿，甚至任何其他类型的铁电材料，包括二维铁电体等。

这项研究为理解和表征已知铁电材料以及发现和设计具有改进性能的新候选化合物开辟了一条新途径。该论文近期发表于npj Computational Materials 8: 209 (2022)。

Editorial Summaryd

Ferroelectric materials possess a spontaneous electric polarization that can be switched with an external electric field. The spontaneous polarization of the ferroelectric material —barium titanate (BaTiO₃) is thought to be the result of the titanium atom off-centering within the enclosing oxygen octahedron, but the detailed microscopic nature of the ferroelectric transition has been the subject of intense, ongoing research with a variety of experimental and theoretical techniques. 

The two models describing the ferroelectric transition, the displacive model and the order-disorder model, capture some of the phenomena characterized by experiments on BaTiO₃, experimentally observed in characterizing BaTiO₃, such as phonon softening at the transition temperatures—consistent with the displacive model—and diffuse X-ray scattering in all phases except the rhombohedral one—consistent with the order-disorder model—leading also to approaches combining the two models.

In this context, simulations—especially from first principles—can offer a precious microscopic understanding of the nature of the phase transitions. A computer simulation of the ferroelectric phase transition of any given material requires three key ingredients: first, a model of the potential energy surface (PES) that describes the energetic response to atomic and structural distortions, second, the free-energy surface (FES) sampled at the relevant, finite-temperature thermodynamic conditions, and third, the polarization of individual configurations that determines, through averaging over samples, the macroscopic polarization. 

Fig. 10 Temperature and pressure dependence of the imaginary part of the dielectric response spectrum, all computed in the cubic phase on a 4 × 4 × 4 supercell.

Density—functional theory (DFT) calculations have been successful in exploring the PES of BaTiO₃ and soft phonons and so on, but effective models rely on the choice of an explicit parametrization of the Hamiltonian. Therefore, in order to make accurate first-principles predictions of the thermodynamics, it is desirable to use an unbiased, agnostic approach without any prior assumption in the form of the PES. 

Lorenzo Gigli at al. from the Laboratory of Computational Science and Modeling, Institute for Materials, École Polytechnique Fédérale de Lausanne, Switzerland, developed a modern, general machine learning (ML) framework to describe at once the finite-temperature and functional properties (dielectric response) of perovskite ferroelectrics and apply it specifically to model BaTiO₃. 

The framework does not need to compromise between simulation scale and scale when conducting molecular dynamics (MD). This framework, based on a combination of an interatomic ML potential and a vector ML model for the polarization, is used to simultaneously predict the total energy, atomic forces, and polarization of a ferroelectric material in order to explore its complex, temperature-dependent phase diagram as well as to predict its functional properties. This approach can be used to compute macroscopic observables —chemical potentials and dielectric susceptibilities, specifically—with an accuracy equivalent to that of the level of theory of the underlying DFT calculations, but at a much smaller computational cost. Moreover, it is applicable with only minor changes to any perovskite or even any other type of ferroelectric material, including 2D ferroelectrics. 

Fig. 13 Validation of the GAP.

The work opens the door for a new avenue of fruitful research into the understanding and characterization of known ferroelectric materials, as well as the discovery and design of new candidate compounds with improved industrially relevant properties. Thisarticle was recently published in npj Computational Materials 8: 209 (2022).

原文Abstract及其翻译

Thermodynamics and dielectric response of BaTiO₃ by data-driven modeling (数据驱动模拟BaTiO₃的热力学和介电响应)

Lorenzo Gigli, Max Veit, Michele Kotiuga, Giovanni Pizzi, Nicola Marzari & Michele Ceriotti

摘要第一性原理模拟铁电材料是密度泛函理论的成功之一，也是许多发展的驱动力，这需要准确描述电子过程和热力学平衡，它们驱动了自发对称破缺和宏观极化的出现。我们展示了一个集成机器学习模型的开发和应用，该模型描述了BaTiO₃相同的基础结构、能量和功能特性，这是一种典型的铁电学。该模型利用从头计算作为参考，在时间和长度尺度上实现了对能量和极化准确而廉价的预测，这是直接从头模拟无法实现的。这些预测使我们能够评估铁电跃迁的微观机制。Ti离心态的有序–无序跃迁是铁电跃迁的主要驱动因素，即使对称性破缺和晶胞畸变之间的耦合决定了中间相、部分有序相的存在。此外，我们还深入地探索了BaTiO₃在其相图上的静态和动态行为，而不需要引入对铁电跃迁的粗粒度描述。最后，我们应用极化模型，以完全从头算的方式计算了材料的介电响应特性，再次再现了正确的定性实验行为。