鐵電材料具有可與外加電場自由切換的自發(fā)電極化特性。作為一種典型的鐵電材料，鈦酸鋇(BaTiO₃)的自發(fā)極化被認(rèn)為是鈦原子在封閉的氧八面體內(nèi)偏離中心的結(jié)果，但其鐵電躍遷的詳細(xì)微觀性質(zhì)一直是各種實(shí)驗(yàn)和理論激烈研究的主題。鐵電躍遷的兩種描述模型—位移模型和有序–無序模型捕捉了一些實(shí)驗(yàn)表征BaTiO₃的現(xiàn)象，而第一性原理模擬可以提供對相變本質(zhì)的寶貴微觀理解。

計(jì)算機(jī)模擬材料的鐵電相變需要三個(gè)關(guān)鍵成分：描述原子和結(jié)構(gòu)扭曲的能量響應(yīng)的勢能面模型，在相關(guān)的有限溫度熱力學(xué)條件下采樣的自由能面，以及通過對樣本的平均來確定宏觀極化的單個(gè)配置極化。

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

密度泛函理論(DFT)在探索BaTiO₃的勢能面及軟聲子等方面取得了成功，但有效的模型依賴于哈密頓量的顯示參數(shù)化。因此，為了對熱力學(xué)做出第一性原理的準(zhǔn)確預(yù)測，最好使用一種無偏的、不可知的方法，而不以勢能面的形式進(jìn)行任何先驗(yàn)假設(shè)。

來自瑞士洛桑聯(lián)邦理工學(xué)院材料研究所計(jì)算科學(xué)與模擬實(shí)驗(yàn)室的Lorenzo Gigli等，開發(fā)了一個(gè)現(xiàn)代的、通用的機(jī)器學(xué)習(xí)(ML)框架，來描述鈣鈦礦鐵電體的有限溫度和功能性質(zhì)(介電響應(yīng))，并將其具體應(yīng)用于BaTiO₃。

該框架在進(jìn)行分子動力學(xué)時(shí)不需要在模擬規(guī)模和尺度間進(jìn)行妥協(xié)。該框架基于原子間ML勢和極化矢量ML模型的組合，可同時(shí)預(yù)測鐵電材料的總能量、原子力和極化，以探索其復(fù)雜的、隨溫度變化的相圖，并預(yù)測其功能特性。

Fig. 5 Phases of BaTiO3 in CV space.

他們的方法可計(jì)算宏觀的可觀測量，如化學(xué)勢和介電磁化率，其精度相當(dāng)于基礎(chǔ)DFT計(jì)算的理論水平，但計(jì)算成本要小得多。它適用于任何鈣鈦礦，甚至任何其他類型的鐵電材料，包括二維鐵電體等。

這項(xiàng)研究為理解和表征已知鐵電材料以及發(fā)現(xiàn)和設(shè)計(jì)具有改進(jìn)性能的新候選化合物開辟了一條新途徑。該論文近期發(fā)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及其翻譯

Thermodynamics and dielectric response of BaTiO₃ by data-driven modeling (數(shù)據(jù)驅(qū)動模擬BaTiO₃的熱力學(xué)和介電響應(yīng))

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

摘要第一性原理模擬鐵電材料是密度泛函理論的成功之一，也是許多發(fā)展的驅(qū)動力，這需要準(zhǔn)確描述電子過程和熱力學(xué)平衡，它們驅(qū)動了自發(fā)對稱破缺和宏觀極化的出現(xiàn)。我們展示了一個(gè)集成機(jī)器學(xué)習(xí)模型的開發(fā)和應(yīng)用，該模型描述了BaTiO₃相同的基礎(chǔ)結(jié)構(gòu)、能量和功能特性，這是一種典型的鐵電學(xué)。該模型利用從頭計(jì)算作為參考，在時(shí)間和長度尺度上實(shí)現(xiàn)了對能量和極化準(zhǔn)確而廉價(jià)的預(yù)測，這是直接從頭模擬無法實(shí)現(xiàn)的。這些預(yù)測使我們能夠評估鐵電躍遷的微觀機(jī)制。Ti離心態(tài)的有序–無序躍遷是鐵電躍遷的主要驅(qū)動因素，即使對稱性破缺和晶胞畸變之間的耦合決定了中間相、部分有序相的存在。此外，我們還深入地探索了BaTiO₃在其相圖上的靜態(tài)和動態(tài)行為，而不需要引入對鐵電躍遷的粗粒度描述。最后，我們應(yīng)用極化模型，以完全從頭算的方式計(jì)算了材料的介電響應(yīng)特性，再次再現(xiàn)了正確的定性實(shí)驗(yàn)行為。