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铁电材料广泛应用于功能器件中, 对铁电体进行方便、准确的理论建模, 是一个长期被关注的问题. 本文提出了一种基于图卷积神经网络的铁电相变模拟方法, 利用图卷积神经网络对铁电材料的势能面进行原子层面的建模, 并将得到的神经网络势函数作为计算器, 以驱动大体系的分子动力学模拟. 给定原子位置, 训练好的图卷积神经网络能够给出势能的高精度预测, 达到每原子1 meV级别, 与从头算( ab inito)精度基本相当, 同时在计算速度上相比从头算方法有数个数量级的提升. 得益于神经网络的高精度和快速预测能力, 结合分子动力学模拟, 本文对两种不同类型的铁电材料——GeTe和CsSnI 3进行研究, 成功模拟了它们随温度发生的结构相变, 模拟结果和实验相符合. 这些结果说明了图卷积神经网络在铁电体建模和相变模拟应用中的准确性和可靠性, 为铁电体的理论探索提供了一个通用建模方法.Ferroelectric materials are widely used in functional devices, however, it has been a long-standing issue to achieve convenient and accurate theoretical modeling of them. Herein, a noval approach to modeling ferroelectric materials is proposed by using graph convolutional neural networks (GCNs). In this approach, the potential energy surface of ferroelectric materials is described by GCNs, which then serves as a calculator to conduct large-scale molecular dynamics simulations. Given atomic positions, the well-trained GCN model can provide accurate predictions of the potential energy and atomic forces, with an accuracy reaching up to 1 meV per atom. The accuracy of GCNs is comparable to that of ab initocalculations, while the computing speed is faster than that of ab initocalculations by a few orders. Benefiting from the high accuracy and fast prediction of the GCN model, we further combine it with molecular dynamics simulations to investigate two representative ferroelectric materials—bulk GeTe and CsSnI 3, and successfully produce their temperature-dependent structural phase transitions, which are in good agreement with the experimental observations. For GeTe, we observe an unusual negative thermal expansion around the region of its ferroelectric phase transition, which has been reported in previous experiments. For CsSnI 3, we correctly obtain the octahedron tilting patterns associated with its phase transition sequence. These results demonstrate the accuracy and reliability of GCNs in the modeling of potential energy surfaces for ferroelectric materials, thus providing a universal approach for investigating them theoretically.
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Keywords:
- phase transition/
- machien learning/
- potential energy surface
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单位 能量 力 应力 /(meV·atom–1) /(meV·Å–1·atom–1) /(meV·Å–3) GeTe 0.197 1.016 2.371 CsSnI3 0.323 0.825 0.944 Phases a/Å b/Å c/Å α/(°) β/(°) γ/(°) GeTe $ Fm\bar{3}m $ DFT 5.997 5.997 5.997 90 90 90 GCN 5.996 5.996 5.996 90 90 90 error 0.017% 0.017% 0.017% 0% 0% 0% $ R3 m $ DFT 6.076 6.076 6.076 88.04 88.04 88.04 GCN 6.061 6.061 6.061 88.37 88.37 88.37 error 0.244% 0.244% 0.244% 0.375% 0.375% 0.375% CsSnI3 $ Pm\bar{3}m $ DFT 6.270 6.270 6.270 90 90 90 GCN 6.270 6.270 6.270 90 90 90 error 0% 0% 0% 0% 0% 0% $ P4/mbm $ DFT 6.337 6.224 6.224 90 90 90 GCN 6.346 6.211 6.211 90 90 90 error 0.148% 0.195% 0.195% 0% 0% 0% $ Pnma $ DFT 6.243 6.243 6.254 90 90 89.63 GCN 6.225 6.225 6.235 90 90 89.72 error 0.295% 0.295% 0.311% 0% 0% 0.103% -
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