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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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