Analysis of the ionic behavior in zirconia under an applied electric field using machine learning potentials

抄録

Zirconia (ZrO₂) is a widely used ceramic material owing to its high strength and toughness, but overcoming the difficulty in mechanical processing is desired. In this context, previous studies revealed that the ductility of yttria-stabilized zirconia is greatly enhanced by the application of an electric field [1]. However, the microscopic mechanism of this phenomenon has not been well understood yet. As a first step to clarify the mechanism of the ductility enhancement, in this study, we have constructed a machine learning potential to predict the behavior of ions in ZrO₂ under electric fields.

We use a machine learning potential because we can expect to achieve high prediction accuracy and relatively low computational cost simultaneously. As for the type of machine learning potential, we have adopted the high-dimensional neural network potential (HDNNP) [2] in this study. Our group proposed a modified HDNNP scheme to examine ionic motions under applied electric fields by adding a neural network (NN) to predict the Born effective charges [3]. We have adopted this modified scheme in this study. First, ZrO₂ structural data including those with oxygen vacancies were generated using classical molecular dynamics (MD) calculations [4] for a variety of crystal structures (orthorhombic, rhombic, monoclinic, and cubic). Next, density functional theory (DFT) calculations were performed on the structural data obtained by the MD calculations to obtain training data on the energy, forces acting on respective ions, and the Born effective charges. The NN to predict the Born effective charges and HDNNP were constructed using the training data from DFT calculations (8000 structures).

We have confirmed that the constructed HDNNP has good prediction accuracy for both energy and forces: the root mean square errors for energy and force are 5.55 × 10^-3 eV/atom, 1.14 × 10^-1 eV/Å for training data, respectively. Note that we have considered the charge states of O vacancies of 0, +1, and +2 though they take the charge state of +2 in bulk ZrO₂. It is also worth noting that we have obtained anomalously large Born effective charge values for some structures with the 0 and +1 charge states compared to the value for the defect-free bulk. We have found that the anomalous values are caused by the metallic nature due to the Fermi level above the bottom of conduction band (see Figure 1) and insufficient computational conditions for such a case. In fact, we have obtained reasonable values of Born effective charges by setting severer computational conditions such as the number of k points, and successfully constructed the NN to predict Born effective charge. In the presentation, we will discuss behavior of the Born effective charge in detail and also present the results of MD calculations under the application of an electric field.

This study was supported by JST CREST Programs "Novel electronic devices based on nanospaces near interfaces" and "Strong field nanodynamics at grain boundaries and interfaces in ceramics" and JSPS KAKENHI Grant Numbers 19H02544, 20K15013,21H05552, 22H04607, and 23H04100.

References [1] H. Motomura, et. al., J. Eur. Ceram. Soc., 42, 5045 (2022). [2] J. Behler and M. Parrinello, Phys. Rev. Lett., 98, 146401 (2007). [3] K. Shimizu, et al., arXiv.2305.19546 (2023). [4] Y. Wang, et. al., Phys. Rev. B, 85, 224110 (2012).