Many-electron calculations of the phase stability of 
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 polymorphs

Mayr-Schmölzer, Wernfried; Planer, Jakub; Redinger, Josef; Grüneis, Andreas; Mittendorfer, Florian

doi:10.1103/physrevresearch.2.043361

Cited by 12 publications

(16 citation statements)

References 54 publications

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“…Our results are consistent with Ref. [33], which shows that manyelectron calculations such as RPA or coupled cluster singles and doubles theory yield smaller energy differences than DFT for ZrO 2 . To further validate the accuracy of MLFF-RPA ∆ , we show that the energy differences between the three phases, as well as the phonon frequencies at Γ, calculated directly using the RPA are in very good agreement with the predictions by MLFF-RPA ∆ (see Table III and Fig.…”

Section: Energysupporting

confidence: 93%

Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

Liu,

Verdi,

Karsai

et al. 2021

Preprint

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We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and ∆-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.Machine learning based regression techniques have become a prominent tool to construct accurate interatomic potentials for materials modeling and simulations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Machinelearned force fields (MLFF), however, are generally constructed by fitting the energies, forces, and stress tensors derived by density functional theory (DFT) calculations, and therefore the accuracy of the resulting MLFFs is largely limited by DFT. It is not surprising, then, that these MLFFs would fail in problems where DFT is inaccurate, such as in systems where long-range electronic correlation effects play an important role. This implies that pursuing an MLFF beyond DFT is highly desirable.

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Section: Energysupporting

confidence: 93%

Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

Liu,

Verdi,

Karsai

et al. 2021

Preprint

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“…The energy differences between the three phases are also shown in the table. AI calculations based on the PBEsol exchange-correlation functional [44] describe very accurately the relaxed structures compared to experiment, almost on par with benchmark many-electron calculations [45]. The MLFF results are in excellent agreement with the AI ones, the differences being less than 0.2% for the lattice parameters and less than 1 meV per atom for the energies.…”

Section: B Structural and Vibrational Propertiessupporting

confidence: 56%

Thermal transport and phase transitions of zirconia by on-the-fly machine-learned interatomic potentials

Verdi¹,

Karsai²,

Liu³

et al. 2021

Preprint

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Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green-Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

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“…For both approaches, they could not find an intersection of the cubic free energy curve with the tetragonal free energy curve close to the experimental phase transition temperature, which is 2690 °C for ZrO 2 (2800 °C for HfO 2 ). [ 43 ] Also Mayr‐Schmölzer et al [ 19 ] calculated the transition temperature with phonopy but did not find a value using traditional density functionals.…”

Section: Resultsmentioning

confidence: 99%

Characteristics of Low‐Energy Phases of Hafnia and Zirconia from Density Functional Theory Calculations

Antunes

Ganser

Kuenneth

et al. 2022

Physica Rapid Research Ltrs

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A systematic simulation study of low‐energy phases of HfO2 and ZrO2, including 24‐atomic cells derived from 180° interphases, leads to a new monoclinic Pc phase (mIII) with a monoclinic angle and a polarization of 0.3 C m−2. This opens up a new transition path toward the monoclinic P2 1 /c phase (m) starting from the tetragonal P4 2 /nmc phase (t), with comparable lower‐energy barriers, where the high‐symmetric phases show the largest temperature dependence. The tetragonal P4 2 /nmc phase, the cubic (c) phase, and the less investigated cubic (cII) phase are favored.

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Many-electron calculations of the phase stability of ZrO2 polymorphs

Cited by 12 publications

References 54 publications

Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

Thermal transport and phase transitions of zirconia by on-the-fly machine-learned interatomic potentials

Characteristics of Low‐Energy Phases of Hafnia and Zirconia from Density Functional Theory Calculations

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