18 April 2016 Uncertainty analysis of continuum scale ferroelectric energy landscapes using density functional theory
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Abstract
Density functional theory (DFT) provides exceptional predictions of material properties of ideal crystal structures such as elastic modulus and dielectric constants. This includes ferroelectric crystals where excellent predictions of spontaneous polarization, lattice strain, and elastic moduli have been predicted using DFT. Less analysis has focused on quantifying uncertainty of the energy landscape over a broad range of polarization states in ferroelectric materials. This is non-trivial because the degrees of freedom contained within a unit cell are reduced to a single vector order parameter which is normally polarization. For example, lead titanate contains five atoms and 15 degrees of freedom of atomic nuclei motion which contribute to the overall unit cell polarization. Bayesian statistics is used to identify the uncertainty and propagation of error of a continuum scale, Landau energy function for lead titanate. Uncertainty in different parameters is quantified and this uncertainty is propagated through the model to illustrate error propagation over the energy surface. Such results are shown to have an impact in integration of quantum simulations within a ferroelectric phase field continuum modeling framework.
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William S. Oates, William S. Oates, Paul Miles, Paul Miles, Lider Leon, Lider Leon, Ralph Smith, Ralph Smith, } "Uncertainty analysis of continuum scale ferroelectric energy landscapes using density functional theory", Proc. SPIE 9800, Behavior and Mechanics of Multifunctional Materials and Composites 2016, 980004 (18 April 2016); doi: 10.1117/12.2219273; https://doi.org/10.1117/12.2219273
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