3 April 2013 A quantum informed continuum model for ferroelectric and flexoelectric materials
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Correlations between quantum mechanics and continuum mechanics are investigated by exploring relations based on the electron density and electrostatic forces within an atomic lattice in ferroelectric materials. Theoretically, it is shown that anisotropic stress is dependent upon electrostatic forces that originate from the quadrupole density. This relation is directly determined if the nuclear charge and electron density are known. The result is an extension of the Hellmann-Feynman theory used to quantify stresses based on electrostatics. Further, flexoelectricity is found to be proportional to the next two higher order poles. These relations are obtained by correlating a nucleus-nucleus potential and nucleus-electron potential with the deformation gradient and second order gradient. An example is given for barium titanate by solving the electron density using density function theory (DFT) calculations. Changes in energy and stress under different lattice geometric constraints are modeled and compared to nonlinear continuum mechanics to understand differences in formulating a model directly from DFT calculations versus a nonlinear continuum model that uses polarization versus the quadrupole density as the order parameter.
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William S. Oates, William S. Oates, "A quantum informed continuum model for ferroelectric and flexoelectric materials", Proc. SPIE 8689, Behavior and Mechanics of Multifunctional Materials and Composites 2013, 868905 (3 April 2013); doi: 10.1117/12.2009695; https://doi.org/10.1117/12.2009695

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