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(Color online) Equilibrium structures of (from left to right) LAO/PTO, KTO/PTO, and the composite superlattice KAO/PTO/LAO/PTO. The arrows mark various off-centric movements of the cations measured from the centers of their respective oxygen cages. For clarity, only off-centric movements larger than 0.05 are shown. Polar discontinuities arising in each superlattice are shown in terms of formal charges ().
(Color online) (−) for LAO/PTO (circles) and KSO/PTO (squares) plotted as a function of applied strain along the z direction. The inset shows the same plot for KAO/PTO/LAO/PTO. The slope of each curve gives the measure of the piezoelectric coefficient. Note the change in y-scale between the inset and the main plot.
Internal displacement gradients as a function of strain (/) and Born effective charges () for different ions in LAO/PTO and KSO/PTO superlattices. The numbers in parentheses indicate the corresponding numbers for the composite superlattice KSO/PTO/LAO/PTO. Clamped ion contribution to total piezoelectric coefficient (), contribution due to internal microscopic strain (), the total contribution + () and the piezoelectric coefficient obtained from the slopes in Fig. 2 () are also listed.
The phonon modes that contribute significantly to the piezoelectric response (the percentage contribution is denoted by C). Frequencies are listed for the equilibrium geometry and for that under +1% and −1% strain.
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