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33746298779
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note
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Here a lattice displacement ("phonon") mode is described as unstable in a particular phase if the corresponding eigen value of the interatomic force matrix (or dynamical matrix in the case of phonons) is negative. These instabilities are generally found in the cubic phase; the Brillouin zone labels used in this paper refer to that of the cubic structure.
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33746287891
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note
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The quoted numbers are from Ref. [8]. Discrepancy exists among different sets of experiments.
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84890775764
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Somewhat similar issues are addressed for PZT 50/50 supercells in M. Fornari and D. J. Singh, Phys. Rev. B 63, 092101 (2001).
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See, for example, M. J. Haun, E. Furman, S. J. Jang, and L. E. Cross, Ferroelectrics 99, 13 (1989);
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33746291151
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U. V. Waghmare, Ph.D. Thesis (Yale University, 1996).
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0004437878
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0342647339
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33744678467
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55
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33746302636
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note
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We have approximated the crystal as quasi-cubic computing Fourier transform in order to compare with first principles phonon calculations [34]. Accounting for the strain relaxation will break some of the symmetries.
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56
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33746312484
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note
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Within our 3 × 2 × 2 Monkhorst-Pack grid sampling, very small β, less than 0.1°, persists, but this goes away on increasing Brillouin zone sampling.
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57
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33746300662
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note
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R(LT) have vastly different structures, and it appears much more difficult to accurately predict the similar small energy differences between them.
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58
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33746306037
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note
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15 modes becomes more stable with pressure - consistent with analysing the eigen values of the interatomic force matrix, not the dynamical matrix. In this limited case, the former seems to be more appropriate.
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59
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33746307144
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note
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O phase.
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