Rhombohedral ferroelectric phases of lead zirconate titanate

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 10, 2003, Pages

  Leung, Kevin ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL; LEAD; TITANIUM DERIVATIVE; ZIRCONIUM DERIVATIVE;

AB INITIO CALCULATION; ARTICLE; CRYSTAL STRUCTURE; ENTROPY; FINITE ELEMENT ANALYSIS; FOURIER TRANSFORMATION; HIGH TEMPERATURE; LOW TEMPERATURE; MOLECULAR MODEL; MONTE CARLO METHOD; PHASE TRANSITION; TRANSMISSION ELECTRON MICROSCOPY;

EID: 0037741906     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.104108     Document Type: Article

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44. For (formula presented) the equilibrium (formula presented) lattice constant of 4.116 Å is used because its volume per formula unit is close to that of the zero-temperature (formula presented) phase. For (formula presented) the LDA lattice constant of its (formula presented) phase (not seen experimentally) is 3.9119 Å. The energy cutoff and Brillouin sampling are 85 Ry and (formula presented) respectively. Splittings between longitudinal optical (LO) and transverse optical (TO) phonon modes are included in the usual way, by computing Born effective charges and the dielectric matrix and folding these into an Ewald summation (Ref. 30).
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46. In our model, the polar TO phonon mode is not allowed to relax as temperature decreases and the (formula presented) mode emerges. (See Ref. 11.) This underestimates the (formula presented) energy difference by (formula presented) To zeroth order, this approximation should underestimate (formula presented) by a like amount. Despite this, our model still predicts (formula presented) that is too high. This reinforces our conclusion that the LDA tends to overestimate (formula presented)
47. One of the three symmetry-related basis function (formula presented)
48. The parameters listed below are in atomic units: (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) (formula presented) measures the equilibrium lattice constant of the (formula presented) structure, relative to (formula presented) Finite Ti concentration (formula presented) is interpolated from theoretical lattice constants via the Vegard law.
49. This nonlinear (formula presented) coupling may be rationalized to some extent with Pb-O covalent bonding. Assume that the rate of change of this interaction varies more rapidly with Pb-O separation at large Pb-O distances than small. With no or small amplitude of (formula presented) modes present, Pb and O are far apart, and the energetics are expected to be more sensitive to the presence of an (formula presented)-like mode which increases the Pb-O distance. This sensitivity should decrease with increasing (formula presented) amplitude. This is strictly a conjecture; other factors may play a role.
50. Note that this term obtains by assuming certain anharmonicities (e.g. that at the X-point) are zero.