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Predicting morphotropic phase boundary locations and transition temperatures in Pb- and Bi-based perovskite solid solutions from crystal chemical data and first-principles calculations
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10.1063/1.2128049
/content/aip/journal/jap/98/9/10.1063/1.2128049
http://aip.metastore.ingenta.com/content/aip/journal/jap/98/9/10.1063/1.2128049

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Projection of the DFT relaxed structure for PZT supercell on the plane. Pb atoms tend to distort away from the large Zr and toward smaller Ti cations.

Image of FIG. 2.
FIG. 2.

partial PDFs. (a) Pb–Ti (solid) and Pb–Zr (dashed) partial PDFs obtained from the relaxed structures of the PZT supercells at experimental lattice constants. (b) Pb–Sc (solid) and Pb–In (dashed) partial PDFs obtained from the relaxed structures of PSN and PIN at experimental lattice constants.

Image of FIG. 3.
FIG. 3.

Experimental values (circles) for the PZT solid solutions as a function of Ti composition (Ref. 37). The dependence of on PT is well fit by a linear function for the whole compositional range.

Image of FIG. 4.
FIG. 4.

(Color online) Distortion magnitudes (in angstroms) for cations in PT solid solutions. Distortion magnitudes are especially large for Zn and Ti. values of 0.08, 0.07, 0.11, 0.10, 0.13, 0.17, 0.17, 0.25, and 0.25 Å are assigned for Mg, In, Sc, W, Zr, Fe, Nb, Zn, and Ti, respectively.

Image of FIG. 5.
FIG. 5.

(Color online) Plot of the MPB position (in mole fraction PT) vs the end member tolerance factor. Circles indicate non-PT end-member perovskites with no Ti cations and less than full occupation of the site by ferroelectrically active Nb or Fe cations. These display a lower ferroelectric activity on the end-member site. Stars indicate systems where ferroelectric activity of the non-PT end-member site is higher due to presence of Ti ions and/or occupation of more than one half of the sites by ferroelectrically active Fe and Nb ions. Diamonds indicate data for solid solution with 1:1 (low tolerance factor) and 2:1 (high tolerance factor) stoichiometries.

Image of FIG. 6.
FIG. 6.

Correlation between the mole fractions of PT at MPB predicted by Eq. (10) using data in Table III and mole fractions of PT at MPB observed experimentally. The solid solutions for which we have DFT -cation displacement data are marked by filled cirles and diamonds for Pb-based and Bi-based systems, respectively. MPB positions predicted for Pb- and Bi-based systems where -cation displacement data is estimated are marked by open circles and diamonds, respectively. Predicted positions for MPB for solid solutions using 1:1 (predicted ) and 2:1 (predicted ) Mn:W stoichiometries are represented by stars. Taking the effect of -cation off centering into account makes quantitative prediction of MPB location possible.

Image of FIG. 7.
FIG. 7.

Correlation between the mole fractions of PT at MPB predicted by Eq. (11) and (12) using data in Table III and mole fractions of PT at MPB observed experimentally. Solid solutions for which we have DFT -cation displacement data are marked by filled cirles and diamonds for Pb-based and Bi-based systems, respectively. MPB positions predicted for Pb- and Bi-based systems where -cation displacement data is estimated are marked by open circles and diamonds, respectively. Predicted positions for MPB for solid solutions using 1:1 (predicted ) and 2:1 (predicted ) Mn:W stoichiometries are represented by stars. Using separate fits for Pb- and Bi-based end-member perovskites improves the correlation.

Image of FIG. 8.
FIG. 8.

(Color online) vs tolerance factor of the non-PT end member using the data of Table V. End members with lower FE activity on the site are shown by circles, end members with higher FE activity on the site are shown by squares. Low concentration of ferroelectrically active cations on the end-member site shifts the to lower values. Least-squares fit lines for the two cases are shown.

Image of FIG. 9.
FIG. 9.

Experimental data for ratio in solid solution. The material is tetragonal for all compositions studied, with an anomalous strong enhancement in tetragonality. Compositions with less then 0.6 PT content could not be made as a single phase.

Tables

Generic image for table
Table I.

Results of our DFT calculations for ferroelectric compositions of solid solutions. Ground-state cation displacements from center of oxygen cage in angstroms. Rhombohedral, monoclinic, and tetragonal phases are denoted by , , and , respectively.

Generic image for table
Table II.

Position of the MPB in solid solutions. Data for BMW-PT and PSW-PT solutions taken from Refs. 18 and 20, respectively. Data for all other systems taken from Ref. 6. End members with high ferroelectric activity on the site are marked by an asterisk. For solid solution, data is given for and possible end-member stoichiometries. For –PT solid solution the average position of the MPB region that extends from 0.2 to 0.4 PT content (Ref. 45) is given.

Generic image for table
Table III.

Ionic data and predictions for PT content at MPB using Eqs. (11) and (12) for Pb- and Bi-based end member perovskites. Shannon-Prewitt -cation ionic radii and displacements obtained by DFT calculations are in angstroms. Fe displacement value is taken from Ref. 36. -cation displacement data marked with an asterisk are estimated based on crystal chemical arguments. For , data is given for and stoichiometries.

Generic image for table
Table IV.

at the MPB in solid solutions. Data for for and solid solutions taken from Refs. 18 and 24, respectively. Solid solutions with lower ferroelectric activity on the site are marked by an asterisk.

Generic image for table
Table V.

Predicted and values for and solid solutions discussed in Sec. IV. Predicted are obtained using Eqs. (11) and (12), (in °C) are obtained by using Eqs. (13) and (14). Ionic size and displacement data in angstroms.

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/content/aip/journal/jap/98/9/10.1063/1.2128049
2005-11-11
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Predicting morphotropic phase boundary locations and transition temperatures in Pb- and Bi-based perovskite solid solutions from crystal chemical data and first-principles calculations
http://aip.metastore.ingenta.com/content/aip/journal/jap/98/9/10.1063/1.2128049
10.1063/1.2128049
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