Temperature dependent XAFS studies of local atomic structure of the perovskite-type zirconates

Temperature dependent preedge and extended x-ray absorption fine structure measurements at the Zr $K$ edge for the perovskite-type zirconates $\mathrm{Pb}{\mathrm{Zr}}_{0.515}{\mathrm{Ti}}_{0.485}{\mathrm{O}}_3$ (PZT), $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ (PZ), and $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_3$ are performed. To carry out a more accurate study of the weak reconstruction of the local atomic structure we employed a combination of two techniques: (i) analysis of the preedge fine structure, and (ii) analysis of the Fourier transform of the difference between $\chi \left(k\right)$ functions obtained at different temperatures. A detailed investigation of local atomic structure in the cubic phase for all the crystals is also performed. It is shown that neither the displacive nor the order-disorder model can describe correctly the changes of local atomic structure during phase transitions in PZ and PZT. A spherical model describing the local atomic structure of perovskite-type crystals suffering structural phase transitions is proposed.

Figure 1

The potential surfaces for the atom $B$ in different $AB{\mathrm{O}}_3$ perovskites: (a) $\mathrm{Eu}\mathrm{Ti}{\mathrm{O}}_3$ and $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_3$, (b) $\mathrm{K}\mathrm{Nb}{\mathrm{O}}_3$, $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$, $\mathrm{Pb}{\mathrm{Zr}}_{0.515}{\mathrm{Ti}}_{0.485}{\mathrm{O}}_3$, and (c) $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, $r$ is the distance from the atom $B$ to the center of the $B{\mathrm{O}}_6$ octahedron.

Figure 2

Preedge region of the Zr $K$ spectrum at different temperatures for $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_3$. Inset: difference between the spectra for 100, 300, and $500°\mathrm{C}$ and that for $20°\mathrm{C}$.

Figure 3

Preedge region of the Zr $K$ spectrum at different temperatures for $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$. Inset: difference between the spectra for 100, 300, and $500°\mathrm{C}$ and that for $20°\mathrm{C}$.

Figure 4

Preedge region of the Zr $K$ spectrum at different temperatures for $\mathrm{Pb}{\mathrm{Zr}}_{0.515}{\mathrm{Ti}}_{0.485}{\mathrm{O}}_3$. Inset: difference between the spectra for 100, 300, and $500°\mathrm{C}$ and that for $20°\mathrm{C}$.

Figure 5

The results of PEFS calculations for $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_3$ performed for different displacements $r_0$ of the Zr atom from its centrosymmetrical position in the cubic lattice. Inset: difference between the spectra calculated for different Zr atom displacements and that for ideal perovskite lattice.

Figure 6

(Color online) Absolute values [dashed (blue) lines] and real parts [solid (black) lines] of the $k^3$ weighted FT of the Zr EXAFS signal measured at $500°\mathrm{C}$ (on the top) and the differential FT for $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_3$. The temperatures are indicated in the figure.

Figure 7

(Color online) The results of fitting performed for different structural models for $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$: (a) one-, (b) eight-, and (c) 12-site model. Left panels: absolute values of the Fourier transform of the $k^3$ weighted $\chi \left(k\right)$ [solid (black) lines, experiment; dashed (blue) lines, fitting results]. Right panels: pair radial distribution functions.

Figure 8

(Color online) The results of fitting performed for different structural models for $\mathrm{Pb}{\mathrm{Zr}}_{0.515}{\mathrm{Ti}}_{0.485}{\mathrm{O}}_3$: (a) one-, (b) eight-, and (c) 12-positional model. Left panels: absolute values of the Fourier transform of the $k^3$ weighted $\chi \left(k\right)$ [solid (black) lines, experiment; dashed (blue) lines, fitting results]. Right panels: pair radial distribution functions.

Figure 9

(Color online) Absolute values [dashed (blue) lines] and real parts [solid (black) lines] of the $k^3$ weighted FT of the Zr EXAFS signal measured at $500°\mathrm{C}$ (on the top) and the differential FT for $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$. The temperatures are indicated in the figure.

Figure 10

(Color online) Absolute values [dashed (blue) lines] and real parts [solid (black) lines] of the $k^3$ weighted FT of the Zr EXAFS signal measured at $500°\mathrm{C}$ (on the top) and the differential FT for $\mathrm{Pb}{\mathrm{Zr}}_{0.515}{\mathrm{Ti}}_{0.485}{\mathrm{O}}_3$. The temperatures are indicated in the figure.