Effect of $B$-site randomness on the antiferroelectric/relaxor nature of the ground state: Diffuse and inelastic x-ray scattering study of $\mathrm{Pb}\left({\mathrm{In}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3$

We have investigated the effect of $B$-site randomness on the antiferroelectric/relaxor nature of the ground state by studying diffuse and inelastic x-ray scattering from ordered and disordered $\mathrm{Pb}\left({\mathrm{In}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3$ (O- and D-PIN) single crystals. The diffuse scattering measurement of O-PIN, which is antiferroelectric at low temperatures, shows that the ferroelectrically interactive local polarization exists in the cubic phase, above the transition temperature $T_{\mathrm{N}}$. Inelastic x-ray scattering analysis of the diffuse scattering shows that the transverse-acoustic (TA) and transverse-optic (TO) modes are dominant at high temperatures ($\sim 800$ K), while the central peak (CP) and TA modes, which are coupled, contribute majorly to diffuse scattering near $T_{{}_{\mathrm{N}}}$ and show critical behavior at temperature close to $T_{{}_{\mathrm{N}}}$. The TO mode shows no anomaly at temperature close to $T_{{}_{\mathrm{N}}}$. Furthermore, the phonon spectra are broad, indicating that a strong damping mechanism exists even in the sample with weak chemical disordering, O-PIN. No clear difference between O- and D-PIN is observed at temperatures above $\sim 500$ K. Here, the major difference between them is the property of the CP mode, which shows no drop and increases rapidly with decreasing temperatures in D-PIN. The CP mode is thought to be directly related to the local polarization and to originate in a combination of Pb flipping and the TO mode. The $B$ site is considered to control the antiferroelectric/ferroelectric instability of lead-based perovskite materials. Finally, the $B$-site randomness is discussed in terms of suppressing the antiferroelectric instability and enhancing the polarization fluctuation.

Figure 1

Relationship between typical temperatures ($T_{\mathrm{N}}$, $T_{\mathrm{C}}$, $T_{\max }$) and Shannon's ionic radius [16] of the $B^{\prime }$ ion in ordered and disordered Pb($B_{1/2}^{\prime }{\mathrm{Nb}}_{1/2}){\mathrm{O}}_3$. The ionic radii of ${\mathrm{Pb}}^{2+}$, ${\mathrm{Nb}}^{5+}$, and ${\mathrm{O}}^{2-}$, which are common to all materials, are 1.49, 0.64, and 1.35 Å, respectively. The temperatures are representative; that is, they are not uniquely determined since they depend strongly on the sample preparation conditions and a slight change in $B$-site randomness results in a slight variation in temperature. The data are from Refs. [17, 18, 19] (for $B^{\prime }$ = Fe), [20, 21, 22] (for $B^{\prime }$ = Sc), [23, 24, 25] (for $B^{\prime }$ = In), [26] (for $B^{\prime }$ = Lu), [24, 27, 28] (for $B^{\prime }$ = Yb), and [29] (for $B^{\prime }$ = Ho).

Figure 2

(a) Temperature-anneal-temperature (chemical order parameter) phase diagram of $\mathrm{Pb}\left({\mathrm{In}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3$ [32]. Typical temperature dependence of the dielectric permittivity ${\epsilon }^{\prime }$ of both (b) O- and (c) D-PIN [23]. $H0L$ mesh scans of (b${}^{\prime }$) O- and (c${}^{\prime }$) D-PIN are shown as well [11]. The inset shows that the reciprocal space corresponds to (b${}^{\prime }$) and (c${}^{\prime }$).

Figure 3

$H0L$ mesh scans of O-PIN taken at 800, 700, 560, 480, 440, 435, 430, and 425 K across $T_{\mathrm{N}}$.

Figure 4

Temperature dependences of superlattice intensities (open circle) and diffuse scattering intensities (solid circle) measured at (3.25, 0, 0.75) and (3.125, 0, 0.875), respectively.

Figure 5

Selected IXS profiles of O-PIN measurements at (a) (3, 0, 0.12) [38] and (b) (2.92, 0, 0.11) as a function of temperature. The fitting results are shown by the solid lines.

Figure 6

Obtained fitting parameters of CP, TA, and TO modes of O-PIN at (a) (3, 0, 0.12) and (b) (2.92, 0, 0.11) as a function of temperature. The energies and widths (the middle and bottom panels) are resolution corrected.

Figure 7

Selected IXS profiles of D-PIN measurements at (a) (3, 0, 0.12) and (b) (2.92, 0, 0.11) as a function of temperature. Fitting results are shown by the solid lines. Owing to the contribution of strong elastic scattering, the IXS profiles cannot be separated by fitting, especially in the lower-temperature region.

Figure 8

Obtained fitting parameters of CP, TA, and TO modes of D-PIN at (a) (3, 0, 0.12) and (b) (2.92, 0, 0.11) as a function of temperature. The energies and widths (the middle and bottom panels) are resolution corrected.

Figure 9

Schematic drawing of (a) Pb-flipping motion and (b) the TO phonon (last) mode. Their mutual interaction is strong.