Local strain heterogeneity and elastic relaxation dynamics associated with relaxor behavior in the single-crystal perovskite $\mathrm{Pb}\left(\mathrm{I}{\mathrm{n}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3\text{−}\mathrm{PbZr}{\mathrm{O}}_3\text{−}\mathrm{Pb}\left(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}\right){\mathrm{O}}_3\text{−}\mathrm{PbTi}{\mathrm{O}}_3$

Recently, $\mathrm{Pb}\left(\mathrm{I}{\mathrm{n}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}\right){\mathrm{O}}_3\text{−}\mathrm{PbZr}{\mathrm{O}}_3\text{−}\mathrm{Pb}\left(\mathrm{M}{\mathrm{g}}_{1/3}\mathrm{N}{\mathrm{b}}_{2/3}\right){\mathrm{O}}_3\text{−}\mathrm{PbTi}{\mathrm{O}}_3$ (PIN-PZ-PMN-PT) relaxor single crystals were demonstrated to possess improved temperature-insensitive properties, which would be desirable for high-power device applications. The relaxor character associated with the development of local random fields (RFs) and a high rhombohedral-tetragonal (R-T) ferroelectric transition temperature $(T_{\mathrm{R}-\mathrm{T}}>120{}^{\circ }\mathrm{C})$ would be critical for the excellent properties. A significant effect of the chemical substitution of $\mathrm{I}{\mathrm{n}}^{3+}$ and $\mathrm{Z}{\mathrm{r}}^{4+}$ in PMN-PT to give PIN-PZ-PMN-PT is the development of local strain heterogeneity, which acts to suppress the development of macroscopic shear strains without suppressing the development of local ferroelectric moments and contribute substantially to the RFs in PIN-PZ-PMN-PT. Measurements of elastic and anelastic properties by resonant ultrasound spectroscopy show that PIN-PZ-PMN-PT crystal has a quite different form of elastic anomaly due to Vogel-Fulcher freezing, rather than the a discrete cubic-$T$ transition seen in a single crystal of PMN-28PT. It also has high acoustic loss of the relaxor phase down to $T_{\mathrm{R}-\mathrm{T}}$. Analysis of piezoresponse force microscopy phase images at different temperatures provides a quantitative insight into the extent to which the RFs influence the microdomain structure and the short-range order correlation length $\langle \xi \rangle$.

Figure 1

Segment of the XRD pattern obtained from the as-prepared ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal. The insets (a), (b), and (c) show high-resolution XPS spectra of the In $3d$, Zr $3d$, and O $1s$ signals, respectively.

Figure 2

Temperature-dependent dielectric permittivity for poled ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal. The inset shows the frequency of maximum permittivity as a function of $T_{max}$ and the curve is a fit of the Vogel-Fulcher equation.

Figure 3

(a) Stack of RUS spectra collected in a heating sequence, room temperature to $\sim 700\mathrm{K}$, from the ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal. Each spectrum has been offset up the $y$ axis in proportion to the temperature at which it was collected. (b) Similar stack of spectra collected from the ${\left[001\right]}_{\mathrm{C}}$ PMN-28PT single crystal. (c) ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal. Temperature dependence of the squared frequency ($f^2$) and inverse mechanical quality factor $\left(Q^{-1}\right)$ from fitting to a resonance peak with frequency near 283 kHz at high temperatures. These have been combined with data for a resonance peak near 507 kHz from spectra collected in a heating sequence from 10 to 295 K. $f^2$ values of the latter have been scaled to match up with the high-temperature data set at room temperature. (d) ${\left[001\right]}_{\mathrm{C}}$ PMN-28PT single crystal. Data for $f^2$ and $Q^{-1}$ obtained in a similar manner to that shown in (c).

Figure 4

Comparison of permittivity 1/$f^2$ to represent elastic compliance, tanδ to represent dielectric loss and $Q^{-1}$ to represent acoustic loss for (a) ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal and (b) ${\left[001\right]}_{\mathrm{C}}$ PMN-28PT single crystal. The RUS and dielectric data were collected in heating sequences from poled crystals.

Figure 5

Piezoresponse images of the (001) surface of the ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal acquired in situ during a sequence of increasing temperature.

Figure 6

(a) Cross section of the autocorrelation image along the direction of most pronounced oscillations of domains in PFM images from the (001) face of the ${\left[001\right]}_{\mathrm{C}}$ crystal of PIN-PZ-PMN-PT, as shown in Fig. 5. (b1) 303 K, (b2) 323 K, (b3) 373 K, (b4) 423 K, (b5) 453 K, and (b6) 503 K show the averaged autocorrelation function at different temperatures and fits of the equation $C\left(r\right)={\sigma }^{2}exp[-{\left(\frac{r}{\langle \xi \rangle }\right)}^{2\mathrm{h}}]$ used to extract values of the short-range correlation length $\langle \xi \rangle$.

Figure 7

Temperature dependence of the average correlation length $\langle \xi \rangle$ for microstructures observed by PFM on (001) surface of ${\left[001\right]}_{\mathrm{C}}$ PIN-PZ-PMN-PT single crystal.