Two-component model of the neutron diffuse scattering in the relaxor ferroelectric PZN-4.5%PT

We report measurements of the neutron diffuse scattering in a single crystal of the relaxor ferroelectric material $95.5\mathrm{\%}\text{Pb}\left({\text{Zn}}_{1/3}{\text{Nb}}_{2/3}\right){\text{O}}_3\text{−}4.5\mathrm{\%}{\text{PbTiO}}_3$. Our results suggest that the nanometer scale structure in this compound exhibits both $⟨100⟩$ and $⟨110⟩$ polarizations, which contribute to different portions of the total diffuse scattering intensity. These contributions can be distinguished by the differing responses to an electric field applied along [001]. While diffuse scattering intensities associated with $⟨110⟩$ (T2-type) polarizations show little to no change in a [001] field, those associated with $⟨100⟩$ (T1-type) polarizations are partially suppressed by the field at temperatures below the Curie temperature $T_C\sim 475\text{K}$. Neutron spin-echo measurements show that the diffuse scattering at (0.05,0,1) is largely dynamic at high temperature and gradually freezes on cooling, becoming mostly static at 200 K.

Figure 1

(Color online) (a) Schematic of the neutron-scattering measurements made in the $\left(H0L\right)$ scattering plane with an electric field applied along [111]. The large (red) and small (blue) ellipses illustrate how the T2-diffuse scattering intensity is redistributed after the sample is FC. (b) Measurements of the diffuse scattering intensity near (002) [see scan (i) in panel (a)] at 200 K (data taken from Ref. 14). Scans were made along $\left(H,0,2.1\right)$ because they intercept both wings of the butterfly sufficiently far from (002) that significant contamination from unwanted Bragg peak scattering can be avoided, thus making it possible to monitor how intensities of the two wings change with field and temperature. Open circles represent ZFC data and closed circles represent FC data. (c) Transverse scan across (003) measured at 300 K on a PZN-8%PT. (d) Schematic identical to that in panel (a) except with the electric field applied along [001]. Dashed lines denote linear $q$ scans measured across or near various Bragg peaks. (b) Measurements of the T2-diffuse scattering intensity near (003) [see scan $\left({\text{i}}^{″}\right)$ in panel (d)] at 200 K. (f) Transverse scans at 200 K along [100] measured across (003) [see scan (i) in panel (d)]. Error bars represent the square root of the number of counts.

Figure 2

(Color online) (a) (100) Bragg peak intensity versus temperature. The intensity increase near $T_C$ is the result of a release of extinction at the phase transition. (b) Diffuse scattering intensity measured at (3,0,0.06) (open black symbols) and $\left(-0.06,0,3\right)$ (closed green symbols) after cooling (FC) in a field $E=4\text{kV}/\text{cm}$ applied along [001]. The lines are guide to the eyes, and the error bars represent the square root of the number of counts.

Figure 3

(Color online) Diffuse scattering intensity measured at 400 K. ZFC data are shown as (black) open circles and FC data are shown as (green) closed circles. Data were taken around (a) $\left(3,0,L\right)$ [scan (ii) in panel (d) of Fig. 1]; (b) $\left(H,0,3\right)$ [scan (i) in panel (d) of Fig. 1]; (c) $\left(1,0,1+L\right)$ [scan (iv) in panel (d) of Fig. 1]; and (d) $\left(1+H,0,1\right)$ [scan (iii) in panel (d) of Fig. 1]. (e) $\left(2,0,2+L\right)$ [scan (v) of panel (d) in Fig. 1]; and (f) $\left(2+H,0,2\right)$ [scan (vi) of panel (d) in Fig. 1]. The solid lines are based on least-square fits to the data described in the text. The error bars represent the square root of the number of counts.

Figure 4

(Color online) Contour maps of the diffuse scattering measured near (300) and (003) at 400 K under both ZFC and FC conditions. Mechanical constraints on the $Q$ range on BT9 prevented us from measuring complete mesh scans at both (003) and (300). The solid and dashed lines are guide to the eyes.

Figure 5

(Color online) Contour maps of the fitted diffuse scattering intensities versus temperature along directions transverse to (300) and (003) under both ZFC and FC conditions.

Figure 6

(Color online) Neutron spin-echo data for different temperatures and electric field effect at 200 K (blue); 300 K (red); 400 K (black; green); and 550 K (purple). The error bars were determined from the square root of $I$ and $I_0$. All data were taken under ZFC conditions shown with open circles except for the 400 K FC data shown with closed symbols. Lines are least-square fits to the databased on the model described in the text.

Figure 7

(Color online) The relaxation time $\tau$ from neutron spin-echo measurements for PZN-4.5%PT (blue) and PMN (red from Ref. 45) plotted as a function of temperature. The solid line is a fit of PMN data to an Arrhenius law $\left(\tau ={\tau }_0{e}^{U/k_{B}T}\right)$ with $U=1100\text{K}$.