Composition dependence of the diffuse scattering in the relaxor ferroelectric compound $(1-x)\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3-x{\mathrm{PbTiO}}_3(0\le x\le 0.40)$

We have used neutron diffraction to characterize the diffuse scattering in five single crystals of the relaxor ferroelectric $(1-x)\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3-x{\mathrm{PbTiO}}_3$ $\left(\mathrm{PMN}\text{−}x\mathrm{PT}\right)$ with $x=0$, 10, 20, 30, and 40%. The addition of ferroelectric ${\mathrm{PbTiO}}_3$ modifies the well-known “butterfly” and “ellipsoidal” diffuse scattering patterns observed in pure PMN $(x=0)$, which are believed to be associated with the presence of randomly oriented polar nanoregions. In particular, the anisotropy of the diffuse scattering diminishes as the PT content increases. The spatial correlation length $\xi$ along the $\left[1\overline{1}0\right]$ direction derived from the width of the diffuse scattering at room temperature increases from $12.6\mathrm{\AA }$ for PMN to $350\mathrm{\AA }$ for PMN-20%PT. In addition, the diffuse scattering intensity at $q=0$ grows and reaches a maximum value around the morphotropic phase boundary (MPB), which suggests that it is proportional to the dielectric susceptibility. Beyond $x=30\%$, a concentration very close to the MPB, no diffuse scattering is observed below $T_C$, and well-defined critical behavior appears near $T_C$. By contrast, the diffuse scattering for $x\le 20$% persists down to low temperatures, where the system retains an average cubic structure $(T_C=0)$. Finally, the anisotropic soft transverse optic (TO) modes observed in PMN are found to be isotropic for PMN-30%PT, which strongly suggests a connection between the anisotropic diffuse scattering and the TO modes.

Figure 1

Temperature dependence of the diffuse scattering in PMN-10%PT measured by (a) neutron scattering (Ref. 7) at $\left(3qq\right)$ and (b) x-ray scattering (Ref. 8) near (300). Inset in (a) shows a schematic of the diffuse scattering intensity contours observed in PMN. The dotted line in the inset denotes the trajectory of the $q$ scans shown in Fig. 4.

Figure 2

Zero-field phase diagram of PMN-$x$PT. Crosses locate the temperature at which the real part of the dielectric constant, measured at a frequency of $1\mathrm{kHz}$ by Noblanc et al., is maximum (Ref. 11). Open circles denote the value of the local $T_C$ at which either a zero-field- or field-induced cubic (C) to rhombohedral (R) transition was observed for PMN, and a structural phase transition was observed by x-ray diffraction (Refs. 12, 13), or by dielectric measurements ($0.05\le x\le 0.15$, Ref. 11), but not by neutron diffraction (Refs. 7, 14). A bulk C to R phase transition, however, was observed for $x=0.27$. For $0.31\le x\le 0.37$, the PMN-$x$PT system exhibits a cubic to tetragonal (T) phase transition on cooling, and then a monoclinic major phase (Mc) at low temperatures, which coexists with the R phase on the lower-PT side (PMN-31%PT) and the T phase on the higher-PT side $(33\le x\le 37\%)$.[17]

Figure 3

Constant intensity contours of the diffuse scattering near (110) and (100) for PMN and PMN-10%PT measured at room temperature. Each contour corresponds to a logarithmic change in intensity of 0.25 (base 10). Thick lines represent the contour intensity of ${10}^{2.3}\sim 200(\mathrm{arb}.\mathrm{units})$. Counts are plotted on the same intensity scale after normalizing by crystal volume and counting time.

Figure 4

Diffuse scattering measured near (110) along the $\left[1\overline{1}0\right]$ direction at room temperature for PMN, PMN-10%PT, and PMN-20%PT. Intensities are plotted on a logarithmic scale. The $q$-scan trajectory is shown schematically in the inset of Fig. 1a. Solid lines are fits to the data as described in the text.

Figure 5

Temperature dependence of the normalized integrated intensity $I_0$ and correlation length $\xi$ extracted from fits to $q$ scans of the diffuse scattering near (110) along the $\left[1\overline{1}0\right]$ direction for the PMN-10%PT and PMN-20%PT samples. Data for PMN were taken from published results by Xu et al. (Ref. 14) measured near (100) along the $\left[1\overline{1}0\right]$ direction. The parameter $I_0$ has been normalized to 1 at $T=300\mathrm{K}$. Dashed lines in (a) and (b) are guides to the eye.

Figure 6

Intensity contours of the diffuse scattering near (110) for PMN-10%PT measured at $400\mathrm{K}$.

Figure 7

Intensity contours of the diffuse scattering near (110) for PMN-20%PT, PMN-30%PT, and PMN-40%PT measured below $\left(300\mathrm{K}\right)$ and above $T_C$. Thick lines represent contours of intensity of ${10}^{2.3}\sim 200$, the same as shown in Fig. 3.

Figure 8

Temperature dependence of the neutron scattering intensities at $(1+q,1-q,0)$ for PMN-20%PT, PMN-30%PT, and PMN-40%PT. The vertical dashed line in (a) indicates $T_C^{loc}$, which is determined from the temperature dependence of the (200) Bragg intensity. Arrows indicate those temperatures where the scattering intensities suggest kinks or divergences. The inset in (a) shows the temperature dependence of the scattering intensity at the (200) Bragg peak.

Figure 9

Constant-$Q$ scans at $T=550\mathrm{K}$ showing TA and TO phonon modes at $Q=(2.15,1.85,0)$ and $(2,-0.21,0)$ for PMN and PMN-30%PT.