Diffuse scattering anisotropy and inhomogeneous lattice deformations in the lead magnoniobate relaxor PMN above the Burns temperature

Neutron diffuse scattering measurements on single crystal PbMg${}_{1/3}$Nb${}_{2/3}$O${}_3$ above the Burns temperature are reported. The high temperature elastic diffuse component is highly asymmetric near reciprocal lattice points not corresponding to high-symmetry directions. This asymmetry can be described using Huang scattering formalism assuming that the scattering originates from mesoscopic lattice deformations due to elastic defects. Qualitative agreement between this model and the experimental data is achieved with simple, isotropic defects. It is demonstrated that the weak satellite maxima near Bragg reflections can be interpreted in terms of a finite resolution effect.

Figure 1

Isointensity contours of the diffuse scattering measured in PMN at 650 K in three BZs (top) and the corresponding isointensity contours produced by model calculations described in text (bottom). The arrows through the zone centers denote the direction of the reciprocal lattice vector $\tau$. The positions of the Al powder rings are marked by dashed lines. The straight solid lines perpendicular to the vector $\tau$ indicate the positions in which the slices depicted in Fig. 2 are made. The maximum intensity used for the plots in the top row is limited to a value that allows for an adequate intensity scale in which to see the diffuse scattering distributions.

Figure 2

1D slices through the 2D DS maps performed along lines perpendicular to the vector $\tau$ (see text for details). These slice trajectories are indicated by the straight lines shown in the upper panels of Fig. 1. The solid lines in this figure are guides for the eye.

Figure 3

(a) A set of modeled radial scans through the DS (without Bragg and background contributions) near the (3 0 0) Bragg reflection under different resolution conditions. The thick, solid line corresponds to the estimated resolution of the current experiment, the dashed line corresponds to the estimated resolution of experiment from Ref. 25. The uppermost line corresponds to the ideal resolution, the second uppermost line corresponds to $\Delta Q_Y=\Delta Q_Z=0.011$ Å${}^{-1}$, the resolution conditions for the other lines are indicated on the plot. The intensity for each line is scaled to allow for a clear representation of multiple lines on a single plot. (b) Projections of the resolution ellipsoids (thick lines) for (A) $q=0$ (zone center), (B) $q=-0.125$, and (C) $q=0.125$ and isointensity contours of the scattering intensity calculated using the parameters described in the text.

Figure 4

The slices of 3D model scattering intensity in (3 0 0) Brillouin zone determined by Eqs. (2) and (4) along the vertical $l$ axis with fixed value of $k=0$ and different values of $h$ described on the graph. Bold line represents the resolution function.

Figure 5

Calculated DS intensity in the (110) Brillouin zone. Corresponding experimental data are reported in Ref. 25.

Figure 6

Data from a longitudinal (radial) scan through the DS along the [h, 0, 0] in PMN at $T=650$ K in the vicinity of the (3 0 0) Bragg reflection (circles), our model fit (solid line), and a decomposition of the fit into Bragg, DS, and background components (dashed lines).