Figure 1

(Color online) Temperature dependence of diffuse scattering in $\left(hk0\right)$ plane from x-ray diffraction at ambient pressure, experiments (red/dark background), and simulations at $P=18\text{GPa}$ (white background with intensity range {11,15} in logarithmic scale) (a) Characteristic butterfly- and rod-shaped diffuse scattering [enhanced intensity along [110] and $\left[1\overline{1}0\right]$ directions avoiding $\mathbf{Q}=\left(000\right)$] is observed in the relaxor phase around $\left\{h00\right\}$ and $\left\{hh0\right\}$ Bragg spots, respectively, in experiments (400 K) and simulations (200 K). (b) In the ferroelectric phase, the characteristic shapes diminish in experiments (250 K), similar to simulations (10 K). (c) In the paraelectric phase, simulations (320 K) only show radial diffuse scattering in good agreement with experiments (Ref. 15). (d) The partial contribution to the diffuse scattering from COR-COR correlations $\left(I_{cc}\right)$ show the butterfly and rod shapes, while the partial contribution from CDR-CDR correlations $\left(I_{dd}\right)$ show only the radial patterns in the simulated relaxor phase.Reuse & Permissions

Figure 2

(Color online) Pressure dependence of diffuse scattering in simulations at 180 K (white background) and experiments (red/dark background) in $\left(hk0\right)$ plane. (a) Simulated diffuse scattering in the ferroelectric $\left(P=14\text{GPa}\right)$, relaxor $\left(P=18\text{GPa}\right)$, and the paraelectric $\left(P=25\text{GPa}\right)$ phases, respectively, show characteristic relaxor-phase butterfly- and rod-shaped diffuse scatting and radial diffuse scattering in the pressure induced paraelectric phase. (b) Experiments at 300 K show weak diffuse scattering in the ferroelectric phase (ambient pressure) but strong butterfly- and rod-shaped scattering in the relaxor phase $\left(P=1.4\text{GPa}\right)$. In the paraelectric phase $\left(P=1.8\text{GPa}\right)$ the butterfly and rod shapes disappear. (c) At 50 K, we observe superlattice peaks in the ferroelectric phase $\left(P=0.6\text{GPa}\right)$. In the relaxor phase $\left(P=2.7\text{GPa}\right)$ on top of the butterfly and rod shapes we observe satellite spots. Further increase in pressure to 10 GPa destroys the diffuse scattering, leading to a pressure induced relaxor to paraelectric phase transition. (The bright spot near the center of the image is due to the beam stop.)Reuse & Permissions

Figure 3

(Color online) Simulated diffuse scattering results at $T=200\text{K}$ and $P=18\text{GPa}$ in $\left(hk0\right)$ plane. (a) Diffuse scattering from simulations with spherical CORs, i.e., no shape anisotropy, show butterfly- and rod-shaped features, suggesting that the details of shapes of CORs, which act as PNRs, are unimportant. (b) Diffuse scattering from a simulation with a single COR in a CDR matrix. Absence of butterfly- and rod-shaped diffuse scattering suggests that a single COR is not responsible for the observed diffuse scattering. (c) Diffuse scattering from a simulation with only CDR. Again, no butterfly- or rod-shaped scattering is observed. Rather radial scattering is seen and can hence be attributed to the chemically disordered region. (d) Diffuse scattering from polar oxygen displacements from the same simulation as in Fig. 1. Here the intensity range is {8,15} in the logarithmic scale. Butterfly- and rod-shaped scattering is observed. The spatial extent of the scattering is smaller compared to those from Pb displacements.Reuse & Permissions

Figure 4

(Color online) Real-space correlations [Eq. (3)] projected along [100] and [110] directions and their direct Fourier transforms. The real-space correlation figures have sides of length $40a$, where $a$ is the lattice parameter and the Fourier-space is in units of $2\pi /40a$. (a) and (d) show correlations between all Pb atoms, which reproduce the experimentally observed butterfly- and rod-shaped diffuse scattering. (b) and (e) show the correlations between COR-COR regions which are extended in the real space along directions normal to the butterfly and rod directions. Their Fourier transform gives the characteristic diffuse scattering. (c) and (f) show the correlations between the CDR-CDR regions which when Fourier transformed give the radial patterns.Reuse & Permissions