Reassessment of the Burns temperature and its relationship to the diffuse scattering, lattice dynamics, and thermal expansion in relaxor $\text{Pb}\left({\text{Mg}}_{1/3}{\text{Nb}}_{2/3}\right){\text{O}}_3$

We have used neutron scattering techniques that probe time scales from ${10}^{-12}$ to ${10}^{-9}\text{s}$ to characterize the diffuse scattering and low-energy lattice dynamics in single crystals of the relaxor ${\text{PbMg}}_{1/3}{\text{Nb}}_{2/3}{\text{O}}_3$ (PMN) from 10 to 900 K. Our study extends far below $T_c=213\text{K}$, where long-range ferroelectric correlations have been reported under field-cooled conditions, and well above the nominal Burns temperature $T_d\approx 620\text{K}$, where optical measurements suggest the development of short-range polar correlations known as “polar nanoregions” (PNR). We observed two distinct types of diffuse scattering. The first is weak, relatively temperature independent, persists to at least 900 K, and forms bow-tie-shaped patterns in reciprocal space centered on $\left(h00\right)$ Bragg peaks. We associate this primarily with chemical short-range order. The second is strong, temperature dependent, and forms butterfly-shaped patterns centered on $\left(h00\right)$ Bragg peaks. This diffuse scattering has been attributed to the PNR because it responds to an electric field and vanishes near $T_d\approx 620\text{K}$ when measured with thermal neutrons. Surprisingly, it vanishes at 420 K when measured with cold neutrons, which provide approximately four times superior energy resolution. That this onset temperature depends so strongly on the instrumental energy resolution indicates that the diffuse scattering has a quasielastic character and demands a reassessment of the Burns temperature $T_d$. Neutron backscattering measurements made with 300 times better energy resolution confirm the onset temperature of $420\pm 20\text{K}$. The energy width of the diffuse scattering is resolution limited, indicating that the PNR are static on time scales of at least 2 ns between 420 and 10 K. Transverse acoustic (TA) phonon lifetimes, which are known to decrease dramatically for wave vectors $q\approx 0.2{\text{Å}}^{-1}$ and $T_c<T<T_d$, are temperature independent up to 900 K for $q$ close to the zone center. This motivates a physical picture in which sufficiently long-wavelength TA phonons average over the PNR; only those TA phonons having wavelengths comparable to the size of the PNR are affected. Finally, the PMN lattice constant changes by less than $0.001\text{Å}$ below 300 K but expands rapidly at a rate of $2.5\times {10}^{-5}{\text{K}}^{-1}$ at high temperature. These disparate regimes of low and high thermal expansions bracket the revised value of $T_d$, which suggests the anomalous thermal expansion results from the condensation of static PNR.

Figure 1

Top—temperature dependence of the TA phonon energy width ${\Gamma }_{\text{TA}}$ measured with thermal neutrons by Wakimoto et al. (Ref. 27). Middle—diffuse scattering intensity contours measured at (110) below (300 K) and just above (650 K) the Burns temperature $T_d$ using cold neutrons by Hiraka et al. (Ref. 28). Bottom-diffuse scattering temperature dependence measured with cold neutrons (open circles) and thermal neutrons (dashed line) by Hiraka et al. (Ref. 28).

Figure 2

Diffuse scattering intensity contours in PMN measured on SPINS near (100) are shown using a linear gray scale at (a) 300, (b) 650, and (c) 900 K. Diffuse scattering intensity contours measured on BT9 at 900 K near (300) using thermal neutrons are shown in (d). The data shown in panels (a) and (b) are from Hiraka et al. (Ref. 28). Schematic diagrams of the diffuse scattering intensity contours below (low-$T$) and at $T_d$ (high-$T$) are shown in the upper right.

Figure 3

(Color online) Contour plot of the difference in diffuse scattering intensity near (110) measured at 550 and 400 K. The result is the characteristic figure 8 pattern, observed previously by Vakhrushev et al. (Ref. 40).

Figure 4

(Color online) Diffuse scattering intensity measured on BT9 at 300 K as a function of reduced momentum transfer relative to (100) (open circles) and (200) (solid circles). The dotted lines isolate the diffuse scattering component from the Bragg peak. The inset shows the orientation of the scan relative to the familiar butterfly pattern measured near (200) at 100 K.

Figure 5

(Color online) Diffuse scattering contours measured on BT9 near (200) are shown at (a) 100, (b) 300, and (c) 600 K.

Figure 6

Diffuse scattering intensity contours in PMN measured on the NCNR DCS near (100) are plotted on a logarithmic gray scale at 300 K. Open circles represent the reciprocal space locations of the detectors of the high-flux backscattering spectrometer relative to the butterfly-shaped intensity contours. Each open circle is a separate detector, and the detector numbers are indicated. These DCS data are taken from Xu et al. (Ref. 18).

Figure 7

(Color online) (a) Contour plot of the diffuse scattering intensity measured on the HFBS as a function of energy transfer and temperature. Contours are shown on a linear intensity scale; dashed lines indicate the FWHM of the peak linewidth at each temperature. Data were summed over detectors 10–16 as illustrated in Fig. 6. Panels (b)–(d) show inelastic scans at 700, 300, and 100 K. The horizontal bar in panel (c) represents the instrumental FWHM elastic energy resolution $\left(2\delta E\right)$.

Figure 8

(a) Temperature dependence of the diffuse scattering measured on the HFBS; data are integrated in energy from $\pm 5\mu \text{eV}$ and in $Q$ over detectors 10–16 as illustrated in Fig. 6. (b) Temperature dependence of the diffuse scattering intensity measured on SPINS at (1.05,0.95,0) by Hiraka et al. (Ref. 28). The SPINS energy resolution of $\delta E=120\mu \text{eV}$ HWHM provided the energy integration.

Figure 9

TA phonon line shapes in PMN measured on SPINS with cold neutrons at $\vec{Q}=\left(1.035,0.965,0\right)$ and (1.1,0.9,0) from 100 to 900 K.

Figure 10

TA and TO phonon line shapes in PMN measured on BT9 with thermal neutrons near the waterfall wave vector at $\vec{Q}=\left(3,-0.14,0\right)$ and $\left(1,-0.14,0\right)$ from 300 to 900 K.

Figure 11

The square of the phonon energy is plotted versus temperature for the zone-center TO modes measured at (200) (open diamonds) and (220) (solid diamonds) taken from Wakimoto et al. (Ref. 27) and Stock et al. (Ref. 29), as well as for three TA modes measured at (1.035,0.965,0) (open triangles), (1.1,0.9,0) (open circles), and $\left(3,-0.14,0\right)$ (solid circles). Linear behavior is consistent with that expected for a conventional ferroelectric soft mode.

Figure 12

Lattice strain of single crystal PMN derived from the (220) Bragg reflection measured from 30 to 580 K on BT9. Data were obtained on heating using a perfect Ge(004) analyzer, an incident neutron energy $E_i=14.7\text{meV}$, and horizontal beam collimations of $15^{\prime }\text{−}47^{\prime }\text{-S-}20^{\prime }\text{−}40^{\prime }$ to obtain extremely high $q$ resolution. X-ray data from Dkhil et al. (Ref. 64) are indicated by the open squares for comparison.