Reassessment of the Burns temperature and its relationship to the diffuse scattering, lattice dynamics, and thermal expansion in relaxorPb(Mg1/3Nb2/3)O3

Abstract

We have used neutron scattering techniques that probe time scales from ${10}^{\ensuremath{-}12}$ to ${10}^{\ensuremath{-}9}\text{ }\text{s}$ 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 ${T}_{c}=213\text{ }\text{K}$, where long-range ferroelectric correlations have been reported under field-cooled conditions, and well above the nominal Burns temperature ${T}_{d}\ensuremath{\approx}620\text{ }\text{K}$, 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 $(h00)$ Bragg peaks. We associate this primarily with chemical short-range order. The second is strong, temperature dependent, and forms butterfly-shaped patterns centered on $(h00)$ Bragg peaks. This diffuse scattering has been attributed to the PNR because it responds to an electric field and vanishes near ${T}_{d}\ensuremath{\approx}620\text{ }\text{K}$ 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 $420\ifmmode\pm\else\textpm\fi{}20\text{ }\text{K}$. 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 $q\ensuremath{\approx}0.2\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$ and ${T}_{c}lTl{T}_{d}$, 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 $0.001\text{ }\text{\AA{}}$ below 300 K but expands rapidly at a rate of $2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }{\text{K}}^{\ensuremath{-}1}$ 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.