Neutron scattering measurements of the lowest-energy TO phonons in the relaxor Pb(Mg 1/3 Nb 2/3 )O3 (PMN) are reported for 10 ≤ T ≤ 750 K. The soft mode, which is overdamped by the polar nanoregions below the Burns temperature T d = 620 K, surprisingly recovers below 220 K. The square of the soft mode energy (hω0) 2 increases linearly with decreasing temperature, and is consistent with the behavior of a ferroelectric soft mode. At 10 K hω0 reaches 11 meV, the same value observed in ferroelectric Pb(Zn 1/3 Nb 2/3 )O3 at low-T . An unusual broadening of the TA phonon starts at T d and disappears at 220 K, coincident with the recovery of the TO mode. These dynamics suggest that a well-developed ferroelectric state is established below 220 K.

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The temperature and zone dependence of the lattice dynamics in Pb(Mg 1/3 Nb 2/3 )O3 is characterized using neutron inelastic scattering. A strong correlation between the diffuse and phonon scattering is measured. The lattice dynamics in Brillouin zones where the diffuse scattering is strong is observed to display qualitatively different behavior than that in zones where the diffuse scattering is weak. In the ( 220) and ( 200) zones, where there is a weak diffuse component, the dynamics are well described by coupled harmonic oscillators. Compared with SrTiO3, the coupling is weak and isotropic, resulting in only a small transfer of spectral weight from one mode to another. A comparison of the scattering in these zones to that in the (110) zone, where a strong diffuse component is present, reveals a strong coupling of the diffuse (or central) component to the acoustic mode. We speculate that the coupling to the central peak is the reason for several recent conflicting interpretations of the lattice dynamics based on data from zones with a strong diffuse component.

Using x-ray scattering, we have studied the nematic to smectic- phase transition of the liquid crystal butyloxybenzilidene-octylaniline confined in an aerosil network. We find that the disorder introduced by the aerosil network destroys the long-range nature of the phase transition, and that the transition becomes similar to that observed in a finite-size system, with finite low-temperature correlation lengths of the ordered moments and a power-law behavior of the order parameter with respect to the reduced temperature observable in a limited temperature range. We also show evidence for a systematic evolution of the effective order parameter critical exponent beta with increasing disorder.