R A Cowley

The theory of structurally incommensurate systems. II. Commensurate-incommensurate phase transitions

For pt.I see ibid., vol.11, no.17, p.3578 (1978). The authors studied the behaviour of systems undergoing structural transformations between commensurate and incommensurate ordered phases. They reviewed the theory developed by McMillan, and by Bak and Emery (1976) in which the order parameter for such phase transitions is visualised as a soliton density, and give a critique of this theory. They extended the analysis to those cases where the commensurate phase ordering is characterised by a wavevector of the Lifschitz type, such as the Brillouin zone corner. In both cases they found the phase transition to be first order, in agreement with experiment. They also briefly analysed an n=2 component model system which is shown to exhibit a continuous commensurate-incommensurate phase transition entirely analogous to one promoted by an acoustic phonon instability.

The theory of structurally incommensurate systems. I. Disordered-incommensurate phase transitions

The authors examined the behaviour of a wide variety of systems undergoing structural phase transitions to a phase incommensurate with the high-temperature structure. With the aid of renormalisation group methods they argued that, in the cases examined, either the critical behaviour is effectively that of the n=2 component Heisenberg model or the phase transition is first order.

Paraelectric, piezoelectric and pyroelectric crystals: I. Dielectric properties

The dielectric properties of crystals are studied on the basis of the weakly anharmonic crystal model. Particular emphasis is placed on the low frequency behaviour of the dielectric susceptibility and on the possibility of a coupling between the dielectric properties and the fluctuations in the phonon density distribution. These fluctuations cannot be treated by low-order perturbation theory but can be discussed by solving the appropriate transport equation. The approximate solution to this equation is obtained following the techniques developed for ultrasonic attenuation.

Paraelectric, piezoelectric and pyroelectric crystals: II Phase transitions

For pt. I, see ibid., vol. 6, 121 (1973). The response of a crystal in the neighbourhood of a structural phase transition is discussed. It is shown that the behaviour of the scattering cross section is very dependent upon the symmetry of the two phases. The weakly anharmonic crystal model is used within the framework of the Landau theory of phase transitions to discuss nonpiezoelectric/ ferroelectric, piezoelectric/ferroelectric and transitions involving an increase in the size of the unit cell both of the improper ferroelectric kind and otherwise. In every case it is shown that the theory gives rise to the possibility of quasi-elastic as well as inelastic scattering below Tc, but above Tc quasi-elastic scattering is expected in the piezoelectric/ferroelectric and improper ferroelectric phase transitions.

Lattice dynamics of strontium titanate: anharmonic interactions and structural phase transitions

An anharmonic model of strontium titanate has been developed which gives reasonable agreement with the temperature-dependent frequency and linewidth of both the zone-centre and zone-corner soft modes. The model is based upon harmonic models derived from the results of neutron inelastic scattering experiments, and extended to include anharmonic interactions of short range. The anharmonic parameters were determined by constraining the model to fit anharmonic properties, for which particularly simple expressions can be derived. Other anharmonic effects were then computed and found to give reasonable agreement with experiment. The main conclusions drawn from the work are: firstly, it is possible to explain the temperature dependence of the zone-corner soft mode with an anharmonic model that is consistent with other properties; secondly, it is found that the soft-mode self-energy below the transition is different in the thermodynamic and collisionless regimes by an amount that is about 10% of the square of the mode frequency. This result questions the validity of using the conventional phenomenological models to correlate low-frequency (thermodynamic) properties with high-frequency (dynamic) properties such as the results of Raman or neutron scattering.

Dielectric response in piezoelectric crystals

Raman scattering measurements in KDA and CsDA are used to show that the soft mode in a piezoelectric ferroelectric may not be described as a classical damped oscillator. The discrepancy arises because of a contribution to the selfenergy of the mode at low frequencies which arise from the coupling of the mode with fluctuations in the phonon density.

Raman scattering at structural phase transitions

The Raman scattering of light from the ferroelectric fluctuations of the uniaxial ferroelectric lead germanate is analysed and found to be well described by models for which the self-energy has appreciable dispersion at frequencies comparable with the soft-mode linewidth. A model is developed to calculate the self-energy arising from phonon-density fluctuations of the modes belonging to the same branch. The model shows that this contribution to the self-energy of the soft mode is particularly large if the modes with which it is interacting are overdamped. In detail, however, the model suggests that close to Tc there is an appreciable contribution to the Raman scattering from the interference terms between the one- and two-phonon scattering.

Magnetic excitations in antiferromagnetic Mn1-cZncF2 at large Zn concentrations

Neutron inelastic scattering techniques have been used to study Zn-substituted MnF2 crystals with average Zn concentrations c=0.22+or-0.02 and 0.7+or-0.1. For c=0.22 the results gave scattered distributions whose peaks were at frequencies less than those of the excitations of pure MnF2 and whose width was considerably larger than the experimental resolution. The other specimen had a concentration gradient such that one end of the crystal ordered magnetically at 4.2K whereas the other end did not. There were no significant differences between the scattering from the different ends, and it consisted of an overdamped distribution the width of which decreased as the wavevector of the excitation decreased.

Application of the Wilson theory of critical phenomena to a structural phase transition

The techniques of the renormalization group and the epsilon -expansion are used to discuss static critical effects near a structural phase transition. In the case of the transition in strontium titanate the theory suggests that the static critical exponents are those of the classical isotropic Heisenberg antiferromagnet.

The two phonon Raman spectra of alkali halide crystals

The two phonon Raman spectrum of KBr is calculated. The calculation is based on the shell model and assumes a nonlinear coupling between the shell and the core of the negative ions. It is found that the results are considerably improved by using a breathing shell model rather that a rigid shell model. The theory then contains three parameters which may be chosen to give a reasonable description of the experimental results. An investigation of the importance of inter-ionic nonlinearities suggests that they are far less important for describing Raman scattering than are the intra-ionic terms.