E. Roger Cowley

Study of a simple model ferroelectric using the effective potential method

Abstract We have applied the effective potential formalism to a simple one-dimensional model of a ferroelectric crystal. The method incorporates quantum effects into a partition function of classical form, which greatly simplifies the calculation. Our results for the nature of the phase transitions, the transition temperatures, and the temperature dependence of the ordering parameter, are all in very good agreement with a full quantum mechanical calculation. Pacs 63.70, 77.80, 64.60.C

Soft mode behavior in a one-dimensional model ferroelectric

Abstract We use a moment-expansion method for the spectral functions to show that a one-dimensional molecular field model of a ferroelectric crystal has a soft zone-center mode of vibration. The frequency of the mode goes towards zero at the transition point but the mode becomes overdamped very close to the transition. Within the limitations of the moment-expansion method, we see no central peak behavior.

Another surprise in mechanics

We recently published a note describing a spectacular mechanics demonstration. It illustrated simultaneously the three conservation laws of mechanics for momentum, energy, and angular momentum and resulted in an amazingly counterintuitive outcome. In this article we are reporting on a follow-up of a conjecture by Professor John Mallinckrodt of the California State Polytechnic University.

A thought-provoking demonstration

We present and discuss a physics demonstration, similar to, but distinct from, the ballistic-pendulum demonstration, one that illustrates all three conservation laws of mechanics (for energy, momentum, and angular momentum) simultaneously.

Molecular field models for ferroelectric crystals

The application of molecular field models to the calculation of the thermal properties of ferroelectric crystals is discussed, with particular emphasis on the sequence of phase transitions occurring in barium titanate. The parameters of the model are related to first-principles energy calculations on the one hand, and to the Landau-Devonshire thermodynamic method on the other. The necessary conditions for the model to display a first-order transition to the disordered, cubic, phase are discussed. Results are presented for one- and three-dimensional models which show most of the features displayed by barium titanate.

Selected topics in lattice dynamics: A critical review (including breathers)

We present a review of lattice dynamics to provide the underpinnings for the study of nonlinear localized modes, the so-called breathers. After a historical survey we address the following topics: harmonic theories, anharmonic perturbation theory, self-consistent theories, classical simulation techniques, path-integral theories, realistic crystal potentials, and intrinsic localized modes. We discuss both static and dynamic properties of crystals, e.g., neutron and x-ray scattering. We do not consider transport properties. Throughout, our emphasis is on discussing the major advances in the field and citing the appropriate references. Our aim is to achieve clarity and simplicity for readers who wish to move on to the study of breathers. We have made a special effort to set up the language and notation that is generally accepted in the field. In order to acquaint the reader with the techniques used in lattice dynamics we have analyzed a number of key problems in detail including a comparison with the available experimental data.

On the applicability of the frequency moments method for the calculation of the spectral shape of a one-dimensional crystal

Abstract Using the anharmonic perturbation theory developed by Maradudin and Fein [Phys. Rev. 128 (1962) 2589] we investigate the reliability of the application of the frequency moments method to the calculation of the spectral shape of a one-dimensional Lennard-Jones crystal in both the classical and quantum regime.

Monte carlo calculations of the equation of state of alkaline earth oxides

Abstract We are currently performing Monte Carlo calculations to determine the equation of state of magnesium oxide and related materials. Initially a rigid-ion model was used, but we are presently applying the potential induced breathing model. This has the important advantages of being a first-principles based model which predicts a many-body deviation from the Cauchy relation.

Generalized sum rules for the moments of a one-phonon spectral function

The low-order moments of the one-phonon spectral function of a crystal are shown to be related directly to the self-energy of the phonon. These relationships are generalizations of the Placzek sum rule and of a well-known high-temperature extension. The rules can be used to simplify a lattice-dynamical calculation of the moments, or, if the moments have been calculated by some other method, such as a Monte Carlo simulation, the rules can be applied in the other direction to yield information about the self-energy of the mode. This information can, in turn, be used to test the quality of a lattice-dynamical approximation. As an illustration, the rules are applied to transverse and longitudinal zone-boundary phonons in argon at 81 K.

Studies of the phase transition in a model of tin telluride

Abstract We have constructed a fully-specified model of a diatomic crystal showing a soft-mode phase transition, loosely patterned on tin telluride. The model can be used to test the accuracy of different techniques for studying the phase transition. Here we apply the self-consistent phonon theory (SCI). Using this theory, we do find a soft mode in the high-temperature, cubic phase, and the free energy shows the Landau form, consistent with a mean-field theory of a second-order phase transition. However, the frequency of the soft mode calculated in the self-consistency iterations does not go to zero at the phase transition. It is pointed out that, even within the SC1 approximation, the frequencies associated with the response functions of the crystal should include additional contributions, corresponding to cubic and bubble-diagram shifts. With these contributions included, the frequency does go to zero at the transition. The shape of the spectral function is also discussed.