Shigeo Naya

A Theory of X-Ray Scattering by Disordered Polymer Crystals

A theory of X-ray diffractions from disordered crystals, which are composed of the polymer molecules of helical structures, is developed. This theory gives the relationships between various disorders in polymer crystals and the diffuse streak diffraction patterns on layer lines as well as Laue-Bragg reflections. The results derived here include those given by Clark and Muus in 1962.

Orientational Phase Transition and Dynamic Susceptibility of Hindered-Rotating Dipolar System –A Librator-Rotator Model–

A microscopic theory is presented to study the two-directional orientational phase transition of the interacting dipolar system and its dynamic susceptibility in the paraelectric phase. On the basis of a classical mechanical model that the librational and the rotational motion for a dipole in the hindered-rotation potential can be treated exactly, the statistical mechanical calculations are carried out in the framework of the molecular field approximation and the linear response theory. In this approximation, several characteristic quantities such as Curie temperature, specific heat, static and dynamic susceptibilities, etc. are all obtained rigorously. The present model recovers the dynamics proper to the dipolar motion in the studies of the orientational phase transition and its dynamic susceptibility, so that it offers an approach different from the conventional pseudo-Ising spin model.

A Theory of Orientational Phase Transition and X-Ray Critical Scattering –Random Phase Approximation–

A statistical theory of random phase approximation for the orientational phase transition is proposed, which is an extension of Brouts theory for the Ising spin system. This theory is used to obtain a general formula for the intensity of X-ray scattering in a compact form. An illustrative example of the X-ray critical scattering near the transition temperature is also given.

On the X-Ray Diffuse Scattering by Molecular Crystals

A general theory for the intensities of X-rays scattered by molecular crystals was under harmonic approximation given by taking account of the molecular translational and librational lattice vibrations as well as their mutual coupling. The molecules were taken as rigid bodies. The relationship of this theory to the other ones hitherto given for the diffuse scattering by molecular crystals was discussed.

Phase Transition and Dynamic Susceptibility of the Anharmonic Oscillator System. An Effective Analysis of Double Morse Potential Based on the Unified Oscillator Model.

An effective analysis for the static and the dynamic properties of an assembly of classical anharmonic oscillators moving in the double Morse potential (DMP) is made in the framework of the molecular field approximation and the linear response theory. By using the effective (trial) potential V 0 ( x )= A x 4 + B x 2 with the temperature-dependent coefficients A and B , some characteristic effects of the higher anharmonicities in DMP are quantitatively considered. The present method offers an extension of the self-consistent Einstein theory, which enables us to make discussions on the static and the dynamic properties of the system from the unified mechanical point of view whether the relevant potential is of single- or of double-minimum.

A Statistical-Mechanical Theory of Structural Phase Transition in Helical Polymer Crystals

The structural phase transition in helical polymer crystal is investigated from a statistical-mechanical point of view. Starting from an effective Hamiltonian per chain molecule, the self-consistent equation is obtained in a mean field approximation. On the basis of this equation, some types of possible phase transitions are investigated. The pressure-dependence of the transition point is also considered. As an application of the theory, the structural phase transition in polytetrafluoroethylene (PTFE) crystal is qualitatively discussed.

Critical Dynamics of Polyorientational Phase Transition —Linear Relaxation Theory—

A critical dynamics of the polyorientational phase transition is presented, which is an extension of the statistical equilibrium theory in random phase approximation previously given by one of the authors. In the approximation of the linear theory, a relaxation equation for the critical slowing down as well as a formula for the dynamical susceptibility tensor are derived. The present theory covers Matsubaras one for the X-ray scattering by orientationally disordered crystals in the thermal equilibrium limit, and reduces naturally to the study of Suzuki and Kubo for the dynamical susceptibility of magnetic system in the Ising spin limit. As an illustrative example, the application of the present theory to an electric dipolar system with the polyorientational ordering and disordering is also given.

Freeze-In Transition of Anharmonic Oscillator System with Quenched Random Interactions

A simple model of strongly disordered systems composed of anharmonic oscillators with quenched random interactions is introduced and its structural phase transition is studied by making use of the replica method. A freeze-in transition characterized by Edwards and Anderson types order parameter (q *0), the phase diagram (para-ferrodistortive-frozen), and a constant susceptibility below the transition temperature are derived in the mean field (Einstein oscillator) approximation. The self-consistent phonon approximation is also used to study the effect of spatial fluctuations, and it is shown that the phase diagram undergoes a qualitative change at the spatial dimension d=4. The relationship between our model and the Ginzburg-Landau theory of spin.glasses are discussed.

Phase Transition of Spherical Phonon System

A critical behaviour of “spherical phonon system” is studied, which is a tentative model useful for the consideration of the ferroelectric phase transitions in anharmonic lattices. The mechanism of the phase transition in this system can be interpreted as a Bose-Einstein condensation of spherical phonons based upon a freeze of chemical potential. The results obtained by the classical and the quantum-mechanical treatments are compared with that of previous theories given by Lines, Tokunaga and Matsubara, Larkin and Vaks, et al.