Takeshi Shigenari

Poisson Ratio Beyond the Limits of the Elasticity Theory

Elastic media can be stable only if the Lame coefficients are positive. This suggests that the Poisson ratio (PR) σ of a regular isotropic elastic media can range from −1 to 0.5. The regular elastic media, described by conventional elasticity theory, means the media which is homogeneous and deforms affinely, that is without formation of hollows or overlapping. In contrast, there are examples of the so-called micropolar media or Cosserat continua, where each microscopic element itself has rotational degrees of freedom. For most of the materials in nature σ lies in the range from 0 to 0.5. For example, cork shows almost zero σ, and σ = 0.5 (constant volume media) is observed for rubber or for the plastic deformation of metals. The materials with a negative σ are quite rare. Usually, the negative σ is attributed to the anisotropy or to the microscopic rotations. The anisotropy is the reason for the negative σ in highly anisotropic crystals like arsenic, antimony and bismuth and also in many single crystals of cubic metals deformed in an oblique direction with respect to the cubic axis. The rotational degrees of freedom cause the negative σ of foams and near the α−β phase transition of quartz and cristobalite. A microscopic model with particles having rotational degrees of freedom has been offered by Ishibashi and Iwata. The model nicely explains the variation of PR from −1 to 0. In the present Short Note we present a microscopic model which demonstrates PR beyond the limits of conventional elasticity. We consider the two-dimensional microscopic model of a crystal shown in Fig. 1. This structure can be found in ref. 11. The model consists of the rigid bars joined to each other by the hinges (open circles in Fig. 1). The bars simulate the rigid clusters of atoms and they have rotational degrees of freedom. The three parameters, the bar lengths a, b and the angle γ (|γ| < π/2), define the geometry of the model. The unit cell has parameters X = 2b cos γ, Y = 2(a− b sin γ). (1)

Inelastic three-soliton collisions in a weakly discrete sine-Gordon system

The three-soliton solutions to the sine-Gordon equation describing the collision of a kink with a breather or with a kink-antikink pair are given and several separatrix three-soliton solutions are extracted from these solutions. The influence of a small perturbation on the three-soliton collisions is studied numerically. As the perturbed system the Frenkel-Kontorova model with a small degree of discreteness is considered. We show that in the three-soliton collisions, in the presence of small perturbation, energy exchange between solitons can take place. The degree of inelasticity of a three-soliton collision is extremely sensitive to the parameters of the collision.

Magnetic Hyperfine Structure and Zeeman Effect of the J=1, K-1=1 Transition of H2CO

The hyperfine structure and the Zeeman effect in the 1 10 →1 11 transition of H 2 CO has been studied with a high resolution beam maser spectrometer. The frequency of the most intense F =2→ F =2 hyperfine component transition was measured to be 4829.649±0.0005 MHz. Theory of the magnetic hyperfine interaction in the presence of external static magnetic field was developed to analyze the experimental result. The spin-rotation interaction constants of proton nuclei in H 2 CO were determined as C x x =-5.0±1.5 KHz, C y y =4.2±1.5 KHz and C z z =-5.3±0.2 KHz. The rotational g -factors of H 2 CO were also obtained as G x x =-0.14±0.03, G y y =-0.14±0.03, G z z =-2.90±0.05 and | G x x - G y y |<0.036.

Domain Wall Solutions for EHM Model of Crystal.

For a one-dimensional discrete model of a crystal the solution of the form of a moving domain wall in an odd-periodic commensurate structure was derived in the continuum approximation. The energy of the commensurate odd-periodic structure, the width and the energy of domain wall were expressed in terms of the amplitudes of harmonics of carrying commensurate structure. With the use of the result by Ishibashi, the relation between domain wall solutions in odd-periodic and even-periodic commensurate structures was established. The applicability and the accuracy of the solutions were also discussed. The obtained solutions were found to be more accurate and general than those by other authors.

Simulation of Modulated Structures in Quartz

We report the results of molecular-dynamics calculation of equilibrium modulated phases of quartz in the vicinity of pressure induced α-β transition. A numerical method suitable for simulation of modulated phases in the vicinity of transition point was developed. The phase diagram with respect to the unit cell deformations was obtained from the pairwise interatomic potentials by [Tsuneyuki et al .: Phys. Rev. Lett. 61 (1988) 869]. The results show that the modulated structures with various wavevectors appear between α- and β-phases suggesting that the softening may occur at any point on the Σ line in the Brillouin zone and that a structure with large wavevector seems to be more probable than one with a small wavevector.

A new interpretation of incommensurate phase of quartz

Abstract Optical and lattice dynamical studies were performed on the incommensurate(IC) phase in quartz. There are two different regions (fog- and m- zone) near the boundary between α and IC phase. The birefringence in the fog-zone was found to be much larger than that expected from the currently accepted model. The lattice dynamical calculation using the Tsuneyuki potential (Phys. Rev. Lett., 61, 869(1988)), revealed that a stable modulated structure with a short period exists between α and β phases. Both results qualitatively agree with the new model recently proposed by Aslanyan et al. (J. Phys. Condens. Matter, 10, 4575(1998)) which assumes that the softening would occur near b/3 rather than close to γ point.

Comments on the characteristics of incommensurate modulation in quartz: discussion about a neutron scattering experiment.

From analysis of the elastic neutron scattering data of Dolino et al. [J. Phys. (Paris) (1984), 45, 361-371], it is shown that, besides the well identified components u(x) and u(y) of the acoustic displacements in the incommensurate (IC) phase of quartz, there also exists a strong component of the u(z) vector of the modulation. The existence of the large u(z) is not consistent with the currently accepted model for the IC transition in quartz, since the long-period IC modulation observed in quartz cannot induce any noticeable acoustic component u(z). The need for a new model is keenly felt in order to understand the origin of the IC modulation in quartz.

Phonon emission from a discrete sine-Gordon breather

Phonon emission from a large-amplitude discrete sine-Gordon breather was studied numerically for a small degree of discreteness. In contrast to the case of highly discrete system investigated by Boesch and Peyrard (Phys. Rev. B 43 (1991) 8491), it was found that the resonance between the breather’s oscillation and the phonons of the lower phonon band edge (ja 0) takes place for a small degree of discreteness. ” 2000 Elsevier Science B.V. All rights reserved.

Reply to the comment on `Inhomogeneities and birefringence in quartz'

The ferroelasticity effect of the incommensurate phase of quartz is discussed. It is pointed out that the effect discussed in the paper by Saint-Gregoire et al (Saint-Gregoire P, Snoeck E, Roucau C, Lukyanchuk I and Janovec V 1996 JETP Lett. 64 410) is negligibly small, and cannot explain the anomalous observations near the transition in quartz.