Transverse Lattice Waves Research Articles

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System**Supported by the National Natural Science Foundation of China under Grant Nos 11675261 and 21403297, and the Scientific Research Foundation of Ludong University under Grant No LY2014010.

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.

Oscillations of magnetized dusts in electronegative radio-frequency plasma

Oscillations of charged dust grains in the sheath region of a radio-frequency plasma containing negative ions are studied using a one-dimensional model for collisional sheaths. The forces on a dust grain in the sheath region are first analyzed and the force-balance conditions found. Oscillations of the levitated dusts are then investigated. Linear lattice waves, including one-dimensional longitudinal and two-dimensional hexagonal transverse lattice waves, as well as the effects of the negative ions and external magnetic field on the waves, are discussed.

Identification of soft phonon modes in Ge–Sb–Te using electron diffraction

The atomistic structure of crystalline Ge–Sb–Te thin film for phase-change optical recording was investigated using transmission electron microscopy and nanobeam electron diffraction. Nonradial diffuse streaks were observed in electron diffraction patterns obtained from laser-induced crystalline phases of Ge–Sb–Te thin films. The intensities of the diffuse streaks were pronounced in particular directions in this alloy. The diffuse streaks were due to low-frequency transverse lattice waves that occur along directions perpendicular to the near neighbor zigzag atomic chains.

Numerical study of transverse lattice waves connected with martensitic transformation

The behavior of the transverse lattice wave connected with the nucleation process of martensite is studied, taking into account the anharmonicity, by use of one-dimensional model for the crystal. The key factor which determines the behavior of the transverse lattice waves according to the model is its amplitudeA with respect to the critical amplitudeA c. As far asA < A c, the presence of the transverse lattice wave does not lead to the initiation of the martensite. Depending on the variation ofA andA c with temperature, the model suggests two alternative processes for the initiation of the martensitic transformation. 1) In case the variation ofA c with temperature is larger than the variation ofA with temperature, the transverse lattice wave develops into the stable nuclei of the martensite, as soon asA c becomes smaller thanA with decrease of temperature. 2) In case the variation ofA with temperature is larger than the variation ofA c with temperature, the transverse lattice wave represents the heterophase fluctuation whenA « A c. The stable martensite is formed with the reduction ofA as temperature is reduced. The presently available experimental data suggest the process 1) as the nucleation mechanism of the martensite. The prominent role of the interface energy between the martensite and the austenite in determining both the structure of the martensite and the dispersion relationship of the transverse lattice wave in the austenite is pointed out.

Non-Linear Mechanical Model for Martensitic Transformation

A non-linear mechanical model for the martensitic transformation is proposed. The formation process of the nucleus of the martensitic phase is described as the results of the evolution of the transverse lattice waves in a non-linear dispersive lattice of the parent phase. A significant role of the dispersion relationship in the martensitic transformation is found; it is the dispersion relationship of the transverse lattice waves in the parent phase that governs the structure of the martensitic nucleus. However, the presence of such strong anomaly in the dispersion relationship as accompanied by a soft phonon is not required for the nucleation of the martensitic phase.

The specific heat of solid oxygen

Measurements have been made in the temperature range from 1.3° K to about 71°K with particular attention to the behavior at very low temperatures, and in the neighborhood of the α-β transition at about 23.89° K. Assuming that near 0° K each molecule moves as a single mass point with the passage of lattice waves, the effective Debye temperature at 0° K is extrapolated to be 104±2° K. As the temperature rises above 10° K, the specific heat rises more rapidly than a reasonable Debye model would predict, suggesting the appearance of additional degrees of freedom, which are thought to be the superposition of a librational motion of the molecules superposed on the longitudinal and transverse lattice waves controlling the motion of a molecule's center of mass. The specific heat shows a very sharp high “spike” at the α-β transition with an entropy change of aboutR ln 1.65; there is no evidence for a latent heat associated with this transition.

Thermal Diffuse Scattering of X-Rays by Transverse Lattice Waves of Potassium Bromide Crystal

Intensity measurements of X-ray diffuse scattering by single crystals of KBr were made on and around the symmetry axes [010] passing through the reciprocal lattice point 400 and [110] passing through the point 004 in the reciprocal space at 293°K. The measured intensities were compared with the calculated intensities in which the first-order thermal diffuse scatterings by the transverse lattice waves were computed on the bases of a simple-shell model and a rigid-ion model. The measurements were found to be closer to the calculated values based on the shell model than to those based on the rigid-ion model. The intensity correction of diffuse scattering till up to 20% for the divergence of X-rays was found to be necessary for the calculation corresponding to the measurements on the symmetry axis [010] passing through the reciprocal lattice point 400.

Ultrasonic Shear Wave Attenuation in Superconducting Tin

The superconducting attenuation of transverse ultrasonic waves was studied experimentally in single crystal tin. The attenuation was found to be consistent with the relation $\frac{{\ensuremath{\alpha}}_{s}}{{\ensuremath{\alpha}}_{n}}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\frac{\mathcal{E}}{\mathrm{kT}})$ at low reduced temperatures in tin; $\frac{{\ensuremath{\alpha}}_{s}}{{\ensuremath{\alpha}}_{n}}$ is the superconducting-to-normal attenuation ratio and $\mathcal{E}$ is the superconducting energy gap. This functional form satisfied the low-temperature observations for all principal propagation and polarization orientations. Anisotropy in the apparent superconducting energy gap was demonstrated. It was found that anisotropy can be associated with polarization orientation as well as propagation orientation of the transverse lattice waves. Observed values of total and residual shear wave attenuation were found to suggest the importance of shear deformation interactions between the electron system and lattice waves in tin.

Temperature Dependence of the Pure Quadrupole Resonance Frequency and Spin—Lattice Relaxation Time in NaBrO3 at Low Temperature

The pure quadrupole resonance frequency of Br79 and Br81 in NaBrO3 has been measured between 4.2° and 77.3°K. The spin—lattice relaxation times have been measured between 4.2° and 16°K. The frequency measurements were compared with the Bayer—Kushida theory. While qualitative agreement with the theory is found over the entire temperature interval investigated, the theory does not fit the data in detail. The spin—lattice relaxation times were compared with the theory developed by Chang for NaClO3. If a linear or parabolic temperature dependence of the Br quadrupole frequency is used, as has been the case in all previous work, the theory can be made to agree with the data by appropriately choosing the Debye temperature. However, if the more nearly correct temperature dependence of the quadrupole frequency given by Bayer is inserted into the theory, it is found that no reasonable adjustment of the Debye temperature gives agreement. Fair agreement with the data can be obtained in this case by adjusting the velocities of the longitudinal and transverse lattice waves. Furthermore, at low temperatures the frequency dependence of Bayer leads to nearly equal contributions to the relaxation of Δm=±1 and Δm=±2 transitions, in contrast to the assumption of a linear or parabolic temperature dependence which leads to negligible contribution by the Δm=±2 transitions.

The Lattice Component of the Thermal Conductivity of Metals and Alloys

Makinson's (1938) theory of the lattice component of the thermal conductivity of metals and alloys, when limited at low temperatures by interaction with the conduction electrons, is re-examined, and the magnitude of the lattice conductivity is related to the electronic thermal conductivity at low temperatures, thus avoiding uncertainties in the theory at high temperatures. The result depends on whether transverse lattice waves can interact with the electrons.