Lattice dynamics of wurtzite-type crystals—II

We evaluated, in the preceding paper, the effective ionic charge and electronic polarizability for wurtzite-type crystals on the basis of the polarizable-ion model given by Born and Huang. With use of the quantities so evaluated, we here estimated the short-range force constants from observed frequencies, elastic constants, and piezoelectric constants after simplifying Born and Huang's procedures. The resulting set of force constants can reproduce the observed data except for the piezoelectric constants. This poor reproduction of the piezoelectric constants is due to the fact that the long-range force is emphasized in the polarizable-ion model.     

Effective dielectric constant model of electromagnetic backscattering from stratified air–sea surface film–sea water medium

Studies of surface film medium on the sea surface are carried out in this paper for developing the technology to automatically detect and classify sea surface films, and an effective dielectric constant model of electromagnetic backscattering from a stratified air–ocean interface. Numerical results of the new model show the characteristics of effective dielectric constants for the air–sea surface film–sea water medium as follows. The effective dielectric constants decrease with increasing relative dielectric constants of the sea surface films. The effective dielectric constants decrease in horizontal polarization(abbr. HH polarization) and increase in VV vertical polarization(abbr. VV polarization) with increasing radar incident angle. Effective dielectric constants vary with relative sea surface film thickness as a cosinusoidal function of sea surface film thickness. Effective dielectric constant of VV polarization is larger than that of HH polarization. Two potential applications are found with our model, i.e., the retrieval of dielectric constants from the sea surface film, and the film thickness retrieval with our model. Our model has a highly significant influence on improving the technology related to the remote sensing of sea surface films.     

The molecular-statistical calculation of the elastic constants of uniaxial nematics

Using the molecular-statistical theory of the thermodynamic properties of nematics and perturbation theory, the expressions for the elastic constants of uniaxial nematics are derived in terms of the mutual interactions between their constituent molecules. Next the elastic constants of the Maier-Saupe model are calculated and compared with the original result. The appearing difference is discussed briefly. Finally, in view of existing discrepancies, the elastic constants of the Onsager model are recalculated. For that purpose the hard rod interaction is conceived as the limit of a non-singular interaction. The elastic constants of hard core models are shown to increase with increasing temperature at constant density. In view of this behaviour the usefulness of hard core models for an understanding of the nematic state seems rather limited.     

DETERMINATION OF ELASTIC CONSTANTS OF ANISOTROPIC LAMINATED PLATES USING ELASTIC WAVES AND A PROGRESSIVE NEURAL NETWORK

In this paper, a procedure is suggested to inversely determine the elastic constants of anisotropic laminated plates using a progressive neural network (NN). The surface displacement responses are used as the inputs for the NN model. The outputs of the NN are the elastic constants of anisotropic laminated plates. The hybrid numerical method (HNM) is used to calculate the displacement responses of laminated plates to an incident wave for given elastic constants. The NN model is trained using the results from the HNM. A modified back-propagation learning algorithm with a dynamically adjusted learning rate and an additional jump factor is developed to tackle the possible saturation of the sigmoid function and to speed up the training process for the NN model. The concept of orthogonal array was adopted to generate the representative combinations of elastic constants, which reduces significantly the number of training data while maintaining its data completeness. Once trained, the NN model can be used for on-line determination of the elastic constants if the dynamic displacement responses on the surface of the laminated plate can be obtained. The determined elastic constants are then used in the HNM to calculate the displacement responses. The NN model would go through a progressive retraining process until the calculated displacement responses using the determined results are sufficiently close to the actual responses. This procedure is examined for an actual glass/epoxy laminated plate. It is found that the present procedure is very robust and efficient for determining the elastic constants of anisotropic laminated plates.     

Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry

We present a reflection-type terahertz time-domain spectroscopic ellipsometry (THz-TDSE) technique for measuring the complex dielectric constants of thin-film materials without replacement of the sample. THz-TDSE provides complex dielectric constants from the ratio of the complex amplitude reflection coefficients between p- and s-polarized THz waves. The measured dielectric constants of doped GaAs thin films show good agreement with predictions of the Drude model, even though the film thickness is of the order of a tenth of the penetration depth of the THz waves. In addition, we demonstrate the measurements of soft-phonon dispersion in SrTiO(3) thin films deposited on a Pt layer. The obtained dielectric constants agree well with the predictions of a generalized harmonic oscillator model.     

DFT Study of HFI in Halogen-Containing Gold, Silver and Copper Complexes

We have analyzed the nuclear quadrupole coupling constants in copper, silver and gold halides and related compounds an the basis of the calculations with use of pseudo-potentials. The geometrical parameters and NQR halogen quadrupole constants obtained by these calculations substantially corresponded to the data of microwave spectroscopy in the gas phase. The analysis of the quality of the calculations with use of pseudo-potentials and the expanded basis set for the copper compounds was carried out. The ZORA model is shown to be a viable alternative to the computationally demanding B3LYP/SDD model for the calculation of halogen coupling constants in molecules. Besides the ZORA model as against BXYP/SDD model have been caused to realistic values of gold nuclear quadrupole coupling constants. In this case of the gold compounds the main contribution of the chemical Mössbauer shift comes from the 6s-orbiral population of the gold atoms.     

Experimental constants, characterizing the process of a plasma polymer modification

In the following paper, empirical constants are determined by a plasma-chemical model and experimental data of the wetting contact angle. The constants characterize the alteration of the contact angle as a function of the time of the polymer treatment and the kind of the plasma-creating gas. The presented equations of the model connect the contact angle with the empirical constants for arbitrary time intervals of treatment and arbitrary percentage content of the researched gas mixtures and gasses. The chemical rate constants, which describe the process of the plasma modification of the polymer material, are determined.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Testing Transition State Theory on Kac-Zwanzig Model

A variant of the Kac-Zwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a double-well external potential and coupled to N free particles through linear springs. While the Kac-Zwanzig model is deterministic, under appropriate choice of the model parameters the evolution of the distinguished particle can be approximated by a two-state Markov chain whose transition rate constants can be computed exactly in suitable limit. Here, these transition rate constants are compared with the predictions of TST and VTST. It is shown that the application of TST with a naive (albeit natural) choice of dividing surface leads to the wrong prediction of the transition rate constants. This is due to crossings of the dividing surface that do not correspond to actual transition events. However, optimizing over the dividing surface within VTST allows one to eliminate completely these spurious crossings, and therefore derive the correct transition rate constants for the model. The reasons why VTST is successful in this model are discussed, which allows one to speculate on the reliability of VTST in more complicated systems.     

Multiple-quantum relaxation in the magic-angle-spinning NMR of 13C spin pairs.

We determine the decay rate constants of zero-, double- and single-quantum coherence for 13C spin pairs in magic-angle-spinning solid-state NMR. The double-quantum coherence is excited by a C7 pulse sequence and converted into zero-quantum coherence by a frequency-selective pair of pi/2 pulses. The zero-quantum coherence is reconverted into observable magnetization by a second pair of pi/2 pulses followed by a second C7 sequence. In a magnetically dilute system where the 13C-13C distance is 0.296 nm, the relaxation rate constants are consistent with a model of uncorrelated random fields at the two labeled 13C sites. In a fully-labelled system with a short 13C-13C distance of 0.153 nm, the measured rate constants are inconsistent with the uncorrelated random field model.     

Elastic constants of natural quartz

The elastic constants of a natural-quartz sphere using resonance-ultrasound spectroscopy (RUS) are measured. The measurements of the near-traction-free vibrational frequencies of the sphere are matched with the predicted frequencies from the dynamic theory of elasticity, with optimized estimates for the elastic constants driving the differences between these sets of frequencies to a minimal value. The present computational model, although based on earlier approaches, is the first application of RUS to trigonal-symmetry spheres. Quartz shows six independent elastic constants, and our estimates of these constants are close to those computed by other means. Except for C14, after a 1% mass-density correction, natural quartz and cultured quartz show the same elastic constants. Natural quartz shows higher internal frictions.     

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences.The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction onds.The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method.The critical points and all the critical exponents are obtained.The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices.When all the Gaussian distribution constants are the same,the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.     

A Theory of Non-Linear Elasticity Compatible With the Murnaghan Equation of State

We present an equation of state for a cubic non-linear elastic material in a general state of finite strain. For hydrostatic pressure, the predictions closely follow Murnaghan's well-known equation of state. At 170 kbar, our model differs from Murnaghan's equation by only 1.3%, which contrasts with the currently accepted non-linear elasticity theory that differs by 10% at this pressure. The theory is based on expressing the variation of the elastic constants as a linear function of stress rather than strain. We define a different set of third-order elastic constants, which involve a derivative with respect to stress, and relate these to the conventional third-order elastic constants. We apply the model to GaAs under hydrostatic pressure and we compare the predictions of the conventional non-linear theory with those of the model we present.     

尺寸相关的弹性常数对应变硅纳米线电学性质的影响

从Keating模型出发,基于离散化思想建立了计算单晶硅纳米线弹性常数和杨氏模量的半连续原子晶格力学模型. 从微扰理论和形变势理论出发,采用有限差分方法建立了计算不同晶向应变硅纳米线价带结构的数值模型. 结合上述的两个计算模型,进而应用经典弹道传输模型研究了轴向应力和弹性常数对p型硅纳米线弹道晶体管电学特性的影响. 研究结果表明,硅纳米线的弹性常数和杨氏模量呈现尺寸效应,该结果与分子动力学的模拟结果具有很好的一致性. 同时发现尺寸相关的弹性常数对硅纳米线晶体管输运电流的影响强烈依赖于单轴应力对输运电流的影 关键词： 应变硅纳米线 弹性常数 弹道电流 价带结构模型     

Third-order elastic constants of ZnS and ZnSe

The complete set of non-vanishing third-order elastic constants of the semiconductors ZnS and ZnSe is obtained theoretically. The strain energy density is estimated using finite strain elasticity theory by considering the interactions up to two nearest neighbours of each atom in the unit cell of these compounds. This energy density is compared with the strain dependent lattice energy density from the continuum model approximation. The second-order parameter of the potential function φ is obtained from the measured principal axis C_ij. The third-order potential parameter is estimated by assuming a Lennard-Jones type of interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the six third-order elastic constants of ZnS and ZnSe. Using these second- and third-order elastic constants of ZnS, the pressure derivatives of second-order elastic constants are evaluated. The second- and third-order elastic constants of ZnSe are compared with the available experimental values. The third-order elastic constants show anisotropy in different directions.     

Renormalization of a spontaneous symmetry-breaking model in the unitary gauge

For the Weinberg-Salam model of leptons a comparison is made between the subtraction constants in the unitary gauge and the subtraction constants in a renormalizable gauge. It is also shown that second-order corrections in muon decay are the same in both gauges.     

Van der waals constants of rare gases in an interpolation model

The possibility is investigated of determining the dispersion constants for pairs of rare-gas atoms directly from the homoatomic and heteroatomic interaction potentials. A simple interpolation model is proposed which makes it possible to find the constant C₆ from the known values of the potentials close to the minimum point. Calculations of the van der Waals constants C₆ performed using the potentials obtained by different authors demonstrated the good accuracy of the model and a definite correlation between the accuracy of the calculated van der Waals constants and the closeness to experiment of the pair potential employed in the model. Kabardino-Balkarian State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 70–73, August, 1997.     

Unification of coupling constants without a covering GUT

We discuss the possibility of unification of gauge coupling constants of the standard model and its extensions at some high scale without the assuption of the existence of a covering GUT at that scale. In our analysis we examine (i) the standard model, (ii) its supersymmetric extension and (iii) an extension in which the spontaneous symmetry breaking is based on the condensation of high-colour fermions. The latter case is favoured for perturbative coupling constants unification while the supersymmetric extension of the standard model, with five families, is favoured for non-perturbative unification.