On the lattice dynamics of AgGaS2

Summary The vibrational spectrum and one-phonon density of states of a chalcopyrite crystal AgGaS₂ are calculated in an extended Keating’s model with two-bond-stretching and one-bond-bending force constants. Three charges of ions and three force constants are determined by a least-square fitting to experimental frequencies of long-wave phonons taken from Raman-scattering experiments. The calculated constant-volume specific heat, Debye temperature and elastic constants, of AgGaS₂ are in agreement with the experimental data of other authors.     

Matrix-continued fraction solutions of some stochastic equations with random telegraph noise

The seven independent adiabatic elastic constants of CaWO₄ are calculated using Born's longwave method and the rigid ion model of Steinman et al. (1972). Good agreement exists between the calculated elastic constants and those measured by Gluyas et al. (1973). The sign of C₁₆ is consistent with the observation of Farley et al. (1972). Further the dynamical equilibrium conditions are also found to be satisfied for this model.     

A phenomenological approach for the phonon dispersion curves of barium

A phenomenological model which combines the axially symmetric ion-ion interaction with the electron-ion interaction scheme of Bhatia has been successfully used to calculate the phonon dispersion curves of bcc Ba. In particular, when the elastic constants determined by Mizukiet al are used as input data, the model successfully reproduces the anomalous feature of the dispersion curves measured by them. On the other hand, when the elastic constants determined by Buchenauet al are used, the model produces a cross over of the longitudinal and transverse branches in the [100] direction, a feature not established in their measurements. Thus the features of the dispersion curves in the [100] direction which is due to the hybridization of thes andd states are evident in the measured elastic constants and are consistent with the values of C₁₂-C₄₄.     

Magneto-elastic properties of Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> (TGG)

The temperature dependence of the elastic constants in Tb₃Ga₅O₁₂ was measured and analysed with a simple crystal field model. The magneto-elastic coupling constants have been deduced from this experiment. The coupling constant g_Γ5, related to the c₄₄ mode, is anomalously large. These coupling constants are important for the interpretation of the phonon Hall effect.     

Cartesian Dynamics of Simple Molecules. IX. Pyramidal Quadratomics (C3v Symmetry)

The vibrations of pyramidal AB₃ type molecules with C_3v symmetry are analyzed in terms of Cartesian co-ordinates, and analytical expressions for the four normal mode frequencies are derived as functions of two stretching and two bending force constants. Optimized values of these force constants are obtained for a number of tri-hydride and tri-halide molecules by substitution of available spectroscopic and geometric data. The physical validity of the model is confirmed by comparing the calculated and observed frequencies of several isotopic species.     

Determination of the anisotropy of the optical constants of electrochemically formed platinum oxide films by reflection spectroscopy and Kramers-Kronig analysis

Reflection spectroscopy in connection with Kramers-Kronig analysis was used to evaluate the complex optical constants of a thin anisotropic film of assumed uniaxial symmetry. The change in reflectivity of a platinum electrode, due to the formation of an oxide layer, was measured between 0.9 eV and 5.2 eV for parallel and perpendicular polarization. The corresponding phase-shifts were calculated from these data. The complex optical constants normal n?_n and tangential n?_t to the surface are now obtainable. The spectral dependence of the complex optical constants shows the expected anisotropic behaviour. The results are explained by means of a simple band model.     

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.     

Symmetry-relations and dynamics of molecular crystals in the long wave limit

Symmetry relations for macroscopic constants are derived. Especially it is shown that the Voigt-symmetry holds for the indices of the elastic constants. This has been doubted several times for lattices of particles with additional degrees of freedom. In the second part a simple model for Br₂- and J₂-lattices is discussed. The intermolecular forces are assumed to be van-der-Waals-forces. The influence of the internal degrees of freedom on lattice dynamics is calculated especially for the elastic constants. Further the limiting frequencies forq?0 are given and compared with experimental values.     

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.     

Interionic potentials and force constant models for rocksalt structure crystals—II

A lattice dynamical model for rocksalt structure crystals is presented in which the interionic force constants are taken to be central and the departure from the Cauchy relations is accounted for by isotropic and anisotropic deformations of the anions. The model is applied to NaBr, NaI and KBr for which C₁₂ > C₄₄ and it is appropriate to consider only the anisotropic deformations. The model parameters are determined entirely from macroscopic data. By assuming an exponential form for the repulsive part of the interionic potential the cohesive energy of the crystals may be determined from the interionic force constants. The cohesive energies are in surprisingly good agreement with experiment although the potential parameters differ considerably from those of other workers. While the dispersion curves obtained from the model are in markedly worse agreement with experiment than those from the standard breathing shell model it is shown that the potentials(in addition to giving good cohesive energies) result in a reasonably consistent dynamical model.     

Elasticity of a magnetic lattice near the magnetic critical point

The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearT _c and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.     

金红石结构TiO2晶体点缺陷形成能的经验途径计算

基于经验参数化途径,通过对晶体结构、晶格形成能、介电性质和弹性实验数据拟合确定金红石结构氧化物晶体TiO₂的电子壳模型参数和非Coulomb互作用势参数.计算点 缺陷形成能.论证Schottky缺陷是金红石结构TiO₂中的本征缺陷. 关键词： 2')" href="#">金红石TiO₂ 点缺陷形成能 电子壳模型 经验途径计算     

P-odd one-meson exchanges revisited: a non-linear chiral model approach

Coupling constants of theP-odd interaction of nucleon with the π-, ρ-, ω-mesons are calculated in the non-linear chiral model. The hierarchy of these constants governed by small parameters sin² θ _w and 1/N _c is established. According to this hierarchy the ratio of the weak πNN and ρNN coupling constants is small, being ?sin² θ _w /N _c . The absolute values of all considered constants prove to be essentially larger than those in theSU(6) _W model, thus pointing that theP-odd effects due to the overlap of the nucleons' wave functions are of importance.     

Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

ERP study of the RKKY interaction in metallic EuxGd1−xB6

The RKKY interaction in metallic Eu_xGd_1?xB₆ compounds has been studied by EPR technique for x = 0.00, 0.20, 0.40 and 0.50. In the region of the absorption maximum the experimental spectra can be fitted to a lineshape function consisting of both Lorentzian absorption and dispersion components. Weiss constants, exchange fields, unbottlenecked g-shifts, and thermal broadening are calculated on the basis of the RKKY model and compared to the experimental results. The predicted Weiss constants and exchange fields are in good agreement with experiment, indicating the validity of the RKKY model. However, the predicted g-shifts and thermal broadening are much greater than those measured experimentally. The reduced g-shifts and thermal broadening are interpreted in terms of a magnetic resonance bottleneck, and the relaxation rates due to the interaction of the conduction electrons with the localized moments and lattice are evaluated.     

Lattice dynamics,third order elastic constants and thermal expansion of Cadmium

The lattice dynamics, second and third order elastic constants, pressure derivatives of the second order elastic constants and the temperature variation of the lattice thermal expansion of Cadmium have been worked out utilising Keating's approach. The ten TOE constants are calculated using four anharmonic parameters. The model used here reproduces the measured pressure derivatives of the SOE constants of Cadmium extremely well. The low temperature limit of the volume Gruneisen function γ_L is found to be nearer to the value of Andres. The high temperature limit γ_v(T) is in good agreement with the value calculated by Gschneidner Jr. from the Cv data for Cadmium. The lattice dynamics of Cadmium is found to be essentially similar to that of Zinc.     

Long-wavelength lattice vibrations of MoS2 and GaSe

The long-wavelength lattice vibrations of MoS₂ and GaSe are interpreted by means of a linear-chain model that includes both intralayer and interlayer force constants.     

Contribution of the multipole polarization to the elastic constants in fluorite structure crystals

Numerical calculations are presented for the contribution of the multipole polarization to the elastic constants in fluorite structure crystals. The multipole polarizability is calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The elastic constants are significantly affected by the multipole polarization of the ions. The contributions of the multipole polarization of the ions to the elastic constant C₁₁, C₁₂, and C₄₄ are about 25%, 40% and 20% of the experimental values, respectively. The calculated values of the deviation from the Cauchy relation are in good agreement with the experimental values.     

Cartesian Dynamics of Simple Molecules III Non-Linear Triatomics (C2v Symmetry)

A simple spring model for the molecular vibrations of non-linear triatomic molecules with C_2v symmetry is described in terms of Cartesian co-ordinates. Analytical expressions for the stretching and bending mode frequencies are obtained and compared with previous derivations. Optimized values of force constants are calculated for models involving two or three adjustable parameters. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. The model provides a simple explanation of the near degeneracy of the symmetric and asymmetric stretching frequencies of H₂S and H₂Se.     

Hubbard model,conserved quantities,and computer algebra

The constants of motion of the half-filled four-point Hubbard model with cyclic boundary conditions are given in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C_4v symmetry and in Bloch representation we have the total momentum operator which is conserved. The anticommutation relations for Fermi operators with spin are implemented using computer algebra. Using computer algebra, all the constants of motion are given. The one-dimensional Hubbard model admits a Lax representation. From the Lax pair we find a new constant of motion.