Significance of model Hamiltonians in energy-band theory

The results of recent ab initio calculations of energy bands are compared with interpolation schemes in order to assess the significance of the latter. When the parameters in the interpolation scheme are required to correspond to those obtainable by an ab initio calculation based on a reasonable one-electron potential, we describe the scheme as a model Hamiltonian. The analytic character of model Hamiltonians for s–p bands (pseudopotential case) or for d bands interacting with s–p bands (resonance case) is summarized. The compatibility of the results of several workers with these analyticity requirements is considered. It is shown that if the empirically-motivated adjustments of parameters are to be regarded as physically significant, these adjustments must satisfy rather strict conditions.     

Theory of the electronic structure of Ga1-yInyNxAs1−x and related alloys

Abstract

We present a quantitative k.P Hamiltonian which describes analytically the composition dependence of the energy gap, interband momentum matrix element, band edge effective masses and conduction band dispersion of GaN_XAs_1?x alloys for low N concentrations (x < ～ 0.05). The model has been confirmed using an sp³s? tight-binding Hamiltonian whose results agree well both with experiment and with previous pseudopotential calculations. The model should be of wide use to guide the future development of this material system and its applications.     

Application of the pseudopotential method to the calculation of the phase transition temperature

Pseudopotential formalism was used to describe the phase transition from a two-phase to a one-phase state in alloys with limited solubility. The combined use of the pseudopotential and static concentration wave methods for calculating the temperature of the order-disorder phase transition was generalized to the case of lattices with a basis. Numerical calculations were carried out for the limiting solubility curves in the system Cd-Zn and the order-disorder transition temperatures for Mg₃Cd, MgCd, and MgCd₃ superstructures.     

Perturbative Handling of the Renner-Teller Effect and Spin-Orbit Coupling in Δ Electronic States of Triatomic and Tetra-atomic Molecules

Second-order perturbative formulae for handling the Renner-Teller effect combined with the spin-orbit coupling in Δ electronic states of triatomic and symmetric (ABBA-type) tetra-atomic molecules with linear equilibrium geometry are derived via two schemes for partition of the model Hamiltonian. The formulae for triatomic molecules are employed to compute the spectrum of the X⁵Δ_g state of FeH₂. The parameters entering the model Hamiltonian are generated by means of ab initio calculations.     

Itenerant magnetic properties of amorphous metallic systems: Numerical studies of the Fe-B alloys

A self-consistent method to compute local magnetic moments and spin polarized electron densities of states and to test the stability of the ferromagnetic vs. the paramagnetic state is developed within the framework of the itinerant electron theory. The tight-binding Hamiltonian, with Coulomb correlation among d electrons, is parametrized according to the Slater-Koster interpolation scheme. The method goes beyond the rigid band splitting approximation. We apply it to the Fe_1−xB_x amorphous system for 0 ⩽x⩽0.6 and obtain the magnetization for T=0 as a function of x in agreement with experimental data in the experimentally-accessible concentration region.     

Tight-binding studies of the electronic band structure of GaAlN and GaInN alloys

The semi-empirical tight-binding (TB) approach with an sp³s^* orbital basis is used to investigate the electronic band structure of cubic Ga_1-xAl_xN and Ga_1-xIn_xN alloys. The spin–orbit splitting in the Hamiltonian and first- and second-neighbour interactions are considered to explore the gap evolution as a function of the concentration x. The TB parameters used in the studies were obtained within the virtual crystal approximation using those of the binary compounds AlN, GaN, and InN. The binary parameters are calculated by applying an empirical TB Hamiltonian taking into account first- and second-neighbour interactions. A direct to indirect gap transition is obtained for Ga_1-xAl_xN at x=0.60. In contrast, the Ga_1-xIn_xN alloys exhibit direct-gap characteristics as a consequence of being formed by the direct-gap binary compounds GaN and InN. PACS 71.20.Nr; 71.23.-k; 71.55.Eq     

Influence of the grain size and structural state of grain boundaries on the parameter of low-temperature and high-rate superplasticity of nanocrystalline and microcrystalline alloys

A model has been proposed for calculating the grain size optimum for the deformation of nanocrystalline and microcrystalline materials under superplasticity conditions. The model is based on the concepts of the theory of nonequilibrium grain boundaries in metals. It has been demonstrated that the optimum grain size d _opt can be calculated as the size at which a high level of nonequilibrium of grain boundaries is combined with a high intensity of the accommodation of grain boundary sliding. The dependences of the quantity d _opt on the rate and temperature of the strain and the thermodynamic parameters of the material have been derived. The results obtained have been compared with the experimental data on the superplasticity of nanocrystalline and microcrystalline aluminum and magnesium alloys.     

Mössbauer study of amorphous Fe-Sb alloys with large composition range

Amorphous Fe_x Sb_100-x alloys with large composition range of 3<-x<-80 have been investigated with⁵⁷Fe Mössbauer spectroscopy. The concentration dependence of quadrupole splitting and its distribution reveal a similar atomic packing scheme in the range of 3<-x<-50. Significantly, the quadrupole splitting of crystalline FeSb₂ is larger than that of amorphous FeSb₂ by a factor of 3. The isomer shifts have been analyzed based on the Miedema-van der Woude's model of isomer shift. The distribution of magnetic hyperfine field P(H) indicates that the alloys are rather magnetically inhomogeneous around x=55.     

A simple analytical EAM model for bcc metals including Cr and its application

An analytical embedded atom method (EAM) model, which can treat bcc transition metal Chromium, has been developed. In this model, a new potential was presented, and a modified term has been introduced to fit the negative Cauchy pressure P _c=(C₁₂-C₄₄)/2 for element Cr. The new model was applied to calculating the thermodynamic properties of binary alloys of all bcc transition metals V, Nb, Ta, Cr, Mo, W and Fe. The calculated dilute-solution enthalpies and formation enthalpies of random alloys are in good agreement with the experimental data available, the results from the first-principles calculations, and the results of thermodynamic calculations.     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

非晶态二元合金模型偏干涉函数的计算及应用

本文从计算非晶态材料散射强度的Debye方程,推导出非晶态二元合金模型的Faber-Ziman偏干涉函数计算公式。利用这些公式,计算了Fe₈₃B₁₇和Ni₆₄B₃₆金属玻璃模型的S_FeB(Q)和S_NiB(Q),并和实验结果及模型计算的偏散射强度I_FeB(Q)和I_NiB(Q)作了比较。文中还计算了Hg₂Na液态合金模型的偏干涉函数,并把它们外推到零衍射角时的数值。最后讨论了具有化学短程序合金的全干涉函数在零衍射角附近的行为。 关键词：     

Symmetrization of Wave Functions of 4- and 5-Atom Molecules

Symmetrized wave functions of 4- and 5-atom molecules with two, three, or four identical atoms are constructed in general form. The symmetrization of the angular and radial parts of the vibrational-rotational wave function is examined in detail. The representation matrix and the Clebsch-Gordan coefficients of the permutation group S _n (n = 3, 4) are adapted for the use in molecular spectroscopy. This makes it easier to draw analogies with the theory of effective Hamiltonian. The use of symmetrized wave functions is shown to significantly alleviate the problem of calculating the vibrational-rotational energy levels from the potential energy surface for such molecules as CH₄, CH₃D, CH₃Cl, etc.     

Equilibrium correlation functions of the spin-boson model with sub-Ohmic bath

The spin-boson model is studied by means of flow equations for Hamiltonians. Our truncation scheme includes all coupling terms which are linear in the bosonic operators. Starting with the canonical generator η_c=[H₀,H] with H₀ resembling the non-interacting bosonic bath, the flow equations exhibit a universal attractor for the Hamiltonian flow. This allows to calculate equilibrium correlation functions for super-Ohmic, Ohmic and sub-Ohmic baths within a uniform framework including finite bias.     

Three-dimensional ab initio dipole moment surfaces and stretching vibrational band intensities of the XH3 molecules

Stretching vibrational band intensities of XH₃ (X=N, Sb) molecules are investigated employing three-dimensional dipole moment surfaces combined with the local mode Hamiltonian model.The dipole moment surfaces of NH₃ and SbH₃ are calculated with the density functional theory and at the correlated MP2 level,respectively. The calculated band intensities are in good agreement with the available experimental data. The contribution to the band intensities from the different terms in the polynomial expansion of the dipole moments of four group V hydrides (NH₃, PH₃,AsH₃ and SbH₃) are discussed. It is concluded that the breakdown of the bond dipole approximation must be considered. The intensity “borrowing” effect due to the wave function mixing among the stretching vibrational states is found to be less significant for the molecules that reach the local mode limit.     

Polarised neutron study on Ni rich NiCr alloys

Magnetic structure amplitudes in Ni_1-xCr_x alloys (x = 0.023 and 0.034) are measured using the polarised neutron diffraction technique. The structure amplitudes are analysed using the projection operator formalism. In this framework a new approach for defining local site moment, diffuse moment and asphericity in the site moment are discussed. A detailed multiband Coherent Potential Approximation (CPA) calculation for ferromagnetic $\text{Ni}$Cr alloys using the Hubbard Hamiltonian with realistic parameters is discussed. The results of these calculations are compared with the existing bulk measurements like magnetisation and transport properties. The evolution of site moment and its asphericity with impurity concentration are obtained and compared with the present polarised neutron results.     

Lattice dynamics of some binary alloys

Summary The phonon dispersion frequencies for Cu₃Au, Cu₃Zn and Ni₃Fe alloys have been calculated using the model potential approach. The contribution of a short-range three-body interaction to the dynamical matrix has also been included in the present study. The theoretically computed phonon dispersion curves of these alloys are found to be in good agreement with the experimental data.     

Characteristic features of the extrinsic electric resistance in ferromagnets with low carrier density

Switching from simple semiconductors to more complicated chemical compositions, we encounter mainly nonstoichiometric or undoped compounds. Combined with other characteristic features of d(f) compounds, this can lead, together with the ordinary scattering by spin disorder in magnetic semiconductors, to an unusual impurity contribution to the total scattering of carriers even in intrinsic semiconductors. A unique scheme for calculating the energy structure of the conduction-band bottom of a ferromagnetic semiconductor and the temperature and field dependences of the impurity contribution to the resistivity is proposed on the basis of a model Hamiltonian. The computed magnetoresistance ratio is negative and has a maximum near T _c . A qualitative comparison is made between the results and the experimental temperature dependences of the Hall mobility and magnetoresistance ratio in the ternary semiconductor n-HgCr₂Se₄, which is nonstoichiometric with respect to the chalcogen. To identify previously unobserved temperature oscillations of the resistance, a careful analysis is made of the low-temperature part of the resistance using the relations obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 68–76 (January 1999)     

The chemical potential in surface segregation calculations: AgPd alloys

We put forward a technique for calculating the surface segregation profile in substitutional disordered alloys. The surface internal energy and the effective bulk and surface chemical potentials are calculated using the full charge density exact muffin-tin orbitals method, combined with the coherent potential approximation. The application of our approach is demonstrated to the close-packed surface of Ag_cPd_1−c random alloys with 0 < c < 1. The surface concentration profile, surface energy and segregation energy are investigated as functions of bulk composition. The present results are compared with former theoretical and experimental data. It is found that at low temperature, Ag segregates to the surface layer for the entire bulk composition range. At 0 K, the subsurface layer contains 100% Pd for c ? 0.4, and somewhat more than (2c − 1) Ag in alloys with c > 0.5. The temperature dependence of the segregation profile is significant for Pd rich alloys and for alloys with intermediate concentrations. At temperatures ?600 K, the subsurface layer is obtained to be almost bulk like.     

A General Variational Algorithm to Calculate Vibrational Energy Levels of Tetraatomic Molecules

A general variational method for calculating vibrational energy levels of tetraatomic molecules is presented. The quantum mechanical Hamiltonian of the system is expressed in a set of coordinates defined by three orthogonalized vectors in the body-fixed frame without any dynamical approximation. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm, which requires the evaluation of the action of the Hamiltonian operator on a vector. The Lanczos recursion is carried out in a mixed grid/basis set, i.e., a direct product discrete variable representation (DVR) for the radial coordinates and a nondirect product finite basis representation (FBR) for the angular coordinates. The action of the potential energy operator on a vector is accomplished via a pseudo-spectral transform method. Six types of orthogonal coordinates are implemented in this algorithm, which is capable of describing most four-atom systems with small and/or large amplitude vibrational motions. Its application to the molecules H₂CO, NH₃, and HOOH and the van der Waals cluster He₂Cl₂ is discussed.     

Model calculation of the surface tension of liquid Ga-Bi alloy

A convenient model, based on some assumptions, for calculating the composition and temperature dependence of the surface tension of binary liquid alloys is reported. The theoretical calculations of the surface tension of gallium-rich-bismuth alloys are presented. The calculated results are compared with the reported experimental data. A relatively good agreement with experimental behavior of the composition dependence of the surface tension was found, but a disagreement was observed with experimental temperature behavior of the surface tension of these alloys. The calculations were conducted in the temperature range from almost 320 K to about 800 K. The surface tension was calculated from eutectic composition (x_Bi = 0.0022) to x_Bi = 0.1, and worked out by linear equations. The model calculation and analysis indicate a first order surface phase transition in this system, which is in accord with experimental findings. For this system, γ decreases linearly with increasing temperature at fixed Bi mole fraction x_Bi, and thus, suggesting a positive surface excess entropy. It is also found that the surface tension isotherms show the linear dependence on the concentration, in the logarithm scale of x_Bi, in the very narrow concentration range.