体心立方晶格的布里渊区形状不是正十二面体

介绍了可能的五种正多面体,指出正十二面体是晶体结构及其布里渊区不可能具有的正多面体形状.体心立方晶格的布里渊区是菱形十二面体,不是正十二面体.     

Phonon spectra and the one-phonon and two-phonon densities of states of UO<Subscript>2</Subscript> and PuO<Subscript>2</Subscript>

The vibrational spectra of uranium dioxide UO₂ and plutonium dioxide PuO₂, as well as the one-phonon densities of states and thermal occupation number weighted two-phonon densities of states, have been calculated within the framework of the phenomenological rigid ion model. It has been shown that the acoustic and optical branches of the spectra are predominantly determined by vibrations of the metal and oxygen atoms, respectively, because the atomic masses of the metal and oxygen differ from each other by an order of magnitude. On this basis, the vibrational spectra can be represented in two Brillouin zones, i.e., in the Brillouin zone of the crystal and the Brillouin zone of the oxygen sublattice. In this case, the number of optical branches decreases by a factor of two. The two-phonon densities of states consist of two broad structured peaks. The temperature dependences of the upper peak exhibit a thermal broadening of the phonon lines L01 and L02 in the upper part of the optical branches. The lower peak is responsible for the thermal broadening of the lowest two optical (T02, T01) and acoustic (LA, TA) branches.     

On the Brillouin delta function of cubic and hexagonal lattices

In many problems of solid state physics one faces the task of integrating functions over polyhedra. This is necessary, for example, for the form factor in the theory of scattering, the Wannier function in band theory, and the Brillouin delta function in pseudocontinuum theory of crystal lattices. The integrands of these quantities are of similar form; the last two require integration over Brillouin zones. In the paper the properties of the Brillouin delta function are shortly rewieved. This function allows, in pseudocontinuum theory, the establishment of a unique relationship between functions of discrete and continuous arguments.A method of simplifying the integration of functions over polyhedra is proposed. The method is based on dividing a polyhedron into simplexes and calculating the integral in new barycentric coordinates. This method is applyied to the calculation of Brillouin delta functions for body centred and face centred cubic crystals. Explicit formulae for hexagonal and orthorhombic lattices are also given and discussed.     

Modeling band spectra of compound crystals in the basis of states of their sublattices

A technique for simulation of band spectra of compound crystals in the basis of states of their sublattices is developed. The Hamiltonian of the crystal is written as a sum of sublattice Hamiltonians and a perturbation operator resulting from hybridization of the sublattice states. The simplest models are proposed to account for the sublattice hybridization. The methods for calculating the average crystal potential are discussed to represent the band spectra of sublattices in a common energy scale when calculating band structures by the pseudopotential method. The band spectra of MgO and MgS crystals are calculated to show the application of the methods under consideration. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 81–84, July, 2006.     

Application of the sublattice method to the investigation of phonon spectra and frequency density of fluorite-structure crystals

Phonon spectra and state densities of MeF₂ (Me = Ca, Sr, Cd, Ba, or Pb) crystals are calculated in the basis of sublattice state vectors using the Born–Mayer model. The phonon spectra and the sublattice state densities are calculated in the field of the second frozen sublattice. It is demonstrated that optical crystal branches are mainly due to oscillations of fluorine ions; moreover, the topology of optical branches in the spectrum and the crystal state densities are close to the topology of the spectra and state densities of the fluorine sublattice in the frozen metal sublattice. Exception is CaF₂ whose ion and cation masses are close in values.     

Electronic structure and hyperfine fields in non-stoichiometric magnetite above the Verwey transition

The NMR spectra of ⁵⁷Fe nuclei were measured below and above the Verwey transition temperature T_V in single crystal samples of Fe_3(1?δ)O₄ (0?δ?0.009). The measured crystals were grown from the melt using the cold crucible technique. In a cubic phase above T_V the satellite structure induced by vacancies in the octahedral sublattice is clearly resolved. The satellite lines originate from those iron nuclei in the tetrahedral sublattice that are nearest to the vacancy. Temperature dependence of satellite lines indicates that the presence of vacancy leads to a redistribution of the electrons in octahedral sublattice and the appearance of iron ions possessing appreciable orbital momentum.     

The Raman effect in crystals

A review is given of progress in the theoretical and experimental study of the Raman effect in crystals during the past ten years. Attention is given to the theory of those properties of long-wavelength lattice vibrations in both cubic and uniaxial crystals which can be studied by Raman scattering. In particular the phenomena observed in the Raman scattering from crystals which lack a centre of inversion are related to the theory. The angular variations of the scattering by any type of lattice vibration in a crystal having any symmetry can be easily calculated using a complete tabulation of the Raman tensor. Recent measurements of first-order lattice vibration spectra are listed. A discussion of Brillouin scattering is included. The relation of second-order Raman spectra to critical points in the lattice vibration density of states is discussed, and measurements of the second-order spectra of diamond and the alkali halides are reviewed.

The theory and experimental results for Raman scattering by electronic levels of ions in crystals are examined, and proposals for Raman scattering by spin waves, electronic excitations across the superconductive gap and by plasmons are collected together.

Finally, the prospects for applying lasers as sources for Raman spectroscopy are discussed, and progress in the new technique of stimulated Raman scattering is reviewed.     

The Raman effect in crystals

A review is given of progress in the theoretical and experimental study of the Raman effect in crystals during the past ten years. Attention is given to the theory of those properties of long-wavelength lattice vibrations in both cubic and uniaxial crystals which can be studied by Raman scattering. In particular the phenomena observed in the Raman scattering from crystals which lack a centre of inversion are related to the theory. The angular variations of the scattering by any type of lattice vibration in a crystal having any symmetry can be easily calculated using a complete tabulation of the Raman tensor. Recent measurements of first-order lattice vibration spectra are listed. A discussion of Brillouin scattering is included. The relation of second-order Raman spectra to critical points in the lattice vibration density of states is discussed, and measurements of the second-order spectra of diamond and the alkali halides are reviewed. The theory and experimental results for Raman scattering by electronic levels of ions in crystals are examined, and proposals for Raman scattering by spin waves, electronic excitations across the superconductive gap and by plasmons are collected together. Finally, the prospects for applying lasers as sources for Raman spectroscopy are discussed, and progress in the new technique of stimulated Raman scattering is reviewed.     

布里渊区中的对称平均点

本文提出了一些布里渊区中的对称平均点,用它可以方便地计算布里渊区中的平均值,其精度可以和特殊点相比而计算量却要小得多。文内给出了立方和六角晶格的对称平均点,并用具体的数值计算例子说明了它的计算精度。 关键词：     

一种晶体表面自由能的计算方法

采用“断键模型”计算了立方晶体理想表面的悬键密度，进而计算了其表面自由能(SFE).结 果表明：对于理想(1×1)-(hkl)表面，SFE可以表示为键能、键长和表面方向的函数.该 模型简单地解决了晶体SFE各向异性的理论问题.根据该模型和Wulff定则得出的晶体平衡形 状与理论完全一致；同时，计算结果也表明面心立方和体心立方晶体的平衡形状与其三维第 一布里渊区重合. 关键词： 表面自由能 晶体 悬键 平衡形状     

Multiple Bragg diffraction in low-contrast photonic crystals based on synthetic opals

The phenomenon of multiple Bragg diffraction in low-contrast photonic crystals based on synthetic opals has been studied both experimentally and theoretically. The transmission and reflection spectra of opal films near the K point of the Brillouin zone of the face-centered cubic lattice in s-polarization exhibit the effect of anticrossing of dispersion curves corresponding to the (111) and ([`1]11)(\bar 111) photonic stop bands. The effect of quasi-Brewster suppression of stop bands is clearly pronounced in p-polarization. The experimental data are analyzed using the calculation of the band structure of opal with the inclusion of the polarization of incident light.     

Manifestation of the specific structural features of lithium niobate single crystals of different composition in their Raman spectra

The Raman spectra of nominally pure lithium niobate single crystals of congruent, close to stoichiometric, and stoichiometric compositions and congruent lithium niobate single crystals doped with Gd³⁺, Y³⁺, and Mg²⁺ ions have been investigated. Weak lines whose widths anomalously decrease with an increase in cation sublattice disordering at a change in the single crystal composition were found for the first time. These lines may be indicative of fine ordering processes involving structural units of the cation sublattice, as a result of which this sublattice is disordered as a whole.     

Polar Kerr rotation spectra in yttrium iron garnet and lithium ferrite: A comparative study

Polar Kerr rotation (PKR) spectra in the range 2.0–5.7 eV at 295 K of lithium ferrite and yttrium iron garnet (YIG) single crystals are reported. The spectra show more details and cover a more extended energy region than those published so far. The interpretation of the spectra is based on the assumptions that 1) PKR is an odd function of the sublattice magnetic moments 2) the origin of PKR in both compounds is of similar nature, the differences due to the different crystal structures (garnet and spinel) being less important. The calculated PKR sublattice components show some similarities in their energy dependences, the magnitude of the tetrahedral sublattice component being higher than that of the octahedral one. The components were used in the calculation of the PKR spectra in diamagnetically substituted yttrium iron garnet (J. Appl. Phys.49, 2212, 1978). The results correctly predict the trends observed experimentally.     

钽铌酸锂晶体的布里渊散射研究

研究了钽铌酸锂(LiTa_xNb_(1-x)O_3,x=0.0013,0.0052,0.015,0.06)晶体在室温的布里渊散射.给出了它们的弹性刚度常数和压电应力常数.测量了一种组份晶体的布里渊散射频移在50K～580K范围内的温度特性.发现某些声子散射谱中除三个正常峰外还存在一个异常峰.     

Formation of nanodefects in LiF crystals under gamma irradiation

The absorption spectra, photoluminescence spectra, and microhardness of LiF crystals exposed to gamma radiation from a shutdown reactor and a ⁶⁰Co source at a dose rate of 7.65 Gy/s are investigated. The structure of these crystals is determined using x-ray diffraction analysis. It is revealed that the Li sublattice contains not only point and complex radiation-induced defects but also 28-nm LiOH particles induced by gamma radiation. It is shown that the formation of defects occurs more efficiently upon exposure to radiation from a shutdown reactor than from a ⁶⁰Co source.     

Photoluminescence decay and time-resolved spectroscopy of cubic yttria-stabilized zirconia

The time-resolved spectra and luminescence decays of cubic yttria-stabilized zirconia single crystals were investigated in the 100–300 K temperature range. At each temperature the time-resolved spectra are dominated by a yellow-orange broad band with a shoulder in the green region, and their shapes appear similar to those displayed in fluorescence. In addition, the shapes remain almost independent of the delay times over the range between 0.04 and 0.4 ms after excitation. The luminescence decays can be satisfactorily described by the superposition of two exponential functions, as well as by two expressions commonly given for decays related to disorder. In the three cases, the temperature dependences of the time constants and the other parameters derived from these expressions are analyzed. The time constants can be accounted for by assuming a radiative decay from two metastable levels with a typical separation of 0.057±0.005 eV. Some correlations between the parameters from the luminescence-decay formulae are given. The results are in good agreement with luminescence due to radiative recombinations at donor F-type levels in which complexes formed by oxygen vacancies in a disordered sublattice are involved.     

Elastic waves in cubic crystals with positive or negative anisotropy of second-order elastic moduli

Elastic waves in cubic crystals are considered. A new classification of cubic crystals is proposed based on their elastic properties. All cubic crystals are shown to be divided into crystals with a positive or negative anisotropy of their second-order elastic moduli. The vibrational-branch spectra of crystals of these two types differ qualitatively in shape. The angular dependences of the polarization vectors are analyzed. The transverse component in quasi-longitudinal vibrations in cubic crystals is shown to be small and can be neglected. The longitudinal component in quasi-transverse modes is not small: its maximum value is 16.5% for Ge and reaches 27% for KCl.     

β → γ structural phase transition in RbCrCl3 - crystals

A lattice vibration analysis of the β → γ phase transition in RbCrCl₃ - crystals is performed. Symmetry properties of the order parameter are also studied. The soft mode transforms according to a reducible representation belonging to the Γ and A points of the monoclinic Brillouin zone. A free-energy expansion that accounts for the symmetry properties of the order parameter is constructed and analysed.     

Special points for calculating integrals over the primitive cell of a periodic system

A method is proposed for constructing appropriate sets of special points in the Brillouin zone in which the extended unit cell method is used with a subsequent shift from the center of the reduced Brillouin zone. The proposed method offers several advantages over the commonly used Monkhorst-Pack method. The difference in the construction of sets of special points for the direct and reciprocal lattices is discussed for crystals belonging to a nonsymmorphic space group. The cases of a planar square lattice and an fcc lattice are considered to illustrate general results.     

Properties of optical and acoustic phonons in diamond crystals

The dependence of the energy on the quasi-momentum of optical and acoustic phonons in diamond-type crystals is analyzed. It is shown that the dispersion relation of optical branches near the Brillouin zone center in such crystals can be derived based on the modified Klein-Gordon equation corresponding to quasiparticles (optical phonons) with negative effective mass. Analytical expressions are derived for dispersion curves of acoustic and optical branches in the entire Brillouin zone, based on the sinusoidal approximation. The obtained analytical dependences of dispersion relations are compared to the experimental results of the study of inelastic neutron scattering spectra in diamond crystals. The law of the coordinate and time transformation for optical phonons with negative effective rest mass when going to the new inertial reference frame, similar to Lorentz transformations in relativistic mechanics, is determined.