Calculation of the dielectric function of Li metal

The inverse microscopic dielectric function of Li metal is evaluated within the time dependent local density approximation (TLDA) using one-electron energies and wave-functions obtained by SCF band structure calculations. Even at larger values of transferred momentum the influence of exchange and correlation is found to be quite small. Local fields are approximated by considering all elements of the dielectric matrix corresponding to the first and second shell of the reciprocal lattice vectors. Their influence is found to be orientation-dependent but in most cases quite small. However, in some cases they even cause a change of the shape of the inverse dielectric function. Our theoretical results agree quite well with measurements of the dynamic structure function by use of inelastic X-ray scattering with transferred energy up to 18 eV. Unrealistic oscillations at still higher energies as well as the narrow width of the peaks indicate the limits of a one-particle scheme.     

Broadband third-harmonic generation in two-dimensional short-range ordered nonlinear photonic structure

We study parametric frequency conversion in two-dimensional nonlinear photonic crystal with short-range ordered ferroelectric domains. We demonstrate that the short-range order enables broadband third-harmonic generation via cascading of two second-order quasi-phase matched nonlinear processes. We obtain conversion efficiencies that are much higher than those achieved from a randomized medium, owing to the unique distribution of reciprocal lattice vectors in the short-range ordered structure.     

Study of the structure and spectral properties of dianions of Zn complexes of porphyrins by the method of density functional theory

The structure, solvation energies, and electronic absorption spectra of products corresponding to the second stage of reduction of Zn porphin (Zn-P) with metallic sodium are calculated using methods of density functional theory. Calculated solvation energies of free and bound ions make it possible to assume that, in commonly used aprotic solvents, reduction products form [2Na⁺ · Zn-P^2?] anion-cation contact complexes. The relative energies of the four stable isomers [2Na⁺ · Zn-P^2?] detected in the gas phase and solvents are considerably different. The arrangement of Na⁺ on different sides of the macrocycle and along the NN axis favors the interaction with the solvent and stabilization in the solution. This conclusion is consistent with the data of calculations of electronic absorption spectra and of modeling of the spectral manifestations of the electron photodetachment from dianions of Zn-tetraphenylporphyrin (Zn-TPP) in frozen matrices. The behavior of the calculated transitions in the series of neutral and charged forms of Zn-P and Zn-TPP is well consistent with experimental data. Despite the fact that the spectral properties of the neutral and dianionic forms of Zn-P and Zn-TPP in the visible range are similar, the nature of their excited states is different.     

Finite diffraction models for electron bandstructures

Truncations of the infinite determinant resulting from the plane wave expansion method for an electron in a periodic potential are analysed to determine how well they can reproduce the low-lying eigenvalues or energy bands. The availability of rigorous expansions for the solutions of the Mathieu equation, essentially the Schrödinger equation for an electron in a one-dimensional cosine potential, suggests that problem for definitive comparisons. Since the only models which can reproduce the fundamental quadratic behaviour of bands at the zone centre have symmetric (odd) sets of reciprocal lattice vectors, the lowest order candidate has an odd determinant of size 3 × 3 through the reciprocal lattice vectors which define the 1st. Brillouin zone of the one-dimensional lattice. As zone centred determinants are not symmetric about zone boundaries they will not give a vanishing group velocity at that point and the effects of truncation will be at their worst. The 3 × 3 or cubic model factorises at the zone centre and a detailed analysis in closed form is straightforward. Agreement with the rigorous results is better than 1% everywhere. The next largest model, with a 5 × 5 determinant, gives errors which are several orders of magnitude smaller throughout the 1st. Brillouin zone. In addition it is found that even the 3 × 3 model gives much better results for the lowest eigenvalue than does second order perturbation theory. Numerical comparisons are also made for the group velocity and (inverse) effective mass using a Hellman-Feynmann approach to calculate the derivatives. Extensions to complex periodic potentials and higher dimensions are briefly discussed.     

The reciprocal lattice construction from axial coordinates of diffraction spots on Weissenberg photographs

An alternative method for constructing of the reciprocal lattice planes from Weissenberg photograph is presented. The radial coordinates of the diffraction spots necessary for the reciprocal lattice plane construction in current method are not introduced into this procedure. The method takes advantage of the coupling of the rotational and translatory motion of the Weissenberg camera. Both the magnitudes and the mutual orientations of the reciprocal lattice vectors can be then determined solely from the measured axial coordinates of the diffraction spots on the Weissenberg photographs. The knowledge of the camera radius as well as the non-uniformity of the radial adhesion of the film to the camera are thus fairly eliminated. The method was successfully applied to the interpretation of Weissenberg photographs of small fragments of lunar olivines from the Sea of Fertility (Luna 16 sample).     

How to do mean field theory in Feynman gauge and doing it for U(1) with corrections to fourth order

It is demonstrated how mean field theory with corrections from fluctuations may be applied to lattice gauge theories in covariant gauges. By fixing the gauge at tree level the importance of fluctuations is decreased. This is understood as inclusion of terms of next-to-leading-order in d in the definition is the mean field tree approximation, d being the dimension of the lattice. The gauge group U(1) and Wilson's action are used as testing ground. Tree and one-loop results comparable to those previously obtained in axial gauge are obtained for d = 4. The next three correction terms to the free and plaquette energies are evaluated in Feynman gauge. The truncated asymptotic series thus obtained is compared to that of the ordinary weak coupling expansion. The mean field series gives, to those orders studied, a much better approximation. The location of phase transitions in 4d and 5d are predicted with 1% error bars.     

约化胞与电子衍射谱的标定

对应于14种布喇菲点阵有44种约化胞,不但约化矢的选法是唯一的,而且可以根据约化矢标量积矩阵(a·a b·b c·c b·c c·a a·b)的不同形式,确定布喇菲点阵类型。在晶体点阵已知的情况下,从点阵参数计算出倒易点阵中的平面约化胞,并与试验得到的电子衍射谱对比以标定衍射斑点的指数。在晶体点阵未知的情况下,从已知转角的两个电子衍射谱中选三个接近中心的衍射斑点,相当于三个低指数倒易矢量。由它们构成倒易点阵的一个初基胞,变换成正点阵的初基胞后,经过约化得出约化胞和相应的布喇菲单胞的类型和参数,同时标定衍射斑点的指数。这些标定计算已编成电子计算机程序,可以用来直接确定晶体点阵类型和进行物相分析。     

Bose-Einstein condensates in rotating lattices

Strongly interacting bosons in a two-dimensional rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries.     

Evolution of a Non-Uniform Deformed State in the Structure of Zinc-Chalcogenide Cubic Crystals Doped by 3 d Ions

The real structure of bulk Zn1 – хМхSe (S) crystals of diluted magnetic semiconductors with М = V, Cr, Fe, Co, Ni 3d impurities is characterized by neutron diffraction. These impurities are known to greatly destabilize even the initial lattices of pure zinc chalcogenides. Data on the resulting non-uniform microstrain field induced by atomic displacements are obtained from the structural peaks along the tangential and radial directions on the above crystals within a dopant concentration range of 0.01 ≤ х ≤ 0.10. Additional nodes with q = (1/3 1/3 1/3) 2π/a (q is the wave vector and a is the cubic unit cell) emerging in the reciprocal lattice of the cubic structure are considered as evidence for a pre-transition to the fcc (face-centered cubic)–hcp (hexagonal close-packed) phase state, which implies transitions from the fcc lattice along an 8-ray non-Lifshitz star with the wave vector k5 = μ(b1 + b2 + b3), where b1, b2, b3 are the reciprocal lattice vectors and μ ≈ 1/3.     

Collinear second harmonic generation of 20 wavelengths in a single two-dimensional decagonal nonlinear photonic quasi-crystal

We report on the observation of quasi-phase matched collinear second harmonic generation (SHG) at 20 wavelengths in a two-dimensional nonlinear photonic quasi-crystal with decagonal lattice. We show that at some wavelengths the second harmonics are generated via standard quasi-phase matching, namely a reciprocal vector exists that equals the phase-mismatch vector, while at others the SHG is as a result of the projection-based quasi-phase matching in which the momentum conservation is satisfied up to a projection of a reciprocal vector onto the direction of propagation. In spite of different generation mechanisms, the reciprocal vectors (or their projections) involved in the collinear QPM SHG can be described by a generalized equation.     

Equation of state and thermodynamics of fcc transition metals: A pseudopotential approach

A simple pseudopotential model is used for the calculation of the phonon spectra at the equilibrium volume and under pressure. The model is based on the secondorder perturbation theory with the local pseudopotential acting on thes electrons while thed electrons contribution is simulated by the repulsive Born-Mayer interatomic potential. Pressure influence on the lattice properties was studied for small compressions (mode Grüneisen parameters) as well as for ultrahigh pressure (equation of state up to 1 TPa). Results of the lattice dynamics calculations were used for determining temperature dependence of the lattice heat capacity and of the macroscopic Grüneisen parameter. The Kohn anomaly at the small wave vectors obtained previously in palladium, platinum and rhodium affects strongly the temperature dependence at low temperature.     

Refined Prediction and Observation of Dislocation Structures in Low Σ Symmetric Grain Boundaries

The grain boundary dislocation structures of three Fe–4at.% Si bicrystals with an additional misorientation of the order of 2° were studied by transmission electron microscopy (TEM), one S5 [001] (310) and two S9 [110] (1 [`1]\overline 1 4). It was found that in the S5 case two Burgers vectors of the structure are not simple basic complete displacement shift lattice (DSC) vectors and are larger than any one of them. This enabled formation of the preferred grain boundary dislocation (GBD) structure with a hexagonal net composed of three screw dislocations and an independent set of parallel edge dislocations. In the S9 case the GBD structure comprises three apparently independent sets of parallel dislocations. The Burgers vectors of two sets could be established as basic DSC vectors in screw and edge orientation, respectively, with respect to the GB plane. For the third set formed by separated groups of four dislocations no corresponding basic DSC vector exists. This case needs further investigation. The previously published table of predicted GBD structures for symmetrical coincidence boundaries up to S11 was refined according to the new results.     

New Form for the Coulomb Potential in Complex Crystals. Part III

The present paper continues our works [1, 2] devoted to the construction of the Coulomb potential at an arbitrary point of the unit cell of crystals with a close-packed hexagonal (CPH) lattice by the Green's function method. Convergence of the real space and reciprocal lattice sums in the Green's function is investigated and the optimal convergence parameter is chosen. The method is used to construct the Coulomb potential in Ti, Co, and Zn metals. Calculations are performed for four directions. Nonmonotonic behavior of nuclear and electron components of the potential in the cell is established. The crystal potential is also calculated for these metals with allowance for the exchange interaction in the Slater approximation.     

New findings in phase transitions of spinel Li1.07Mn1.93O4-delta studied by transmission electron microscopy

Phase transitions and the related phase identifications at different temperatures for spinel Li(1.07)Mn(1.93)O(4-delta) crystals have been studied by transmission electron microscopy. The preliminary results clearly show the existence of at least two types of low-temperature phase: monoclinic and orthorhombic. Oxygen deficiency may raise the phase-transition temperature for the high-temperature (HT) cubic to low-temperature (LT) tetragonal, monoclinic, or orthorhombic phases. When the oxygen deficiency delta is very close to zero, the transition temperature is below room temperature (RT). Therefore, only the HT cubic spinel is observed at RT. When delta=0.182, the transition temperature is higher than RT, so the structures of the LT phases can be studied at RT. This study reveals the structural relationships between the LT phase and the HT phase. These relationships can be summarized as follows: (1) Two orthogonal cubic [440](Cubic)(*) and [440](Cubic)(*) reciprocal vectors are divided into two parts by {220} and {220} super reflections, respectively. This situation resembles the structures caused by correlated tilting and/or distortion of the octahedra in perovskites. (2) One of the cubic <440>Cubic(*) reciprocal vectors is divided into three parts by weak super-reflections. This situation resembles the modulated structure caused by the charge- and orbital-ordering in the perovskite La(1/3)Ca(2/3)MnO(3) of the space group Pnma. (3) One of the cubic <440>(Cubic)(*) reciprocal vectors, e.g. [440](Cubic)(*), is divided into three parts by stronger super-reflections, at the same time some strong reflections of the cubic spinel, e.g. (111)(Cubic)=(320)(Ortho)/2 disappear, indicating that there is a phase transition containing atomic movement. Items (2) and (3) are new findings in the present work.     

The adsorption of hydrogen on iron; A surface orbital modified occupancy — bond energy bond order calculation

A Surface Orbital Modified Occupancy — Bond Energy Bond Order (SOMO-BEBO) model calculation of hydrogen adsorption on iron is presented. This calculation represents a novel approach to the CFSO-BEBO method in that the calculation is correlated in a consistent way with the thermal desorption spectra of the hydrogen-iron system. Heats of molecular adsorption calculated are ?32.88, ?35.68 and ?49.57 kJ/mol for the iron (110), (100), and (111) surfaces, respectively. Heats of dissociative adsorption calculated are ?54.40, ?75.30 and ?87.90 kJ/mol for the three states on the iron (111) surface; ?51.21 and ? 73.62 kJ/mol for the two states on the iron (100) surface; and ?63.78 kJ/mol for the one state on the iron (110) surface. Activation energies for dissociative adsorption were found to be small or zero for the iron (111) surface while non-zero activation energies of 49.27 and 45.05 kJ/mol were calculated for the iron (100) and (110) surfaces, respectively. The FeH single-order bond energy has been calculated to be 298.2 kJ/mol. The radius of the hydrogen surface atom has been estimated to be 1.52 × 10^?10 m consistent with the expected size of an H^? ion. The elimination of certain surface sites for molecular adsorption as a result of the ferromagnetism of iron is suggested by the calculation. The reason for the absence of well defined LEED patterns for hydrogen adsorption on the iron (111) and (100) surfaces [Bozso et al., Appl. Surface Sci. 1 (1977) 103] is explained on the basis of the size of the H^? surface ion. The adsorption of hydrogen on the iron (110) surface is consistent with a relatively stable, small-sized H⁺₂ surface ion giving, therefore, a regular LEED pattern and a positive surface potential upon adsorption of hydrogen on this surface.     

Incommensurate Magnetic Fluctuations in the Underdoped Copper Oxide Materials

The doping dependence of magnetic fluctuations in the underdoped copper oxide materials are studied within the t-J model. It is shown that away from the half-filling, the magnetic Bragg peaks from the dynamical spin structure factor spectrum S(k,ω) are incommensurate with the lattice. Although the incommensurability δ(x) is almost energy-independent, the dynamical spin susceptibility χ^'(k,ω) at the incommensurate wave vectors is changed dramatically with energies, which is consistent with the experiments.     

Structural relative stabilities and pressure-induced phase transitions for lanthanide trihydrides REH3 (RE=Sm,Gd, Tb,Dy, Ho,Er, Tm,and Lu)

The structures, structural relative stabilities, pressure-induced phase transitions, and equations of state for lanthanide trihydrides REH₃ (RE=Sm, Gd, Tb, Dy, Ho, Er, Tm, and Lu) are systematically studied using ab initio calculations under a core state model (CSM). The obtained ground-state parameters, such as lattice constants and bulk modulus, agree well with the available data. Among the P6₃/mm, P3?c1, and P6₃cm structures, the P6₃cm structure is found to be the most stable structure for lanthanide trihydride via the comparison of the calculated total energies. With the help of Birch–Murnaghan equation of state, the structural transitions from hexagonal to cubic for REH₃ (RE=Sm, Gd, Ho, Er, and Lu) under pressure are affirmed; especially, the similar behavior of REH₃ (RE= Tb, Dy, and Tm) is reasonably predicted for the first time by this means. For the transitions, the repulsive interactions of H–H atoms may play an important role in terms of the analysis of the structures in the vicinity of the theoretical phase transition.     

二维斜方晶格光子晶体的第一布里渊区分析

二维斜方晶格光子晶体在光学聚焦器件及光子晶体波导中有重要的应用价值。对二维斜方晶格的第一布里渊区进行研究发现,保持斜方晶格基矢模长比R不变,改变倾斜角θ,第一布里渊区形状将在矩形和平行六边形间交替变化,所需的倒格矢也相应地变化,利用倒格矢正交临界条件可以对第一布里渊区的形状和所需的倒格矢进行划分。最后,利用平面波展开法对一种斜方晶格光子晶体进行带隙计算,验证了这种划分的正确性。     

Lattice relaxation and charge-transfer optical transitions due to self-trapped holes in nonstoichiometric LaMnO3 crystal

We explore the role of electronic and ionic polarization energies in the physics of “colossal” magnetoresistive (CMR) materials. We use the Mott-Littleton approach to evaluate polarization energies in the LaMnO₃ lattice associated with holes localized on both the Mn³⁺ cation and the O^2?anion. The full (electronic and ionic) lattice relaxation energy for a hole localized at the O site is estimated at 2.4 eV, which is appreciably greater than that of 0.8 eV for a hole localized at the Mn site, indicating a strong electron-phonon interaction in the former case. The ionic relaxation around the localized holes differs for anion and cation holes. The relaxation associated with Mn⁴⁺ is approximately isotropic, whereas ionic displacements around O^? holes show axial symmetry with the axis directed towards the apical oxygens. Using the Born-Haber cycle, we examine thermal and optical energies of the hole formation associated with the electron ionization from Mn³⁺, O^2?, and La³⁺ions in the LaMnO₃ lattice. For these calculations, we derive a phenomenological value for the second electron affinity of oxygen in the LaMnO₃ lattice by matching the optical energies of the La⁴⁺ and O^? hole formation with maxima of binding energies in the experimental photoemission spectra. The calculated thermal energies predict that the electronic hole is marginally more stable in the Mn⁴⁺ state in the LaMnO₃ host lattice, but the energy of a hole in the O^? state is only higher by a small amount, 0.75 eV, suggesting that both possibilities should be treated seriously. We examine the energies of a number of fundamental optical transitions, as well as those involving self-trapped holes of Mn⁴⁺ and O^? in the LaMnO₃ lattice. The reasonable agreement of our predicted energies, linewidths, and oscillator strengths with experimental data leads us to plausible assignments of the optical bands observed. We deduce that the optical band near 5 eV is associated with the O(2p)-Mn(3d) transition of a charge-transfer character, whereas the band near 2.3 eV is rather associated with the presence of Mn⁴⁺ and/or O^? self-trapped holes in the nonstoichiometric LaMnO₃ compound.     

He原子与HI分子碰撞截面的密耦计算

基于发展的分子间相互作用势, 采用密耦方法计算了入射能量从1到140?meV范围内He原子与HI分子碰撞的微分截面、分波截面和积分截面.通过与He-HX（X=F,Cl,Br）体系分波截面的比较, 印证了He-HI体系相互作用势以及密耦计算结果的可靠性.结果表明：小角散射的概率大于大角散射的概率;碰撞能量越高,散射概率就越小, 尾部效应也越弱.总积分截面主要来自弹性碰撞的贡献;非弹性积分截面以00→01和00→02跃迁的贡献为主,其中00→02跃迁的贡献最大. 关键词： 碰撞截面 密耦计算 HI-He体系