Electron density calculations for MgCO3 using the sublattice technique

Self-consistent valence electron densities of a MgCO₃ crystal and of its constituent sublattices are calculated on the basis of the local-density functional theory. The coupling between the sublattices is characterized by the density difference, introduced as the difference between the total electron density and the densities of individual sublattices. Intra-and interlattice hybridization effects are considered. It is shown that the density difference is in qualitative agreement with the experimental deformational density.     

Effect of electron irradiation on the structure and properties of the MgB2 superconductor

This paper reports on the results of an investigation into the effect of irradiation of the Bardeen-Cooper-Schriefer superconductor MgB₂ by electrons with a mean energy ē ～ 10 MeV at low doses (0 ≤ Φt ≤ ～5 × 10¹⁶ cm^?2) on the lattice parameters, the intensity and width of diffraction lines, the superconducting transition temperature T _c , and the temperature dependence of the resistivity ρ(T) in the normal state. The results of structural investigations have revealed regularities in the defect formation in the magnesium and boron sublattices of the MgB₂ compound as a function of the electron fluence. At the initial stage, irradiation leads to the formation of vacancies, originally in the magnesium sublattice and then in the boron sublattice. For fluences Φt ≥ ～1 × 10¹⁶ cm^?2, vacancies are formed in both sublattices. The evolution of the electrical and physical properties [T _c , ρ_{273 K}, residual resistivity ratio RRR = ρ_{273 K}/ρ_{50 K}, parameters of the dependence ρ(T)] under electron irradiation is in agreement with the regularities revealed in the formation of radiation-induced defects in the crystal lattice of the MgB₂ compound.     

Optical activity of imperfect 1D superlattices with vacancies in impurity layers

The concentration dependence of the specific rotation angle of a gyrotropic photonic crystal (imperfect 1D superlattice with an arbitrary number of sublattices one of which (potassium dithionate K₂S₂O₆) is optically active) is numerically simulated. Specific gyrotropic features of the photonic crystal related to the random substitution of layers of a model molecular crystal with vacancies for the layers of the K₂S₂O₆ sublattice are revealed using microscopic analysis of the specific rotation angle of the optical polarization in the molecular crystal with a primitive lattice in the exciton spectral range.     

Electronic structure of crystalline sulfites

The band spectra, densities of states, and distributions of the valence and difference densities in Na₂SO₃ and K₂SO₃ crystals with a hexagonal lattice are calculated in terms of the local-density functional theory. It is found that the absorption edge of these crystals is curvilinear. The partial compositions of the bundles of valence bands are determined. It is shown that the polarizing effect of the cations on the anions substantially depends on the symmetry and the number of metal sublattices.     

Vacancy induced changes in the electronic structure of titanium carbide—II. Electron densities and chemical bonding

In a recent paper, we presented the band structure and the state densities for an ordered model structure for TiCn_0.75 and discussed the changes which occur in comparison with stoichiometric TiC. Starting from these results, we investigate in the present paper, on the basis of calculated electron densities, how the bonding situation is influenced by the vacancies on the carbon sublattice in TiC_0.75. The results can be summarized as follows: The presence of empty lattice sites leads to the formation of new types of bonds not present in TiC; i.e., weak bonds between second nearest Ti neighbors across the vacancy sites and stronger Ti-Ti bonds in the Ti octahedra around the vacancies caused by the reduction of the number of C-Ti bonds. An analysis of the electron densities also shows a strengthening of the covalent Ti-Ti bonds involving Ti atoms not immediately adjacent to a vacancy as well as an increase of the ionic character of the C-Ti bonds.     

The genesis of energy bands formed by sublattice states in alkaline-earth metal oxides and sulfides

The self-consistent electron energy band spectra of crystals and charged sublattices of alkaline-earth metal oxides and sulfides are calculated in the framework of the density functional theory within the pseudopotential approximation in the basis set of localized orbitals. The charge states of sublattices (such as neutral sublattices, empty metal sublattices, and doubly charged anion sublattices) are analyzed with due regard for the electrical neutrality of the crystal. It is demonstrated that the valence bands of the studied crystals are very similar to the valence bands of the doubly charged anion sublattices. The distributions of the valence electron densities of the crystals are virtually identical to those of the anion sublattices. The lower conduction bands of the crystals and doubly charged anion sublattices also almost coincide with each other for MgO and MgS but differ substantially for CaO and CaS. This is associated with the difference between the contributions from the anions and cations to the conduction band of the crystals. It is found that these contributions depend on the relative energy positions of p and d unoccupied states.

     

Relationship between short- and long-range orders in nonstoichiometric titanium monoxide (TiO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>)

The relationship between the short- and long-range orders in various phases of nonstoichiometric titanium monoxide (TiO _y ) has been analyzed for the first time. The types of the local environment of lattice sites in the metal and nonmetal (oxygen) sublattices of Ti₅O₅, Ti₃O₂, Ti₂O₃, and Ti₄O₅ superstructures are described. It is established that, in phases where ordering takes place simultaneously in both sublattices, all parameters of the superstructural short-range order determining the positions of atoms and vacancies in the first three coordination spheres can be uniquely expressed via the long-range order parameters. If the ordering takes place only in one sublattice, then five of the six short-range order parameters vanish. It is shown that, using data on the maximum absolute values of six short-range order parameters and on the fractions of occupied atomic positions in titanium and oxygen sublattices, it is possible to predict the type of ordered phase expected to form in the nonstoichiometric titanium monoxide TiO _y .     

Anomalous states of the crystal structure of (Rb0.1(NH4)0.9)2SO4 solid solutions in the temperature range 4.2–300 K

Crystals of (Rb_0.1(NH₄)_0.9)₂SO₄ solid solutions are studied using x-ray diffractometry. It is revealed that the temperature dependence of the lattice parameter a exhibits an anomalous behavior, namely, the “invar effect” at temperatures above the ferroelectric phase transition point T _c and an anomalous increase in the temperature range from T _c to the liquid-helium temperature. An anomalous increase in the lattice parameter a and an increase in the intensity of Bragg reflections with a decrease in the temperature are interpreted within the model of the coexistence of two sublattices hypothetically responsible for the ferroelectric phase transition. A series of superstructure reflections observed along the basis axes corresponds to a sublattice formed in the matrix of the host structure. Analysis of the ratio between the lattice parameters of these structures allows the inference that, in the temperature range 4.2–300 K, the structure of the crystal under investigation can be considered an incommensurate single-crystal composite.     

Magnetic interactions in Pr1−xTbxMn2Ge2

The magnetic moments in the rare earth and Mn sublattices of RMn₂Ge₂, where R is a rare earth element, feature a variety of ordering configurations. In PrMn₂Ge₂ and TbMn₂Ge₂, the interlayer magnetic coupling in the Mn sublattice is, respectively, ferromagnetic and antiferromagnetic below about 350 K. At low temperatures, the rare earth sublattice also orders and reconfigures the ordering in the Mn sublattice. In this study, we investigate the variations in the magnetic properties of Pr_1−xTb_xMn₂Ge₂ as a function of rare earth concentration by examining the evolution of the features in the temperature dependence of the magnetization. The results of earlier neutron diffraction and Mössbauer studies on samples with x=0 and 1 are also used for interpreting the magnetization data and to give an account of the competing effects between various magnetic structures in the Mn and rare earth sublattices. The results are summarized in the Pr_1−xTb_xMn₂Ge₂ magnetic phase diagram.     

Effects of magnetic anisotropy and exchange in Tm2Fe17

Neutron diffraction experiments have been carried out to study the magnetocrystalline anisotropy of two (2b and 2d) Tm sublattices and four (4f, 6g, 12j, and 12k) Fe sublattices in ferrimagnetic compound Tm₂Fe₁₇ (space group P6₃/mmc). We have determined the temperature dependence of the magnitude and orientation of magnetization for each of the thulium and iron sublattices in the range (10?C300) K. A spontaneous rotation (at about 90 K) of the Tm and Fe sublattice magnetizations from the c-axis to the basal plane is accompanied by a drastic change in the magnetization magnitude, signifying a large magnetization anisotropy. Both Tm sublattices exhibit an easy-axis type of the magnetocrystalline anisotropy. The Fe sublattices manifest both the uniaxial and planar anisotropy types. The sublattice formed by Fe atoms at the 4f position reveals the largest planar anisotropy constant. The Fe atoms at the 12j position show a uniaxial anisotropy. We find that the inelastic neutron scattering spectra measured below and above the spin-reorientation transition are remarkably different.     

Magnetic and electronic structure studies of the perovskite oxide Nd2/3Sr1/3MnO3 from the first principle calculation

Generalized gradient approximation (GGA) and GGA + U (U denotes on-site Coulomb interactions) methods are applied to investigate the magnetic and electronic structures of the perovskite oxide Nd_2/3Sr_1/3MnO₃. Under GGA the compound prefers ferrimagnetic ordering in which Nd sublattice is spin-antiparallel to Mn sublattice. Nd 4f states cross over the Fermi level under GGA, leading the ferrimagnetic Nd_2/3Sr_1/3MnO₃ to a metallic character. The on-site Coulomb interactions should be included to emphasize the localized feature of Nd 4f states. Under GGA + U, the spins of Nd and Mn sublattices tend to be parallel in the ground state, and fully spin-polarized Mn 3d electrons yield a half-metallic band structure for the ferromagnetic Nd_2/3Sr_1/3MnO₃. The ferromagnetic coupling between Nd and Mn sublattices is ascribed to the super-exchange interaction between Nd 4f and Mn 3d (t2g) electrons via O 2p electrons.     

Magnetic phase transition and the corresponding magnetostriction of intermetallic compounds RMnsGe2（R=Sm,Gd）

The temperature dependence of lattice constants a and c of intermetallic compounds RMn₂Ge₂ (R=Sm, Gd) is measured in the temperature range 10－800K by using the x-ray diffraction method. The magnetoelastic anomalies of lattice constants are found at the different kinds of spontaneous magnetic transitions. The transversal and longitudinal magnetostrictions of polycrystalline samples are measured in the pulse magnetic field up to 25T. In the external magnetic field there occurs a first-order field-induced antiferromagnetism－ferromagnetism transition in the Mn sublattice, which gives rise to a large magnetostriction. The magnitude of magnetostrictions is as large as 10^-3. The transversal and longitudinal magnetostrictions have the same sign and are almost equal. This indicates that the magnetostriction is isotropic and mainly caused by the interlayer Mn－Mn exchange interaction. The experimental results are explained in the framework of a two-sublattice ferrimagnet with the negative exchange interaction in one of the sublattices by taking into account the lattice constant dependence of interlayer Mn－Mn exchange interaction.     

Atomic displacements in the V<Subscript>52</Subscript>O<Subscript>64</Subscript> superstructure and the short-range order in superstoichiometric cubic VO<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> vanadium monoxide with metal vacancies

Atomic displacements in the lattice of the tetragonal V₅₂O₆₄ superstructure have been experimentally determined. It has been found that atomic displacement waves, which are attributed to the formation of the short-range displacement order, appear in the vanadium and oxygen sublattices of this superstructure. It has been shown that the V₅₂O₆₄ superstructure is formed on the basis of disordered superstoichiometric cubic vanadium monoxide with the short-range order in the metallic sublattice. The character of the short-range order is such that vanadium atoms occupying tetrahedral positions are in the environment of four vacant sites of the vanadium sublattice. This means that the superstoichiometric VO_>1.0 vanadium monoxide has a cubic structure differing from the B1-type structure characteristic of most of the strongly nonstoichiometric cubic compounds MX _y (X = C, N, O) of transition metals.     

Influence of the sublattice symmetry on the band structure of a MgSiN<Subscript>2</Subscript> crystal

It is demonstrated that the MgSiN₂ crystal structure can be reduced to a superposition of the Bravais approximate highly symmetric sublattices. The combined Brillouin zones are constructed for the crystal lattice and sublattices. Results of calculations of the electronic MgSiN₂ structure in the context of the local approximation of density functional theory are presented. The influence of the existing hidden symmetry of the crystal on its band spectrum is described.     

Annealing of a unique structural defect in crystalline PbF2 near the sublattice melting temperature

Structural defects whose size and concentration vary dramatically with temperature near the F^- ion sublattice melting temperature were observed in good, optical quality single crystals of PbF₂. Light scattering, optical microscopy and electron microprobe studies suggest that these defects are lattice strains surrounding clusters of neutral lead atoms which anneal at the sublattice melting temperature.     

Diffusion in ordered Fe-Si alloys

The measurement of the diffusional Mössbauer line broadening in single crystalline samples at high temperatures provides microscopic information about atomic jumps. We can separate jumps of iron atoms between the various sublattices of Fe-Si intermetallic alloys (D0₃ structure) and measure their frequencies. The diffusion of iron in Fe-Si samples with Fe concentrations between 75 and 82 at% shows a drastic composition dependence: the jump frequency and the proportion between jumps on Fe sublattices and into antistructure (Si) sublattice positions change greatly. Close to Fe₃Si stoichiometry iron diffusion is extremely fast and jumps are performed exclusively between the three Fe sublattices. The change in the diffusion process when changing the alloy composition from stoichiometric Fe₃Si to the iron-rich side is discussed.     

Die magnetische Struktur und das magnetische Verhalten von ErFe2: Eine Neutronenbeugungsuntersuchung

The magnetic structure of ErFe₂ has been determined from neutron diffraction measurements on a powderd sample in the temperature region between 4.2°K and 700°K. ErFe₂ exhibits ferrimagnetic ordering below 600°K with the Er- and Fe-ions being antiparallel oriented. The separate sublattice magnetisations of the Er- and Fe-sublattices have been determined. The saturation moments at 4.2°K have been found to beμ(Fe)=1.97μ _B andμ(Er)=8.47μ _B. The coupling between the two sublattices is by an antiparallel spin-spin interaction of the Er and Fe ions. The temperature dependence of the sublattice magnetization of the Er-ions is explained by a separation into two parts: an induced magnetization at high temperatures and a spontaneous magnetization at lower temperatures.     

Atom transport in random two sublattice structures: analogue of the random alloy sum rule

A simple and often used model of atom transport by the vacancy mechanism on two physically distinct interpenetrating sublattices assumes that each atom–vacancy exchange frequency depends only on the species of the atom and the sublattice from which it jumps. In the kinetic theory of this model, the phenomenological coefficients can be expressed as sums of partial correlation functions, each labelled by the sublattices associated with the atoms making the first and last jumps in the sequence of correlated jumps which it represents. A sum rule, a set of exact relations among these partial correlation functions, is derived for the model, assuming arbitrary vacancy content and any number of chemical species. It reduces to a widely used sum rule for the random lattice gas [L.K. Moleko and A.R. Allnatt, Phil. Mag. A 58 677 (1988)] in the limit that atom jump frequencies are made independent of sublattice. For the two sublattice model at very low vacancy contents, a more powerful sum rule is also derived; it is essentially the same as that of Belova and Murch [Defect Diffus. Forum 194/199 547 (2001)]. The efficiencies of the three sum rules are briefly compared. The low vacancy concentration sum rule is illustrated by numerical simulations for a binary two sublattice system.     

Zone structure and its genesis from the states of sublattices in orthorhombic MgGeN<Subscript>2</Subscript>

It is demonstrated that the crystalline structure of MgGeN₂ can be reduced to the superposition of “approximated” high-symmetry Bravais sublattices by shifting atoms in a unit cell within the range of 5% of the lattice constant. The superimposed Brillouin zones were plotted for crystal lattices and sublattices. The computational results are presented for the electronic structure of MgGeN₂ in terms of the theory of the density function. The influence of “hidden” symmetry in this crystal on zone spectra is described.     

Molecular dynamics simulation of the superionic conductor BaF2

Molecular dynamics simulations of the BaF₂ fluoride crystal were carried out over a wide range of temperatures in order to study structural and transport characteristics in the low-temperature, the high-temperature superionic, and the molten state. The experimental temperature dependence of the lattice constant was taken into account. A sharp change in total energy of the system in the vicinity of T=1200 K indicates a phase transition to the high-temperature state with a transition energy U=(18.8±0.2) kJ/mol which is close to the value of the latent heat Q=18.36 kJ/mol obtained experimentally at 1275 K. Calculation of the radial distribution functions g(r) shows that in the high-temperature superionic state the F^– sublattice is already disordered while the Ba²⁺ sublattice stays regularly ordered, which keeps the crystal in the solid state. In the low-temperature state both sublattices are regularly ordered, and in the molten state both sublattices are disordered. The calculated diffusion constants of F^– in the superionic state is about 10^–9m²/s which is a typical value for superionic conductors. The temperature dependence of the diffusion constant obeys the Arrhenius equation. Higher statistical moments of the trajectories are used to characterise the type of ion movement.