Formation of a monolayer <Emphasis Type="Italic">h</Emphasis>-BN nanomesh on Rh (111) studied using <Emphasis Type="Italic">in-situ</Emphasis> STM

As a member of the 2D family of materials, h-BN is an intrinsic insulator and could be employed as a dielectric or insulating inter-layer in ultra-thin devices. Monolayer h-BN can be synthesized on Rh (111) surfaces using borazine as a precursor. Using in-situ variable-temperature scanning tunneling microscopy (STM), we directly observed the formation of h in real-time. By analyzing the deposition under variable substrate temperatures and the filling rate of the h-BN overlayer vacant hollows during growth, we studied the growth kinetics of how the borazine molecules construct the h-BN overlayer grown on the Rh surface.     

Electronic band structure and x-ray spectra of boron nitride polytypes

The electronic band structures of boron nitride crystal modifications of the graphite (h-BN), wurtzite (w-BN), and sphalerite (c-BN) types are calculated using the local coherent potential method in the cluster muffin-tin approximation within the framework of the multiple scattering theory. The specific features of the electronic band structure of 2H, 4H, and 3C boron nitride polytypes are compared with those of experimental x-ray photoelectron, x-ray emission, and K x-ray absorption spectra of boron and nitrogen. The features of the experimental x-ray spectra of boron nitride in different crystal modifications are interpreted. It is demonstrated that the short-wavelength peak revealed in the total densities of states (TDOS) in the boron nitride polytypes under consideration can be assigned to the so-called outer collective band formed by 2p electrons of boron and nitrogen atoms. The inference is made that the decrease observed in the band gap when changing over from wurtzite and sphalerite to hexagonal boron nitride is associated with the change in the coordination number of the components, which, in turn, leads to a change in the energy location of the conduction band bottom in the crystal.     

Theory of the microstructure of disordered <Emphasis Type="Italic">AA</Emphasis>′BO<Subscript>3</Subscript> and <Emphasis Type="Italic">ABB</Emphasis>′O<Subscript>3</Subscript> perovskite-structure solid solutions

A model is considered in which atoms A and A′ or B and B′ of disordered solid solutions A _x A _1?x ^′ BO₃ and AB _x B _1?x ^′ O₃ are distributed over a regular system of points 1(a) and 1(b) of the symmetry group O _h ¹ characterizing the ideal perovskite structure. The probabilities P(G _i |x) of unit cells having crystal-field symmetry at their center lowered to G _i =T _d , D_3d, C_3v, C_4v, D_2h, C_2v, C _s , or C₂ are calculated as a function of the concentration x. The limits for x in which the Jahn-Teller and/or dipole ordering mechanism is probable are determined. In the approximation taking into account only effective pair interactions, the scattering amplitude F _hkl is found to depend on a single parameter r₀. The theory predicts that the dependence of the intensities of even and odd reflections on sin θ/λ is nonmonotonic and that the distributions of nonuniform strains and of values of the lattice parameters in solid solutions are discrete.     

Formation and composition of the clathrate phase in the H<Subscript>2</Subscript>O-H<Subscript>2</Subscript> system at pressures to 1.8 kbar

The transition of the hexagonal ice phase I_h to the clathrate phase sII has been found in the H₂O-H₂ system at a pressure of about 1 kbar under conditions of an excess of gaseous hydrogen. The pressures of the I_h → sII and sII → I_h transitions have been determined over a temperature range from ?36 to ?18°C, and the pressure dependence of the synthesis temperature of the clathrate phase from a liquid at pressures from 1.0 to 1.8 kbar has been constructed. The solubility of hydrogen in the I_h and sII phases and in liquid water has been measured. The concentration of hydrogen in the clathrate phase sII is about 1.2 wt % (10 mol %) near the boundary of the sII → I_h transition, and it increases to 2 wt % (16 mol %) at a pressure of 1.8 kbar.     

Analytic properties of the effective dielectric constant of a two-dimensional Rayleigh model

Analytic properties of the dimensionless static effective dielectric constant f(p, h) of a two-dimensional Rayleigh model (p is the concentration and h is the ratio of the dielectric constants of components) are considered as a function of the complex variable h. It is shown that the only singularities of the function f(p, h) are first-order poles for real h = h _n < 0 (n = 1, 2, ...) with the condensation point h = ?1, which form an infinite discrete (countable) set. The positions of the first ten poles of the function f(p, h) and the residues at these points are calculated and represented graphically versus the concentration. Based on the results obtained, a pole-type approximate formula is proposed that describes the behavior of the function f(p, h) over a wide range of p and complex h.     

Withdrawal of Electrodynamical Forbiddance and Peculiarities of the SERS Spectra in Fullerene C<Subscript>70</Subscript>

It is demonstrated that in fullerene C₇₀, which can be considered as a deformed fullerene C₆₀ in some mean sense there is a withdrawal of an Electrodynamical forbiddance of a strong quadrupole light-molecule interaction, which is realized in the fullerene C₆₀. This situation occurs because of the reduction of symmetry of C₆₀ from the icosahedral symmetry group Y_h to the group D_5h. The withdrawal results in appearance of the lines in the SERS spectra of C₆₀, which are forbidden in usual Raman scattering and are active in the infrared absorption spectra. The experimentally measured SERS spectra of C₇₀ demonstrates existence of such lines that strongly confirms our ideas about the dipole-quadrupole SERS mechanism.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Transmission of the spin-spin coupling constants through hydrogen bonds in ammonia clusters

Spin-spin coupling constants are reported using six ab initio and fifteen DFT methods for dimers and larger clusters of ammonia. An analysis of components (Fermi contact, spin dipole, paramagnetic spin-orbit, and diamagnetic spin-orbit) of more relevant coupling constants ¹J_NH′, ^1hJ_NH′ and ^2hJ_NN has been carried out. Fermi contact is the dominant term in the total value for all constants. For dimers, a relationship between the addition of direct and intermolecular coupling constants gives the direct constants of monomer. From the comparison of all ab initio and DFT methods for dimers, SOPPA(CCSD) and S55VWN5 methods are, respectively, more reliable taking into account their accuracy and the computing time. Both methods are employed for the analysis of the transmission of coupling constants through the hydrogen bond for ammonia clusters. A linear relation between the intermolecular constants ^1hJ_NH′ and the length of the hydrogen bond is found.     

Intensity of singlet-triplet transitions in C<Subscript>60</Subscript> fullerene calculated on the basis of the time-dependent density functional theory and taking into account the quadratic response

The singlet-singlet and triplet-triplet absorption spectra of C₆₀ fullerene are calculated using the density functional method and taking into account the theory of linear and quadratic responses. The B3LYP density functional and the 6–31G and 3–21G atomic basis sets are used. The calculations are performed using the D_2h and D_5d symmetry groups, although the real symmetry of the ground state is described by the I _h symmetry group. The matrix elements of the operator of the spin-orbit coupling are calculated and the probabilities of some singlet-triplet transitions are estimated. Taking into account the data in the literature on vibronic interactions of vibrations of the t_1u, t_2u, g _u , and h _u symmetry species, the radiative lifetime of the 1³T_2g → 1¹A _g phosphorescence was estimated to be 45 s. The fact that this time proved to be considerably greater than the experimentally observed total lifetime of the triplet testifies to a fast nonradiative deactivation of the lowest triplet state of C₆₀ fullerene and agrees with a low phosphorescence intensity. The zero-field splitting of some triplets and the intensities of magnetic dipole transitions are discussed.     

Morphological transformations of diblock copolymers in binary solvents: A simulation study

Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent C _S2, the concentration of the polymer C _p , and the polymer–solvent interactions ε _ij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of C _p , C _S2, and/or ε _AS2. The copolymer morphological sequence from dissolved → sphere → rod → ring/cage → vesicle is obtained upon increasing C _S2 at a fixed C _p . This morphology sequence is consistent with previous experimental observations. It is found that the selectivity of the selective solvent affects the self-assembled microstructure significantly. In particular, when the interaction ε _BS2 is negative, aggregates of stacked lamellae dominate the diagram. The mechanisms of aggregate transformation and the formation of stacked lamellar aggregates are discussed by analyzing variations of the average contact numbers of the A or B monomers with monomers and with molecules of the two types of solvent, as well as the mean square end-to-end distances of chains. It is found that the basic morphological sequence of spheres to rods to vesicles and the stacked lamellar aggregates result from competition between the interfacial energy and the chain conformational entropy. Analysis of the vesicle structure reveals that the vesicle size increases with increasing C _p or with decreasing C _S2, but remains almost unchanged with variations in ε _AS2.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Intermediate phases in [111]- and [001]-oriented PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>–29PbTiO<Subscript>3</Subscript> single crystals

Phase transformations in [111]- and [001]-oriented PbMg_1/3Nb_2/3O₃–29PbTiO₃ single crystals have been studied using dielectric and optical measurements before and after applying an electric field. It is shown that the subsequence of phase transitions rhombohedral (R)—tetragonal (T)—cubic (C) phases is observed in nonpolarized samples of both orientations as temperature increases. In the [111]-oriented crystal, an additional intermediate monoclinic phase (it is possible, M _a ) is induced after preliminary polarization at room temperature and the R–M _a –T–C phase transitions are observed on heating. In the [001]-oriented crystal, after its polarization, the monoclinic phase forms instead of the rhombohedral phase even at room temperature and the M _a –T–C transitions occur on heating. The results are discussed from the point of view of the existence polar nanoregions with different local symmetries in a glasslike matrix.     

Rotation of the inner shell in a C<Subscript>20</Subscript>@C<Subscript>80</Subscript> nanoparticle

The stability of a C₂₀@C₈₀ nanoparticle and the rotation of its inner shell are studied theoretically within the tight-binding approximation. It is found that the C₂₀ skeleton in the free state is described by space group D_3d; in the case where C₂₀ is placed into the C₈₀(I _h ) fullerene field, the space group of C₂₀ is raised to I _h due to isomerization. The total energy surface of the C₂₀@C₈₀ compound is scanned over two rotation angles. Based on an analysis of the surface relief and energy isoline map, orientational melting of the nanoparticle is predicted. A nanoparticle gyroscope—C₂₀ rotating in the field of C₈₀ at a certain relative orientation and energy supply—is also predicted to exist.     

Colossal room-temperature magnetoresistance in thin La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>y</Subscript>MnO<Subscript>3</Subscript> epitaxial films

The first thin La_1?xAg_yMnO₃ epitaxial films (_y ≤ x) were grown on SrTiO₃ (110) substrates with silver present in the ionized state (Ag⁺) only. The Curie temperatures T_C of the compositions with x = y = 0.05, x = y = 0.1, and x = 0.3 and y = 0.27 crystallizing in the hexagonal structure \(R\bar 3c\) above or close to room temperature. The temperature dependences of electrical resistivity ρ and of magnetoresistance ¦Δρ/ρ/¦ = ¦(ρ_H ? ρ _H = 0)/ρ_H=0¦ pass through maxima near T_C, with the magnetoresistance being negative and reaching colossal values of ～7–20% in a magnetic field H = 8.2 kOe not only at T_C but also at room temperature. The magnetic moment per formula unit as derived from the saturation magnetization at T = 5 K is substantially smaller than expected for complete ferromagnetic ordering. The magnetization in fields of up to 6 kOe depends on the actual sample cooling conditions, and the hysteresis loop of a field-cooled sample is displaced along the H axis by ΔH. The above properties can be accounted for by the fact that the films are in a two-phase magnetic (ferromagnetic-antiferromagnetic) state induced by strong s-d exchange. The maximum value of Δ H was used to calculate the energy of exchange coupling between the ferromagnetic and antiferromagnetic parts of a sample.     

Elastic properties of D<Subscript>2</Subscript>O ices in solid-state amorphization and transformations between amorphous phases

Nonequilibrium phase transformations in D₂O ices, including the solid-state amorphization of ice 1h (1h-hda) and the heating-induced transition cascade hda-lda-1c-1h from high-density amorphous (hda) ice to low-density amorphous (lda) ice followed by crystallization in cubic ice 1c and phase transition to ordinary hexagonal ice 1h, were studied using an ultrasonic technique. It has been shown that, as in H₂O ice, the softening of a crystal lattice or an amorphous network precedes nonequilibrium transformations. However, noticeable isotopic differences in the behavior of the elastic properties of H₂O and D₂O, in particular, their 1h and hda modifications, call for a more detailed study of the structural features of these H₂O and D₂O phases.     

Radiation defect formation in strontium and calcium fluoride crystals doped by divalent cadmium and zinc ions

Ionization radiation is shown to reduce impurity ions to the univalent state in strontium and calcium fluoride crystals doped by divalent cadmium and zinc ions. In this case, a univalent ion is surrounded by eight equivalent fluorine ions and exhibits cubic symmetry O _h . At room temperature, the symmetry of the center is revealed to be sequentially lowered to C _3v and then to C _2v owing to the addition to the nearest environment of the impurity univalent ion of one or two anion vacancies, respectively, which are intrinsic defects not forming in undoped strontium and calcium fluoride crystals. Stable intrinsic defects are assumed to form through the separation of anion vacancy-interstitial fluorine ion pairs in the electric field induced by the reduced impurity ions. This electric field lowers the energy barrier to thermal separation of charged intrinsic defects.     

Optical and x-ray diffraction studies of the symmetry of distorted phases of the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>ZrF<Subscript>7</Subscript> crystal

(NH₄)₃ZrF₇ single crystals were grown, and polarization-optical and x-ray diffraction studies were performed on powders and crystalline plates of various cuts over a wide temperature range. Phase transitions are revealed at temperatures T _1↑ = 280 K, T _2↑ = 279.6 K, T _3↑ = 260–265 K, and T _4↑ = 238 K on heating and at T _1↓ = 280 K, T _2↓ = 269–270 K, T _3↓ = 246 K, and T _4↓ = 235 K on cooling. The sequence of changes in symmetry is established to be as follows: O _h ⁵ (Z = 4) ? D _2h ²⁵ (Z = 2) ? C _2h ³ (Z = 2) ? C _i ¹ (Z = 108) ? monoclinic²(Z = 216).     

Fundamental Entangling Operators in Quantum Mechanics and Their Properties

For the first time, we introduce so-called fundamental entangling operators \(e^{iQ_{1} P_{2}}\) and \(e^{iP_{1} Q_{2} }\) for composing bipartite entangled states of continuum variables, where Q_i and P_i (i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation (q₁, q₂) → (Aq₁ + Bq₂, Cq₁ + Dq₂), where AD?BC = 1, which means even the basic coordinate transformation (Q₁, Q₂) → (AQ₁ + BQ₂, CQ₁ + DQ₂) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.