On the superconducting transition temperature for metallic nanocrystals

A new approach is proposed for calculating the Debye temperature of a nanocrystal in the form of an n-dimensional rectangular parallelepiped with an arbitrary microstructure and the number of atoms N ranging from 2ⁿ to infinity. The geometric shape of the system is determined by the lateral-to-basal edge ratio of the parallelepiped. The size dependences of the Debye and melting temperatures for a number of materials are calculated using the derived relationship. The theoretical curves thus obtained agree well with the experimental data. The calculated dependences of the superconducting transition temperature T _c on the size d of aluminum, indium, and lead nanocrystals are also in reasonable agreement with the experimental estimates of T _c (d). It is demonstrated that, as the nanocrystal size d decreases, the greater the deviation of the nanocrystal shape from an equilibrium shape (in our case, a cube), the higher the temperature of the superconducting transition T _c (d). The superconducting transition temperature is calculated as a function of the thickness (diameter) of a plate (rod) with an arbitrary length. It is found that a decrease in the thickness (diameter) of the plate (rod) leads to an increase in the temperature T _c (z): the looser the microstructure of the metallic nanocrystal, the higher the temperature T _c (z).     

Influence of particle size,stoichiometry, and degree of long-range order on magnetic susceptibility of titanium monoxide

In situ measurements of the magnetic susceptibility of ordered and disordered titanium monoxides TiO_y in the temperature range from 300 to 1200 K have revealed that it depends on the size of crystals, their stoichiometry, and long-range order parameters. Analysis of the data for both the ordered and disordered TiO_y has demonstrated that the dependence of the Van Vleck paramagnetism on the nanocrystal size is inversely proportional due to the breaking of symmetry of the local environment of titanium and oxygen atoms near the surface of nanocrystals. It has been found that the Van Vleck contribution from the atomic vacancy disorder in monoxide nanocrystals of superstoichiometric composition, as well as in the crystalline stoichiometric monoxide, is proportional to the deviation of the degree of long-range order from the maximum value.     

Dependence of Van-Vleck paramagnetism on the size of nanocrystals in superstoichiometric TiO<Subscript> <Emphasis Type="Italic">y</Emphasis> </Subscript>

In situ measurements of the magnetic susceptibility of titanium monoxide nanocrystals with superstoichiometric composition TiO_y (y > 1) in the 300–1200 K temperature range showed that this value depends not only on the structural state of a sample, but also on the size of crystals. Analysis of data obtained for both ordered and disordered TiO_y showed that the Van-Vleck paramagnetism is inversely proportional to the nanocrystal size because of breakage of the symmetry of local environment of the near-surface atoms of titanium and oxygen. The Van-Vleck paramagnetism contribution due to atomic-vacancy disorder in superstoichiometric titanium monoxide nanocrystals, as well as in the stoichiometric composition, is proportional to a deviation of the degree of long-range order from its maximum value.     

The influence of anchoring energy on the prolate shape of tactoids in lyotropic inorganic liquid crystals

A model was constructed to describe the prolate shape of anisotropic regions, tactoids, coexisting with the isotropic phase in lyotropic inorganic liquid crystals. The elastic energy of the tactoid, the surface energy, and the interaction energy between the director field and the boundary of the tactoid were taken into account. Large-sized tactoids were shown to be prolate because of the competition between the elastic energy of the nematic phase of the tactoid and the surface energy. Small-sized tactoids were prolate because of the competition of the surface energy with the anchoring energy between the director and the boundary of the tactoid. The suggested model was applied to experimental data to determine the ratio of the elastic constants K₃/K₁ and the ratio between the anchoring energy W and the surface tension σ depending on the “time of aging” of vanadium pentoxide sols in water.     

Quantum-Size Dependence of the Energy for Vacancy Formation in Charged Small Metal Clusters. Drop Model

Self-consistent computations of the monovacancy formation energy are performed for Na _N , Mg _N , and Al _N (12 < N ≤ 168) spherical clusters in the drop model for stable jelly. Scenarios of the Schottky vacancy formation and “bubble vacancy blowing” are considered. It is shown that the asymptotic behavior of the size dependences of the energy for the vacancy formation by these two mechanisms is different and the difference between the characteristics of a charged and neutral cluster is entirely determined by the difference between the ionization potentials of clusters and the energies of electron attachment to them.     

Thermodynamische Stabilität makromolekularer Kristalle

The density of free energy of a chain crystal contains two terms of opposed sign dependent on the numberN of chain elements in the straight section of the macromolecules between the surfaces of the crystal perpendicular to thec-axis. The surface energy contributes a positive term decreasing withN. The amplitude Φ of the periodic lattice field opposing the chain translation in thec-axis yields the negative term. Due to the incoherent longitudinal thermal vibration of the four first-order neighbours of any chain the fieldΦ is smeared out. Its amplitude decreases the more the higherN and hence yields an increase in free energy density with increasingN. As a consequence of the opposite sign of surface energy and lattice field changes withN the free energy density shows a minimum at finiteN corresponding to the thermodynamically stable crystal thickness. With increasing temperature and lower interaction between adjacent chainsN increases in perfect qualitative agreement with experimental data.     

Treatment of pairing in small systems by Green functions

A finite system of fermions with pairing interaction is treated by the Green function method. It is shown that a finite number of “bound pairs” must be assumed to get the correct properties of the system in that region of the interaction strength where the BCS-solution is incorrect. Also the difference betweenE ₀(N+2)?E ₀(N) andE ₀(N)?E ₀(N?2),E ₀(N) being the ground state energy of theN-particle system, has to be considered. The formulae derived give an interpolation between the region where perturbation theory applies and the region of validity of the BCS-equations.     

Superconductivity in two-band systems with a variable carrier density: The case of MgB<Subscript>2</Subscript>

A theory of the thermodynamic properties of a two-band superconductor with a low carrier density is developed; it is based on a phonon superconductivity mechanism with a strong electron-phonon coupling. This theory can describe the variation of the critical temperature T _c, the energy gaps Δ₁ and Δ₂, and the relative electronic specific heat jump (C _S ? C _N)/C _N at T = T _c with the carrier density in the compound MgB₂ when substitutional impurities of various valences are introduced into this system. The values of T _c, Δ₁, and Δ₂ are shown to decrease as this compound is doped by electrons and to remain constant (or almost constant) as it is doped by holes. This behavior follows from the mechanism of filling the σ and π energy bands, which overlap at the Fermi surface. The theory agrees qualitatively with experimental data. This agreement is found to be better when intra-and interband electron scattering by an impurity potential is taken into account.     

Neutral Particle Motion around a Schwarzschild Black Hole in Modified Gravity

We investigate circular motion of neutral test particles on equatorial plane near a black hole in scalar-tensor-vector gravity. We consider three cases (i) α < G/G_N (ii) α = G/G_N and (iii) α > G/G_N to find the regions where motion can exist. The corresponding effective potential, energy, angular momentum and center of mass energy are evaluated. Further, we define four different cases for α > G/G_N and identify stable and unstable regions of circular orbits. It is found that circular orbits having zero angular momentum exist at r = αGNM due to repulsive gravity effects. We conclude that the structure of stable regions for α < G/G_N as well as α = G/G_N case is completely different from that of α > G/G_N.     

Surface and volume phase states of Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>x</Subscript>BO<Subscript>3</Subscript> crystals in the vicinity of the Néel point

The behavior of the magnetic system of a surface layer of macroscopic Fe_1?xGa_xBO₃ crystal (x=0, 0.3) in the vicinity of the Néel temperature T_N was studied. The studies were made by a method involving simultaneous gamma, x-ray, and electron Mössbauer spectroscopy that made it possible to obtain information simultaneously from surface layers and from the bulk of a macroscopic crystal. It was found that the temperature T_N(L) at which a thin layer at a depth L from the surface switches to a disordered state is lower than T_N for the bulk and is lower the closer this layer is to the surface. In the vicinity of T_N, a nonuniform state is observed in which the bulk of the crystal is magnetically ordered and the surface layer is disordered. The transition temperature T_N(L) decreases from T_N to its surface value within a surface layer of a “critical” thickness.     

Theoretische Untersuchungen über die Lage des Zwischengitteratoms in Kupfer

The different stable atomic configurations, formation energies and changes in volume of the crystal for an interstitial in copper are calculated with the help of the electronic digital computer Z 22 using a general method developed byTewordt. For the interaction between a pair of ions the Born-Mayer potentialV ₁, given byHuntington, and the Morse potentialV _M, given byGirifalco-Weizer, are employed. Two equilibrium configurations for an interstitial are found. In the stable configuration“A” the interstitial and one next neighboured atom are symmetrically located relative to one of the elementary cube faces along a cubic axis passing through the cube center. In the stable configuration“B” the interstitial and one next neighboured atom are symmetrically located relative to a cube corner along a {111}-axis. The interstitial is found not to reside at the center of an elementary cube. Neglecting electronic contributions to the relaxation of the lattice due to the redistribution of the electrons the calculations showed that the interstitial moved along a cubic axis about 0.4a/2 away from the elementary cube center into a stable configuration“A”. Moreover the crowdion is found to be unstable. It is shown that the crowdion decays into an interstitial lying in a next neighboured configuration“A”. The configuration“B” is separated from surrounding“A” and unstable “body-centered” and “crowdion” configurations by energy barriers. The number of atoms around the mobile interstitial treated as movable discrete particles is about 150 for the configuration“A” and about 50 for the configuration“B”. Using the Born-Mayer potentialV ₁ the changes in volume of the crystal arising from the interstitial are found to be 1.126 atomic volumes for the configuration“A” and 1.432 atomic volumes for the configuration“B”. The contributions to the formation energy of an interstitial arising from the potentialV ₁ turn out to be 3.548 eV for the configuration“A” and 4.098 eV for the configuration“B”. The results of the theoretical calculations are discussed in connection with recent radiation damage experiments performed at low temperatures on copper.     

On the dependence of the single-spin asymmetry of charged pions on kinematical variables

The experimental single-spin asymmetry (A _N ) of charged pions produced in proton-proton and proton-nucleus collisions is analyzed phenomenologically as a function of kinematical variables. It is shown that the c.m. pion threshold energy (E ₀ ^c.m. ) above which |A _N | is positive depends on the reaction energy √s and on the particle-production angle θ ^c.m.. The dependence of the single-spin asymmetry on the kinematical variables in the region specified by the inequalities 0.7 < p _T < 2.7 GeV/c and E ^c.m. > E ₀ ^c.m. exhibits a scaling behavior. The dependence of A _N on √s proves to be significant at moderate and low energies. Formulas that make it possible to predict the behavior of A _N for charged pions over a broad region of kinematical variables are derived.     

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s ₁ x ₁ + s ₂ x ₂ + ? + s _N x _N is proposed. Here x = (x ₁, … , x _N ), x _j ∈ R and the coefficients s = (s ₁, … , s _N ), s _j ∈ N. Given the interpolation values \((f(1), f(2),...,f(N))=\vec {y}\), the unknown coefficients \(s = (s_{1}(\vec {y}),\dots , s_{N}(\vec {y}))\) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.     

Dependence of the upper critical field on the defect concentration in MgB<Subscript>2</Subscript> and the electronic structure parameters

The upper critical field H _c 2 (H ‖ c) of the two-band superconductor MgB₂ is studied as a function of the residual resistivity ρ_n. It is found that the superconductor follows the standard trend: the slope-dH_c2/dT of the temperature dependence of H_c2(T) increases with the number of defects. The upper critical field in the clean limit is found, and direct estimations of the parameters of carriers in the 2D σ band (including the Fermi velocity and the coherence length) are made. The contribution of the electron scattering to the magnitude of H_c2 is determined, and the mean free path of electrons in samples with various defect concentrations is estimated. The density of states of σ electrons at the Fermi level is calculated using the dependence of the slope-dH_c2/dT on ρ_n and a band structure model. It is impossible to estimate this density of states directly, because the upper critical field is determined by the carriers of one band, whereas the resistivity depends on the carriers in both bands.     

Phase diagrams of bosonic AB<Subscript>n</Subscript> chains

The AB_{N ?1} chain is a system that consists of repeating a unit cell withN siteswhere between the A and B sites there is an energy difference ofλ. Weconsidered bosons in these special lattices and took into account the kinetic energy, thelocal two-body interaction, and the inhomogenous local energy in the Hamiltonian. We foundthe charge density wave (CDW) and superfluid and Mott insulator phases, and constructedthe phase diagram for N =2 and 3 atthe thermodynamic limit. The system exhibited insulator phases for densitiesρ =α/N, with α being an integer. Weobtained that superfluid regions separate the insulator phases for densities larger thanone. For any N value, we found that for integer densitiesρ, thesystem exhibits ρ +1 insulator phases, a Mott insulator phase, and ρ CDW phases. Fornon-integer densities larger than one, several CDW phases appear.     

Density of states of two-dimensional aluminum nanoclusters in the Hubbard model

The density of states of a two-dimensional square nanosystem composed of N × N aluminum atoms (N = 3?30) is calculated in the framework of the Hubbard model. It is demonstrated that, at a small parameter N, the density of states depends substantially on the number of atoms and on the position of a particular atom in the lattice. As the parameter N increases, the density of states for the vertex and edge atoms tends to the value of the density of states for the bulk atoms. The temperature of the system is implicitly included by specifying the energy of hopping in the initial Hamiltonian.     

Monomer counterrotations and tunneling splitting in CO dimer by data of millimeter wave spectroscopy

Analysis of the rotational spectrum of the molecular dimer (CO)₂ measured in the millimeter wave range has been performed and four new rotational states are revealed. Three of these states are characterized by almost free rotations of both monomers in the dimer. These states have approximately the same first term σ in the expansion of the rotational energy in powers of the rotational angular momentum J for various values of the momentum projections on the dimer axis (K=0, 1, 2) and various rotational constants B. The intrinsic rotational angular momenta of CO dimers, j₁=j₂=1, are determined from the σ value. In addition, a state with K=2 is found which corresponds to one of the known shape isomers of (CO)₂. The values of the tunneling splitting for each of the new states are determined. The results indicate that previous data on the suppressed tunneling are determined by the asymmetry of internal rotations in the CO monomers rather than by the _K value.     

Effect of Doping on the Properties of Hydrogenated Amorphous Silicon Irradiated with Femtosecond Laser Pulses

A comparative analysis of the effect of femtosecond laser irradiation on the structure and conductivity of undoped and boron-doped hydrogenated amorphous silicon (a-Si: H) is performed. It is demonstrated that the process of nanocrystal formation in the amorphous matrix under femtosecond laser irradiation is initiated at lower laser energy densities in undoped a-Si: H samples. The differences in conductivity between undoped and doped a-Si: H samples vanish almost completely after irradiation with an energy density of 150–160 mJ/cm².