X-Ray Diffraction Study of Correlated Electron System at Low Temperatures

By using an ultra-low temperature X-ray diffractometer, we studied low temperature phase transitions of several materials. These phase transitions are classified into a ferro quadrupole ordered phase, that is, Jahn–Teller distortion (TmVO, ZnCrO), an antiferro quadrupole ordered phase (CeB, PrPb), and a superconducrivity (MgB). We also investigated unknown phases, such as the low temperature phase in PrPtBi and the 4th phase in CeLaB. Our low temperature X-ray measurement gives rise to a fruitful information about the phase transition. Not only a whole profile of the reflection peaks, which can be analyzed by the Rietveld method, we also made the precise measurement of the temperature dependence of the integrated intensity of the reflection peak, the full width at half maximum, and the lattice spacing for some fixed reflections. The temperature dependence of the integrated intensity (I.I.) can be expressed by the Debye–Waller expression. At low temperatures, the change of the phonon frequency can be obtained from the I.I. through the Debye–Waller factor. In MgB we observed the hardening of the phonon and the softening of phonon above and below the superconducting transition temperature, respsctively. This result suggests the relevant mechanisim of superconductivity in MgB is the electron–phonon interaction. From the precise measurement of the lattice constant, we found the negative thermal expansion at low temperatures in many correlated electron system. This negative thermal expansion can be explained by the Fermi liquid theory by Misawa.     

Linear Response Theory Around a Localized Impurity in the Pseudogap Regime of an Anisotropic Superconductor

We compare and contrast the polarizability of a d-wave superconductor in the pseudogap regime, within the precursor pairing scenario (dPG), and of a d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Our study is motivated by STM imaging experiments around an isolated impurity, which may in principle distinguish between precursor pairing and dDW order in the pseudogap regime of the high- superconductors. In both cases, the -dependence of the polarizability is characterized by an azimuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector , albeit imperfect, due to a nonzero value of the hopping ratio in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also reflected by the dependence of the retarded polarizability.     

Bi2212 c-Axis Twist Bicrystal and Artificial and Natural Cross-Whisker Josephson Junctions: Strong Evidence for s-Wave Superconductivity and Incoherent c-Axis Tunneling

We discuss the latest data from c-axis twist Josephson junction experiments on Bi₂Sr₂CaCu₂O (Bi2212) bicrystals and on artificially and naturally formed cross whiskers. All three experiments provide strong evidence for a dominant s-wave order parameter for . The bicrystal and natural cross-whisker data also provide strong evidence for incoherent c-axis tunneling across the intrinsic Bi2212 junctions, consistent with a strongly inhomogeneous material.     

Thermodynamic Functions of Fermi Gas with Quadruple BCS-Type Binding Potential with dx2 - y2 d_{x^2 - y^2 } -Wave-Pairing Symmetry

A gas of spin 1/2 fermions with an interaction V+W = -||^-1 _k,k g _k,k(k)(k) b _k b _-k - 2 _k(k)n _k+ n _k-, where n _k± = a _k±, b _k = a _k+ a _k- and a _k, satisfy Fermi anticommutation relations, is investigated in the -pairing case. W+V₄ is nonzero only within a thin layer of one-fermion energies around the chemical potential , and (k) denotes the characteristic function of the corresponding range of momenta. Two cases are studied: 1⁰ = 0, 2⁰ = 0.10025 eV. In the first case the system exhibits a first order transition, in the second, the transition is second order. Temperature dependence of the system's thermodynamic functions is examined and compared with that of the s-pairing case.     

Excitonic Collective Mode and Negative Compressibility in Electron Liquids

A highly self-consistent theory maintaining the exact functional relations between the electron self-energy and the vertex part is employed to calculate the dielectric function very accurately in the homogeneous electron gas in two- and three-dimensions. By investigating the full dynamical properties of thus obtained, we find that the softening of excitonic collective modes is responsible for making the compressibility of the system negative at sufficiently low densities.     

EPR study of V2O5–P2O5–Li2O glass system

glass system, with 0 < x 50 mol%, was prepared and investigated by EPR method. For low content of V₂O₅ all the spectra present a hyperfine structure typical for isolated V⁴⁺ ions. With the increasing of V₂O₅ content, the EPR absorption signal showing hyperfine structure is superposed by a broad line without hyperfine structure characteristic for clustered ions. At high V₂O₅ content, the vanadium hyperfine structure disappears and only the broad line can be observed in the spectra. Spin Hamiltonian parameters g , g , A , A , dipolar hyperfine coupling parameters, P, and Fermi contact interaction parameters, K, have been calculated.The composition dependence of line widths of the first two absorptions from the parallel band and of the broad line characteristic to the cluster formations was also discussed.     

On perfect nonlinear functions (Π)

Perfect nonlinear functions are of importance in cryptography. By using Galois ring, relative trace and investigating the character values of corresponding relative difference sets, we present a construction of perfect nonlinear functions from to , where m′ is a divisor of 2m, and a construction of perfect nonlinear functions from to where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from to if and only if p = 2, and there doesn’t exist a perfect nonlinear function from to if m > n and l(l is odd) is self-conjugate modulo 2 ^k (k ≥ 1).      

Finite-size Effects on the Thermal Resistivity of 4He Near the Superfluid Transition

We present measurements of the thermal resistivity () near the superfluid transition temperature of ⁴He at saturated vapor pressure and confined in glass capillary arrays with rectangular capillary cross-sections of spacing L = 1 μm, width m, and length mm. We expect the finite-size effect in this rectangular geometry to provide a good approximation to that in the ideal parallel-plate geometry. The data coincide within our resolution with previous measurements for cylindrical capillaries of 1 m radius, indicating that the finite-size scaling-functions for these two geometries are indistinguishable. This stands in contrast to the scaling functions for static properties which, near the transition temperature, depend on the dimensionality of the confinement. The results are consistent with recent Monte Carlo and spin-dynamics simulations, and with renormalization-group calculations for capillaries with square cross section and .     

Implication of Striped Hole Structurization on the Evolution of Cuprate Electronic Properties with Doping

The striped hole structurization in cuprate CuO₂ layers is discussed in the framework of the earlier introduced string model implying the direct overlap of O 2p-like orbitals. In the lightly doped compounds with the mean hole density , each dopant ion and the nearest quantized hole orbital of rank η can be viewed as a pseudoatom. The growth of above 1/24 stimulates condensation of the pseudoatoms into pancakes where some part of hole orbitals is expected to be collectivizing into bosonic stripes (BS). The formation of BS among the fermion-like hole surroundings has to be displayed in electronic spectra first as a bulge, and then as the coherent peak flanking to the broad hump of incoherent origin (the so called “peak-dip-hump structure”). Accumulating and broadening BS with increase of give rise to percolation superconductivity below a border of critical temperatures . It is shown, that the cuprate characteristics calculated without fitting parameters are consistent with measurements.      

Excess Volumes, Densities, Speeds of Sound, and Viscosities for the Binary Systems of 1-Octanol with Hexadecane and Squalane at (298.15, 303.15 and 308.15) K

Excess molar volumes, , excess molar isentropic compressibilities, , and deviations of the speeds of sound, u ^D, from their ideal values u ^id in an ideal mixture for binary mixtures of 1-octanol, C₈H₁₇OH, with hexadecane, C₁₆H₃₄, and squalane (2,6,10,15,19,23-hexamethyltetracosane), C₃₀H₆₂, at T = (298.15, 303.15, and 308.15) K and at atmospheric pressure were derived from experimental density, ρ, and speed-of-sound data, u. Viscosity measurements were also carried out for the same mixtures. The Prigogine-Flory-Patterson (PFP) theory has been applied to analyze of these systems. Furthermore, the apparent molar volumes, and apparent molar compressibility, of the components at infinite dilution have been calculated.     

Construction of binary minimal product parity-check matrices

A parity-check matrix H of a given code is called minimal if it has minimum number of nonzero entries among all parity-check matrices representing . Let and be two binary linear block codes with minimal parity-check matrices H ₁ and H ₂, respectively. It is shown that, using H ₁ and H ₂, one can efficiently generate a minimal parity-check matrix for the product code .     

Microstructure studies of ZnO nanoneedles

ZnO nanoneedles with uniform diameter and length have been synthesized using thermal evaporation approach. Their microstructure and anisotropic growth mechanism have been studied by means of scanning electron microscopy, high-resolution electron microscopy and convergent-beam electron diffraction. The ZnO polarity induces fast [0001] axial growth of the ZnO nanoneedles which are directed either by high index and planes or by ZnO nanoparticle nuclei formed at the (0001)-Zn growth fronts. Moreover, the {0002} stacking faults are believed to assist the ZnO nanoneedle growth. The slope surfaces at the inactive -O bottom geometrically favor ZnO nanorods growth through twinnings.     

Orientation relations between carbon nanotubes grown by chemical vapour deposition and residual iron-containing catalysts

Orientation relationships between the growth direction of carbon nanotubes and encapsulated residual iron-containing particles have been determined using transmission electron microscopy. The nanotubes that are prepared by Fe-catalysed chemical vapour deposition on sol–gel Fe(NO₃)₃-tetraethyl orthosilicate substrates are the helical multiwall type. Nanoscale particles of both the low-temperature α-Fe (ferrite) and high-temperature γ-Fe (austenite) were found in the cavity of the carbon nanotubes with , and parallel to the tube growth direction, respectively. Cementite Fe₃C, the most abundant Fe-containing phase in present samples was also found to be entrapped in nanotubes with or parallel to the tube axis. The metastable retention of γ-Fe particles at room temperature is ascribed to the strain energy induced at the particle-nanotube interface due to volume expansion upon the γ- → α-Fe phase transformation. The decomposition of initially high aspect-ratio, rod-shape particles into a string of ovulation, while encapsulated in carbon nanotubes is accounted for by the Rayleigh instability. Ovulation leading to reduced particle size has also contributed to increase the surface energy term that counterbalances the total free energy change of phase transformation from γ- to α-Fe and further aids to the metastable retention of γ-Fe.     

Thermal impurity reactions and structural changes in slightly carbonated hydroxyapatite

Lattice and surface impurity reactions and structural changes induced by them in slightly carbonated hydroxyapatite (SCHA) treated at 25–1100oC were comprehensively studied. The SCHA was processed by a conventional wet synthesis at a high possible temperature (96oC) using ammonium containing parent reagents. IR-spectroscopy, XRD, TG-DTA technique and mass spectrometric thermal analysis (MSTA) were employed for characterization of the samples. with in cationic- and (A- and B-positions) with in anionic sites, and H₂O, () , N _x H _y on the surface of particles were found and considered as impurity groups. Complicated changes in lattice constants of the SCHA stepwise annealed in air (for 2 h) were revealed; the changes were associated with reactions of the impurity groups. Filling the hexed sites with hydroxyl ions above 500oC was shown to happen partly due to lattice reactions but was mainly owing to hydrolysis of the SCHA by water molecules in air. Decomposition of groups proceeded through both thermal destruction and reactions with some of the impurity ions. The decarbonation in A-sites occurred at much lower temperatures (450–600oC) than in B-sites (700–950oC) and was first revealed to happen in two stages: due to an impurity reaction around 500oC, and then through thermal destruction at 570oC. A redistribution of ions, decreasing in amount on the whole, was observed upon annealing above 500oC. To avoid possible erroneous conclusions from TG-data, a sensitive method was shown to be required for monitoring gaseous decomposition products (such as the MSTA in this study), in case several impurity groups were present in a SCHA.     

Reference Viscosities of H<Subscript>2</Subscript>, CH<Subscript>4</Subscript>, Ar,and Xe at Low Densities

The zero-density viscosity of hydrogen, methane, and argon was determined in the temperature range from 200 to 400 K, with standard uncertainties of 0.084% for hydrogen and argon and 0.096% for methane. These uncertainties are dominated by the uncertainty of helium’s viscosity , which we estimate to be 0.080% from the difference between ab initio and measured values at 298.15 K. For xenon, measurements ranged between 200 and 300 K and the zero-density viscosity was determined with an uncertainty of 0.11%. The data imply that xenon’s viscosity virial coefficient is positive over this temperature range, in contrast with the predictions of corresponding-states models. Furthermore, the xenon data are inconsistent with Curtiss’ prediction that bound pairs cause an anomalous viscosity decrease at low reduced temperatures. At 298.15 K. the ratios , and were determined with a relative uncertainty of less than 0.024% by measuring the flow rate of these gases through a quartz capillary while simultaneously measuring the pressures at the ends of the capillary. Between 200 and 400 K, a two-capillary viscometer was used to determine with an uncertainty of 0.024% for H₂ and Ar, 0.053% for CH₄, and 0.077% for Xe. From was computed using the values of calculated ab initio. Finally, the thermal conductivity of Xe and Ar was computed from and values of the Prandtl number that were computed from interatomic potentials. These results may help to improve correlations for the transport properties of these gases and assist efforts to develop ab initio two- and three-body intermolecular potentials for these gases. Reference viscosities for seven gases at 100 kPa are provided for gas metering applications.     

The trace spectra of polynomial bases for $${\mathbb{F}}_{2^{n}}$$

In this paper we study the trace spectra of polynomial bases for over . Shparlinski showed that there exists a polynomial basis having O(log n) elements of trace one. Here we show that for every t ≤ n, there exists a polynomial basis having t + O(log n) elements of trace one. We also study consequences of our results to the existence of irreducible polynomials of certain weights.     

On primitive and free roots in a finite field

In this paper them-dimensional extension of the finite field of orderq is investigated from an algebraic point of view. Looking upon the additive group as a cyclic module over the principal ideal domain , we introduce a new family of polynomials over which are the additive analogues of the cyclotomic polynomials. Two methods to calculate these polynomials are proposed. In combination with algorithms to compute cyclotomic polynomials, we obtain, at least theoretically, a method to determine all elements in of a given additive and multiplicative order; especially the generators of both cyclic structures, namely the generators of primitive normal bases in over , are characterized as the set of roots of a certain polynomial over .     

On stabilized models in micromagnetics

The effective behaviour of stationary micromagnetic phenomena is modelled by a convexified Landau–Lifshitz minimization problem for the limit of large and soft magnets Ω with no exchange energy. The numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side-constraint and the stray-field energy on the unbounded domain . A penalty method models the side-constraint and the exterior Maxwell equation is recast via a nonlocal integral operator . This paper gives an overview of the available results and implementational details.     

Notes on classification of toric surface codes of dimension 5

This is an addendum to the beautiful paper by Little and Schwarz (Appl Algebra Eng Commun Comput 18:349–367, 2007) in which one case of toric surface codes of dimension 5 was missing in their classification result of toric surface codes of dimension less than 6. Our main purpose is to fill the gap of this paper. We find that our new code enjoys more symmetry, and it has more codewords of minimum distance in general. However, over some special fields , and have the same number of the codewords of minimum distance. H. Zuo was supported by NSFC and PSSCS of Shanghai.     

Effect of boundary plane on the atomic structure of [0001] Σ 7 tilt grain boundaries in ZnO

The atomic structure of [0001] Σ 7 tilt grain boundaries with { }‖ { }, { }‖ { }, and { }‖ { } boundary planes in ZnO was investigated through high-resolution transmission electron microscopy observation of fiber-textured thin films and atomistic calculations. These boundaries were found to comprise three kinds of common structural units that are characterized by fourfold- to eightfold-coordinated channels along the [0001] direction in contrast to sixfold-coordinated channels in wurtzite structure. The boundary structural units are very similar to the multiple core structures of edge dislocations with Burgers vectors of 1/3 < > . Transformation between two of the three configurations can easily occur through an atom flipping corresponding to dislocation glide. Depending on the orientation of boundary planes with respect to the Burgers vectors, the dislocation-like units exhibit straight or zigzag arrangements with periodicities corresponding to the Σ 7 misorientation.