Defect structure of quenched γ-BICOVOX by combined X-ray and neutron powder diffraction

A detailed investigation of the defect structure of the Co doped BIMEVOX solid electrolyte, Bi₂V_{1 − x}Co_xO_{5.5 − 3x/2} (x = 0.1 and x = 0.2), quenched from high temperature, has been carried out using X-ray and neutron powder diffraction data measured at room temperature. The structure is built up from alternating layers of [Bi₂O₂]_n²ⁿ⁺ and [V_{1 − x}Co_xO_{3.5 − 3x/2}]_n²ⁿ⁻ with disorder limited to the vanadate layer. The ideal V/Co co-ordination is octahedral with corner sharing of equatorial oxygens. The refinements show that the true structure is distorted, with disorder in both apical and equatorial oxygens and oxygen vacancies concentrated in the equatorial positions. Detailed analysis of the oxygen site occupancies reveals two main types of V/Co co-ordination viz. distorted octahedral and distorted tetrahedral. The majority of the sites in both compositions are tetrahedral.     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Nuclear effects in the F3 structure function for finite and asymptotic Q

We study nuclear effects in the structure function F₃ which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of the nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of a Q⁻² series caused by nuclear effects (“nuclear twist” series). Basing ourselves on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F₃. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q⁻² correction. Special attention is paid to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on the Q² and x dependence of nuclear structure functions is found.     

Characterization of nonstoichiometric nickel manganite spinels NixMn3−x□3δ/4O4+δ by temperature programmed reduction

Cation deficient spinels Ni_xMn_3−x□_3δ/4O_4+δ (0≤x≤1) have been prepared by thermal decomposition of mixed oxalates Ni_x/3Mn_(3−x)/3(C₂O₄)·nH₂O in air at 623 K. They have been characterised by temperature programmed reduction (TPR) under H₂, the reaction being followed by gravimetric and powder X-ray diffraction measurements. It has been shown that TPR proceeds in several steps. The first steps correspond to the loss of nonstoichiometric oxygen leading to the formation of a stoichiometric oxide. During the following stages the manganese cations are reduced, causing the spinel structure to be destroyed, and the formation of solid solution of NiO in a cubic MnO. Subsequently, Ni²⁺ cations undergo a reduction to metallic nickel, and, finally, a mixture of nonstoichiometric MnO_1−δ and metallic nickel is formed. These oxides contain a high level of vacancies which vary with the nickel content with a maximum of δ≈1 near x=0.6. This nonstoichiometry is ascribed both to the presence of Ni³⁺ and excess of Mn⁴⁺.     

Low frequency impedance of a round superconducting wire

We calculated the electric field E on the surface of a straight superconducting wire with circular cross-section carrying AC transport current I=I_acosωt. Performing the Fourier analysis of E, we found that both components of the first harmonic have the same form: the critical current I_c in prefactor and the rest depending on the ratio F=I_a/I_c. The in-phase component leads to the classical result of loss calculation, while the out-of-phase component was derived for the first time. Thus the wire can be symbolized by a complex self-inductance L₁(I)=L₁′(I)−jL₁″(I) where L₁′ represents the reactive power while L₁″ the losses. When the lock-in amplifier, used to sort out the components of the first harmonic, is utilized in the wide-band mode, it allows one to determine the magnetic flux penetrated in the wire volume at two significant moments of the AC cycle: at zero current (remanent flux) and at the amplitude value of current.     

Minimal renormalization without ε-expansion: Three-loop amplitude functions of the 0(n) symmetric Φ theory in three dimensions below Tc

We present an analytic three-loop calculation for thermodynamic quantities of the O(n) symmetric Φ⁴ theory below T_c within the minimal subtraction scheme at fixed dimension d = 3. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the three-loop terms of the amplitude functions ƒ_Φ, F₊ and F₋ of the order parameter and the specific heat above and below Tc, respectively, without using the e = 4-d expansion. A Borel resummation for the case n = 2 yields resummed amplitude functions f_Φ and F₋ that are slightly larger than the one-loop results. Accurate knowledge of these functions is needed for testing the renormalization-group prediction of critical-point universality along the λ₋line of superfluid ⁴He. Combining the three-loop result for F₋ with a recent five-loop calculation of the additive renormalization constant of the specific heat yields excellent agreement between the calculated and measured universal amplitude ratio A⁺/A^- of the specific heat of ⁴He. In addition we use our result for f_Φ to calculate the universal combination Rc of the amplitudes of the order parameter, the susceptibility and the specific heat for n = 2 and n = 3. Our Borel-resummed three-loop result for R_c is significantly more accurate than the previous result obtained from the ε-expansion up to O(ε².     

Saturation and BFKL dynamics in the HERA data at small-x

We show that the HERA data for the inclusive structure function F₂(x,Q²) for x10⁻² and 0.045Q²45 GeV² can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x₀ of x at which the saturation scale Q_s equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.     

径向积分的解析计算

本文阐明的方法能方便地求出径向积分ⁿ₁^l₁F_Lⁿ₂^l₂(q)≡∫₀^∞> (R_n1^l₁(αr)jL(Kr)R_n2^l₂(αr)r²dr(q≡(K)/(α))的解析表达式。文中给出了L=0,1,2情况下各个径向积分的解析式,同时还以多重求和的形式络出了对各种量子数L,n₁,l₁,n₂,l₂适用的径向积分表达式。     

Magnetic properties of Lu2Co17−xSix single crystals

The Co-sublattice anisotropy in Lu₂Co₁₇ consists of four competitive contributions from Co atoms at crystallographically different sites in the Th₂Ni₁₇-type of crystal structure, which result in the appearance of a spontaneous spin-reorientation transition (SRT) from the easy plane to the easy axis at elevated temperatures. In order to investigate this SRT in detail and to study the influence of Si substitution for Co on the magnetic anisotropy, magnetization measurements were performed on single crystals of Lu₂Co_17−xSi_x (x=0−3.4) grown by the Czochralski method. The SRT in Lu₂Co₁₇ was found to consist of two second-order spin reorientations, “easy-plane”–“easy-cone” at T_SR1≈680 K and “easy-cone”–“easy-axis” at T_SR2≈730 K. Upon Si substitution for Co, both SRTs shift toward the lower temperatures in Lu₂Co₁₆Si (T_SR1≈75 K and T_SR2≈130 K) with the further onset of the uniaxial type of magnetic anisotropy in the whole range of magnetic ordering for Lu₂Co_17−xSi_x compounds with x>1 due to a weakening of the easy-plane contribution from the Co atoms at the 6g and 12k sites to the total anisotropy.     

Quenching of spin fluctuations by high magnetic fields

The quenching of spin fluctuations by magnetic fields has been observed in heat capacity and electrical resistivity measurements at low temperatures for a series of highly exchange enhanced magnetic materials. These include: the weak itinerant electron ferromagnets Sc₃In, Zr_1−xHf_xZn₂ (0 x 0.2) and Ni₃Al; the strong Pauli paramagnets RCo₂ (R = Sc, Y and Lu), TiBe₂ and Pd_1−xNi_x (0 x 0.01); and the heavy fermion systems CeSn₃, CeSi_x (x ≈ 1.85) an d UAl₂. The reported quenching of spin fluctuations in scandium and palladium by magnetic fields is reviewed, and it appears that the initial observations and conclusions are incorrect, and that fields greater than 10 and 40 T, respectively, will be necessary to quench spin fluctuations in these metals. The behaviors of these spin fluctuators have been grouped into six classes.     

The evolution of parton distributions at small x

We investigate parton distributions at small x using moments of the Gribov-Lipatov-Altarelli-Parisi (GLAP) evolution equation with respect to x. In this representation the kernel of the GLAP equation contains singularities in the moment variable ω at ω = 0. We show that the importance of these singularities at small x depends on the form of the starting distributions. We examine the range of x in which the GLAP equation is valid. The restrictions on the range of x depend on the form of the starting distributions. We investigate whether the GLAP equation can be used to interpolate data in the HERA region. Results are given for the structure function F₂ at small x. A possible method of determining the gluon distribution from F₂ is discussed.     

Magnetic properties and percolation threshold in diluted B-spinel ZnCr2xAl2−2xS4: a study through high-temperature expansions

By making use of high-temperature series expansions (HTSE) of the correlation functions, we study the thermal and disorder variation of the short-range order (SRO) in the particular B-spinel ZnCr_2xAl_2−2xS₄. We developed the HTSE for the q-dependent static structure factor S(q) to the order 6 in reciprocal temperature including both the nearest- and next-nearest-neighbour interactions J₁ and J₂, respectively. Respecting the experimental fact that the broad diffuse peak of the neutron is situated at the particular wave vector q₀=[0 0 0.79] and is insensitive to the temperature for a given ratio of dilution x, we have estimated the thermal variation of J₁ and J₂ in the case of the pure compound.

The bond percolation threshold x_p of the ZnCr_2xAl_2−2xS₄ is determined by studying the disorder variation of the correlation length ξ. The x_p is considered as the concentration at which ξ vanishes. The obtained values are x_p=0.27 when only J₁ is considered and 0.23 when both J₁ and J₂ are taken into account.     

Synthesis and electrophysical properties of novel lithium ion conducting oxides

Novel lithium ion conducting oxides with perovskite structure have been synthesized and studied. It has been found that the La_2/3−xLi_3xTiO₃ and La_2/3−xLi_3xNb₂O₆ compounds have a perovskite structure at 1/24 < x < 1/6 and 0 < x < 3/10, respectively. The results of investigating the electrical properties of both groups of perovskites indicate a high lithium ion conductivity.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

Very strong interlayer exchange coupling in epitaxial Fe/Fe1−xSix/Fe trilayers (x=0.4–1.0)

Fe/Fe_1−xSi_x/Fe (x=0.4–1.0) wedge-type epitaxial trilayers with improved homogeneity are grown by co-evaporation from two electron-beam sources. The coupling strengths of the bilinear (J₁) and biquadratic (J₂) coupling terms are derived from Brillouin light scattering (BLS) spectra and longitudinal MOKE hysteresis loops. The total coupling strength J=J₁+J₂ increases dramatically with increasing x and reaches values in excess of 6 mJ/m².     

A piecewise linear model for the zones of instability of an area-preserving map

In this note we study the global behavior of the piecewise linear area-preserving transformation x₁ = 1 − y₀ + |x₀|, y₁ = x₀, of the plane. We show that there are infinitely many invariant polygons surrounding an elliptic fixed point. The regions between these invariant polygons serve as models for the “zones of instability” in the corresponding smooth case. For our model we show that some of these annular zones contain only finitely many elliptic islands. The map is hyperbolic on the complement of these islands and hence exhibits stochastic behavior in this region. Unstable periodic points are dense in this region.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

Positive linear magnetoresistance in Fex–C1−x composites

A large positive magnetoresistance (MR) has been found in micro-sized Fe_x–C_1−x composites. At a magnetic field of 5 T, the Fe_0.2–C_0.8 composite has the largest MR, 53.8% and 190% at room temperature and at 5 K, respectively. The magnetic field dependence of the MR can be described approximately as MR∝Bⁿ, and the value of exponent n is determined by the Fe weight concentration and temperature, ranging from 1/4 to 6/4. It appears that Fe_x–C_1−x has a linear field dependence of the positive MR at different temperatures. The possible mechanism for the positive MR is discussed.     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.