A spectroscopic ellipsometric investigation of new critical points of Zn1−xMnxS epilayers

Zn_1−xMn_xS epilayers were grown on GaAs (1 0 0) substrates by hot-wall epitaxy. X-ray diffraction (XRD) patterns revealed that all the epilayers have a zincblende structure. The optical properties were investigated using spectroscopic ellipsometry at 300 K from 3.0 to 8.5 eV. The obtained data were analyzed for determining the critical points of pseudodielectric function spectra, (E) = ₁(E) + i₂(E), such as E₀, E₀ + Δ₀, and E₁, and three E₂ (Σ, Δ, Γ) structures at a lower Mn composition range. These critical points were determined by analytical line-shapes fitted to numerically calculated derivatives of their pseudodielectric functions. The observation of new peaks, as well as the shifting and broadening of the critical points of Zn_1−xMn_xS epilayers, were investigated as a function of Mn composition by ellipsometric measurements for the first time. The characteristics of the peaks changed with increasing Mn composition. In particular, four new peaks were observed between 4.0 and 8.0 eV for Zn_1−xMn_xS epilayers, and their characteristics were investigated in this study.     

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.     

Hyperscaling for polymer rings

The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a d-dimensional lattice obeys hyperscaling. The combination p_NR²_N^d/2μ^−N (where p_N is the number of configurations of an oriented and rooted N-step ring, R²_N a typical average size squared, and μ the SAW effective connectivity constant of the lattice) is equal for N å ∞ to a lattice-dependent constant times a universal amplitude A(d). The latter amplitude is calculated directly from the minimal continous Edwards model to second order in 4 − d. The case of rings at the upper critical dimension d = 4 is also studied. The results are checked against field-theoretical calculations, and former simulations. As a consequence, we show that the universal constant λ appearing to second order in in all critical phenomena amplitude ratios is equal to .     

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.     

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.     

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.     

Disruption of antiferromagnetic order in Zn-doped La2CuO4

The magnetic phase diagram of La₂(Cu_1−xZn_x)O₄ has been determined from zero-field muon-spin-rotation (ZF-μSR) data taken at LAMPF for 0 ≤ x ≤ 0.10. Antiferromagnetic onset temperatures follow T_N(x) from susceptibility measurements on the same samples. However, the order becomes long range, as evidenced by a well-defined internal magnetic field, only at temperatures well below T_N. Extrapolation of our results yields T_N → 0 K at x = 0.11 for a single (Cu_1−xZn_x)O₂ plane, and comparison with YBa₂(Cu_1−xZn_x)₃O₆ implies identical disruption of magnetism by Zn doping in the single- and double-plane systems.     

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.     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Measurements of fragment mass, charge and kinetic energy distributions in thermal neutron fission of U with a back-to-back ΔE-E detector system

A simultaneous measurement of mass (M), charge (Z) and kinetic energy (E_k) distributions of fragments in thermal-neutron fission of ²³⁵U has been carried out using a back-to-back ΔE-E detector system. A pair of gridded ionization chambers filled with P-5 gas measured the energy losses ΔE₁, ΔE₂ of the complementary fragments in the gas, and the residual fragment energies were measured with a pair of semiconductor detectors. The four-parameter data were analysed to obtain fragment Z-distributions using the mass-momentum conservation relations to obtain M and then using the dependence of ΔE on E/M and Z. The charge resolution for the light-fragment group was determined at the gas pressures of 44, 150, 270 Torr and the best Z-resolution was obtained at 270 Torr. The data at this latter gas pressure were analysed to obtain the variances σ²_z of the fragment charge distributions for different E_k windows and this was compared with the measured variances σ²_A of the fragment mass distribution as a function of E_k as obtained by twoparameter measurements of the correlated fragment energies. The dependence of the measured variances σ²_A, σ²_Z on E_k is considered with a view to learning about the degree of neutron-proton correlations in the nucleon exchanges taking place during the mass division in fission, in analogy with that used in the case of heavy-ion deep inelastic collisions (DIC). The variation of σ²_A/σ²_z with E_k observed in the present work, which is somewhat similar to that seen in heavy-ion DIC, implies that the fragment mass division in fission is governed by nucleon-exchange processes, where the degree of neutron-proton correlations is dependent on the total kinetic energy E_k. While for very large E_k the neutron-proton motion in the exchange processes is found to be uncorrelated, for lower E_k values the motion is seen to be correlated. Implications of these results regarding the applicability of fission models such as statistical model are pointed out.     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

Structure, oxygen stoichiometry and electrical conductivity in the system Sr-Ce-Co-O

Mixed oxides in the system S-Ce-Co-O were prepared by solid state reaction and by freeze-drying of precursor compounds followed by thermal treatment. Two types of perovskite oxides exist in the system: Solid solutions of the type Sr_{1 − y}Ce_yCoO_{3 − x} and mixed oxides of the type (1 − y)SrCeO₃ − ySrCoO_{3 − x}. Microstructures and phase compositions were determined by electron microscopy and X-ray diffraction. SrCoO_{3 − x} forms a solid solution of ceria on the A-site in the strontium cobaltite lattice up to 0.15 mol Ce. This solid solution corresponds to the high-temperature structure of pure SrCoO_{3 − x} and is characterized by high oxygen exchange and electrical conductivity. The oxygen deficiency x was measured by solid electrolyte coulometry. The oxygen deficiency of solid solutions Sr_{1 − y}Ce_yCoO_{3 − x} increases with temperature and decreases with pO₂ in the ambient atmosphere and with increasing Ce dopant concentration. The pO₂-T-x diagram of the solid solution was determined. The T, pO₂ and dopant concentration dependencies of electrical conductivity were measured by a four-point d.c. technique. By Ce doping strontium cobaltite becomes a stabilized high-conductive material (maximum conductivity: 500 S cm⁻¹ at 400 °C, E_a = 0.025 eV, p-type). Above this temperature the T-coefficient of the conductivity changes from positive (semiconducting) to negative values.     

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.     

From Planck to GUT via dimensional transmutation

Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev S which defines the GUT scale will be determined via dimensional transmutation at a scale M where the soft-breaking (mass)² vanishes as a result of running from M_P = (8πG_N)^−1/2. Because of the large number of adjoint fields N_A coupled to S, one finds that M can be generically close to M_GUT = 2 × 10¹⁶GeV:

, where λ is a Yukawa 0.7. This work examines the symmetries and dynamical constraints required in a SUSY-GUT in order that the desired flatness in S is achieved, and that this flatness may survive in a supergravity framework.     

Diffusion of W on A W(211) plane

The diffusion of W on a (211) plane of a W field emitter has been re-examined by means of the fluctuation autocorrelation method. Diffusion along channels yielded E = 16.8 ± 0.5 kcal, D₀ = (3 ± 1) × 10⁻⁵ cm² s⁻¹. For diffusion across channels E =6.6 kcal, D₀ = 4 × 10⁻⁹cm² s⁻¹ at T < 752 K, and E = 24 kcal, D₀ = 5 × 10⁻⁴ cm² s⁻¹ at T > 752 K. The results for diffusion along channels yield E and D₀ values intermediate between recent results by Wang and Ehrlich [Surf. Sci. 206 (1988) 451] using field ion microscopy (E = 19 kcal, D₀ = 7.7 × 10⁻³ cm² s⁻¹) and Tringides and Gomer [J. Chem. Phys. 84 (1986) 4049], using the same method as the present work but a larger slit (E = 13.3 kcal, D₀ = 7 × 10⁻⁷ cm² s⁻¹). The results for cross channel diffus good agreement with those of Tringides and Gomer below 752 K, where these authors stopped. The new high temperature results suggest that the channel wall exchange mechanism postulated by Tringides and Gomer for cross channel diffusion at low T gives way to diffusion by climbing over the channel walls with higher E but also higher D₀ above 752 K. Possible reasons for the discrepancies between these three sets of results and the absence of cross channel diffusion in the work of Wang and Ehrlich are briefly discussed.     

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.     

Layer dependence of the superconducting transition temperature of HgBa2Can−1CunO2n+2+δ

High-pressure methods have been used to synthesize multiphase compositions in the Hg---12{n−1}n homologous series. The phase assemblages were examined by optical, electron diffraction and X-ray diffraction techniques, and their stoichiometries verified by electron microprobe. Transport and magnetic susceptibility measurements were combined with the results of the phase analysis to establish superconducting transition temperatures for both as-prepared and O₂- or Ar-annealed materials. It was found that the transition temperature peaks at T_c = 134 K for N = 3 and then decreases abruptly for n>4, reaching T_c<90 K for n7.     

General solutions of the Monge-Ampère equation in n-dimensional space

It is shown that the general solution of a homogeneous Monge-Ampère equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ξ_j/∂x₀ + Σ_k=1ⁿ⁻¹ ξ_k ∂ξ_j/∂x_k = 0 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation.     

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.