Synthesis and characterization of C3N4 crystal (I)

A successful experimental synthesis of pure crystalline β- and α-C₃N₄ films on Si(100) substrate was carried out by bias-assisted hot filament chemical vapor deposition (bias-HFCVD). It is found that a mixed-phase C₃-_I-Si_xN_y buffer layer was formed between the Si substrate and the C-N film. A “lattice match selection” was proposed to study the growth mechanism of C₃N₄ clusters composed of many crystal columns with hexagonal facets. Project supported by the National Natural Science Foundation of China and the Chinese Academy of Sciences.     

Synthesis and characterization of C3N4 hard films

C3N4 films have been synthesized on both Si and Pt substrates by microwave plasma chemical vapor deposition (MPCVD) method. X-ray spectra were calculated for single phase α-C3N4 and β-C3N4 respectively. The experimental X-ray spectra of films deposited on both Si and Pt substrates showed all the strong peaks of α-C3N4 and β-C3N4, so the films are mixtures of α-C3N4 and β-C3N4. The N/C atomic ratio is in the range of 1.0-2.0. X-ray photoelectron spectroscopy (XPS) analysis indicated that the binding energy of C 1s and N 1s are 286.2 eV and 399.5 eV respectively, corresponding to polarized C-N bond. Fourier transform infrared absorption (FT-IR) and Raman spectra support the existence of C-N covalent bond in the films. Nano-indentation hardness tests showed that the bulk modulus of a film deposited on Pt is up to 349 GPa.     

Preparation and optical properties of GaSb nanoparticles embedded in SiO2 composite films

The composite films of GaSb nanoparticles embedded in SiO₂ matrices were fabricated by radio-frequency magnetron co-sputtering. Transmission electron microscope and X-ray diffraction pattern indicate that the GaSb nanoparticles were uniformly dispersed in SiO₂ matrices. Room temperature transmission spectra exhibit a blue shift of about 2.73 eV. The blue shift increases with decreasing size of GaSb nanoparticles, suggesting the existence of quantum size effects. Room temperature Raman spectra show that there is a larger Raman peak red shift and broadening of the composite films than that of bulk GaSb. This phenomenon is explained by photon confinement effect and tensile stress effect     

Preparation, structure, magnetic properties and special magnetoresistance effect of Lao.67Sr0.33Mn03+δ/Pr0.7Cao.3 Mn03+δ/Lao.67Sro.33Mn03+δ trilayered thin films

The La_0,67Sr_0.33Mn0_{3 +δ}/Pr_0.7Ca_o.3Mn0_3+δ/La_0.67Sr_0.33Mn0_3+δ(LPL) trilayered films on (100)LaA-1O₃ substrates are prepared by using direct current (DC) magnetron sputtering method. The results obtained by means of X-ray powder diffractometer show that all films are the high quality epitaxial films. The results gained by SQUID magnetometer indicate that there is a magnetic coupling in the LPL trilayered films. The resistivities of LSMO, PC-MO and LPL films are measured using standard four-probe method and analyzed log_p-1/T curve. From the results it is concluded that the middle-layered PCMO which is ferromagnetic may play a role of intra-magnetic field, which weakens the paramagnetism of LSMO film, lowersp _max and enlargesT _p which is the transition temperature from metal to insulator, just as the applied magnetic field does. And the middle-layered PCMO may induce the change of the density of states in the LSMO’s gap. The two reasons above make the resistivity andT _p of the samples in zero field change with the thickness of PCMO layers. Project supported by the Chinese Academy of Sciences and the Foundation of State Science and Technology Commission of China.     

Phase transition in layered perovskite-like manganate Ca3Mn2O7 under high pressure

In situ high pressure energy dispersive X-ray diffraction measurements on the layered perovskite-like manganate Ca₃Mn₂O₇ powder under pressures were performed by using the diamond anvil cell with synchrotron radiation. The results show that the structure of layered perovskite-like manganate Ca₃Mn₂O₇ is unstable under pressure due to the easy compression of NaCl-type blocks. The structure of Ca₃Mn₂O₇ underwent two phase transitions under pressures in the range of 0–35 GPa. One was at about 1.3 GPa with the crystal structure changing from tetragonal to orthorhombic. The other was at about 9.5 GPa with the crystal structure changing from orthorhombic back to another tetragonal.     

Irreducible characters of the group S n that are semiproportional on A n

Previously, we dubbed the conjecture that the alternating group A_n has no semiproportional irreducible characters for any natural n [1]. This conjecture was then shown to be equivalent to the following [3]. Let α and β be partitions of a number n such that their corresponding characters χ^α and χ^β in the group S_n are semiproportional on A_n. Then one of the partitions α or β is self-associated. Here, we describe all pairs (α, β) of partitions satisfying the hypothesis and the conclusion of the latter conjecture. Supported by RFBR (grant No. 07-01-00148) and by RFBR-NSFC (grant No. 05-01-39000). __________ Translated from Algebra i Logika, Vol. 47, No. 2, pp. 135–156, March–April, 2008.     

On a class of hyperbolic 3-orbifolds of small volume and small heegaard genus associated to 2-bridge links

We consider a class of hyperbolic 3-orbifoldsO(α/β); the underlying topological space of such an orbifold is the 3-sphere and the singular set is obtained by adding the two standard (upper and lower) unknotting tunnels to a 2-bridge linkL(α/β) (and associating branching order two to both unknotting tunnels). These 3-orbifolds are extremal with respect to the notion of Heegaard genus or Heegaard number of 3-orbifolds; it is to be expected that they are also extremal with respect to the volume, that is the smallest volume hyperbolic 3-orbifolds should belong to this or some closely related class. We show that an orbifoldO(α/β) has a uniqueD ₂-covering by an orbifoldℒ _n(α/β) wose space is the 3-sphere and whose singular set is the same 2-bridge linkL(α/β) used for the construction ofO(α/β); moreoverO(α/β) is hyperbolic if and only ifℒ _n(α/β) is hyperbolic. As the volumes of the orbifoldsℒ _n(α/β) are known resp. can be computed, this allows to compute the volumes of the orbifoldsO(α/β). The problem of computation of volumes remains open for some closely related classes of 3-orbifolds which are also extremal with respect to the Heegaard genus (for example associating a branching order bigger than two to one or both unknotting tunnels).     

Epitaxial growth and electrical transport properties of La0.5Sr0.5Co03 thin films prepared by pulsed laser deposition

Epitaxial growth of the La_0.5Sr_{0.5 3}(LO) thin films has been realized on Lin3, SrTiC₃ and MgO substrates by pulsed laser deposition. The epitaxial growth behavior and the electrical transport properties of these films were studied systematically. The temperature dependencies of the resistivity of the film have been determined. Studies indicate that close dependencies exist between the crystal structures and the electrical transport properties of the epitaxial LSCO films, and that the epitaxial thin films are of low resistivity and metallic conductive features. The epitaxial films deposited on the LaA10₃ substrates at about 700 °C possess the optimal properties compared with the others. Discussions of the dependencies and the mechanisms of the epitaxial structures on the electrical transport properties of the LSCO films have been made. Project supported by the National Natural Science Foundation of China (Grant No. 19574003 and No. 19674001).     

Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R ₁, R ₂, R ₃) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI. M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023.     

2-Summing operators on C([0, 1], lp) with values in l1

Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U ^#, U _# two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π _s (C(Ω, X), Y); (β)U ^# ∈ Π _s (C(Ω), Π _s (X, Y)); (γ) U _# ε Π _s (X, Π _s (C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l _p ) with values in l ₁ satisfies (α), (β) and (γ), which show that the above implication is the best possible result.     

Microstructure of a-SiOx:H

A set of a-SiO_x:H (0.52 <x< 1.58) films are fabricated by plasma-enhanced-chemical-vapor-deposition (PECVD) method at the substrate temperature of 250°C. The microstructure and local bonding configurations of the films are investigated in detail using micro-Raman scattering, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It is found that the films are structural inhomogeneous, with five phases of Si, Si₂O:H, SiO:H, Si₂O₃:H and SiO₂ that coexist. The phase of Si is composed of nonhydrogenated amorphous silicon (a-Si) clusters that are spatially isolated. The average size of the clusters decreases with the increasing oxygen concentration x in the films. The results indicate that the structure of the present films can be described by a multi-shell model, which suggests that a-Si cluster is surrounded in turn by the subshells of Si₂O:H, SiO:H, Si₂O₃:H, and SiO₂.     

Liquid structure of undercooled Cu70Ni30 alloy

Experiments of X-ray diffraction for liquid Cu₇₀Ni₃₀ alloy above and below its liquidus (l 230°C) have been carried out. By the analysis of experimental results, it is discovered that difference between structures of liquid and undercooled Cu₇₀Ni₃₀ alloy is their cluster sizes. The correlation radius of cluster is 1.125 nm and the atom number of cluster is 403 at l 250—l 400°C, and they are 1.3 nm and 704 respectively at the undercooled liquid state (1 200°C). The structure of liquid Cu₇₀Ni₃₀ alloy is fcc short order and its solid structure, fcc, is kept from liquid fcc short order.     

Irreducible characters with equal roots in the groups Sn and An

We show that treating of (non-trivial) pairs of irreducible characters of the group S_n sharing the same set of roots on one of the sets A_n and S_n \ A_n is divided into three parts. This, in particular, implies that any pair of such characters χ^α and χ^β (α and β are respective partitions of a number n) possesses the following property: lengths d(α) and d(β) of principal diagonals of Young diagrams for α and β differ by at most 1. Supported by RFBR grant No. 04-01-00463 and by RFBR-NSFC grant No. 05-01-39000. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 3–25, January–February, 2007.     

Synthesis of C3N4 crystals under high pressure and high temperature

C₃N₄ crystals with the size of several micrometers have been synthesized from C₃N₄H₄ in the presence of nickel-based alloy or cobalt as catalyst under high pressure of 7 GPa and temperature of about 1400°C for 10 min. Scanning electron microscopy, energy-disperse X-ray analysis, and X-ray diffraction were used to examine the grown crystals. The general rule on selecting the starting materials for synthesis of carbon nitride crystals at high pressures and high temperatures is suggested.     

Magnetovolume and chemical bonding effects of Ni atom in γ’-(Fe1- x Ni x )4N compounds

By X-ray diffraction and high pressure Mossbauer spectroscopy, the structure and the hyperfine parameters of Ni substituted γ’-Fe₄N were investigated. The results of X-ray diffraction indicate that single phase γ’-(Fe₁-_xNi_x)₄N compounds can be prepared in the composition range of 0⩽x⩽0.6, and with the increase of Ni content the lattice parameter is fit for the relationshipa ₀(x)=3.790 5-0.021 57x-0.031 67x ². By high pressure Mossbauer spectra, effects of magnetovolume and chemical bonding of Ni atom on hyperfine magnetic field and isomer shift of iron were distinguished for the first time, and their composition dependences for different lattice sites were studied simultaneously. It is found that the magnetovolume and chemical bonding have different influences on the properties of γ’-(Fe₁-_xNi_x)₄N, and the latter one plays a key role in the property changes of γ’-(Fe₁-_xNi_x)₄N. Project supported by the National Natural Science Foundation of China, the Natural Science Fund of Gansu Province and the Postdoctoral Fund of China.     

On the Spectral Function of Some Higher Order Elliptic or Degenerate-elliptic Operators

^m σ/|α|=|β|=m D^α(a _αβD^β) is a higher order degenerate-elliptic operator on L²(R^N) and V ∈ L¹(R^N) we show in particular that s(λ) > 0 for all λ > 0 provided that ∫_RN V(x)dx≥ 0, V not equivalent to 0 and N ≤ 2m.     

The decomposition of Kv into K2×K5''''s

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25).     

The structure and magnetic properties of Fe- N thin films

200 nm Fe-N thin films deposited on glass substrates by RF sputtering were vacuum annealed at 250-350℃ under 12000 A/m magnetic field. Heat treatment was effective in improving the soft magnetic properties of the Fe-N film. When the nitrogen content was in the range of 5-7 at. %,the thin films consisted of α′ + α" after heat treatment and had excellent soft magnetic properties of 4πMs = 2.4 T, Hc ＜ 80 A/m, μr = 1500 under 2-10 MHz. The properties of the films meet the needs of a write head material used in the dual element GMR/inductive heads. The fromation mechanism and lattice constants of the α′ phase in Fe-N thin film are different from Jack's results obtained from γ→α′transformation in bulk samples. The linear relationship between a, c and Ca'N for thin film was obtained asc = 2. 866+ 1.559Ca'N,a = 2.866 + 0.181Ca'N.``     

A geometrical problem arising in a signal restoration algorithm

Let ℤ_2N={0, ..., 2N-1} denote the group of integers modulo 2N, and let L be the space of all real functions of ℤ_2N which are supported on {0,...N−1}. The spectral phase of a function f:ℤ_2N→ℝ is given by φ_f(k)=arg for k ∈ ℤ_2N, where denotes the discrete Fourier transforms of f. For a fixed s∈L let K_s denote the cone of all f:ℤ_2N→ℝ which satisfy φ_f ≡ φ_s and let M_s be its linear span. The angle α_s between M_s and L determines the convergence rate of the signal restoration from phase algorithm of Levi and Stark [3]. Here we prove the following conjectures of Urieli et al. [7] who verified them for the N≤3 case:

The pressure in operator algebras

We introduce two notions of the pressure in operator algebras, one is the pressure Pα（π, T） for an automorphism α of a unital exact C^＊-algebra A at a self-adjoint element T in A with respect to a faithful unital ＊-representation π the other is the pressure Pτ,α（T） for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T.