用三个关系式与Mathematica软件求第二类自然数幂和公式

首先介绍三个第二类自然数幂和关系式并对其中的两式给出证明,接着利用这些关系式与数学软件M athem atica4.0,给出求解第二类自然数幂和公式的若干机械计算方法.     

High temperature annealing effect on structural and magnetic properties of Ti/Ni multilayers

High temperature annealing effect on structural and magnetic properties of Ti/Ni multilayer (ML) up to 600 °C have been studied and reported in this paper. Ti/Ni multilayer samples having constant layer thicknesses of 50 Å each are deposited on float glass and Si(1 1 1) substrates using electron-beam evaporation technique under ultra-high vacuum (UHV) conditions at room temperatures. The micro-structural parameters and their evolution with temperature for as-deposited as well as annealed multilayer samples up to 600 °C in a step of 100 °C for 1 h are determined by using X-ray diffraction (XRD) and grazing incidence X-ray reflectivity techniques. The X-ray diffraction pattern recorded at 300 °C annealed multilayer sample shows interesting structural transformation (from crystalline to amorphous) because of the solid-state reaction (SSR) and subsequent re-crystallization at higher temperatures of annealing, particularly at ≥400 °C due to the formation of TiNi₃ and Ti₂Ni alloy phases. Sample quality and surface morphology are examined by using atomic force microscopy (AFM) technique for both as-deposited as well as annealed multilayer samples. In addition to this, a temperature dependent dc resistivity measurement is also used to study the structural transformation and subsequent alloy phase formation due to annealing treatment. The corresponding magnetization behavior of multilayer samples after each stage of annealing has been investigated by using Magneto-Optical Kerr Effect (MOKE) technique and results are interpreted in terms of observed micro-structural changes.     

掺铥氟磷玻璃的结构、热学性质和光谱性质

制备了不同Al(PO3)3含量的掺铥系列氟磷玻璃,研究了其结构、热稳定性和光谱性质。随着Al(PO3)3含量的增加,该系列玻璃的密度降低,折射率增加,差热分析表明,转变温度、析晶起始温度、析晶峰温度和熔化温度增加。Al(PO3)3摩尔浓度在7%~9%时析晶稳定性最佳。采用归一化的拉曼光谱分析了材料的结构和声子状况,对于该系列氟磷玻璃,Al(PO3)3含量的增加不会影响声子能量,但使声子密度增大。测试了样品的吸收光谱,Tm3 的3H6→3F4在第三通信窗口的L波段有明显吸收。与在其它玻璃基质中相比,Tm3 的3F4能级对应能量偏高,3H4能级对应能量偏低,使得3H4→3F4跃迁波长较大,接近于增益迁移光纤放大器的放大波长。扎得奥菲而特(Judd-Ofelt)理论分析表明随着Al(PO3)3含量增加,离子强度参量Ω2增大,Ω6保持相对稳定,Tm3 的能级寿命降低。     

Molecular dynamics simulations on the structures and properties of ε-CL-20-based PBXs ——Primary theoretical studies on HEDM formulation design

Five polymer bonded explosives (PBXs) with the base explosive ε-CL-20 (hexanitrohexaazaisowurtzi- tane), the most important high energy density compound (HEDC), and five polymer binders (Estane 5703, GAP, HTPB, PEG, and F2314) were constructed. Molecular dynamics (MD) method was employed to investigate their binding energies (Ebind), compatibility, safety, mechanical properties, and energetic properties. The information and rules were reported for choosing better binders and guiding formula- tion design of high energy density material (HEDM). According to the calculated binding energies, the ordering of compatibility and stability of the five PBXs was predicted as ε-CL-20/PEG > ε-CL-20/ Estane5703 ≈ε-CL-20/GAP > ε-CL-20/HTPB > ε-CL-20/F2314. By pair correlation function g(r) analyses, hydrogen bonds and vdw are found to be the main interactions between the two components. The elasticity and isotropy of PBXs based ε-CL-20 can be obviously improved more than pure ε-CL-20 crystal. It is not by changing the molecular structures of ε-CL-20 for each binder to affect the sensitivity. The safety and energetic properties of these PBXs are mainly influenced by the thermal capability (C°p) and density (ρ) of binders, respectively.     

Optical properties of cadmium sulfide nanocrystal film prepared by electrochemical synthesis at liquid-liquid interface

Dendritic nanocrystalline CdS film was deposited at liquid-liquid interface of surfactants and an electrolyte containing 4 mmol L⁻¹ cadmium chloride (CdCl₂) and 16 mmol L⁻¹ thioacetamide (CH₃CSNH₂) with an initial pH value of 5 at 15 °C by electrochemical synthesis. The nanofilm was characterized by transmission electron microscopy (TEM), field emission scanning electron microscope (FE-SEM), atomic force microscopy (AFM), ultraviolet visible (UV-vis) absorption spectroscopy and fluorescence spectroscopy. The surface morphology and particle size of the nanofilm were investigated by AFM, SEM and TEM, and the crystalline size was 30-50 nm. The thickness of the nanofilm calculated by optical absorption spectrum was 80 nm. The microstructure and composition of the nanofilm was investigated by X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS), showing its polycrystalline structure consisting of CdS and Cd. Optical properties of the nanofilm were investigated systematically by UV-vis absorption and fluorescence spectroscopy. A λ_onset blue shift compared with bulk CdS was observed in the absorption spectra. Fluorescence spectra of the nanofilm indicated that the CdS nanofilm emitted blue and green light. The nanocomposites film electrode will bring about anodic photocurrent during illumination, showing that the transfer of cavities produces photocurrent.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003     

Annealing behavior of gel‐spun polyethylene fibers at temperatures lower than needed for significant shrinkage

The annealing at 373 K of ultrastrong, gel‐spun polyethylene (PE) has been studied. At this temperature, the fibers show no significant shrinkage. Still, a significant decrease in the mechanical properties is observed. The fibers have been analyzed with differential scanning calorimetry (DSC), temperature‐modulated differential scanning calorimetry (TMDSC), atomic force microscopy (AFM), and small‐angle X‐ray scattering (SAXS). During the annealing, the glass transition of the intermediate phase is exceeded, as shown by DSC. When split for structure analysis by AFM, the annealed fibers undergo plastic deformation around the base fibrils instead of brittle fracture. The quasi‐isothermal TMDSC experiments are compared to the minor structural changes seen with SAXS and AFM. The loss of performance of the PE fibers at 373 K is suggested to be caused by the oriented intermediate phase, and not by major changes in the structure or morphology. The overall metastable, semicrystalline structure is shown by TMDSC to posses local regions that can melt reversibly. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 403–417, 2003     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

The non-isotropic character of electric and dielectric properties of ammonium zinc chloride crystal

The dielectric constant, ε, and the d.c. conductivity, σ, were measured along the a-, b- and c-axes of (NH₄)₂ZnCl₄ (AZC) crystal in the 300-450 K temperature range. Crystals of AZC grown from aqueous solutions containing excess of ZnCl₂ were used. The value of the dielectric permittivity of AZC is extremely small compared to other ferroelectric crystals. Pronounced broad or step-like peaks at the phase transition temperatures were detected along the a- and b-axes, while ε along the c-axis is temperature independent up to the end of the measuring range. Reciprocal of the dielectric permittivity in the range of the commensurate to incommensurate phase transition obeys a relation similar to the Curie-Weiss law that is valid for second order ferroelectric/paraelectric phase transitions. The constants of the proposed relationship applied to the cooling run are given. The J-E characteristics along the three crystallographic axes were measured in the normal, incommensurate, commensurate and antiferroelectric phases. Hence, the type of conduction mechanism has been estimated. Parameters of Poole-Frenkel and Richardson-Schottky types of conduction mechanism have been determined. The effect of applied electric field on the conductivity measurement was also tested. Conductivity anomalies with different character were observed at the phase transition temperatures. The lnσ−1000/T dependence revealed thermal activation energy of conduction along the a-, b- and c-axes with different values in different phases of AZC.     

On the origin of irreproducible behaviour of Na1−xLixNbO3 solid solutions

The irreproducibility of electrical properties of Na_0.88Li_0.12NbO₃ solid solution on thermal cycling reported by M.A.L. Nobre and S. Lanfredi is explained by gradual decomposition of the supersaturated solid solution below ca. 800 °C.