Standing-wave solutions of the Enneper (sine-Gordon) equation

The present paper investigates the real solutions of the partial differential equations (∂²ω/∂u²) − (∂²ω/∂ν²) = sin ω (Enneper or sine-Gordon equation) that are of the FORM = F(|₁(u) · |₂(ν)). In the application of the Enneper equations to crystal physics such solutions may represent standing waves. A complete classification of these solutions and its degenerate cases is given.     

Spectroscopic Evidence for Anionic Coordination Complexes of the Transition Metals with C70 and the Higher Fullerenes C76, C78, C82, C84, C86, C90, and C92

The carbonylate anions [M(CO)₅]^- (M = Mn, Re), [Co(CO)₄]^-, [CpFe(CO)₂]^-, and [CpM(CO)₃]^- (M = Mo, W) react with C₇₀ via single electron transfer processes to give, respectively, the corresponding 17-electron, metal-centered radicals Co(CO)₄, M(CO)₅ (M = Mn, Re), CpFe(CO)₂, and CpM(CO)₃ (M = Mo, W) in addition to the radical anion C₇₀^-. In secondary thermal or photochemical processes, the metal-centered radicals Co(CO)₄ and M(CO)₅ (M = Mn, Re) combine with the C₇₀^- to form the new η²-C₇₀ complexes [Co(CO)₃(η²-C₇₀)]^- and [M(CO)₄(η²-C₇₀)]^-. However, the metal-centered radicals CpM(CO)₃ (M = Mo, W) require photolysis to react with C₇₀^- to form [CpM(CO)₂(η²-C₇₀)]^-, whereas neither thermolysis nor photolysis induces reaction between CpFe(CO)₂ and C₇₀^-. The photochemical reaction of [Mn(CO)₅]^- with a mixture of higher fullerenes known to contain at least C₇₆, C₇₈, C₈₄, C₈₆, and C₉₀ resulted similarly in the formation of the higher fullerene complexes [Mn(CO)₄(η²-C_n)]^- (n = 76, 78, 80, 82, 84, 86, 88, 90, 92, 96, and 98), all identified using electrospray mass spectrometry.     

Thaumasite––direct, woodfordite and other possible formation routes

Two main formation routes for thaumasite exist below 15 °C. One is the direct route from C–S–H reacting with appropriate carbonate, sulfate, Ca²⁺ ions and excess water. The other route is the woodfordite route from ettringite reacting with C–S–H, carbonate, Ca²⁺ ions and excess water, in which thaumasite arises through the intermediate formation of the solid solution woodfordite. The woodfordite route for thaumasite formation appears to be relatively quicker (although still slow) than the direct route, presumably because with the former the ettringite already has the octahedral [M(OH)₆] units that can facilitate the critical change from [Al(OH)₆]³⁻ to [Si(OH)₆]²⁻ groupings. Both routes are mutually dependent on each other. The presence of magnesium salts can modify the path to thaumasite formation. High pressure might be able to stabilise [Si(OH)₆]²⁻ groupings and allow thaumasite to become formed above 15 °C. This possibility is discussed.     

Structure, nucleation and Eu luminescence in alkaline earth rare earth borate glass

In La₂O₃-MO-B₂O₃ ternary system, various glasses/ glass ceramics with M=Ca, Sr and Ba have been prepared. In this ternary system, homogeneous nucleation occuring in the B₂O₃ melt appears to be the cause for the formation of nanocrystallites, hence glass ceramics. The nucleation process is very much dependent on the alkaline earth used viz., with smaller alkaline earths like Ca, boron prefers (BO₄)⁵⁻ tetrahedral coordination with oxygen, while in the case of bigger alkaline earths like Ba and Sr, (BO₃)³⁻ triangular coordination seems to be predominant. Eu³⁺ in this glass system yields intense ⁵D₀→⁷F_j emission. A cursory view on the dependence of the various Judd-Ofelt parameters (Ω_k) indicates that Ω₂ parameter is very much dependent on the immediate vicinity of the luminescent ion (Eu³⁺) while Ω₄ is not. Various results based on these are discussed.     

Incorporating Runs Rules into Hotelling's χ2 Control Charts

This paper illustrates a simple and effective method of incorporating runs rules into Hotelling χ² control charts. A Markov chain will be used to obtain a desired in-control average run length (ARL). Comparisons between the basic multivariate χ² control chart and the multivariate χ² control chart, which incorporates the various runs rules, are based on their respective ARL performances. All multivariate χ² control charts that incorporate the various runs rules have shown better ARL performance compared to the basic multivariate χ² control chart for small shifts in distance λ from the in-control mean vector μ₀ to the out-of-control mean vector μ_s. An example of the application, based on the proposed method, is also given.     

Ordered Langmuir-Blodgett films of a substituted lutetium bisphthalocyanine

High-quality LB multilayers have been prepared from the Lu(III) sandwich complex of 2,3,9,10,16,17,23,24-octa (n-butoxy)phthalocyanine (LuPc₂(OBu)₁₆). Surface pressure-area isotherms were characterized and indicate that a stable monolayer is formed corresponding to an area per molecule of 2.4 nm² at 30 mN m⁻¹. The LB films were highly birefringent, and polarized spectra gave dichroic ratios of 3.3 for the 670 nm absorption band and between 0.5 and 2.8 for infrared absorptions. The results indicate that the phthalocyanine rings were highly oriented perpendicular to the dipping direction but somewhat tilted from the substrate normal. The order was shown to be absent when (i) unsubstituted LuPc₂ was used for LB films, or (ii) the horizontal lifting method of film deposition was used, or (iii) the surface pressure was increased to 50 mN m⁻¹, causing a molecular rearrangement. The ordering was improved at 100 °C and finally lost at 280 °C by annealing on a hot stage. The d.c. electrical conductivity of LB films of LuPc₂(OBu)₁₆ was low (σ ≈ 2 × 10⁻⁷ Ω⁻¹ m⁻¹), in contrast with unsubstituted LuPc₂ (σ ≈ 10⁻¹ Ω⁻¹ m⁻¹) and showed no evidence for anisotropy. The findings are in broad agreement with related studies and illustrate some of the many factors involved in improving the structure of phthalocyanine LB films for possible applications.     

Up-conversion dynamics in GdAlO3:Er single crystal fibre

Green fluorescence has been obtained under continuous laser excitation in the 780–860 nm range in GdAlO₃:Er³⁺. With the help of the Judd-Ofelt treatment we built a model based on population rate equations to describe its time evolution. We found the intensity parameters to be Ω₂ = 2.045 × 10⁻²⁰ cm², Ω₄ = 1.356 × 10⁻²⁰ cm² Ω₆ = 1. 125 × 10⁻²⁰ cm². Even if a two-photon absorption and a looping mechanism are necessary to well describe the dynamics, the main process responsible for up-conversion is energy transfer between erbium ions.     

Stress relaxation in the interface between creep particle and elastic matrix-strengthening mechanism

The effect of a power law creep particle on interface behavior between the particle and elastic matrix is investigated by stress analysis. Using the results obtained through the stress analysis, the forces due to interaction of an applied stress and stress concentration with an edge dislocation are determined. The direct interaction between the edge dislocation and the creeping particle is studied under fully relaxed stress conditions. Through the investigation the following results are derived. Stress relaxation in the interface can be caused by power law creep along or by diffusion, or a combination of both mechanisms. The degree of stress relaxation caused by diffusion can be defined in terms of the relaxation time for both boundary diffusion and volume diffusion. The amount of stress relaxation caused by the power law creep particle is characterized by the quantity ₂ which is a function of Γ₀ = 2(1/√3)^{1 + m} × (σ_∞/2μ)^m(σ₀/σ_∞t^m), where m is strain rate hardening exponent, σ_∞ is applied stress, μ is the shear modulus, σ₀ is the material constant of the power law creep particle, and t is elapsed time. The value ₂ = 1.0 corresponds to the fully relaxed condition and ₂ = −0.6 corresponds to the initial state. The time to reach a fully relaxed condition is very sensitive to the strain rate exponent, with the smaller m values leading to longer times. The stress state of complete relaxation in the elastic matrix is equivalent to the solution of a void in an elastic matrix superposed on the solution of positive surface traction on the void. This result is identical to that obtained by Srolovitz et al. [Acta. Metall.32, 1979 (1984)]. When the stress is completely relaxed in the particle, all stress components (σ_r, σ_θand σ_rθ) are relaxed, while in the matrix relaxations are observed only for σ_rand σ_θ. The critical resolved shear stress and critical stress to climb the dislocation in the neighborhood of the particle exceed the Orowan stress. Also, the particle attracts the dislocation. Therefore the strengthening of a power law creep particle in an elastic matrix is caused by the Orowan mechanism and by attraction of the dislocation.     

Solid-Phase Syntheses of Two Deacetyl-Thymosin β4 Analogues with Substitution at Position 12 and Their Effects on Impaired Blastogenic Response of T Lymphocytes of Uremic Patients

Two deacetyl-thymosin β₄ analogues containing Phe(4Br) or D-Phe(4Br) as position 12 were synthesized by the manual solid-phase method, and their immunological effects on the impaired blastogenic response of phytohemagglutinin-stimulated T lymphocytes of uremic patients with infectious diseases were studied. Bromination of the p-position of Phe¹² resulted in a marked restorative effect on the impaired blastogenic response of T lympocytes compared with that of our synthetic deacetyl-thymosin β₄ The synthetic [Phe(4Br)¹²]deacetyl-thymsin β₄ was approximately equal in potency to our synthetic [Phe(4F)¹²]deacetyl-thymosin β₄ in uremic patients, but the other analogue, [D-Phe(4Br)¹²]deacetyl-thymosin β₄, had no effect.     

Formation of Transparent and Photo Conducting Films by High Temperature Chemical Conversion of Solution Grown Precursor Films

The formation of photoconducting ZnO and transparent conducting CdO films by high temperature oxidation and thermal decomposition of chemically deposited ZnS and Cd(OH)₂ precursor films respectively is reported. The ZnS to ZnO and Cd(OH)₂ to CdO conversions were confirmed by x-ray diffraction (XRD)₂ electrical and optoelectronic studies. As deposited ZnS and Cd(OH)₂ films exhibited very low dark conductivity and no photoconductivity. Air oxidation of ZnS films at about 400°C for at least 15 minutes converted them to ZnO films with higher dark and photoconductivity. Cd(OH)₂ to CdO conversion occurred at about 300°C. CdO films exhibited a dark conductivity of the order of 10³ (Ωcm)^-1 and an optical transmittance in the range of 90%. These characteristics of ZnO and CdO films make them suitable candidates for the development of low cost photoconductors and solar cell structures.     

Temperature dependencies of excited states lifetimes and relaxation rates of 3–5 phonon (4–6 μm) transitions in the YAG, LuAG and YLF crystals doped with trivalent holmium, thulium, and erbium

The temperature dependencies of the nanosecond multiphonon relaxation (MR) rates of the ³F₃ state of Tm³⁺ in the YLF crystal and of the ⁵F₅ state of Ho³⁺ ion in the YAG and LuAG crystals and of the microsecond MR rates of the ⁴F_9/2 (²H_9/2) state of Er³⁺ ions in YLF were measured in the wide temperature range using direct laser excitation and selective fluorescence kinetics decay registration. For YLF the observed relations are explained by 4-phonon process in the frame of a single-frequency model with hω_eff=450±30 cm⁻¹ for the ³F₃ state of Tm³⁺ and by 5-phonon process with hω_eff=445 cm⁻¹ for the ⁴F_9/2 (²H_9/2) state of Er³⁺. For YAG and LuAG crystals these dependencies are explained by the 3-phonon process with hω_eff=630 cm⁻¹. The decrease of the relaxation rate with the temperature in the range from 13 to 80 K was observed for the ⁴F_9/2 (²H_9/2) state of Er³⁺ in the YLF crystal. It is explained by the redistribution of excited electronic states population of erbium ions over the higher lying Stark levels with different MR probabilities. A good fit of experimental temperature dependence (including the dropping part of the experimental curve) was obtained for single-frequency model (hω_eff=450 cm⁻¹) with W₀₁=8.0×10⁴ s⁻¹ and W₀₂=4.7×10⁴ s⁻¹ accounting Boltzmann distribution of population over two excited Stark levels of the excited state of erbium ions. Employment of this model improves the fit between the experiment and the theory for the ⁵F₅ state of Ho³⁺ ion in YAG as well. Strong influence of the parameters of the non-linear theory of MR, i.e. the reduced matrix elements U^(k) of electronic transitions and the phonon factor of crystal matrix η on the spontaneous MR rates was observed experimentally. The smaller these parameters the slower the spontaneous MR W₀. This fact can be used for searching new active crystal laser media for the mid-IR generation.     

RADIATION CHEMICAL AND PHOTOPHYSICAL PROPERTIES OF C60(C4H8SO3Na)n IN AQUEOUS SOLUTION: A LASER FLASH PHOTOLYSIS AND PULSE RADIOLYSIS STUDY

Optical absorption studies on aqueous solutions of C₆₀(C₄H₈SO₃Na)_n (n = 4-6) revealed deviation from the Beer-Lambert law in the 250-350 nm region, which is assigned to the formation of solute aggregates at concentrations higher than 1 × 10^-3 mol dm^-3. Dynamic light scattering experiments showed aggregates with an average size of ∼100 nm. The solute has a broad weak fluorescence emission (ϕ_f = 1.8 × 10^-3) in the 450-650 nm region, which remained independent of solute concentration. The broad transient absorption band in the 450-900 nm region (ε₆₆₀ = 2170 dm³ mol^-1 cm^-1), which formed immediately on laser flash photolysis (λ_ex = 355 nm, 35 ps), is assigned to singlet-singlet transition. It decays to a triplet excited state whose absorption is observed to depend strongly on solute concentration. In dilute solutions, an absorption band with λ_max = 590 nm is seen, and at high solute concentration a broad absorption in the 500-900 nm region is observed. The e_aq^- reacts with the solute with a bimolecular rate constant of 1.7 × 10⁸ dm³ mol^-1 s^-1 and forms weak broad absorption bands at 440, 540, 620, 870, 940, and 1020 nm. Isopropanol radicals also react with the solute with a bimolecular rate constant of 2.3 × 10⁸ dm³ mol^-1 s^-1 with the formation of a transient optical absorption spectrum similar to that observed on reaction with e_aq^- and assigned to a solute radical anion. The ^•H and ^-OH radicals react with bimolecular rate constants of 3.2 × 10⁹ and 4.4 × 10⁹ dm³ mol^-1 s^-1, respectively, and form transient absorption bands at 440, 510, and 660 nm. Based on electron transfer studies with suitable electron donor/acceptor substrates, the ranges of the reduction and oxidation potentials of the solute an estimated.     

Evaluation of neutron thermalization parameters and benchmark reactor calculations using a synthetic scattering function for molecular gases

Using a synthetic incoherent scattering function which describes the interaction of neutrons with molecular gases we provide analytical expressions for zero- and first-order scattering kernels, σ₀(E₀ → E), σ₁(E₀ → E), and total cross section σ₀(E₀). Based on these quantities, we have performed calculations of thermalization parameters and transport coefficients for H₂O, D₂O, C₆H₆ and (CH₂)_n at room temperature. Comparison of such values with available experimental data and other calculations is satisfactory. We also generated nuclear data libraries for H₂O with 47 thermal groups at 300 K and performed some benchmark calculations (²³⁵U, ²³⁹Pu, PWR cell and typical APWR cell); the resulting reactivities are compared with experimental data and ENDF/B-IV calculations.     

Experimental determination of the gyromagnetic ratio of thehelium-4 atom in terms of that of the helium-3 nucleus

The ratio R=γ_4He(2³S₁)/γ_3He (1¹S₀) has been measured using gaseous samples in low magnetic field. The result, R=864.02276±3×10 ^-8, leads to a value of γ_4He=1760.78798(3×10^-7)×10⁸ ×rad×s^-1×T^-1     

Synthesis and the luminescent properties of europium-activated Ca2SnO4 phosphors

The synthesis and photoluminescent (PL) properties of calcium stannate crystals doped with europium grown by mechanically activated in a high energy vibro-mill have been investigated. The characteristics of Ca₂SnO₄:Eu³⁺ phosphors were found to depend on the amounts of europium ions. The XRD profiles revealed that the system, (Ca_1−xEu_x)₂SnO₄, could form stable solid solutions in the composition range of x = 0–7% after being calcined at 1200 °C. The calcined powders emit bright red luminescence centered at 618 nm due to ⁵D₀ → ⁷F₂ electric dipole transition. Both XRD data and the emission ratio of (⁵D₀ → ⁷F₂)/(⁵D₀ → ⁷F₁) reveal that the site symmetry of Eu³⁺ ions decreases with increasing doping concentration. The maximum PL intensity has been obtained for 7 mol% concentration of Eu³⁺ in Ca₂SnO₄.     

Optical properties of rare earth ion (Nd, Er and Tb)-doped alumina films prepared by the sol–gel method

Rare earth ion (Nd³⁺, Er³⁺ and Tb³⁺)-doped alumina films were prepared by the sol–gel method using aqueous alumina sol. The effects of dopant concentration and treatment temperature on the optical properties, absorption and emission were examined for the doped films. Alumina films prepared by this method gave a high dopant concentration (0–15 mol% per alumina). Significant concentration quenching did not occur in this concentration range. The emissions from ⁵D₃ and ⁵D₄ of Tb³⁺-doped film reflected sensitively a matrix environment around Tb³⁺ ions. Er³⁺- and Nd³⁺-doped alumina films resonantly excited by cw Ti–sapphire laser (800 nm) showed upconversion emission at room temperature. The former gave 548 nm (⁴S_3/2→⁴I_15/2) and 640 nm (⁴F_9/2→⁴I_11/2) signals, and the latter 640 nm (⁴G_7/2→⁴I_11/2), which were dependent on alumina.     

Charge carrier transport in Cu(COOH)2 organic molecular single crystal

The temperature dependences of the d.c. electrical conductivity (σ) and thermoelectric power (TEP) of low-dimensional Cu(COOH)₂ single crystal have been studied. The electrical conductivity is highly anisotropic (σ_‡/σ = 3.0 × 10²) and the crystal undergoes a Peierls transition at 208 K and two polymorphous phase transitions, namely → β and β → at 327 and 377 K respectively. The conductivity in this crystal is found to be mainly due to a non-adiabatic hopping mechanism. TEP measurements carried out at various temperatures show that the conductivity is due to the mobility of holes.     

A theoretical study on the second-order nonlinear optical susceptibilities of lithium formate monohydrate crystal, HCOOLi·H2O

Ab initio calculations of the first hyperpolarizabilities of (HCOOLi·H₂O)_2n supermolecules, as the building-blocks of lithium formate monohydrate (LFM) crystal with extended system, were performed for the first time. The dependence of the static β_ijk⁰ values on chain length was explored, and the frequency dependence of β_ijk(−2ω;ω,ω) was measured, and the influences of electron correlation and basis set on β_ijk⁰ were evaluated. Finally, we predicted the second-order nonlinear optical coefficients of LFM crystal. The β_ijk⁰ value of (HCOOLi·H₂O)_2n is linearly dependent on the chain length of supermolecule, which is quite unusual for an extended system connected by the O–Li bonds with ionic characters. Although the static component of β_zzz⁰ tensor is the static largest in these three components under study, the absolute value of frequency-dependent β_zyy(−2ω;ω,ω) element, transforming the smallest into the largest, is the most sensitive to frequency. After the fundamental wavelength is smaller than 500 nm, it is found that the β_ijk(−2ω;ω,ω) value is resonantly enhanced to a great extent due to the double frequency lies in the region of resonance. In addition, the β_zxx⁰ value goes from negative to positive with changes of electron correlation and basis set. Obviously, it is very necessary to take into account the effect of electron correlation, if the hyperpolarizability tensor components must be accurately calculated. Moreover, it is also very important whether it is adopted a complete basis set with diffuse and polarization functions. The calculated nonlinear coefficients at high level suggest that the scaled set reported by Robert seem more reasonable.     

Structural and optical characterization of β-FeSi2 layers on Si formed by ion beam synthesis

Structural and optical properties have been investigated for surface β-FeSi₂ layers on Si(100) and Si(111) formed by ion beam synthesis using ⁵⁶Fe ion implantations with three different energies (140–50 keV) and subsequent two-step annealing at 600 °C and up to 915 °C. Rutherford backscattering spectrometry analyses have revealed Fe redistribution in the samples after the annealing procedure, which resulting in a Fe-deficient composition in the formed layers. X-ray diffraction experiments confirmed the existence of /gb-FeSi₂ by annealing up to 915 °C, whereas the phase transformation from the β to phase has been induced at 930 °C. In photoluminescence measurements at 2 K, both β-FeSi₂/Si(100) and β-FeSi₂/Si(111) samples, after annealing at 900–915 °C for 2 h, have shown two dominant emissions peaked around 0.836 eV and 0.80 eV, which nearly coincided with previously reported PL emissions from the sample prepared by electron beam deposition. Another β-FeSi₂/Si(100) sample has shown sharp emissions peaked at 0.873 eV and 0.807 eV. Optical absorption measurements at room temperature have revealed the allowed direct bandgap of 0.868–0.885 eV as well as an absorption coefficient of the order of 10⁴ cm⁻¹ near the absorption edge for all samples.     

Ultrafast nonlinear optical effect in CdTe-doped glasses fabricated by the laser evaporation method

The laser evaporation method is an attractive technology to synthesize composite materials. We tried to apply the laser evaporation method on fabrication of CdTe-doped glasses for the first time. CdTe microcrystallites embedded in SiO₂ films were confirmed by transmission electron microscope images. The third-order nonlinear susceptibility χ⁽³⁾ and the decay time τ of CdTe-doped glasses were measured by three-beam forward type degenerate four-wave mixing. The maximum value of χ⁽³⁾ was estimated 4.2 x 10^-7 esu when the absorption coefficient was 6000 cm^-1. From the limitation of pulse duration of 5 ps, τ was not exactly measured but imagined to be shorter than 10 ps, which was much faster than the other semiconductor-doped glasses ever reported. The figure of merit defined as χ^(3)/τ is probably larger than 7.