Determination of the (Na) Sternheimer antishielding factor by Na NMR spectroscopy on sodium oxide chloride, Na3OCl

The (Na⁺) Sternheimer antishielding factor γ_∞ (Na⁺) was determined by ²³Na NMR spectroscopy on sodium oxide chloride, Na₃OCl. The quadrupolar coupling constant of the sodium ion in Na₃OCl was determined to QCC=11.34 MHz, which presents the largest coupling constant of a sodium nucleus observed so far. Applying a simple point charge model, the largest principal value of the electric field gradient at the sodium site was calculated to V_zz=−6.76762·10²⁰ V/m². From these values we calculated the (Na⁺) Sternheimer antishielding factor to γ_∞ (Na⁺)=−5.36. In sodium oxide, Na₂O, we observed an isotropic chemical shift of δ_CS=55.1 ppm, referenced to 1 M aqueous NaCl (δ=0 ppm).     

Adsorption of Na onto γ-alumina studied by solid-state Na and Al nuclear magnetic resonance spectroscopy

The adsorption of Na⁺ on γ-alumina surfaces at four coverages of Na₂CO₃ [5, 10, 15 and 20% (w/w)] was characterized by solid-state ²³Na and ²⁷Al nuclear magnetic resonance (NMR) spectroscopy. The experimental results suggest that two distinct adsorbed species are present on the alumina surface: surface species and surface salts. At the lower coverages of Na₂CO₃ (5 and 10%), the surface species is predominant, in which the Na⁺ cations are associated with the oxygen atoms of γ-alumina. Increasing the loading level to 15% results in the appearance of a second adsorbed species that is attributed to the surface salt, Na₂CO₃, deposited on the solid surface. Further adsorption of Na₂CO₃ leads to an increase in the amount of surface salt while the amount of surface species remains unchanged. ¹H---²⁷Al Cross-polarization magic angle spinning (CP-MAS) experiments give the evidence that some Na⁺ cations in the form of surface species are coordinated with the Brönsted acid sites of γ-alumina. This may be the main driving force that improves appreciably the catalytic efficiency of an Na₂CO₃---Al₂O₃ catalyst.     

Ionic conduction and dielectric relaxation in Ag/Na ion-exchanged aluminosilicate glasses: mixed mobile ion effect and KWW relaxation

Ag⁺/Na⁺ ion-exchanged aluminosilicate glasses with uniform concentration profiles were prepared, and their electrical conductivities were investigated as functions of the ion-exchange ratio and the initial glass compositions. In the case of the ion-exchanged glasses of x20Ag₂O–(1−x)20Na₂O–10Al₂O₃–70SiO₂ in mol%, the conductivity, σ, and its activation energy, E_σ, showed a minimum and a maximum at the same ion-exchange ratio x=0.3, respectively, and the mixed mobile ion effect (MMIE) was observed. The fully ion-exchanged sample attained σ=3.5×10⁻⁵ S/cm at 200 °C, which was 1.5 orders of magnitude larger than that of initial glass. In the case of x25Ag₂O–(1−x)25Na₂O–25Al₂O₃–50SiO₂, the mixed mobile ion effect was also observed at x=0.5. The maximum conductivity of 2×10⁻⁴ S/cm at 200 °C was obtained in the fully ion-exchanged glass sample.

The electric relaxation analysis was also conducted on both systems, and Kohlrausch–Williams–Watts (KWW) fractional exponent β was obtained as a function of x. The decrease of β was observed near x≈0.3 in the former system, while that of the later system was independent of the ion-exchange ratio. Based on the structural analysis results, the observed behaviors were investigated from the point of view of the occupation of Ag⁺ ions on the non-bridging oxygen-site (NBO-site) and the charge compensation-site (CC-site) of AlO₄ tetrahedral unit.     

Measurement of the slope parameter for the neutral pion spectrum in KL → πππ decay

The π⁰ spectrum in the K_L⁰ → 3π decay was measured using a wire chambers magnetic spectrometer. In the usual approximation, the matrix element can be expressed as: M² ≈ 1 + 2a₀(M_K/M_π²)(2T_π⁰−T_π⁰max) + a₁(M_K²/M_π⁴)(2T_π⁰−T_π⁰max)². We obtained a₀ = −0.282 ± 0.011 and a₁ consistent with zero.     

Ionic conduction properties of layer-type oxides NaxMx/2Ti1−x/2O2 (M=Ni, Co; 0.60≤x≤1.0)

Layer-type oxide Na_xM_x/2^IITi_1−x/2^IVO₂ (M=Co, Ni; 0.60≤x≤1.0) has been prepared by solid state reactions. In both series, two structural variants of type -NaFeO₂ (O3) and β-RbScO₂ (P2) have been obtained consecutively as x decreases with a borderline composition around x_c0.7. With the decrease of x, the ionic conductivity has been found to increase up to 8.4×10⁻² S cm⁻¹ at 770 K (Na_0.67Co_0.33Ti_0.67O₂). Compositions of P2 have been found to exhibit the conductivity values two to five times greater than those of O3, primarily due to the larger rectangular threshold available for the diffusion of Na⁺ ions. Such a structural effect has also been considered to depend on the polarizability of alkali ion. HT-XRD and ²³Na-NMR data of Na_0.67Co_0.33Ti_0.67O₂ strongly suggest that the diffusion of Na⁺ ion is deeply related with the local distortion of trigonal prismatic sites, leading to the change of activation energy around 430 K.     

A new measurement of the weak magnetism term in the betaspectra of B and N

The betaspectra of ¹²B and ¹²N have been measured with a NaI crystal as spectrometer. Assuming a shape correction factor 1 + aW + bW² and b₋ = 1.106 × 10⁻⁴ MeV⁻², b₊ = −1.397 × 10⁻⁴ MeV⁻², the spectra yield a₋ = (+0.91 ± 0.11) × 10⁻² MeV⁻¹ and a₊ = (−0.07 ± 0.09) × 10⁻² MeV⁻. the a₋ − a₊ = (+0.98 ± 0.09) × 10⁻² MeV⁻¹ is in agreement with the weak magnetism prediction.     

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.     

Asymptotics of eigenvalues of the Schrödinger operator with a strong δ-interaction on a loop

In this paper we investigate the operator H_β=−Δ−βδ(·−Γ) in , where β>0 and Γ is a closed C⁴ Jordan curve in . We obtain the asymptotic form of each eigenvalue of H_β as β tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of H_β in the strong coupling asymptotic regime.     

Deuterium conductivity, diffusion and implantation in Sr-doped LaYO3

A study of deuterium conductivity and diffusion in the oxide perovskite La_0.9Sr_0.1YO_3−δ is presented in this work. Deuterium ions were implanted into La_0.9Sr_0.1YO_3−δ (50 keV, 1×10¹⁶ atoms/cm²) and the corresponding deuterium depth profile was determined by SIMS and compared with a Monte Carlo simulation (TRIM96). This implant was used as a standard for the determination of deuterium concentration in a La_0.9Sr_0.1YO_3−δ sample pre-treated in D₂O atmosphere. In this way, it was fully confirmed that La_0.9Sr_0.1YO_3−δ incorporates water at high temperatures. The conductivity of La_0.9Sr_0.1YO_3−δ was measured in D₂O atmosphere and compared with other proton (deuteron) conductors. Concentration and conductivity data were used in conjunction to estimate the deuterium diffusivity and the constant of reaction of (heavy) water incorporation into LaYO₃. Some comments on the catalytic activity of this oxide are made.     

Study of superconducting state parameters of alkali–alkali binary alloys by a pseudopotential

A detailed study of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ^*, transition temperature T_C, isotope effect exponent and effective interaction strength N_OV of ten alkali–alkali binary alloys i.e. Li_1−xNa_x, Li_1−xK_x, Li_1−xRb_x, Li_1−xCs_x, Na_1−xK_x, Na_1−xRb_x, Na_1−xCs_x, K_1−xRb_x, K_1−xCs_x and Rb_1−xCs_x are made within the framework of the model potential formalism and employing the pseudo-alloy-atom (PAA) model for the first time. We use the Ashcroft’s empty core (EMC) model potential for evaluating the superconducting properties of alkali alloys. Five different forms of local field correction functions viz. Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used to incorporate the exchange and correlation effects. A considerable influence of various exchange and correlation functions on λ and μ^* is found from the present study. Reasonable agreement with the theoretical values of the SSP of pure components is found (corresponding to the concentration x = 0 or 1). It is also concluded that nature of the SSP strongly depends on the value of the atomic volume Ω₀ of alkali–alkali binary alloys.     

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⁺.     

Conductance studies of NaBPh4, NBu4I, NaI, NaCl, NaBr, NaClO4 and the limiting ionic conductance in water + propan-1-ol mixtures at 298.15 K

The electrical conductivities of NaBPh₄, NBu₄I, NaI, NaCl, NaBr and NaClO₄ have been studied in the mixtures of propan-1-ol with water. The obtained results were analysed using the Fuoss–Justice equation. The individual limiting ionic conductivities of Na⁺, NBu₄⁺, BPh₄⁻, I⁻, Cl⁻, Br⁻, ClO₄⁻ ions have been determined using the Fuoss–Hirsch assumption. The dependencies of the limiting molar conductances Λ_o and Walden products Λ_oη versus mixed solvent composition have been discussed.     

Neutrino oscillations induced by two-loop radiative mechanism

Two-loop radiative mechanism, when combined with an U(1)_L′ symmetry generated by L_e − L_μ − L_τ (=L′), is shown to provide an estimate of Δm²/Δm²_atm εm_e/m_τ, where ε measures the U(1)_L′-breaking. Since Δm²_atm 3.5×10⁻³ eV², we find that Δm² ε10⁻⁶ eV², which will fall into the allowed region of the LOW solution to the solar neutrino problem for ε 0.1.     

Experimental study of the time-dependent rate of K → πππ

The time-dependence of the decay rate of initially pure K⁰ into the final state (π⁺π⁻π⁰) has been studied in search for the decay k_S⁰→π⁺π⁻π⁰. No evidence is found in a sample of 384 observed events. The ratio of the CP -violating K_S⁰ amplitude and the K_L⁰ amplitude is η₊₋₀ = (0.13_−0.20^+0.17) + i(0.17_−0.26^+0.27); the ratio of the CP-conserving K_S⁰ amplitude and the K_L⁰ amplitude is < 0.4. The energy dependence of the K⁰→π⁺π⁻π⁰ matrix element is found to be a₊₋₀ = −0.31 ± 0.03.     

Study of the ferroelectric–paraelectric phase transition of NaH3(SeO3)2 single crystals by H and Na NMR

The ¹H and ²³Na spin–lattice and spin–spin relaxation times of NaH₃(SeO₃)₂ single crystals grown using the slow-evaporation method were measured as functions of temperature and frequency in the ferroelectric and paraelectric phases. The changes in the symmetry of the (SeO₃)²⁻ dimers as a result of the ferroelectric–paraelectric phase transition are associated with large changes in the spin–lattice and spin–spin relaxation times, and in the number of resonance lines. The large changes in the relaxation times at 195 K indicate that the H and Na ions are significantly affected by this transition. The change in the number of resonance lines for the ¹H and ²³Na nuclei means that the orientations of the (SeO₃)²⁻ dimers and the environments of the Na ions change at T_C. Therefore, the orientations of the (SeO₃)²⁻ dimers and the environments of the Na ions play important roles in the phase transitions. In conclusion, the ferroelectric–paraelectric phase transition of NaH₃(SeO₃)₂ is accompanied by changes in hydrogen-bond structure and distortions of the (SeO₃)²⁻ and Na⁺ ion lattices, which form a slightly distorted octahedron.     

Lattice sternheimer factor of Eu(OH)3 from Mössbauer spectral study

The Mössbauer spectra of powdered Eu(OH)₃ were recorded between 300 and 4.2 K, with ¹⁵¹SmF₃ as source. The spectra showed one single absorption line having definite width but without any fine structure. The lattice Sternheimer factor γ_∞ of ¹⁵¹Eu in Eu(OH)₃ was estimated with the help of these spectra as well as by using the values of some physical parameters obtained from spectral and magnetic susceptibility measurements on pure single crystal of Eu(OH)₃, The value of lattice Sternheimer factor (= -87) thus evaluated is slightly larger than that value ( = - 80) for ¹⁵⁴Eu in ethylsulphate host. This result is consistent with the γ_∞ values of other rare-earth ions and also with the results obtained from magnetic and optical experiments on Eu(OH)₃.     

Sr-doped LaInO3 and its possible application in a single layer SOFC

The effects of dopants on the electrical conductivity of the perovskite-type oxide LaInO₃ have been investigated. Replacement of La by Sr is the most effective way to enhance the conductivity of LaInO₃, whereas Ca substitution for In is rather difficult due to the large difference in the ion radii. The optimum composition is La_0.9Sr_0.1InO_3−δ whose maximum conductivity is 7.6×10⁻³ S cm⁻¹ at 900°C. The electrical conductivity of La_0.9Sr_0.1InO_3−δ has been measured over a wide range of oxygen partial pressure from pO₂=1 to 10⁻²⁵ atm. P-type and n-type behavior at high and low oxygen partial pressure have been observed, respectively, while at intermediate oxygen partial pressures, the electrical conductivity changes only slightly with the oxygen partial pressure. The concept of a single layer solid oxide fuel cell based on a La_0.9Sr_0.1InO_3−δ ceramic pellet has been tested. A maximum power density of 3 mW cm⁻² at 800°C was achieved when dilute H₂ and air were used as fuel and oxidizing agent, respectively.     

The pion form factor at a timelike momentum transfer of approximately 1 fm from π electroproduction at threshold

From an extrapolation of threshold π⁺ electroproduction data combined with a kinematical constraint at an unphysical point, we derive the value of the pion form factor at a time-like value of the momentum transfer k²_π 1 fm⁻². The result is F_π(k²_π) = 1.19 ± 0.1. From this value, using a twice subtracted dispersion relation, we obtain r_π 0.98 ± 0.24 fm.     

H MAS and H[Na] double resonance NMR studies on the modification of surface hydroxyl groups of γ-alumina by sodium

The modification of surface hydroxyl groups with sodium in a series of Na₂CO₃-γ-Al₂O₃ catalysts was investigated as a function of both the Na₂CO₃ loading and the calcination temperature by means of ¹H magic angle spinning (MAS) and ¹H[²³Na] spin-echo double resonance NMR techniques. The ¹H NMR experiments revealed that sodium ions are homogeneously distributed over the alumina surface and closely coordinated with the surface hydroxyl groups. In the catalysts calcined at 250 °C, the acidic hydroxyl groups (with a chemical shift of 2.0 ppm) are preferentially associated with sodium ions at low Na₂CO₃ coverages (5 and 10%), while both the acidic and the basic (0 ppm) hydroxyl groups are accessible for sodium ions at high coverages (15 and 20%). The coordination causes a low-field shift of about 2 ppm in the ¹H MAS spectra, and a broad signal at 4.5 ppm appears. It is interesting that the 4.5 ppm signal is completely suppressed in the ¹H[²³Na] MAS experiments, providing direct evidence that a strong interaction exists between adsorbed sodium ions and the surface hydroxyl groups. Increasing the calcination temperature to 450 °C results in preferential removal of the acidic hydroxyl groups, and only the most basic hydroxyl groups remain when the calcination temperature is raised to 600 °C. This is attributed to the formation of the coordinated species which enhances the acidity of the surface hydroxyl groups and prompts their dehydroxylation, especially at high calcination temperature. Correlation of the ¹H MAS NMR results and catalytic activity measurements indicates that the basic hydroxyl groups are essential for the carbonyl sulfide hydrolysis reaction.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.