On the arithmetic of the endomorphisms ring {{\rm End}(\mathbb{Z}_{p} \times \mathbb{Z}_{p^{2}})}

For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that End(\mathbbZ_p×\mathbbZ_p²){{\rm End}(\mathbb{Z}_{p}\times \mathbb{Z}_{p^{2}})} is a semilocal ring with p ⁵ elements that cannot be embedded in matrices over any commutative ring. We identify the elements of End(\mathbbZ_p ×\mathbbZ_p²){{\rm End}(\mathbb{Z}_{p} \times \mathbb{Z}_{p^{2}})} with elements in a new set, denoted by E _p , of matrices of size 2 × 2, whose elements in the first row belong to \mathbbZ_p{\mathbb{Z}_{p}} and the elements in the second row belong to \mathbbZ_p²{\mathbb{Z}_{p^{2}}}; also, using the arithmetic in \mathbbZ_p{\mathbb{Z}_{p}} and \mathbbZ_p²{\mathbb{Z}_{p^{2}}}, we introduce the arithmetic in that ring and prove that the ring End(\mathbbZ_p ×\mathbbZ_p²){{\rm End}(\mathbb{Z}_{p} \times \mathbb{Z}_{p^{2}})} is isomorphic to the ring E _p . Finally, we present a Diffie-Hellman key interchange protocol using some polynomial functions over E _p defined by polynomials in \mathbbZ[X]{\mathbb{Z}[X]}.     

One weight $$\mathbb {Z}_2\mathbb {Z}_4$$ additive codes

We study one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes. It is shown that the image of an equidistant \(\mathbb {Z}_2\mathbb {Z}_4\) code is a binary equidistant code and that the image of a one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive code, with nontrivial binary part, is a linear binary one weight code. The structure and possible weights for all one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes are described. Additionally, a lower bound for the minimum distance of dual codes of one weight additive codes is obtained.     

Distribution of relaxation times investigation of $$\hbox {Co}^{3+}$$ doping lithium-rich cathode material $$\hbox {Li}[\hbox {Li}_{0.2} \hbox {Ni}_{0.1} \hbox {Mn}_{0.5} \hbox {Co}_{0.2}]\hbox {O}_{2}$$Li[Li0.2Ni0.1Mn0.5Co0.2]O2

The element \(\hbox {Co}^{3+}\) was introduced into lithium-rich material \(0.5\hbox {Li}_{2}\hbox {MnO}_{3} \cdot 0.5 \hbox {LiNi}_{0.5}\hbox {Mn}_{0.5}\hbox {O}_{2}\) by a polyacrylamide-assisted sol–gel method to form \(\hbox {Li}[\hbox {Li}_{0.2} \hbox {Ni}_{0.1} \hbox {Mn}_{0.5} \hbox {Co}_{0.2}]\hbox {O}_{2}\) and better electro-chemical performances were observed. Electrochemical impedance spectroscopy spectra were measured on 11 specific open circuit voltage levels on the initial charge profile. Then they were converted to the distribution of relaxation times (DRTs) g(\(\tau \)) by self-consistent Tikhonov regularization method. The obtained DRTs offered a higher resolution in the frequency domain and provided the number and the physical origins of loss processes clearly. Through the analysis of DRTs, the rapid augmentation of resistance to electronic conduction and charge transfer within the voltage range 4.46–4.7 V where the removal of \(\hbox {Li}_{2}\hbox {O}\) from \(\hbox {Li}_{2} \hbox {MnO}_{3}\) component took place was the most remarkable phenomenon and the \(\hbox {Co}^{3+}\) doping greatly reduced the resistance to electronic conduction Re. This gave us more evidence about the complicated ‘structurally integrated’ composite character of the material.     

Correlations for the Dielectric Constants of $$\hbox {H}_{2}\hbox {S}$$, $$\hbox {SO}_{2}$$SO2, and $$\hbox {SF}_{6}$$SF6

A new method is developed for correlating the static dielectric constant of polar fluids over wide ranges of conditions where few experimental data exist. Molecular dynamics simulations are used to establish the temperature and density dependence of the Kirkwood g-factor, and also the functional form for the increase of the effective dipole moment with density. Most parameters in the model are obtained entirely from simulation; a single proportionality constant is adjusted to obtain agreement with the limited experimental data. The method is applied to hydrogen sulfide (\(\hbox {H}_{2}\hbox {S}\)) and sulfur dioxide \((\hbox {SO}_{2})\), both of which are important in geochemistry but have only a few dielectric data available. The resulting correlations agree well with the available liquid data, obey physical boundary conditions at low density and at high temperature, and interpolate in density and temperature in a physically reasonable manner. In addition, we present a more conventional correlation for the dielectric constant of sulfur hexafluoride, \(\hbox {SF}_{6}\), where more data are available.     

Effect of Hafnium Impurities on the Magnetoresistance of $$\hbox {YBa}_{2}\hbox {Cu}_{3}\hbox {O}_{7-\delta }$$

In the present study, we investigate the influence of the hafnium (Hf) impurities on the magnetoresistance of \(\hbox {YBa}_{2}\hbox {Cu}_{3}\hbox {O}_{7-\delta }\) ceramic samples in the temperature interval of the transition to the superconducting state in constant magnetic field up to 12 T. The cause of the appearance of low- temperature “tails” (paracoherent transitions) on the resistive transitions, corresponding to different phase regimes of the vortex matter state is discussed. At temperatures higher than the critical temperature (T > \(T_\mathrm{c})\), the temperature dependence of the excess paraconductivity can be described within the Aslamazov–Larkin theoretical model of the fluctuation conductivity for layered superconductors.     

Temperature effects on the electrical characteristics of $$\mathrm{Al}/\mathrm{PTh}-\mathrm{SiO}_{2}/\mathrm{p\hbox {-}Si}$$ structure

The temperature-dependent current–voltage (\(I\text {--}V\)) and capacitance–voltage (\(C\text {--}V\)) characteristics of the fabricated Al/p-Si Schottky diodes with the polythiopene–SiO\(_{2}\) nanocomposite (\(\hbox {PTh--SiO}_{2}\)) interlayer were investigated. The ideality factor of \(\hbox {Al}/\hbox {PTh--SiO}_{2}/{p}\text {-Si}\) Schottky diodes has decreased with increasing temperature and the barrier height has increased with increasing temperature. The change in the barrier height and ideality factor values with temperature was attributed to inhomogeneties of the zero-bias barrier height. Richardson plot has exhibited curved behaviour due to temperature dependence of barrier height. The activation energy and effective Richardson constant were calculated as 0.16 eV and \(1.79 \times 10^{-8} \hbox {A\,cm}^{-2} \,\hbox {K}^{-2}\) from linear part of Richardson plots, respectively. The barrier height values determined from capacitance–voltage–temperature (\(C\text {--}V\text {--}T\)) measurements decrease with increasing temperature on the contrary of barrier height values obtained from \(I\text {--}V\text {--}T\) measurements.     

Investigation on the impact and compression behavior of wet \upgamma -\hbox {Al}_{2}\mathrm{O}_{3} granules

The material behavior of dominant elastic–plastic \(\upgamma \) - \(\hbox {Al}_{2}\mathrm{O}_{3}\) granules has been experimentally studied by means of quasi static compression tests and dynamic impact tests until fracture. The obtained distributions of breakage velocity and specific breakage energy are compared. Thus, velocity dependent influences at stressing like viscous behavior can be derived. Additionally, the influences of particle size and moisture content on the material behavior are investigated.     

Evolution of the electrical resistance of \bf{\hbox {YBa}_2\hbox {Cu}_3\hbox {O}_{7-\varvec\delta }} single crystals in the course of long-term aging

Investigated are the changes in the basal-plane electrical resistivity of an optimally doped \(\hbox {YBa}_2\hbox {Cu}_3\hbox {O}_{7-\delta }\) single crystal in the course of long-term aging (17 years) at room temperature in air. In consequence of aging the sample has decomposed into three phases with different temperatures of the superconducting transition, while the transition widths of these phases have increased significantly. The temperature dependence of the electrical resistivity has retained a metallic character. The fluctuation conductivity near the critical temperature is described well by the 3D Aslamazov–Larkin model. In the course of aging significant changes in the scattering characteristics have been observed, whereas the Debye temperature has changed slightly and the transverse coherence length has remained constant.     

Structural,elastic, optoelectronic and magnetic properties of $$\mathbf{CdHo }_\mathbf{2}{} \mathbf{S}_\mathbf{4}$$ spinel: a first-principle study

We report the results of the full-potential linearized augmented plane wave (FP-LAPW) calculations on the structural, elastic, optoelectronic and magnetic properties of \(\hbox {CdHo}_{2}\hbox {S}_{4}\) spinel. Both the generalized gradient approximation (GGA) and Trans-Blaha modified Becke-Johnson potential (TB-mBJ) are used to model the exchange-correlation effects. The computed lattice parameter, internal coordinate and bulk modulus are in good agreement with the existing experimental data. According to the calculated elastic moduli, \(\hbox {CdHo}_{2}\hbox {S}_{4}\) is mechanically stable with a ductile nature and a noticeable elastic anisotropy. The ferromagnetic phase of \(\hbox {CdHo}_{2}\hbox {S}_{4}\) is energetically favourable compared to non-magnetic one, with a high magnetic moment of about 8.15 \(\upmu _{\mathrm{B}}\). The calculated band structure demonstrates that the title compound is a direct band gap semiconductor. The TB-mBJ yields a band gap of \(\sim \)1.86 and \(\sim \)2.17 eV for the minority and majority spins, respectively. The calculated optical spectra reveal a strong response in the energy range between the visible light and the extreme UV regions.     

Effect of annealing temperature and $$\hbox {CdCl}_{2}$$ treatment on the photo-conversion efficiency of $$\hbox {CdTe/Zn}_{0.1}$$CdTe/Zn0.1$$\hbox {Cd}_{0.9}$$Cd0.9S thin film solar cells

We report the effects of annealing in conjunction with \(\hbox {CdCl}_{2}\) treatment on the photovoltaic properties of \(\hbox {CdTe/Zn}_{0.1}\hbox {Cd}_{0.9}\)S thin film solar cells. CdTe layer is subjected to dry \(\hbox {CdCl}_{2}\) treatment by thermal evaporation method and subsequently, heat treated in air using a tube furnace from 400 to \(500{^{\circ }}\hbox {C}\). AFM and XRD results show improved grain size and crystallographic properties of the CdTe film with dry \(\hbox {CdCl}_{2}\) treatment. This recrystallization and grain growth of the CdTe layer upon \(\hbox {CdCl}_{2}\) treatment translates into improved photo-conversion efficiencies of \(\hbox {CdTe/Zn}_{0.1}\hbox {Cd}_{0.9}\)S cell. The results of dry \(\hbox {CdCl}_{2}\) treatment were compared with conventional wet \(\hbox {CdCl}_{2}\) treatment. Photo-conversion efficiency of 5.2% is achieved for dry \(\hbox {CdCl}_{2}\)-treated cells in comparison with 2.4% of wet-treated cell at heat treatment temperature of \(425{^{\circ }}\hbox {C}\).     

Influence of the conditions of a solid-state synthesis anode material $$\hbox {Li}_{4}\hbox {Ti}_{5}\hbox {O}_{12 }$$ on its electrochemical properties of lithium cells

Lithium–titanium spinel is a promising electrode material for high power and environmentally friendly batteries. We did research on \(\hbox {Li}_{4}\hbox {Ti}_{5}\hbox {O}_{12 }\) (LTO) samples, which were synthesized via solid-state reaction at various conditions in a temperature range from 800 to \(900{^{\circ }}\hbox {C}\) and they were investigated by XRD, SEM, IS, cyclic voltammetry and the galvanostatic charge–discharge tests. X-ray diffractions show that all of the samples have a spinel structure with Fd-3m space group with a small amount of impurities \(\hbox {TiO}_{2}\) (anatase). Lithium ion batteries with LTO-based electrode exhibit excellent reversible capacity of \(\,\sim 180\hbox { mAh}\hbox { g}^{-1}\) in the current density range from 0.1 to 1 C. As an electrode material for rechargeable lithium-ion batteries, LTO-F demonstrates the best rate and cyclic performance from all of the studied samples.     

Electro-optical properties,decomposition pathways and the hydrostatic pressure-dependent behaviours of a double-cation hydrogen storage material of $$\hbox {Al}_{3}\hbox {Li}_{4}(\hbox {BH}_{4})_{13}$$

Electro-optical properties, the decomposition pathways and the pressure-dependent behaviours of \(\hbox {Al}_{3}\hbox {Li}_{4}(\hbox {BH}_{4})_{13}\) have been investigated using a first-principle plane-wave pseudopotential method. \(\hbox {Al}_{3}\hbox {Li}_{4}(\hbox {BH}_{4})_{13}\) is a kind of double-cation borohydride, consisting of distorted tetrahedral anions \([\hbox {Al}(\hbox {BH}_{4})_{4}]^{-}\) and cations \([\hbox {Li}_{4}(\hbox {BH}_{4})]^{3+}\), which obeys the stability criteria of decomposition reactions. Herein, two possible decomposition reactions of the compound are proposed, which release 18 hydrogen molecules (about 12.03 wt%) in the first reaction and 24 hydrogen molecules (about 16.04 wt%) in the second reaction. On increasing the pressure on the structure, the lattice parameter, the volume of unit cell, the quasiparticle band gap and also enthalpy of the system decrease nearly monotonically; therefore, the acceptor levels gradually get filled and the Fermi level shifts upward. Results of computational investigations of the structural, electronic and thermodynamic parameters and their pressure-dependent behaviours indicate that \(\hbox {Al}_{3}\hbox {Li}_{4}(\hbox {BH}_{4})_{13}\) has intriguing properties. Therefore, it would be a very promising material for hydrogen storage technology.     

Evaluation of the elastic properties of monovalent oxides using $$\hbox {TeO}_{2}$$-based glasses

Quaternary tellurite glasses with composition \(75\hbox {TeO}_{2}\)–\(5\hbox {WO}_{3}\)–\(15\hbox {Nb}_{2} \hbox {O}_{5}\)–\(5\hbox {M}_{x} \hbox {O}_{y}\) in mol%, where \(\hbox {M}_{x}\hbox {O}_{y}\) = (\(\hbox {Na}_{2}\hbox {O}, \, \hbox {Ag}_{2}\hbox {O}\), ZnO, MgO, CuO, NiO, \(\hbox {TiO}_{2}\), \(\hbox {MnO}_{2}\)), were prepared by the normal melt-quenching method. The ultrasonic velocities (longitudinal and shear) were measured in these glasses using the pulse-echo technique at room temperature. Their elastic moduli, microhardness and Debye temperature were calculated and discussed in terms of the modifier’s ionicity and quantitatively in terms of number of bonds per unit volume and the cross-link density. In this study, the values of ultrasonic velocities, elastic moduli, Debye temperature and microhardness were found to be strongly dependent on three factors, namely: (i) modifier’s ionicity; (ii) trigonal pyramid (\(\hbox {TeO}_{3}\))/trigonal bipyramid (\(\hbox {TeO}_{4}\)) ratio; and (iii) glass transition temperature \(T_\mathrm{g}\). We used the Makishima and Mackenzie’s model to calculate the theoretical elastic moduli and to indicate that the experimental values were in good agreement with the theoretical values.     

First-Principles Investigations on Structural,Phonon, and Thermodynamic Properties of Cubic \text {CeO}_{2}

The structural, phonon, and thermodynamic properties of the cubic \(\hbox {CeO}_{2}\) are investigated from first-principles calculations. The calculated lattice parameters, bulk modulus, and phonon dispersion curves are in agreement with available experimental data and other calculations. It is shown that the local density approximation (LDA)+ \(U\) method is more suitable for describing the properties of \(\hbox {CeO}_{2}\) compared with the LDA method. The pressure and temperature dependences of the specific heat, Debye temperature, and the thermal expansion coefficient are successfully obtained from the Debye–Grüneisen model by combining with the phonon density of states.     

$$\hbox {NO}_{2}^{-}$$ and $$\hbox {SCN}^{-}$$SCN--intercalated layered double hydroxides: structure and orientation of anions in the interlayer gallery

\(\hbox {NO}_{2}^{-}\) and \(\hbox {SCN}^{-}\) are two common small inorganic anions. The former is a common industrial pollutant. The latter is linear and is a good mimic for the toxic \(\hbox {CN}^{-}\) ion. The structures of these two anions are refined within the gallery of the [Zn–Al]-layered double hydroxide (LDH). Both LDHs crystallize as mixed anion phases. The nitrite is found to co-exist with the nitrate ion. The nitrite ion is intercalated with its molecular plane inclined to the metal hydroxide layer. In the case of the \(\hbox {SCN}^{-}\) intercalated LDH, no other anion was detected by ion chromatography, suggesting that the \(\hbox {SCN}^{-}\) deficiency is compensated by intercalated hydroxyl ions. In this case, the \(\hbox {SCN}^{-}\) ion is found to be intercalated with its molecular axis inclined to the metal hydroxide layer.