Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1

The solution of a generalized non-relativistic Schrödinger equation with radial potential energy V(r)=V ₀(r/a ₀)^2–2 is presented. After reviewing the general properties of the radial ordinary differential equation, power series solutions are developed. The Green's function is constructed, its trace and the trace of its first iteration are calculated, and the ability of the traces to provide upper and lower bounds for the ground eigenvalue is examined. In addition, WKB-like solutions for the eigenvalues and eigenfunctions are derived. The approximation method yields valid eigenvalues for large quantum numbers (Rydberg states).     

Nonstoichiometry and structural intergrowth in the CaFexMn1−xO3−y (0 ≤ x ≤ 1) system

An electron diffraction and microscopy study of the CaFe_xMn_1−xO_3−y system treated at 1100°C in air has been performed. An increase of y is accompanied by an increase of the cubic perovskite substructure parameter, the nonstoichiometry being accommodated in several ways. The system contains two solid solutions of the perovskite-type (P) and of the brownmillerite-type (B) and also an intermediate phase (x = 0.6) which makes disordered intergrowth with the B-type solid solution. These results are discussed in terms of multitwinning, randomly dispersed oxygen deficiency, and ordered and disordered intergrowth formation.     

Ionic conductivity and crystal chemistry of ramsdellite type compounds,Li2+x(LixMg1−xSn3)O8, 0 ≤ x ≤ 0.5 and Li2Mg1−xFe2xSn3−xO8, 0 ≤ x ≤ 1

Solid solution phases Li_2+x(Li_xMg_1−xSn₃)O₈: 0 ≤ x ≤ 0.5 and Li₂Mg_1−xFe_2xSn_3−xO₈: 0 ≤ x ≤ 1, both with ramsdellite type structure, have been synthesized by solid state reaction at 1773 and 1523 K, respectively. The relationship of the ramsdellite structure to the recently illustrated, tetragonal-packed structure is given. The Li_2+x(Li_xMg_1−xSn₃)O₈ solid solutions exhibit conductivities 4 × 10⁻⁶–5 × 10⁻⁴ (Ω cm)⁻¹ at 573 K and corresponding activation energies, 0.93−0.74 eV. The highest conductivity was observed for Li_2.3(Li_0.3Mg_0.7Sn₃)O₈, x = 0.3. In the solid solution series Li₂Mg_1−xFe_2xSn_3−xO₈, the highest conductivity was exhibited by Li₂Fe₂Sn₂O₈, 2 × 10⁻⁵ (Ω cm)⁻¹ at 573 K.     

Glycolate Ti1 − x Fe x (OCH2CH2O)2 − x/2 as a precursor for the preparation of quasi-one-dimensional (1D) solid solutions Ti1 − x Fe x O2 − 2x/2 (0 ≤ x ≤ 0.1)

Quasi-one-dimensional (1D) solid solutions Ti_{1 ? x} Fe _x (OCH₂CH₂O)_{2 ? x/2} (0 < x ≤ 0.1) with the structure of anatase were prepared by heating the glycolate Ti_{1 ? x} Fe _x (OCH₂CH₂O)_{2 ? x/2} in an atmosphere of air at a temperature of >450°C. The conditions of formation and the properties of the new glycolate Ti₃Fe₂(OCH₂CH₂O)₉ were described. It was found that the synthesized Ti_{1 ? x} Fe _x O_{2 ? 2x/2} solid solutions exhibit photocatalytic activity in the reaction of hydroquinone oxidation in an aqueous solution on irradiation with UV light. A correlation between the rate of oxidation of hydroquinone and the concentration of iron in the catalyst was established. A procedure for the preparation of titanium dioxide with the structure of anatase doped with iron and carbon (Ti_{1 ? x} Fe _x O_{(2 ? x/2) ? yCy)} and also composites on its basis, which contain an excess amount of carbon, was proposed.     

Transition métal—isolant dans V1−xMnxO2−2xF2x (0 < x ≤ 0, 10)e´tude des proprie´te´s structurales,magne´tiques,ete´lectriques

V_1−xMn_xO_2−2xF_2x samples (0 < x ≤ 0, 10) have been prepared by solid state reaction in sealed platinium tubes. The metal ⇄ insulator transition occurs at a quickly decreasing temperatures as MnF₂ increases. The crystallographic, magnetic, transport properties, and DTA have been determined and discussed.     

Variation of radiative lifetimes of NH2(Ã2A1) with rotational levels in the (0, 8, 0) and (0, 9, 0) vibration bands

Radiative lifetimes from the first electronically excited state of the amidogen free radical, NH(2)(A?(2)A(1)), are reported for rotational states in selected vibrational levels ν(2)' using laser-induced fluorescence. Thermal collision of argon, Ar(?)((3)P(0), (3)P(2)) metastable atoms in a microwave discharge-flow system with ammonia (NH(3)) molecules produced ground state NH(2)(X?(2)B(1)). The radiative lifetimes for the deactivation of NH(2)(A?(2)A(1)) were determined by measuring the decay profiles of NH(2)(A?(2)A(1)?→?X?(2)B(1)). In addition to the Fermi resonances with the ground state that lengthen the radiative lifetimes, a systematic increase in the radiative lifetimes with rotational quantum number was observed. Furthermore, the average radiative lifetimes of the (0, 9, 0) Γ, τ(1) = 18.65 ± 0.47 μs and (0, 8, 0) Φ, τ(2) = 23.72 ± 0.65 μs levels were much longer than those of the (0, 9, 0) Σ, τ(3) = 10.62 ± 0.47 μs, and (0, 8, 0) Π, τ(4) = 13.55 ± 0.55 μs states suggesting increased mixing of the first electronic excited and the ground states.     

Using high pressure to prepare polymorphs of the Ba2Co(1-x)Zn(x)S3 (0 ≤ x ≤ 1.0) compounds

In this work, high pressure was used as a tool to induce structural transition and prepare metastable polymorphs of ternary sulfides. Structural transformations under high pressure of compounds belonging to the Ba(2)Co(1-x)Zn(x)S(3) (0 ≤ x ≤ 1.0) series were studied using X-ray diffraction and electron microscopy. All members of the Ba(2)Co(1-x)Zn(x)S(3) series show the Ba(2)CoS(3)-type one-dimensional structure, but, after heating under pressure, the Ba(2)CoS(3) compound (x = 0) separates into BaS and the two-dimensional BaCoS(2-δ) (δ ≈ 0), while Ba(2)Co(1-x)Zn(x)S(3) compounds with x ≥ 0.25 maintain their one-dimensional features but rearrange into polymorphs showing the Ba(2)MnS(3)-type structure. All structural transformations can be linked to shortening in interchain metal-metal distances caused by the high pressure, and the role of the zinc in preventing loss of one-dimensionality is discussed.     

Crystal structural, magnetic, and transport properties of layered cobalt oxyfluorides, Sr2CoO(3+x)F(1-x) (0 ≤ x ≤ 0.15)

The crystal structure of the layered cobalt oxyfluoride Sr(2)CoO(3)F synthesized under high-pressure and high-temperature conditions has been determined from neutron powder diffraction and synchrotron powder diffraction data collected at temperatures ranging from 320 to 3 K. This material adopts the tetragonal space group I4/mmm over the measured temperature range and the crystal structure is analogous to n = 1 Ruddlesden-Popper type layered perovskite. In contrast to related oxyhalide compounds, the present material exhibits the unique coordination environment around the Co metal center: coexistence of square pyramidal coordination around Co and anion disorder between O and F at the apical sites. Magnetic susceptibility and electrical resistivity measurements reveal that Sr(2)CoO(3)F is an antiferromagnetic insulator with the Néel temperature T(N) = 323(2) K. The magnetic structure that has been determined by neutron diffraction adopts a G-type antiferromagnetic order with the propagation vector k = (1/2 1/2 0) with an ordered cobalt moment μ = 3.18(5) μ(B) at 3 K, consistent with the high spin electron configuration for the Co(3+) ions. The antiferromagnetic and electrically insulating states remain robust even against 15%-O substation for F at the apical sites. However, applying pressure exhibits the onset of the metallic state, probably coming from change in the electronic state of square-pyramidal coordinated cobalt.     

Hydrothermal Synthesis and Characterization of Cd1−xMnxS (0≤x<1) Nanocrystals

Cd_1?xMn_xS (0≤x<1) nanocrystals were synthesized in a hydrothermal process. The nanocrystals were characterized by TEM, XRD, and photoluminescence. The results showed that the MnS crystalline phase appeared in high Mn content in the composite Cd_1?xMn_xS. The variation of the Cd_1?xMn_xS emission with Mn content implied different emission mechanisms. The Mn²⁺ ion emission was probably due to energy transfer via the trap states of CdS nanocrystals in our samples.     

SiO_x-based(0<x≤2) composites for lithium-ion batteries

Silicon(Si) materials as anode materials for applications in lithium-ion batteries(LIBs) have received increasing attention.Among the Si materials,the electrochemical properties of SiO_x-based(0x≤2)composites are the most prominent.However,due to the cycling stability of SiO_x being far from practical,there are some problems,such as Iow initial coulombic efficiency(ICE),obvious volume expansion and poor conductivity.Researchers in various countries have optimized the electrochemical properties of SiO_x-based composites by means of pore formation,surface modification,and the choice of constituents.In this review,SiO_x-based composites are classified into three categories based on the valency of Si(SiO_2 composites,SiO composites and SiO_x(0x2) composites).The synthesis,morphologies and electrochemical properties of the SiO_x-based composites that are applied in LIB are discussed.Finally,the prope rties of several common SiO_x-based composites are briefly compared and the challenges faced by SiO_x-based composites are highlight.     

Mechanical properties of mixed conducting La0.5Sr0.5Fe1−x Co x O3−δ (0≤x≤1) materials

Young’s modulus, strain–stress behavior, fracture strength, and fracture toughness of (0≤×≤1) materials have been investigated in the temperature range 20–1,000°C. Young’s moduli of and , measured by resonant ultrasound spectroscopy, were 130±1 and 133±3 GPa, respectively. The nonlinear stress–strain relationship observed by four-point bending at room temperature was inferred as a signature of ferroelastic behavior of the materials. Above the ferroelastic to paraelastic transition temperature, the materials showed elastic behavior, but due to high-temperature creep, a nonelastic respond reappeared above ∼800°C. The room temperature fracture strength measured by four-point bending was in the range 107–128 MPa. The corresponding fracture toughness of , measured by single edge V-notch beam method, was 1.16±0.12 MPa·m^1/2. The measured fracture strength and fracture toughness were observed to increase with increasing temperature. The fracture mode changed from intragranular at low temperature to intergranular at high temperature. Tensile stress gradient at the surface of the materials caused by a frozen-in gradient in the oxygen content during cooling was proposed to explain the low ambient temperature fracture strength and toughness.     

Electronic Structure and Chemical Bonding in Monoclinic and Cubic Li2-xHxTiO3 (0≤ x ≤ 2)

The linear muffintin orbitals method in a tight binding approximation and extended Huckel theory are used to study the electronic structure and chemical bonding of lithium titanate (Li₂TiO₃) and its protonated analogs (Li_1.75H_0.25TiO₃ and H₂TiO₃). The effect of protons on electron spectrum characteristics and bond strength are investigated for the monoclinic and cubic phases of lithium titanate. Phase stability is evaluated by cohesion energy calculations.     

Rubidium-cationic conductivity of Rb2−2x Ga2−x A x O4 (A = P, V, Nb, Ta) solid electrolytes

Solid solutions based on rubidium monogallate RbGaO₂ with a general formula Rb_2?2x Ga_2?x A _x O₄ (A = P, V, Nb, and Ta) are synthesized. Their crystal structure and temperature and concentration dependences of conductivity are studied. The highest rubidium-cationic conductivity is (1.8–3.9) × 10^?3 S cm^?1 at 400°C and (1.4–2.1) × 10^?2 S cm^?1 at 700°C. These results are compared with the data for rubidium monogallate doped with four-charged cations and solid solutions based on RbAlO₂.     

Low Temperature Synthesis and Characterization of Li1.2-y NayV3O8(0≤y≤1.2) from V2O5 Gel

Without overnight heating and stirring,Li1.2V3O8 and its analogs Li1.2-y NayV3O8(0≤y≤1.2) were successfully synthesized by adding mixed solution of LiOH and NaVO3 to V2O5 gel and dehydrating the prepared gel in 150-350℃.The simplicity awards this synthesis process superiority over other low temperature synthesis routes when mass production is concerned.TG-DTA,XRD and TEM experiments were carried out for physical characterization.By galvanostatic charge-discharge and cyclic voltammetry tests,these products showed better electrochemical performance than high temperature products as cathode active materials in secondary lithium batteries.After treatment of Li1.2V3O8 at 250℃,it exhibited a capacity of 350mAh/g when cycled at current rate of about 60 mA/g over the voltage range of 3.8-1.7V vs,Li^ /Li.The influence of partial substitution of Li by Na was also extensively studied.     

Dependence of the Structure and Properties of (M,Cu)Sr2(Ln,Ca)Cu2O8−δ (1212) and (M,Cu)Sr2(Ln,Ce4+)2Cu2O10−δ (1222) Phases on the Cation M

The composition and structure of (M,Cu)(Sr,Ln)₂(Ln,Ca,Sr)Cu₂O_8– phases, where M = B, Al, Cr, Pb, Bi, Ru, or Mo (1212 type), and (M,Cu)(Sr,Ln(₂(Ln,Ce⁴⁺)₂Cu₂O_10– phases, where M = V, Cr, Mn, Ru, or Mo (1222 type), have been determined. The role of the M cation in the formation of the crystal structures and the superconductivity phenomenon was analyzed. The relationship between the type of M cation and structural parameters was discovered.     

Ternary lanthanum sulfide selenides α-LaS2−xSex (0

Christian Bartsch  Thomas Doert 《Journal of solid state chemistry》2012

Synthesis and characterization of a NASICON phase of variable composition Na1 − x Ni1 − x Sc1 + x (MoO4)3 (0 ≤ x ≤ 0.5)

Subsolidus phase ratios in the Na₂MoO₄-NiMoO₄-Sc₂(MoO₄)₃ system have been studied using X-ray diffraction, differential thermal analysis, and vibrational spectroscopy. A phase of variable composition Na_{1 ? x} Ni_{1 ? x} Sc_{1 + x} (MoO₄)₃ (0 ≤ x ≤ 0.5) having NASICON structure (space group \(R\bar 3c\) ) and a triple molybdate crystallizing in triclinic system (space group \(P\bar 1\) ) have been obtained. The high conductivity of Na_{1 ? x} Ni_{1 ? x} Sc_{1 + x} (MoO₄)₃ allows the phase of variable composition to be regarded as a promising sodiumion-conductive solid electrolyte.     

Novel red-emitting phosphors, (Mg(1−x−y)MnxDyy)Al2Si2O8 and (Mg(1−x−y)MnxTmy)Al2Si2O8

Mn⁴⁺ doped and Dy³⁺, Tm³⁺ co-doped MgAl₂Si₂O₈-based phosphors were prepared by conventional solid state reaction at 1,300 °C. They were characterized by thermogravimetry, differential thermal analysis, X-ray powder diffraction, photoluminescence, and scanning electron microscopy. The luminescence mechanism of the phosphors, which showed broad red emission bands in the range of 600–715 nm and had a different maximum intensity when activated by UV illumination, was discussed. Such a red emission can be attributed to the ²E → ⁴A₂ transitions of Mn⁴⁺.     

Untersuchungen in den Systemen: V−B,Nb−B,V−B−Si und Ta−B−Si

Zusammenfassung Mit Hilfe röntgenographischer Messungen werden die Boride von Vanadin und Niob untersucht, wobei eine neue Phase der ungefähren Zusammensetzung V₂B identifiziert wird, welche mit der entsprechenden Nb-Borid-Phase isotyp ist. Dieselbe Kristallart tritt auch im System: Ta–B auf. Die in der Literatur angegebene -Phase im Zweistoff: Nb–B erweist sich als NbO.Im System: V–B–Si wird wie im analogen Mo-System die Existenz einer ternärenT 2-Phase Me₅(Si_1/3, B_2/3)₃ nach-gewiesen¹; ihre Gitterkonstanten werden ermittelt.Im Schnitt Ta₂Si–Ta₂B besteht ein geringes Lösungs-vermögen der beiden Phasen ineinander. Durch Zusatz von 20 Mol-% Ta₂Si zu Ta₂B erhält man die oben erwähnte neue Kristallart.Bei den Borid-Siliziden der Metalle aus der 4a-, 5a- und 6a-Gruppe werden die Stabilitätsbereiche derT 1-,T 2- undD 8₈-Phasen miteinander verglichen.