Synthesis and properties of LiZr2(AsO4)3 and LiZr2(AsO4) x (PO4)3 − x

The LiZr₂(AsO₄)₃ arsenate and LiZr₂(AsO₄) _x (PO₄)_{3 ? x} solid solutions have been prepared through precipitation followed by heat treatment, and characterized by X-ray diffraction, X-ray structure analysis, IR spectroscopy, and impedance spectroscopy. We have established conditions for the crystallization of the arsenate and a continuous series of arsenate phosphate solid solutions (0 ≤ x ≤ 3), which have been obtained as two polymorphs: monoclinic and hexagonal. Using the Rietveld method, we have refined the crystal structures of the polymorphs of LiZr₂(AsO₄)₃ (sp. gr. P2₁/n, a = 9.1064(2), b = 9.1906(2), c = 12.7269(3) Å, β = 90.844(2)°, V =1065.03(5) ų, Z = 4; sp. gr. R $\bar 3$ c, a = 9.1600(4), c = 22.9059(13) Å, V = 1664.44(14) Å, Z = 6) and LiZr₂(AsO₄)_1.5(PO₄)_1.5. Their structural frameworks are built up of AsO₄ tetrahedra—or (As,P)O₄ tetrahedra occupied by arsenic and phosphorus atoms at random—and ZrO₆ octahedra, with the lithium atoms in between. The ionic conductivity of the materials has been measured. The cation conductivity of monoclinic LiZr₂(AsO₄) _x (PO₄)_{3 ? x} with 0 ≤ x ≤ 1 has been shown to exceed the conductivity of lithium zirconium phosphate.     

Effect of CuO addition on structure and electrical properties of low temperature sintered quaternary piezoelectric ceramics

The ceramics were prepared successfully by CuO additions to Pb[(Mn_1/3Sb_2/3)_0·06(Ni_1/2W_1/2)_0·02(Zr_0·49Ti_0·51)_0·92]O₃. Effect of the addition on sintering temperature, structure and electrical properties of ceramics was investigated. The piezoelectric ceramics was prepared by solid-state reaction. Sintering experiments were accomplished at temperature between 950 and 1100 °C added 0· 3–1· 0 wt% CuO. The sintering temperature was reduced from 1250 °C (without CuO additions) to 970 °C when CuO-doped. The ceramics sintered at 970 °C for 2 h with 0· 7 wt% CuO exhibited ε _r = 1845, tan δ = 0· 15%, d ₃₃ = 395 pC/N, k _p = 0· 58 and Q _m = 1830, which were the highest values. With increasing CuO doping, T _c becomes lower. Jahn–Teller effect was used to explain the contraction of c-axis and simultaneous extension of a-axis in the lattice.     

Crystal structure and EPR study of Mn-doped β-tricalcium phosphate

Mn-doped β-tricalcium phosphate was prepared by solid state reaction at 1100 °C. The crystal structure of Ca_2.85Mn_0.15(PO₄)₂, was determined by single crystal X-ray diffraction and found to be rhombohedral, R3c. Unit cell parameters are: a = 10.3419(3); c = 37.025(3) Å (hexagonal setting), Z = 21. Structure refinement data show that from the five Ca positions the Ca(4) site is only half filled and that the Mn²⁺ ions occupy the hexacoordinated Ca(5) site solely. EPR spectroscopy reveals that manganese in solid solutions Ca_3−xMn_x(PO₄)₂ (x = 0.1; 0.28; 0.6) is divalent and supports the structure refinement results that Mn occupies the Ca(5) site with a geometry very near to a regular octahedron.     

Mechanical wave interaction at a diffuse interface

An investigation is made of the reflection coefficientR of an ultrasonic wave impinging on a boundary at which there is a gradual transition of material properties from one material to another. The study is confined to the one-dimensional case of compression waves incident at 90° on the boundary. Both analytical and numerical solutions forR are presented for various interfacial profiles, and are seen in general to be strongly dependent on wave frequency. Measurements are made on diffusion bonded samples of nickel to copper, and the results compared with theory. Significant scatter is found in the experimental results due primarily to the migration of oxygen into the diffusion zone. A second set of measurements on diffusion bonded samples of nickel to carbon steel show general agreement with theory.Nomenclature A _i ,B _i ,C _i ,i=1, 2 coefficients in the expression forX (x) - c _i concentration of speciesi - c _L compression wave velocity - D _i diffusion coefficient for speciesi - diffusion coefficient for a binary mixture - E(x) Young's modulus - stiffness for the case of one-dimensional strain, =(1–v)E(x)/(1+v)(1–2v) - one-dimensional stiffness within bluk materiali - J _i ,i=1, 2 flux of speciesi - k(x) wave number at spatial co-ordinatex, equal to 2/ - k _i ,i=1, 2 wave number within bulk materiali - K(x) pseudo-wavenumber, defined by Eq. (8). - k _B Boltzmann's constant - L thickness of interfacial zone - f wave frequency - m, N material profile parameters, used to specifyK(x) - Q activation energy for diffusion - R reflection coefficient - t time - T transmission coefficient - u(x, t) displacement of molecules due to wave action,u(x, t)=X(x) (t) - X(x) spatial portion of functionu(x, t) - x spatial variable - Y(x, t) (x, t)/ - Z _i ,i=1, 2 mechanical impedance of bulk materiali - strain - wavelength of sound - Poisson's ratio - material density - (x, t) stress - (t) temporal portion of functionu(x, t) - _i (x),i=1, 2 functional form ofX(x) within interfacial region - angular frequency of wave     

Self Modeling Nonlinear Regression

The paper is concerned with parametric models for populations of curves; i.e. models of the form y_i (Z) = f(θ _i ; x) + error, i = I, 2, …, n. The shape invariant model f(θ _i ; x) = θ_0i + θ_1i g([x – θ_2i /θ_3i ) is introduced. If the function g(x) is known, then the θ _i may be estimated by nonlinear regression. If g(x) is unknown, then the authors propose an iterative technique for simultaneous determination of the best g(x) and θ _i . Generalizations of the shape invariant model to curve resolution are also discussed. Several applications of the method are also presented.     

Thermal expansion of NZP-family alkali-metal (Na, K) zirconium phosphates

The thermal expansion of the A _x Zr_2.25-0.25x(PO₄)₃ phosphates with A = Na(x = 0.5,1.0,2.0,3.0,4.0, 5.0) and K(x = 1.0, 3.0, 5.0), crystallizing in structures of the NaZr₂(PO₄)₃ type (sp. gr.R3c or C2/c), was studied by high-temperature x-ray powder diffraction in the range 20–700‡C. The lattice parametersa and c and thea- andc-axis thermal expansion coefficients (α_a and α_c) were determined. The thermal expansion of the phosphates was found to be highly anisotropic (α_a < 0, α_c > 0). The strongest anisotropy was found in NaZr₂(PO₄)₃ (α_a = -4.89 x 10^-6 K^-1, α_c = 22.02 x 10^-6 K^-1), KZr₂(PO₄)₃ (α_a =-5.30 x 10^-6 K^-1, α_c = 5.41 x 10^-6 K^-1), and Na₅Zr(PO₄)₃ (α_a = -5.82 x 10^-6 K^-1, α_c = 20.73 x 10^-6 K^-1). K₅Zr(PO₄)₃ exhibited the smallest thermal expansion and weak anisotropy (α_a = -2.14 x 10^-6 K^-1, α_c = 2.65 x 10^-6 K^-1). The effects of M(l) and M(2) site occupancies on α_a, α_c,a, and c were assessed. The relative magnitudes of crystal-chemical and thermal expansion in the Na and K compounds were analyzed.     

Effect of calcium substitution on superconductivity and hole concentration in La1·5Ba1·5Cu3O z

The superconducting properties of single phase La_1·5−x Ca _x+y Ba_1·5−y Cu₃O _z , 0·0≤x≤0·60 (LC) and 0·0≤y≤0·70 (CB), compounds with tetragonal triple-perovskite structure are studied, using X-ray diffraction for their resistivity, a.c. susceptibility, and oxygen-content. La_1·5−x Ca _x Ba_1·5Cu₃O _z (LC) samples, 0·15≤x≤0·60, are superconducting withT _c ^R=0 between 40 and 74 K. With the increase inx, the oxygen content, hole concentration in the CuO₂ layers as well as theT _c increase. It is interesting to find that although the hole concentration and oxygen stoichiometry of the LaCa_0·5+y Ba_1·5−y Cu₃O _z (CB) compounds increase with the increase iny, theT _c ^R=0 remains nearly constant around 74 K fory=0·0−0·70. A correlation exists between theT _c and the hole concentration for LC and CB compounds.     

The crystal structure of a new sodium zinc arsenate phase solved by “simulated annealing”

The framework structure of a new sodium zinc arsenate, produced by dehydration of the Na₆(ZnAsO₄)₆·8 H₂0 sodalite analog, has been solved by a simulated annealing method. This method utilizes typical tetrahedral-atom bonding schemes with possible space group and unit cell dimensions to randomly generate possible continuous frameworks and their calculated energies. The Rietveld refinement of the Na₆(ZnAsO₄)₆ solution phase was initially performed on room temperature X-ray data and then continued on low-temperature constant wavelength neutron data. This sodium zinc phosphate is a hexagonal polycrystalline material: space group P6₃ (no. 173), with a = b =9.005 (2) Å, c = 8.161 (2) Å, a = β = 90°, γ = 120°, V= 573.1 Å, and Z = 2, with R = 12.35% and R_w = 9.76% for 2756 (CW neutron) powder data points. This tridymite structural analog undergoes a room-temperature transformation to the open-framework sodalite structure.     

Summaries of New Books

Let X ₍₁₎, …, X _(k) be the first k ordered observations of a sample of size m from the distribution with p.d.f. f(x; β₁, θ) = (1/θ) exp [-(x – β₁)/θ] for x ≥ β₁ ≥ 0, θ > 0 and zero elsewhere (2 ≤ k ≤ m); let Y _(i), …, Y _(l) be the first l ordered observations of a sample of size n from the distribution with p.d.f. g(y; β₂, θ) = (1/θ) exp [—(y – β₂)/θ] for y ≥ β₂ ≥ 0, θ > 0 and zero elsewhere (2 ≤ l ≤ n). It is assumed that θ is unknown. A test based on (X ₍₁₎, …, X _(k), Y ₍₁₎, …, Y _(l)) is proposed for the null hypothesis β₁ = β₂ against the alternative β₁ ≠ β₂. The distribution of the test statistic under the null hypothesis is derived. The significance points for various values of k, I, m, n are tabulated for (α = .05 and .Ol.     

A single crystal X-ray diffraction study of Na4(UO2)4(i-C4H9COO)11(NO3)·3H2O

Synthesis and the results of IR and single crystal X-ray diffraction study of Na₄(UO₂)₄(i-C₄H₉COO)₁₁·(NO₃)·3H₂O are reported. The crystals are monoclinic; the unit cell parameters at 100 K are as follows: a = 13.697(2), b = 20.285(3), c = 15.991(3) Å, β = 103.760(3)°, space group P2₁, Z = 2, R = 0.0650. The uraniumcontaining structural units are mononuclear moieties [UO₂(i-C₄H₉COO)₃]^? and [UO₂(NO₃)(i-C₄H₉COO)₂]^?, belonging to crystal-chemical group AB ₃ ⁰¹ (A = UO ₂ ²⁺ , B⁰¹ = i-C₄H₉COO^? and NO ₃ ^? ) of uranyl complexes. The IR data are consistent with the results of the single crystal X-ray diffraction study. The influence of the carboxylate ligand volume on the structure of Na[UO₂L₃]·nH₂O crystals (L = acetate, n-butyrate, isovalerate ion) is analyzed.     

Application du Théorème D'échantillonnage à la Restitution D'objets Partiellement Connus

On cherche à restituer le mieux possible un signal b(x)dont un appareil nous fournit un enregistrement e(x)=b(x)*?(x); la fonction ?(x) est supposée couper toutes les fréquences de b(x) supérieures à une fréquence de coupure μ₁ = a. Il s'agit de rechercher une représentation b _c(x) du signal, identique à celle qu'aurait fourni un appareil de réponse impulsionnelle A _c(x) plus fine que ?(x) (i.e. dont la fréquence de coupure c est supérieure à a). On montre que l'on doit utiliser toutes les informations, même vagues, que l'on possède a priori sur b(x) afin d'imposer ‘des contraintes’ à b _c(x). On recherche alors, parmi les développements qui satisfont à ces contraintes, le développement b _c ⁿ qui rend minimum l'écart quadratique On montre que, grâce aux contraintes introduites, on peut restituer correctement une fraction importante des fréquences coupées : le développement b _c ⁿ ne diffère en effet pratiquement pas de l'approximation en moyenne quadratique sur -∞, +∞ de la représentation cherchée du signal, dans le système des bases     

Synthesis of Cu3(PO4)2 · H2O based solid solutions through Co or Ni substitution for Cu

New substitutional solid solutions have been synthesized: (Cu_{1 ? x} Co_x)₃(PO₄)₂ · H₂O (0 < x ≤ 0.20), (Cu_{1 ? x} Ni_x)₃(PO₄)₂ · H₂O (0 < x ≤ 0.12), and (Cu_{1 ? y} Co_y)₃(PO₄)₂ · H₂O (0.55 ≤ y ≤ 0.65). The first two solid solutions are isostructural with Cu₃(PO₄)₂ · H₂O (monoclinic symmetry, sp. gr. C2/c); the third solid solution also has a monoclinic structure, which is a Cu₃(PO₄)₂ · H₂O related superstructure. The lattice parameter b of (Cu_{1 ? y} Co_y)₃(PO₄)₂ · H₂O (0.55 ≤ y ≤ 0.65) is almost twice that of (Cu_{1 ? x} Co_x)₃(PO₄)₂ · H₂O (0 < x ≤ 0.20), while their a and c parameters differ little. The solid solutions have been characterized by chemical analysis, x-ray diffraction, IR spectroscopy, and thermal analysis.     

Dielectric and piezoelectric properties of Bi<Subscript>0·5</Subscript>(Na<Subscript>0·82</Subscript>K<Subscript>0·18</Subscript>)<Subscript>0·5</Subscript> TiO<Subscript>3</Subscript>-LiSbO<Subscript>3</Subscript> lead-free piezoelectric ceramics

The (1−x)Bi_0·5(Na_0·82K_0·18)_0·5TiO_3−x LiSbO₃ (x = 0−0·03) lead-free piezoelectric ceramics were fabricated by a conventional solid-state reaction method and the effect of LiSbO₃ addition on microstructure and electrical properties of the ceramics was investigated. The results of XRD measurement show that Li⁺ and Sb⁵⁺ diffuse into the Bi_0·5(Na_0·82K_0·18)_0·5TiO₃ lattices to form a solid solution with a pure perovskite structure. The LiSbO₃ addition has no remarkable effect on the crystal structure. However, a significant change in grain size took place. Simultaneously, with increasing amount of LiSbO₃, the temperature for a antiferroelectric to paraelectric phase transition clearly increases. The piezoelectric constant d ₃₃ and the electromechanical coupling factor k _p show an obvious improvement by adding small amount of LiSbO₃, which shows optimum values of d ₃₃ = 175 pC/N and k _p = 0·36 at x = 0·01.     

Homogenization of a degenerate parabolic problem in a highly heterogeneous periodic medium

We consider the homogenization of a time-dependent heat transfer problem in a highly heterogeneous periodic medium made of two connected components having heat capacities c_α(x) and heat conductivities a_α(x), α=1,2 of order one, separated by a third material with thickness of the same order ε than the basic periodicity cell having heat capacity c₃(x) and conductivity λa₃(x) where a₃ is of order one and λ tends to zero with the size ε of the elementary cell. We assume only that c_i(x)?0, i=1,2,3 almost everywhere, such that the problem can be degenerate (parabolic-elliptic). We show that the critical value of the problem is and identify the homogenized problem depending on δ is zero, strictly positive finite or infinite.     

Microwave Response of Perfect YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">x</Emphasis></Subscript> Thin Films Deposited on CeO<Subscript>2</Subscript>-Buffered Saphire: A Probe for Pairing Symmetry

Microwave surface impedance, Z _s(T), of epitaxial YBCO thin films deposited on CeO₂-buffered sapphire substrates, was measured at several discrete frequencies within the range 5–134 GHz by use of coplanar resonator and end-plate cavity resonator techniques. The main features of obtained experimental results are as follows: (i) surface resistance R _s(T) at low temperatures obeys the exponential law: R _s(T) = R _res+R ₀⋅exp [−δ/T] with a small gap δ value (δ≈ 0.7 T _c); (ii) the most perfect quasi-single-crystalline films reveal a distinct two-peak structure of R _s(T) dependence, which is not observable in films with a less ordered crystal structure. These features are believed to reveal some intrinsic electron properties of such films, namely: (i) mixed (d+is) type symmetry of electron pairing, and (ii) dominant role of extended c-oriented defects (e.g., edge dislocation arrays or twin planes) in quasiparticles scattering for the most perfect films, which demonstrate the two-peak anomalous R _s(T) behavior.     

Effect of synthesis conditions on the phase composition and critical current density of Bi1.6Pb0.4Sr2−x KxCa2Cu3F0.8Oy

Effects of the temperature-time schedule on the phase composition, critical current density j _c, critical temperature T _c, and electric resistance in the normal state (ρ) of the samples of Bi_1.6Pb_0.4Sr_2−x K_xCa₂Cu₃F_0.8O_y (x=0 or 0.02) compositions were studied by X-ray diffraction analysis and by measuring resistances and current-voltage characteristics of the samples. The values of j _c=of 583.6 A/cm² (at 77.4 K) and T _c(R=0)=107.1 K were obtained in the samples with x=0.02 upon partial fusion. In order to obtain high j _c values, the samples must be synthesized (sintered) prior to the fusion stage.     

Self Modeling Curve Resolution

This paper presents a method for determining the shapes of two overlapping functions f ₁(x) and f ₂(x) from an observed set of additive mixtures, [α _i f ₁(x) + β _i f ₂(x); i = 1, …, n), of the two functions. This type of problem arises in the fields of spectrophotometry, chromatography, kinetic model building, and many others. The methods described by this paper are based on the use of principal component techniques, and produce two bands of functions, each of which contains one of the unknown, underlying functions. Under certain mild restrictions on the f_j (x), each band reduces to a single curve, and the f_i (x) are completely determined by the analysis.     

Oxide ionic conductivity and crystallographic properties of tetragonal type Bi2O3-based solid electrolyte doped with Ho2O3

Abstract

In the present work, the authors have investigated the binary system of (Bi₂O₃)_1–x(Ho₂O₃)_x. For the stabilisation of the tetragonal type solid solution, small amounts of Ho₂O₃ were doped into the monoclinic Bi₂O₃ via solid state reactions in the stoichiometric range 0·01≤x≤0·1. The crystal formula of the formed solid solution was determined as Bi(III)_4–4xHo(II)_4xO_6–2xVo_(2+2x) (where Vo is the oxide ion vacancy) according to the XRD and SEM microprobe results. In the crystal formula, stoichiometric values of x were 0·04≤x≤0·08, 0·03≤x≤0·09, 0·02≤x≤0·09 and 0·04≤x≤0·09 for annealing temperatures at 750, 800, 805 (quench) and 760°C (quench) respectively. The four probe electrical conductivity measurements showed that the studied system had an oxide ionic type electrical conductivity behaviour, which is increased with increasing dopant concentration and temperature. The obtained solid electrolyte system has an oxygen non-stoichiometry characteristic, and it contains O^2– vacancies, which have disordered arrangements in its tetragonal crystal structure. The increase in the amount of Ho₂O₃ doping and temperature causes an increasing degree of the disordering of oxygen vacancies and a decrease in the activation energy E_a.     

Blended infinite elements for paraboblic boundary value problems

A common method for numerically approximating two-point parabolic boundary value problems of the form u_t = L[u]+f(u) defined of the semi-infinite strip S = [0, 1]×[0, ∞] is to first discretize the spatial operator in the differential equation and then solve for the time evolution. Such an approach typically involves solving a system of algebriaic equations at a sequence of time steps. In this paper we take a different approach and subdivide S into a collection of semi-infinite substrips S_i = [x_i, x_i+1]×[0, ∞], and use blending function techniques to derive finite parameter functions e_i(x, t) defined on S_i. Spectral matching methods are used in deriving e_i to ensure that (u ? e_i) can be made small on S_i. Galerkin's method, with associated integration sover the entire space-time domain S, is then used to generate approximations to u(x, t) based upon the so defined infinite element (e_i, S_i). Approximations are hence found for all (x, t) in S by solving one well structed system of algebraic equations. We apply the method to several linear and non-linear problms.     

Dielectric behaviour of Pb-substituted BZT ceramics

Material series with compositional formula Ba_1·0?x Pb _x Ti_0·90Zr_0·10O₃ (0 ≤ x ≤ 0·20, in steps of 0·05) were prepared by conventional solid state method. All the samples were subjected to X-ray diffraction (XRD) studies and found to be single phase with perovskite structure. SEM measurements were done in order to collect micro-structural information. Different transition temperatures were found to depend on the Pb content. Tetragonality (c/a) and Curie temperature (T _c) increase with increase in lead content x. Dielectric properties were studied as a function of temperature and frequencies.