Solvable lattice models whose states are dominant integral weights of A it−1 (1)

A new hierarchy of solvable IRF models is presented. It is generated from Belavin's Z _n ×Z _n symmetric model. The site variables take values in the set of level l dominant integral weights of A _–1 ⁽¹⁾ . It is conjectured that the local state probabilities are given through the irreducible decomposition of characters for the affine Lie algebra pair (A _n–1 ⁽¹⁾ A _n–1 ⁽¹⁾ ,A _n–1 ⁽¹⁾ ).     

Density functional calculations of Pb1−xCaxSySe1−y alloys lattice matched to different substrates

Density functional calculations are performed to study the structural and electronic properties of technologically important Pb_1?xCa_xS_ySe_1?y quaternary alloys. The calculations are based on the total-energy calculations within the full-potential augmented plane-wave (FP-LAPW) method. For exchange-correlation energy and corresponding potential, the generalized gradient approximation (GGA) by Perdew–Burke–Ernzerhof (PBE) and Engel–Vosko (EVGGA) have been used. We investigated the effect of composition on lattice constant, bulk modulus and band gap for pseudobinary as well as for quaternary alloys, which showed non-linear dependence on the composition x and y. The presented contour maps of energy band gap and lattice constants versus concentrations could be useful for designing new structures with the desired optical properties. In addition, the energy band gap and natural band offset of simple cubic Pb_1?xCa_xS_ySe_1?y quaternary alloys lattice matched to PbS and SrS substrates are investigated. The obtained results show that the quaternary alloys of interest could be appropriate materials for designing heterostructures with desired optical and interfacial properties.     

An−1(1) reflection K-matrices

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the A_n−1⁽¹⁾ affine Lie algebra. We have classified them in two classes of solutions. The first class consists of n(n−1)/2 K-matrix solutions with three free parameters. The second class are solutions that depend on the parity of n. For n odd there exist n reflection K-matrices with 2+[n/2] free parameters. It turns out that for n even there exist n/2 K-matrices with 2+n/2 free parameters and n/2 K-matrices with 1+n/2 free parameters.     

Solution of Potts-3 and Potts-∞ matrix models with the equations of motion method

In this letter, we show how one can solve easily the Potts-3 + branching interactions and Potts-∞ matrix models, by the means of the equations of motion (loop equations). We give an algebraic equation for the resolvents of these models, and their scaling behaviour. This shows that the equations of motion can be a useful tool for solving such models.     

Three-dimensional coupled double-distribution-function lattice Boltzmann models for compressible Navier–Stokes equations

Two three-dimensional (3D) lattice Boltzmann models in the framework of coupled double-distribution-function approach for compressible flows, in which specific-heat ratio and Prandtl number can be adjustable, are developed in this paper. The main differences between the two models are discrete equilibrium density and total energy distribution function. One is the D3Q25 model obtained from spherical function, and the other is the D3Q27 standard lattice model obtained from Hermite expansions of the corresponding continuous equilibrium distribution functions. The two models are tested by numerical simulations of some typical compressible flows, and their numerical stability and precision are also analysed. The results indicate that the two models are capable for supersonic flows, while the one from Hermite expansions is not suitable for compressible flows with shock waves.     

Superconductivity of (Sn1−z Pbz)1−x InxTe alloys

The temperature dependences of the electrical resistivity of (Sn_1?z Pb_z)_1?x In_xTe alloys with different concentrations of lead (z=0–0.60) and indium (x=0.03–0.20) were studied at temperatures T=0.4–4.2 K in magnetic fields from zero to H=15 kOe. A resistivity drop of no less than three-four orders of magnitude was observed in this range of alloy compositions. Application of a magnetic field above a critical level resulted in a recovery of the sample resistivity to the original value. The observed resistivity drop is identified with a superconducting transition. The critical parameters of the superconducting transition (T _c and H _c2) were determined at the drop to one half the normal resistivity level. Experimental dependences of the critical supercon-ducting-transition temperature T _c and of the second critical magnetic field H _c2 on the contents of lead (z) and indium (x) were measured. The data obtained confirm a strong localization of the In impurity states and are evidence of the extrinsic nature of superconductivity in the class of materials under study. It was established that as the Pb content in (Sn_1?z Pb_z)_1?x In_xTe increases, T _c and H _c2 decrease as the Fermi level E _F (fixed in the In impurity resonance band) leaves the Δ extremum and the superconductivity breaks down when E _F leaves the LΣ saddle point in the valence-band energy spectrum.     

Structure and lattice dynamics of solid solutions (1 − x)BiFeO3-xANbO3 (A = K,Na)

The structures and the dynamic characteristics of the lattices of two compositions of solid solutions of multiferroic BiFeO₃ with ferroelectric KNbO₃ and antiferroelctric NaNbO₃, namely, (1 ? x)BiFeO₃-xKNbO₃ and (1 ? x)BiFeO₃-xNaNbO₃, have been studied using X-ray powder diffraction and Raman spectroscopy. For these systems with x = 0.3, 0.5, and 0.7, the symmetry and unit cell parameters at room temperature have been determined. An analysis of the vibrational spectra has revealed sequences of rotational distortions with variations in the concentrations of components.     

Solution synthesis of Y1−xBixVO4 for optical applications

Transparent luminescent Y_0.98?xBi_xEu_0.02VO₄ (0<x<1) ceramic films have been prepared using a polymeric route and heat-treatment at 550 °C. A solid solution of zircon-type Y_1?xBi_xVO₄ is obtained for x values below 0.5 whereas phase separation is observed above this limit. The absorption spectra of the films show a shift of the band edge towards high wavelength with the bismuth content, as theoretical calculi have predicted. Luminescence of the films under a UV excitation is typical of europium ion in the zircon structure. The poor correlation between absorption and excitation spectra at high bismuth content is coherent with desexcitation in localized states of valence band. However, the excitation wavelength could still be tuned from deep-UV to near-UV range by inserting bismuth in YVO₄.     

An extended functional transformation method and its application in some evolution equations

In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact,is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.     

Classical solutions ofℂP n−1 models and their generalizations

We discuss finite action solutions ofP ^n–1 models, of their Grassmannian generalizations and of a classical fermion — boson model based on the supersymmetric extension of theP ^n–1 model.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.I would like to thank Dr. A. M. Din for his collaboration with me on all the topics discussed here. Also I would like to thank E. F. Corrigan, D. B. Fairlie, M. Günyadin, J. Lukierski, I. Singer, R. Stora and many others for discussions and constructive criticisms and Professor J. Niederle for his invitation to present this talk at the symposium and for hospitality in Czechoslovakia.     

Far infrared studies of lattice and free carrier effects in CdxHg1−xSe

Far infrared reflection spectra of Cd_xHg_1−xSe are measured in the region 20 to 600 cm^-1 at temperature between 5 and 77 K. Reflection spectra are explained well by the dynamic dielectric function which is constructed as a sum of interband, intraband and phonon contributions. The plasma-LO phonon coupling and free carrier effects are discussed.     

The phase structure of SU(2) × U(1)Y lattice gauge theory

Using analytic and Monte Carlo techniques, we determine the phase structure and nature of spontaneous symmetry breaking of the SU(2) × U(1)_Y electroweak gauge theory with fixed-length Higgs fields on a lattice. We find that it has two completely separated phases: (a) a disordered, symmetric phase and (b) a phase in which SU(2) × U(1)_Y is spontaneously broken to U(1)_em, which is realized in its deconfined Coulomb phase with massless photons. Exact analytic results and approximate series expansions are given for various special cases of the theory.     

Synthesis,microstructure and dielectric properties of (1−x)PSN−xPLuN

Ceramic lead niobates and their solid solutions PSN–PLuN (pure lutecium niobate) were synthesized by solid state reactions. The sequence of phases formed at PSN–PLuN synthesis has been studied by X-ray analysis. Their symmetry changed from rhombohedral for PSN to pseudo-monoclinic for the 0.75PSN–0.25PLuN compositions. The performed EDS investigations revealed that the samples PSN–PLuN are perfectly sintered. They contain a little glassy phase and their grains are well shaped. The increase of lutecium content in the examined solid solution caused downward shift of the temperature of the phase transition. The decrease of the achieved permittivity values ? was observed as well.     

Dielectric and piezoelectric properties of (Bi1−x−yNdxNa1−y)0.5BayTiO3 lead-free ceramics

New lead-free (Bi_1−x−yNd_xNa_1−y)_0.5Ba_yTiO₃ ceramics were prepared by a conventional ceramic technique and their dielectric and piezoelectric properties were studied. X-ray diffraction studies reveal that Nd³⁺ and Ba²⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a new solid solution with a pure perovskite structure, and a morphotropic phase boundary (MPB) of rhombohedral and tetragonal phases is formed at 0.04 < y < 0.10. The partial substitutions of Nd³⁺ and Ba²⁺ decrease effectively the coercive field E_c and increase significantly the remanent polarization P_r. Because of lower E_c, larger P_r and the formation of the MPB, the piezoelectric properties of the ceramics are significantly enhanced at x/y = 0.02/0.06: d₃₃ = 150 pC/N and k_p = 30.5%. The ceramics exhibit relaxor characteristic, which is probably resulted from the cation disordering in the 12-fold coordination sites. The depolarization temperature T_d shows a strong compositional dependence and reaches a minimum value at the MPB. The temperature dependences of the ferroelectric and dielectric properties suggest that the ceramics may contain both the polar and non-polar regions near the depolarization temperature T_d, which cause the polarization hysteresis loop become deformed near/above T_d.     

An operating regime based on switching effects for photodetectors of Pb1−xSnxTe(in) MBE films

Pb_1−xSn_xTe(In) (x = 0.20) MBE films have been prepared on BaF₂ substrates. The characteristics of resistivity relaxation under the combined effect of a pulsed electric field and IR illumination have been investigated. We have shown that the films can be used as rather fast-response photodetectors operating in a regime of periodic accumulation and quenching of the signal.