Статический и динамический вклады в расщепление основного состояния Eu-=SUP=-2+-=/SUP=- в SrMoO-=SUB=-4-=/SUB=-

The EPR spectrum of an Eu^2+ impurity center in a SrMoO_4 single crystal in the temperature range T = 1.8, 111–300 K has been studied, and the temperature changes in the spin Hamiltonian parameters describing the EPR spectrum of odd europium isotopes have been determined. It is shown that small temperature changes in the diagonal parameters of the spin Hamiltonian (for odd Eu^2+ isotopes) $$b_{2}^{0}$$ ( T ) = b _2( F ) + b _2( L ) and $$P_{2}^{0}$$ ( T ) = P _2( F ) + P _2( L ) are explained by the compensation of spin–phonon contributions b _2( F ) and P _2( F ) by the contributions of the lattice thermal expansion b _2( L ) and P _2( L ). The quantities b _2( L ) and P _2( L ) that are dependent on the static lattice parameters at a given temperature, are estimated in terms of the superposition Newman model. Then, the spin–phonon b _2( F ) and P _2( F ) contributions determined by the lattice ion vibrations are separated. An analysis shows that $$b_{2}^{0}$$ ( F ) and $$P_{2}^{0}$$ ( F ) > 0, b _2( L ) and P _2( L ) < 0, and the temperature behavior of the spin–phonon contribution is well described by G. Pfister’s model of local vibrations.

Влияние решеточного и спин-фононного вкладов на температурное поведение расщепления основного состояния Gd-=SUP=-3+-=/SUP=- в SrMoO-=SUB=-4-=/SUB=-

The temperature behavior of the EPR spectra of the Gd^3+ impurity center in single crystals of SrMoO_4 in the temperature range T = 99–375 K is studied. The analysis of the temperature dependences of the spin Hamiltonian b _2 ^0 ( T ) = b _2( F ) + b _2( L ) and P _2 ^0 ( T ) = P _2( F ) + P _2( L ) (for Gd^157) describing the EPR spectrum and contributing to the Gd^3+ ground state splitting Δ E is carried out. In terms of the Newman model, the values of b _2( L ) and P _2( L ) depending on the thermal expansion of the static lattice are estimated; the b _2( F ) and P _2( F ) spin-phonon contributions determined by the lattice ion oscillations are separated. The analysis of b _2 ^0 ( T ) and P _2 ^0 ( T ) is evidence of the positive contribution of the spin-phonon interaction; the model of the local oscillations of the impurity cluster with close frequencies ω describes well the temperature behavior of b _2( F ) and P _2( F ).

Tetraquark resonances computed with static lattice QCD potentials and scattering theory

We study tetraquark resonances with lattice QCD potentials computed for two static quarks and two dynamical quarks, the Born-Oppenheimer approximation and the emergent wave method of scattering theory. As a proof of concept we focus on systems with isospin I = 0, but consider different relative angular momenta l of the heavy b quarks. We compute the phase shifts and search for S and T matrix poles in the second Riemann sheet. We predict a new tetraquark resonance for l = 1, decaying into two B mesons, with quantum numbers I(JP) = 0(1−), mass [see formula in PDF] MeV and decay width [see formula in PDF] MeV.

Closed-form evaluation of two-dimensional static lattice sums

Closed-form formulae for the conditionally convergent two-dimensional (2D) static lattice sums S 2 (for conductivity) and T 2 (for elasticity) are deduced in terms of the complete elliptic integrals of the first and second kind. The obtained formulae yield asymptotic analytical formulae for the effective tensors of 2D composites with circular inclusions up to the third order in concentration. Exact relations between S 2 and T 2 for different lattices are established. In particular, the value S 2 = π for the square and hexagonal arrays is discussed and T 2 = π /2 for the hexagonal is deduced.

Charge Compensation in Trivalent Doped Ca3(SiO4)Cl2

ABSTRACTCalcium chlorosilicate (Ca3(SiO4)Cl2) is seen as a potential host phase for the immobilization of Cl-rich wastes arising from pyrochemical reprocessing, a waste stream often containing a mix of both di- and trivalent cations. Substitution of trivalent cations into the lattice requires some form of charge compensation to ensure the lattice remains charge neutral overall. Whilst previous work has only examined this through the formation of Ca vacancies, this study investigates the feasibility of charge-balancing via the substitution of a monovalent cation onto the Ca sites of the lattice. To that end, a series of static lattice calculations were performed to determine the site selectivity of monovalent cations of differing size when substituted onto the Ca sites of the calcium chlorosilicate lattice and the solution energies for the overall substitution processes compared with those for charge compensation via vacancy formation. In all cases the monovalent charge-balancing species shows a clear preference for substitution onto the Ca1 site in the calcium chlorosilicate lattice. The solution energy of the substitution process increases with the increasing ionic radii of both the mono- and trivalent species as the steric stresses associated with substitution of larger cations than the Ca2+ host increase. As such, only charge-balancing using Li+, Na+ or K+ is more favourable than via formation of a Ca vacancy.

Effect of Charge-balancing Species on Sm3+ Incorporation in Calcium Vanadinite

ABSTRACTApatites are often seen as good potential candidates for the immobilization of halide-rich wastes. In particular, phosphate apatites have received much attention in recent years, however, their synthesis often produces complicated multi-phase systems, with a number of secondary phases forming [1.2]. Calcium vanadinite (Ca5(VO4)3Cl) demonstrates a much simpler phase system, with only a single Ca2V2O7 secondary phase which can easily be retarded by the addition of excess CaCl2. However, when doping with SmCl3 (as an inactive analogue for AnCl3) the Sm forms a wakefieldite (SmVO4) phase rather than being immobilized within the vanadinite, a result of having to form an energetically unfavourable Ca vacancy in order for the lattice to remain neutral overall. It has been postulated that charge-balancing the lattice via co-substitution of a monovalent cation will be less disfavoured and therefore help stabilise formation of a (Ca5-2xSmxAx)(VO4)3Cl solid solution (A = monovalent cation). This has been investigated using a combined modelling and experimental approach. Static lattice calculations performed using Li+, Na+ and K+ as charge-balancing species have shown the energy cost to be less than half that of charge-balancing via formation of a Ca vacancy. As a result, solid state synthesis of (Ca5-2xSmxLix)(VO4)3Cl, (Ca5−2xSmxNax)(VO4)3Cl and (Ca5-2xSmxKx)(VO4)3Cl solid solutions have been trialled, and analysis of the resulting products has shown a significant reduction in both the SmVO4 and Ca2V2O7 secondary phases across all dopant levels.

MODIFIED BCS GAP EQUATION FOR JAHN–TELLER DISTORTED HIGH TEMPERATURE SUPERCONDUCTORS

In this communication we report the interplay of the normal electron-phonon (EP) interaction, dynamic Jahn–Teller (DJT) distortion and superconductivity in high temperature superconductors in presence of a static lattice strain. This model consists of a degenerate two orbital band separated by Jahn–Teller (JT) energy modified by the DJT interaction in the conduction band. The superconductivity is assumed to be s-wave type present in the same band. The interaction Hamiltonian is solved by Green's function method and a modified BCS gap equation is obtained with a modified conduction band energy [Formula: see text] and modified BCS order parameter [Formula: see text] with α = 1, 2 designating the two orbitals. This interplay displays some new interesting results which are different from the effect of the static lattice strain on superconducting (SC) order parameter. The interplay is studied by varying the normal EP coupling, the DJT coupling, the SC coupling, the phonon vibration frequency, the phonon wave vector and other model parameters of the system.