Site-occupation preferences in quaternary GaInAsSb and CdMnSeTe compounds in tetrahedrally coordinated zinc-blende structures are discussed. Probabilistic eigenfunctions are defined to determine individual component pair-populations from measured average-pair distributions. The methodology and possible traps in interpreting site-occupation preferences of published EXAFS experimental overall average-pair distributions are discussed. The approach allows a deeper understanding of individual pair selective preferences in semiconducting multinary compounds. EXAFS reported departures from Bernoulli random distributions point to changes within elemental tetrahedral average-populations. Resolution requires that for tetrahedral structures experimental data best-fit be a 4th degree polynomial, product of a parabola by the factor x(1-x). The analysis shows that both materials have a marked preference for elemental tetrahedra with odd numbers of competing species of ions around a central ion.
Cu^{2+} ions doped to ZnGeF_6·6H_2O substitute the host Zn^{2+} ions and undergo a strong Jahn-Teller effect producing nearly axial elongation of the Cu(H_2O)_6 octahedra with equal population of the three possible deformations at low temperatures as shown by the EPR spectra. Reorientations between these distorted configurations are observed as a continuous shift of EPR lines leading to averaging of the g- and A-tensors. The full averaging is observed at the phase transition temperature 200 K. Electron spin relaxation was measured up to 45 K only, where the electron spin echo signal was detectable. Electron spin-lattice relaxation is governed by the Raman two-phonon process allowing to determine the Debye temperature asΘ_D=99 K. There is no contribution of the Jahn-Teller dynamics to the spin-lattice relaxation rate. Electron spin echo decay is strongly modulated by dipolar coupling to the ^1H and ^{19}F nuclei. The phase memory time is governed by instantaneous diffusion at helium temperatures and then by spin-lattice relaxation processes and excitation to the first vibronic level of energyΔ=151 cm^{-1}.
Single crystals and powder EPR spectra of Cu^{2+} ions in Cs_{2}Zn(SO_{4})_{6}·6H_{2}O were recorded in the temperature range of 4.2-300 K and the g-factor temperature variations were determined. The g_{z} and g_{y} have the values of 2.443 and 2.134, respectively, at the rigid lattice limit below 20 K, and then continuously tend to an average value on heating. This vibronic averaging produced by reorientations of Cu(H_{2}O)_{6}-complexes between Jahn-Teller distorted octahedral configurations is described in terms of a two-state Silver-Getz model which is known as a good model for diamagnetic non-ammonium Tutton salts. We found, however, that this model is only a crude approximation in Cs_{2}Zn(SO_{4})_{6}·6H_{2}O below 150 K. Above this temperature the model works better and describes the vibronic dynamics between the two lowest energy potential wells in the adiabatic potential surface differing in the energy of δ_{12}=318(9) cm^{-1}=3.7 kJ/mol.
EPR linewidth of Cu^{2+} in the Tutton salt crystals weakly depends on temperature at low temperatures and then it rapidly grows above 60 K. We present detailed results of measurements and analysis for ^{63}Cu^{2+} in K_2Zn(SO_4)_2·6 H_2O, K_2 Zn(SO_4)_2·6D_2O, (NH_4)_2Mg(SO_4)_2·6H_2O and Cs_2Zn (SO_4)_2·6H_2O in a temperature range of 4.2-300 K and compare them with already published electron spin-lattice relaxation data. The relaxation contributes weakly to the linewidth which is dominated by molecular dynamics and grows exponentially with temperature. To describe this we are discussing the influence of jumps between two sites of Cu^{2+} complexes in a slow motion region where the sites are differently thermally populated. This case has not been considered so far. We have derived appropriate expressions describing the contribution of jumps to the linewidth which allows the determination of the jump rate and energy difference δ_{A,B} between the two sites being two Jahn-Teller distorted configurations of the vibronic Cu(H_2O)_6 complexes. The jump rate 1/τ strongly depends on temperature and reaches 10^9 s^{-1} at room temperature, whereas theδ_{A,B} varies from 117 cm^{-1} for K_2Zn(SO_4)_2·6D_2O to 422 cm^{-1} for Cs_2Zn(SO_4)_2·6 H_2O. The comparison with vibronic level splitting, which varies in the range of 67-102 cm^{-1}, indicates that the reorientation mechanism involves phonon induced tunnelling via excited vibronic levels. These reorientations do not contribute, however, to the spin-lattice relaxation which is governed by ordinary two-phonon relaxation processes in the whole temperature range. Thus, the reorientations and spin relaxation are two independent phenomena contributing to the total linewidth.
Transport integrals I_n(Θ_D/T) are reviewed with their applications in solid-state physics, molecular dynamics, and electron spin-lattice relaxation. Analytical approximations of I_n for n=2-8 are proposed as applicable for computer fitting procedures in the range of the variable x=Θ_D/T from 0.1 to 40. The results are applied for description of the spin-lattice relaxation data collected for Cu^{2+} ions in triglycine sulphate and are compared with relaxation data for Cu^{2+} and Mn^{2+} in (NH_4)_2Mg(SO_4)_2·6H_2O.
An expression for the Green function of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states, phase shift and scattering cross-section are expressed in terms of complete elliptic integrals of the first kind.
The effective capacitance between the origin and any other lattice site, in an infinite 3D simple cubic network consisting of identical capacitors, is evaluated in terms of the lattice Green function of the network. The perfect case is reviewed shortly, while the perturbed case (a capacitor is removed) is studied in two cases. Numerical values of the effective capacitance are presented and the asymptotic behavior is studied for the both cases.
We express the equivalent resistance between the origin (0,0,0) and any other lattice site (n_1,n_2,n_3) in an infinite body centered cubic network consisting of identical resistors each of resistance R rationally in terms of known values b_{0} and π. The equivalent resistance is then calculated. For large separations two asymptotic formulae for the resistance are presented and some numerical results with analysis are given.
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