Nonasymptotic critical 3D-XY behavior for the nematic-smectic-A 1 liquid crystal transition

High-resolution X-ray data near the nematic (N)-smectic-A ₁ (SmA ₁) transition are reported for two polar liquid-crystal systems with large nematic ranges. The correlation volume ξ_∥ ξ _⊥ ² , the smectic order-parameter susceptibility σ, and the heat capacityC _p of these systems and two other N-SmA ₁ systems are in excellent agreement with exact theoreticalpreasymptotic 3D-XY predictions. The importance of correction terms for ξ_∥ ξ _⊥ ² and σ as well asC _p is demonstrated. Universal features of the 3D-XY model are obeyed except for anisotropy in the correlation lengths ξ_∥ and ξ_⊥.     

On anomalies of anisotropic thermal expansion near points of electronic topological transitions in noncubic metals. Applications to Zn,Cd and CdMg alloys

Singularities of the low-temperature coefficients of the thermal expansion, α_i(T), near points of electronic topological transitions (ETT) in noncubic metals are investigated. Using a uniaxial metal with a weak pseudopotential of the electron-ion interaction as an example, it is shown that the longitudinal α_∥ and transverse α_⊥ coefficients should be opposite in sign near the ETT point, while the ∥α_i∥ values can considerably exceed the volume coefficient β=α_∥ + 2α_⊥. These conclusions are illustrated by ab initio band structure calculations for the hcp Zn, Cd and CdMg alloys. The results explain the scale and sign of the α_i low-temperature anomalies in Zn and Cd (α_∥ > 0, α_⊥ < 0>). For the Cd_1-xMg_x alloys the anomaly inversion (α_∥ < 0, α_⊥ > 0) is predicted after the first ETT at the point x=x_c1≈0.06, as well as its sharp growth (the ∥α_i∥ increase) after the second ETT at x_c2≈0.12.     

An interpretation of the g factors for the tetragonally-compressed Cr centers in YVO4 and YPO4 crystals

The g factors g_∥ and g_⊥ for the tetragonally-compressed (CrO₄)³⁻ clusters in YMO₄ (M=V, P) crystals are calculated from the high-order perturbation formulas based on the two-mechanism model for the compressed d¹ tetrahedra with the ground state |d_z²〉. From the calculated values and by considering a small admixture of the first excited state |d_x²−y²〉 to the ground state |d_z²〉 due to the vibrational motion of ligands (which leads a twinkling compressed tetrahedron to become an elongated one), the observed g_∥ and g_⊥ for Cr⁵⁺ centers in YMO₄ crystals are explained reasonably. The difficulty of the large deviations of g_∥ from g_e (≈2.0023) in the two systems is therefore removed and the above dynamic effect may be the cause which results in the large deviation of g_∥ from g_e for some (CrO₄)³⁻ clusters in crystals.     

Thermoreflectance of single crystal Gd

Thermoreflectance spectra for E∥c and E⊥c were measured on a Gd single crystal. The thermoconductance spectra, Δσ_∥ and Δσ_t], are very anisotropic. The strong interband edge at about 0.5 eV is shown to arise from a transition to or from the Fermi level for E⊥c. For E∥c additional effects occur.     

Theoretical calculations of the optical band positions and spin-Hamiltonian parameters for Yb at the tetragonal Y site of KY3F10 crystal

The six optical band positions and six spin-Hamiltonian parameters [g factors g_∥, g_⊥ and hyperfine structure constants A_∥(¹⁷¹Yb³⁺), A_⊥(¹⁷¹Yb³⁺), A_∥(¹⁷³Yb³⁺), A_⊥(¹⁷³Yb³⁺)] for Yb³⁺ ion at the tetragonal Y³⁺ site of KY₃F₁₀ crystal are calculated from a diagonalization (of energy matrix) method. In the method, the Hamiltonian of energy matrix contains the free-ion, crystal-field interaction, Zeeman (or magnetic) interaction and hyperfine interaction terms and so a 14×14 complete energy matrix for 4f¹³ ion in tetragonal crystal-field and under an external magnetic field is constructed. Diagonalizing the energy matrix, these optical and EPR spectral data are calculated together and the calculated results are in reasonable agreement with the experimental values. The signs of hyperfine structure constants A_∥, A_⊥ for the isotopes ¹⁷¹Yb³⁺ and ¹⁷³Yb³⁺ in KY₃F₁₀ are suggested. The results are discussed.     

Theoretical examination of optical and EPR spectra for Cu ion in K2PdCl4 crystal

In this work, two d-d transition spectra and four EPR parameters g_∥, g_⊥, A_∥, A_⊥ of K₂PdCl₄/Cu²⁺ are uniformly interpreted based on Zhao's crystal-field model. The calculation result is in good agreement with the experiment findings. The ligand spin-orbit coupling is neglected on the calculation, which is consistent with the ab initio result by Hillier et al. [J. Am. Chem. Soc. 98 (1976) 95]     

Studies of the optical spectrum band positions and spin-Hamiltonian parameters for Pa ion in ThX4 (X=Cl, Br) crystals

The optical spectrum band positions and spin-Hamiltonian (SH) parameters (g factors g_∥ and g_⊥ and hyperfine structure constants A_∥ and A_⊥) for 5f¹ ion Pa⁴⁺ at the tetragonal Th⁴⁺ site of ThX₄ (X=Cl, Br) crystals are calculated from a complete diagonalization (of energy matrix) method (CDM). In the CDM, the magnetic (or Zeeman) interaction and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and so the optical and EPR spectra data can be studied in a unified way. The calculated results are in reasonable agreement with experimental values. The possible misprints or small errors in the experimental g factors for Pa⁴⁺ in ThX₄ crystals are pointed out. The results are discussed.     

Low temperature ESR of K2Pt(CN)4Br0.3. 3.2 H2O

Electron spin resonance has been observed in high purity single crystals of K₂Pt(CN)₄Br_0.3·3.2H₂O, (KCP), in the temperature range of 4.22–80 K. Two types of paramagnetic species are found to dominate the spectrum. One of these is an inhomogeneously broadened line showing no resolved hyperfine splitting and having g_∥ = 1.946 ± 0.003 and g⊥ = 2.340 ± 0.003. The second paramagnet is identified as a Cu²⁺ impurity center with g_∥ = 2.231 ± 0.003, g⊥ = 2.079 ± 0.002 and hyperfine tensor A_∥ = 467 MHz, A_⊥ = 70 MHz.     

Theoretical investigation of EPR and optical spectra of Mo(V) in [Mo6O19][N(C4H9)4]3 salt

The electron paramagnetic resonance (EPR) spectral data (the g factors and hyperfine structure constants) and d–d transition spectra for the tetragonal Mo⁵⁺ centre in [Mo₆O₁₉][N(C₄H₉)₄]₃ salt are theoretically investigated from the complete diagonalization method (CDM) for a 4d¹ ion in tetragonally compressed octahedron. The theoretical results are in good agreement with the experimental data. The dependency of the g factors of the ground state on the R_∥(MoO bond length) has been studied. It is shown that the g factors varied with the R_∥ approximately in a linear way.     

Defect model and spin-Hamiltonian parameters for the tetragonal Nd center in the tetragonal phase of SrTiO3 crystal

The spin-Hamiltonian parameters (g factors g_∥, g_⊥ and hyperfine structure constants ¹⁴³A_∥, ¹⁴³A_⊥, ¹⁴⁵A_∥ and ¹⁴⁵A_⊥) of the tetragonal Nd³⁺ center in the low-temperature (T≈4.2 K) tetragonal phase of SrTiO₃ are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are attached to the conventional Hamiltonian and a 52×52 energy matrix concerning the ground term ⁴H_J (J=9/2, 11/2, 13/2, 15/2) is constructed. The Nd³⁺ center is attributed to Nd³⁺ occupying the 12-fold coordinated Sr²⁺ site in SrTiO₃. Differing from the defect model assumed in the previous paper that the tetragonal distortion of this Nd³⁺ center is due to the association of one interstitial oxygen ion at a nearest neighborhood of Nd³⁺ and the Nd³⁺ displacement Δz along C₄ axis, we suggest that it is due to the distortion of SrTiO₃ lattice in the tetragonal phase. The calculated g factors g_∥ and g_⊥ show good agreement with the experimental values, suggesting that our defect model of Nd³⁺ center in SrTiO₃ is reasonable. The experimental hyperfine structure constants were not reported and so our calculated results remain to be checked by EPR experiment.     

Studies of the zero-field splitting and g-factor for the defect model of Cr in α-LiIO3 crystals at low temperature

The EPR zero-field splitting parameters D and g-factors for Cr³⁺ in α-LiIO₃ single crystal, taking into account both the effect of lattice distortion and two Li⁺ vacancies, have been investigated using a complete diagonalization method (CDM) for 3d³ ions in a trigonal symmetry crystal field. The theoretical results (D=−0.60876 cm⁻¹, g_∥=1.9641, g_⊥=1.9682) are in excellent agreement with experimental results (D=−0.6099(3) cm⁻¹g_∥=1.965±0.001, g_⊥=1.971±0.002). In addition, Macfarlane's perturbation expressions lead to results almost identical with the CDM for Cr³⁺ in an α-LiIO₃ single crystal.     

Effect of the spin-orbit interaction of Ni2+ ions with a triplet orbital ground state on the magnetostriction of NiFe0.5Cr1.5O4 ferrite

The magnetization σ and the longitudinal (λ_∥) and transverse (λ_⊥) magnetostrictions of the NiFe_0.5Cr_1.5O₄ ferrite containing the tetrahedral ions Ni²⁺ with the triplet orbital ground state have been investigated for the first time at a temperature of 4.2 K in fields up to 55 kOe. It is revealed that the NiFe_0.5Cr_1.5O₄ ferrite exhibits an anomalously large magnetic anisotropy (H _c=12.5 kOe) and magnetostrictions (λ_∥≈?870×10^?6 and λ_⊥≈800×10^?6). In strong fields, the magnetostrictions λ_∥ and λ_⊥ are found to be anisotropic in character; i.e., the susceptibility Δλ_∥p and Δλ_⊥p. The conclusion is drawn that the studied compound is characterized by two paraprocesses: one paraprocess in the B sublattice has an exchange nature, and the second process in the A sublattice is due to the spin-orbit interaction of Ni _A ²⁺ ions.     

Thickness dependence of the surface plasmon dispersion in ultrathin aluminum films on silicon

The collective excitation in Al films deposited on Si(1 1 1)-7 × 7 surface was investigated by high-resolution electron-energy-loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS) and scanning tunneling microscopy (STM). At the Al film thickness d < 10 ML, the surface plasmon of Al film has only a small contribution to the observed energy-loss peaks in the long wavelength limit (q_∥≈0), while its contribution becomes significant for q_∥>d^-1. More interestingly, for thin Al films, the initial slope of the surface plasmon dispersion curve is positive at q_∥∼0, in a sharp contrast to bulk Al surface where the energy dispersion is negative. These observations may be explained based on the screening interaction of the space charge region at the Al-Si interface.     

Distribution of electromagnetic transition amplitudes

In this paper the distribution of electromagnetic transition amplitudes 〈W′∥O∥W〉 is described in terms of fluctuations about a gaussian secular variation (as a function of initial and final energies) according to the Porter-Thomas assumption. Explicit formulas are derived both for the case (i) that∑ _w ′¦〈W′∥O∥W〉¦² is replaced by its local average and (ii) that∑ _W ′¦〈W′∥O∥W〉¦² is treated as a stochastic variable showing a χ _d ² -distribution. The resulting distribution function appears to possess a monomial tail. Comparisons with shell-model results are made.     

Quantum probability and Levy Laplacians

The formula Δ _L = lim_?→0 ∫_{∥s–t∥<?} b _s b _t dsdt for the Levy Laplacian is obtained, where b _t stands for an annihilation process. The formula is extended to some generalizations of the Levy Laplacian.     

Inequalities for the Schattenp-norm. IV

We prove some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA,B, andX are operators such thatA +B ≧ |X| andA +B ≧ |X*|, then ∥AX +XB∥ _p ^p + ∥AX* +X*B∥ _p ^p ≧2 ∥X∥ _2p ^2p for 1 ≦p<∞, and max (∥AX +XB∥, ∥AX* +X*B∥) ≧ ∥X∥². Also, for any three operatorsA,B, andX, $$|| |A|X - X|B| ||_2^2 + || |A*|X - X|B*| ||_2^2 \leqq ||AX - XB||_2^2 + ||A*X - XB*||_2^2 .$$      

Theoretical investigation of the optical and EPR parameters for VOion in some complexes

The molecular orbital coefficients and the EPR parameters of trisodium citrate dihydrate, sodium hydrogen oxalate monohydrate, potassium d-gluconate monohydrate and L-Alanine vanadyl complexes are calculated theoretically. Two d-d transition spectra and EPR parameters for the VO²⁺ complex are calculated theoretically by using crystal-field theory. The calculated g and A paramaters have indicated that paramagnetic center is axially symmetric. Having the relations of g_∥〈g_⊥〈g_e and A_∥〉A_⊥ for VO²⁺ ions, it can be concluded that VO²⁺ ions are located in distorted octahedral sites (C_4v) elongated along the z-axis and the ground state of the paramagnetic electron is d_xy.     

Veneziano model for nucleon nucleon and nucleon antinucleon scattering. I

The thermal conductivity has been measured on two niobium samples of different purity (ratio of mean free path to coherence length 220 and 10, respectively), in the mixed state, with heat current parallel (k _∥) and normal (k _⊥) to the magnetic field. The experimental results are compared with theories; the range of validity is discussed. Maki's relation (k-k _n) ～ (H _c2 -H)^1/2 could be verified only for the purer sample in the field range (H _c2 -H)?140 Oe. The relationsk _∥/k ₁>1 forT?T _c andk _∥/k ₁<1 forT?T _c were found to be valid for the whole range of fields in the mixed state.     

Microwave spectrum,dipole moment,and conformation of 3-methylcyclopentanone

The rotational spectrum of 3-methylcyclopentanone has been observed in the frequency region from 18.0 to 26.5 GHz. Both a-type and b-type transitions in the ground vibrational state and a-type transitions in five excited states have been assigned. The ground state rotational constants are determined to be A = 5423.32 ± 0.18, B = 1949.51 ± 0.01, and C = 1529.59 ± 0.01 MHz. Analysis of the measured quadratic Stark effects gives the dipole moment components ∥μ_a∥ = 2.97 ± 0.02, ∥μ_b∥ = 1.00 ± 0.03, ∥μ_c∥ = 0.18 ± 0.06, and the total dipole moment ∥μ_t∥ = 3.14 ± 0.03 D. These data are consistent with a twisted-ring conformation with a methyl group in the equatorial position.     

Tetravalent vanadium in CaF2 and SrF2 crystals: An EPR study

An EPR study of tetravalent vanadium centers created by room temperature X-irradiation in CaF₂ and SrF₂ is presented. The production efficiency of these centers is enhanced by previous annealing of the samples at 1000 K in air. The symmetry of V⁴⁺ ions is tetragonal and its EPR spectrum can be described by an axial spin Hamiltonian including a Zeeman and hyperfine term with $\text{S =}\text{1}\text{2}$ and $\text{I =}\text{7}\text{2}$ (corresponding to ⁵¹V nuclei). The following values for the spin Hamiltonian parameters are obtained g_∥ = 1.947 ± 0.002, g_⊥ = 1.935 ± 0.005, A_∥ = 500 ± 5 MHz, A_⊥ = 150 ± 10 MHz in the case of SrF₂ and g_∥ = 1.945 ± 0.002, A_∥ = 505 ± 5 MHz and A_⊥ < 200 MHz, in the case of CaF₂. A model for the center including an interstitial O^2? ion is tentatively proposed.