Invariance of the Massless Field Equations under Changes of the Metric

It is shown that the Maxwell equations with sources, expressed in terms of the covariant tensor field F_ijand the current density four-vector Jⁱ, are invariant under the change of the metric g_ijby g_ij = g_ij+ l_il_jif l_iis a principal null direction of F_ijand that an analogous result holds in the case of the massless Klein-Gordon equation if l_iis null and orthogonal to the gradient of the field and in the case of the null dust equations if l_iis parallel to the dust four-velocity. An elementary proof of the following generalization of the Xanthopoulos theorem is also given: Let (g_ij, F_ij) be an exact solution of the Einstein-Maxwell equations and let l_ibe a principal null direction of F_ij, then (g_ij+ l_il_j, F_ij) is also an exact solution of the Einstein-Maxwell equations if and only if (l_il_j, 0) satisfies the Einstein-Maxwell equations linearized about the background solution (g_ij, F_ij). Furthermore, analogous theorems, where the source of the gravitational field is a massless Klein-Gordon field or null dust, are presented.     

On the nature of the phase transition in the KDP systems

Using the Landau theory of phase transitions it has been shown that for a second order phase transition Ω/k_BT_c ? 0.01. and its isomorphs 4Ω/J¹ ? 1 and for a first order transition Ω/k_BT_c ? 0.01.     

Evolution of the optical properties and the electrical resistivity of CaMnO3 during the substitution of Mo for Mn ions

The reflectance, the optical density, and the optical conductivity spectra of CaMn_{1 ? x} Mo _x O₃ (x ≤ 0.07) polycrystals are studied over a wide spectral region. The substitution of Mo⁶⁺ ions for Mn⁴⁺ ions leads to a strong decrease in the first high-energy phonon band, which is related to vibrations in the MnO₆ octahedron. The appearance of band-type charge carriers is detected in CaMn_{1 ? x} Mo _x O₃ with x ≤ 0.04, and carrier localization is observed in CaMn_0.93Mo_0.07O₃. This localization increases at T < 160 K, i.e., during the transition from the paramagnetic to the antiferromagnetic state with orbital ordering and a monoclinic structure. The optical conductivity spectrum of CaMn_0.93Mo_0.07O₃ exhibits a strong shift of fundamental absorption bands, which is associated with a change in the band structure because of a decrease in the splitting of the 3d levels of Mn in the crystal field.     

Influence of the electron concentration on the superconducting properties of the spinel system Li1-yTi2O4

In the spinel system Li_1-y Ti₂O₄ the Li content was reduced by oxidative extraction by means of a solution of I₂ as well as Br₂ in CH₃CN or by oxygen. The extraction is associated with a transition of Ti³⁺ to Ti⁴⁺: the system is Li_1-y Ti³⁺_1-yTi⁴⁺_1+y O₄. Consequently, with increasing y the charge carrier concentration decreases from the starting value of 0.5 electrons/Ti ion for LiTi₂O₄. The extraction proceeds in two steps. At the beginning, the Ti₂O₄ framework remains intact and the transition to superconductivity increases with decreasing charge carrier concentration to a maximal value of 13.2 K. Separated by a two-phase region for medium extraction levels for higher y values, a Li depleted material of approximate composition Li_0.3Ti₂O₄ is obtained. The crystal structure of Li_0.3Ti₂O₄ can be deduced from the original spinel lattice by a partial Ti migration from 16d to 16c and 8 a sites (space group Fd3m). Consequently, the Ti₂O₄ framework of Li_0.3Ti₂O₄ is disconnected and the material is no longer superconducting.     

On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

On the temperature dependence of positron lifetimes in tin and the transition from theβ- to theα-phase

The N₂, O₂, H₂O, and CO₂ molecules that have condensed on the surface of a pyroelectric tourmaline crystal were degassed successively by means of electron bombardment. The temperature dependence of the electrostatic field strength on the specimen surface was observed by electron diffraction; it decreased as the degassing advanced. The tourmaline surface behaved as a gas Chromatographic adsorbent.     

Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n_1ef, n_2ef, and n_3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n_1ef, n_2ef, and n_3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n₁, n₂ and n₃ are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n₁, n₂ and n₃ of the holographic gratings generated in the photopolymer material.     

Geometric study of the connection between the Lagrangian and Hamiltonian constraints

The second order differential equation character of the solutions of the dynamical equation i(Γ)ω_L = dE_L for a singular Lagrangian L, as well as the conditions for the existence of such a solution, are studied. We also introduce a couple of maps R (L)_v : T _FL(v)(T¹Q) → T_v(TQ) and T(L)_v : T_FL(v)(T¹Q) → T_FL(v)(T¹Q), with v ϵ TQ, which are shown to be very useful for establishing the connection between the constraints arising in the Lagrangian and Hamiltonian formulations.     

On the relation between the energy gap and the critical temperature

It is shown that the ratio β = ϵ/T_c (ϵ is the energy gap at T = OK) saturates with increasing strength of the electron-phonon interaction; the value β_max is calculated. The special case of a multigap superconductor is discussed. New high-T_c superconductors present a unique oppurtunity to observe a multigap structure.     

NDMAP: the best material to study the Haldane's prediction

As predicted by Haldane, spin, S=1 one-dimensional (1D) Heisenberg antiferromagnet (HAF) has an energy gap between the singlet ground state and first excited triplet. On application of magnetic field, the triplet state Zeeman splits and the energy of one of the triplet state becomes zero at a critical field, H_c. Above H_c the system recovers magnetism. Then, we expect that a quasi-1D HAF will show a magnetic long-range ordering (LRO) at low temperatures due to the inter-chain coupling. This field-induced LRO has not been observed before due to complication of the crystal structure in the materials studied so far and/or technical difficulty.From a heat capacity measurement on a single crystal of an S=1 quasi-Q1D HAF, Ni(C₅H₁₄N₂)₂N₃(PF₆), we found an anomaly at a temperature in finite fields indicating a field-induced phase transition. A magnetic LRO is confirmed by a neutron diffraction measurement on the same sample. The temperature versus magnetic field phase diagram of this compound is constructed and discussed.     

Experimental Investigation into the Low-Molecular-Weight Fluoropolymer for the Storage of Ultracold Neutrons

The experimental setup for examining the low-molecular-weight CF₃(CF₂)₃–O–CF₂–O–(CF₂)₃CF₃ fluoropolymer, which is a promising coating material for the walls of storage chambers for ultracold neutrons, is described. The results are detailed. The measurement data are interpreted in the model of a multilayer complex quantum-mechanical potential of the chamber walls.     

Analysis of the possible reasons for the suppression of superconductivity in the Y1−x PrxBa2Cu3Oy system on the basis of thermoelectric power data

The temperature dependence of the thermoelectric power in samples of Y_1−x Pr_xBa₂Cu₃O_y (x=0−0.6) is investigated. The principal parameters of the system of charge carriers are determined on the basis of an analysis of this dependence within a narrow-conduction-band model, and their variation with increasing praseodymium content is analyzed. It is found that an increase in x leads to a very weak increase in the electron filling and considerable broadening of the conduction band accompanied by strong localization of the charge carriers. It is concluded on the basis of a comparative analysis of the results obtained and data for the YBa₂Cu₃O_y system in the case of aliovalent substitutions in the barium and copper sites that the valence of praseodymium in Y_1−x Pr_xBa₂Cu₃O_y is very close to 3+. It is shown that there is a universal correlation between the effective width of the conduction band and the critical temperature following various cation substitutions in the Y-Ba-Cu-O system. It is concluded that the main reason for suppression of the superconducting properties of Y_1−x Pr_xBa₂Cu₃O_y is the strong modification of the band spectrum caused by praseodymium. Fiz. Tverd. Tela (St. Petersburg) 39, 1520–1525 (September 1997)     

On the nature of the Kaiser effect in metallic glasses

The Kaiser effect was observed in the measurement of acoustic emission (AE) during the course of uniaxial compression of the bulk samples of metallic glasses Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5 and Zr_52.5Ti₅Cu_17.9Ni_14.6Be_22.5. The field-ion microscopy study of bulk Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5 shows that this glass has a polycluster structure. This fact allows one to reveal the nature of AE appearing during the course of deformation of metallic glasses and to interpret the observed Kaiser effect. The dislocations generated at the intercluster boundaries and moving through the glass bulk are the sources of AE.     

Measurement of mass attenuation coefficients in some Cr,Co and Fe compounds around the absorption edge and the validity of the mixture rule

The total mass attenuation coefficients for elements Cr, Co and Fe and compounds CrCl₂, CrCl₃, Cr₂(SO₄)₃K₂SO₄·24H₂O, CoO, CoCl₂, Co(CH₃COO)₂, FePO₄, FeCl₃·6H₂O, Fe(SO₄)₂NH₄·12H₂O were measured at different energies between 4.508 and 14.142 keV using secondary excitation method. Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Br, Rb, Sr were chosen as secondary exciters. 59.5 keV γ-rays emitted from a ²⁴¹Am annular source were used to excite a secondary exciter and K_α(K-L₃, L₂) lines emitted by the secondary exciter were counted by a Si(Li) detector with a resolution of 160 eV at 5.9 keV. It was observed that mixture rule method is not a suitable method for determination of the mass attenuation coefficients of compounds, especially at an energy that is near the absorption edge. The obtained values were compared with theoretical values.      

On the mechanism of the broadening of the proton vibrational IR band in weak hydrogen bonds. Double adiabatic approximation

It is proposed that broadening of the ν_s (AH) IR band is due to the ν_s (AH) and ν_σ (AH…B) mode coupling and to the stochastic variation of the equilibrium distance R_e (A…B) modulating the proton vibration. The R_e disordering variation is caused by a coupling of the ν_σ mode with the low frequency oscillators (ν_Q) of the medium and of the complex as such. Besides, the (ν_σ, ν_Q) and (ν_s, ν_σ) couplings cause a ν_s frequency shift. Both the band broadening and the frequency shift increase with higher force constants responsible for (ν_σ, ν_Q) mode coupling. Furthermore the Q_i low frequency stochastic vibrations directly modulate the ν_σ (AH…B) vibration and the free AH groups stretching vibration (ν^o_s) causing some broadening at their bands which is however several times smaller than the ν_s band broadening in the complex. Several examples are reported to confirm the proposed model.     

Interrelation of the critical magnetic field H c2 and the residual resistivity for the two-band superconductor MgB2

An expression that describes the upper critical magnetic field H _c2 and generalizes the Gor’kov relation has been derived for the two-band two-gap superconductor MgB₂. The expression relates the upper critical magnetic field H _c2 to the residual resistivity and the parameters of the band structure and holds in the range from the clean limit to the dirty limit. The ratios of the relaxation times τ_π/τ_σ and the mean free paths of π- and σ-band electrons for MgB₂ samples with a low defect level and Mg(B_{1 ? x} C _x )₂ samples with a partial substitution of carbon for boron are determined from experimental data.     

Studies of the surface magnetic state of the Sr-M hexagonal ferrites near the phase transition at the Curie temperature

A study is reported of the temperature dependences of the hyperfine (HF) interaction parameters in a ～200-nm thick surface layer and in the bulk of macroscopic hexagonal ferrite crystals of the Sr-M type (SrFe₁₂O₁₉ and SrFe_10.2Al_1.8O₁₉). The method used for the measurements is Mössbauer spectroscopy with simultaneous detection of gamma quanta, characteristic x-ray emission, and electrons, which permits direct comparison of the HF parameters in the bulk and the near-surface layers of a sample. As follows from the experimentally determined temperature dependences of the effective magnetic fields, the fields at the nuclei of the iron ions located in a ～200-nm thick near-surface layer decrease with increasing temperature faster than those of the ions in the bulk. The transition to paramagnetic state in a ～200-nm thick surface layer was found to occur 3° below the bulk Curie temperature. This offers the first experimental evidence for the transition to paramagnetic state in a surface layer of macroscopic ferromagnets to take place below the Curie temperature T _c for the bulk of the crystal. It has been established that the transition temperature T _c (L) of a thin layer at a depth L from the surface of a crystal increases as one moves away from the surface to reach T _c at the inner boundary of the surface layer called critical. In the vicinity of T _c one observes a nonuniform state, with the crystal being magnetically ordered in the bulk but disordered on the surface. The experimental data obtained were used to construct a phase diagram of surface and bulk states for macroscopic magnets near the Curie (or Néel) temperature.     

Superluminal Signals and the Resolution of the Causal Paradox

The experimental evidence for electromagnetic signals propagating with superluminal group velocity is recalled. Transformations of space and time depending on a synchronization parameter, e₁, indicate the existence of a privileged inertial system. The Lorentz transformations are obtained for a particular e₁≠0. No standard experiment on relativity depends on e₁, but if accelerations are considered only e₁=0 remains possible. The causal paradox generated by superluminal signals (SLS) in the theory of relativity does not exist in the theory with e₁=0. The irrelevance of SLS for the Einstein, Podolsky and Rosen paradox is pointed out.     

On the critical temperature in the Al5 compounds

Using a generalized form of the Eliashberg gap equations which includes possible variations of the electronic density of states N(?) with energy, we have calculated the critical temperature for a model density of state which consists of a Lorentzian peak superimposed on a constant background density. By changing the value of the width in the Lorentzian form we discuss the change in T_c with disorder. When the width is reduced to zero T_c saturates (T^s_c) to some finite value which we can calculate. In this region, however, T_c drops sharply with increasing width so that the calculated values of T^s_c are much larger than can be achieved in practice.