Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

T-odd correlations in (n, αγ) reactions

The T-odd correlation (k _α · [σ × k _γ])(k _α · k _γ), where σ is the vector of the neutron polarization and the symbols k denote the respective linear momenta (all vectors are unit ones), in the sequential alpha-gamma cascade induced by a thermal-neutron capture is studied. The study is performed in the one-resonance approximation. Both the final-state interaction of the alpha particle with the residual nucleus and the actual T-noninvariant phase shift are considered as possible origins of the correlation. The problem of suitable target isotopes is analyzed. Related correlations in other neutron- and proton-induced reactions are discussed.     

Diffraction of electrons in the CubicTi5O5 superstructure of titanium monoxide

Annealed titanium monoxide TiO_1.087 has been studied by the electron diffraction method. A cubic model of the Ti₅O₅ superstructure (Ti₅O₅ (Ti₉₀?₁₈O₉₀??₁₈)) of nonstoichiometric titanium monoxide Ti _x O _z has been proposed on the basis of experimental data and representations about the disorder-order transition channel. It has been shown that reflections observed on the electron diffraction pattern are identified in the space group $Pm\bar 3m$ . The period of the unit cell of the cubic Ti₅O₅ superstructure is larger than that for the B1 basic disordered structure of Ti _x O _z monoxide by a factor of 3. The disorder-order transition channel Ti _x O _z (space group $Fm\bar 3m$ )-Ti₅O₅ (space group $Pm\bar 3m$ ) includes 75 superstructure vectors of seven stars {k ₁₀}, {k ₇}, {k ₆₍₁₎}, {k ₆₍₂₎}, {k ₄₍₁₎}, {k ₄₍₂₎}, and {k ₁}. The distribution functions of Ti and O atoms over the sites of the cubic Ti₅O₅ (space group $Pm\bar 3m$ ) superstructure have been calculated.     

Atomic-vacancy ordering in the lowest tungsten carbide W2C

Atomic-vacancy ordering in the lowest tungsten carbide W₂C with an L′3-type basic hexagonal structure has been studied by neutron diffraction and X-ray diffraction. In the temperature range 2700–1370 K, the only ordered phase of the lowest tungsten carbide is shown to be the trigonal ?-W₂C phase (space group P $\overline 3 $ 1m). This trigonal ?-W₂C phase is found to form via a disorder-order phase transition channel, which includes three superstructure vectors (k ₁₅ ⁽¹⁾ , k ₁₅ ⁽²⁾ , k ₁₇ ⁽¹⁾ ) of two Lifshitz stars ({k ₁₅}, {k ₁₇}, and to be described by two long-range order parameters (η₁₅, η₁₇). The distribution function of carbon atoms in the trigonal ?-W₂C superstructure is calculated, and the corresponding region of the allowable values of the long-range order parameters η₁₅ and η₁₇ is found. Symmetry analysis of other possible superstructures of the lowest tungsten carbide W₂C is performed, and the physically acceptable sequence of phase transformations in W₂C is determined.     

Exact solution of the Boltzmann equation in the relaxation approximation,existence of negative differential conductivity for certain types of energy bands and its implication for the fluctuation spectrum and the noise temperature

The Boltzmann equation for the distributionf _k of a system of charged particles obeying classical statistics in a uniform fieldF, $$\frac{{\partial f_k }}{{\partial t}} + F\frac{{\partial f_k }}{{\partial k}} = \smallint d^3 k'(W_{kk'} f_{k'} - W_{k'k} f_k ),$$ will be solved analytically for a special class of transition ratesW _kk′=const·h _k ·ν _k ·ν _k′ for any initial distribution.h _k is the Maxwell distribution andν _k >0 can be interpreted as ak-dependent relaxation frequency. The constant relaxation approximation (ν _k =ν) will be used to discuss the drift velocitiesu for all the fields and temperaturesT for certain types of band structuresE(k). Bands with lineark-dependence for largek give rise to drift velocities saturating for large fields. For bands with the periodicity of the reciprocal lattice, the zero drift-theorem has been proved. It states that $$\mathop {\lim }\limits_{F \to \infty } u (F,T) = \mathop {\lim }\limits_{T \to \infty } u (F,T) = 0$$ for all the periodic band structures. This theorem is even correct for a generalW _kk′ if certain restrictions are made. Finally, making use of the Markov character of the conditional probability (Green's function) solution of the Boltzmann equation, the velocity fluctuation spectrumS is calculated forE(k)=A(1?cosa k). It will be shown thatS(F, T, 0) remains positive for the critical field and all temperatures, and therefore the noise temperature diverges on approaching the critical field.     

Spatial dispersion in polariton spectra of CuGaS2 crystals

The unmodulated and wavelength-modulated reflectivity spectra of CuGaS₂ crystals for the polarization E ‖ c, k ⊥ c at 77 and 8 K have been studied. The states n=1, 2, and 3 of A excitons and n=1 and 2 of B and C excitons are established. The luminescence spectra from the surface at k ‖ c and k ⊥ c are obtained. The fine structure of the reflectivity spectra of excitons are analyzed with due regard for the normal and oblique incidence of light onto the crystal surface. The main parameters of the A, B, and C excitonic series are determined such as the energies of the longitudinal and transverse excitons Γ₄ (E ‖ c) for states n=1 and 2, the longitudinal and the transverse mass of excitons in CuGaS 2, and the effective masses of electrons (m _c1*) and holes (m _v1*, m _v2*, m _v3*). It is shown that the mass m _v1* in the upper valence band at k ‖ c equals (0.7–0.8)m ₀ and at k ⊥ c, 1.87m ₀.     

Ti5O5 superstructures of cubic titanium monoxide

A cubic model is proposed for the Ti₅O₅ (Ti₅?O₅□ ≡ Ti₉₀?₁₈O₉₀□₁₈) superstructure of nonstoichiometric titanium monoxide Ti _x O _z with double imperfection. The unit cell of the cubic Ti₅O₅ superstructure has the threefold lattice parameter of the unit cell of the basis disordered B1 structure of Ti _x O _z monoxide and belongs to space group $Pm\bar 3m$ . The channel of the disorder-order transition, i.e., Ti _x O _z (space group $Fm\bar 3m$ )-Ti₅O₅ (space group $Pm\bar 3m$ ), includes 75 superstructure vectors of seven stars {k ₁₀}, {k ₇}, {k ₆₍₁₎}, {k ₆₍₂₎}, {k ₄₍₁₎}, {k ₄₍₂₎}, and {k ₁}. The distribution functions of Ti and O atoms over the sites of the cubic Ti₅O₅ superstructure are calculated. A comparison of the X-ray and electron diffraction data obtained for ordered TiO_1.087 monoxide with the theoretical simulation results supports the existence of the cubic Ti₅O₅ superstructure. The cubic (space group $Pm\bar 3m$ ) Ti₅O₅ superstructure is shown to be a high-temperature structure relative to the well-known monoclinic (space group C2/m) superstructure of the same type.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Phosphorus(V)corrole- Porphyrin Based Hetero Trimers: Synthesis,Spectroscopy and Photochemistry

‘Axial-bonding’-type hetero trimers have been constructed by employing a simple ‘inorganic’ reaction such as axial bond formation of main group element containing phosphorus corrole. The approach is simple and modular in nature. The architecture of these hetero trimers such that, while a phosphorus(V)corrole forms the basal scaffolding unit, either two free-base porphyrins [(H ₂ ) ₂ –PCor] or Zn^II porphyrins [(Zn) ₂ –PCor] occupy the two axial sites via an aryloxy bridge. Both hetero trimeric species have been completely characterized by mass (FAB), UV/Vis, proton nuclear magnetic resonance spectroscopies and also by the differential pulse voltammetric method. Comparison of their spectroscopic and electrochemical data of these trimers with those of the corresponding reference compounds reveal that there is no apparent ring-to-ring interactions in these ‘vertically’ linked hetero trimers. Reduced fluorescence quantum yields were observed for [(H ₂ ) ₂ –PCor] and [(Zn) ₂ –PCor] when compared to corresponding monomeric chromophores. Finally, a comparison is made between the presently reported phosphorus(V)corrole based hetero arrays and the previously reported analogous arrays based on Ge(IV)corrole with regard to their spectroscopic properties and photochemical activities.     

Pseudogap behavior in the emery model for the electron-doped superconductor Nd2 − x Ce x CuO4: Multiband LDA + DMFT + Σk approach

We propose a generalization of the LDA + DMFT + Σ _k approach to the multiband case, in which correlated and uncorrelated states are present in the model simultaneously. Using the multiband version of the LDA + DMFT + Σ _k approach, we calculate the density of states and spectral functions for the Emery model in a wide energy interval around the Fermi level. We also obtain the Fermi surfaces for the electron-doped high-temperature superconductor Nd_{2 ? x} Ce _x CuO₄ in the pseudogap phase. The self-energy part Σ _k introduced additionally to take into account pseudogap fluctuations describes the nonlocal interaction of correlated electrons with collective Heisenberg short-range spin fluctuations. To solve the effective impurity model, the numerical renorm-group (NRG) method is used for the DMFT equations. Good qualitative agreement of the Fermi surfaces calculated using the LDA + DMFT + Σ _k approach and experimental angle-resolved photoemission spectroscopic data is attained. The stability of the dielectric solution with charge transfer in the Emery model with correction for double counting is analyzed in the Appendix.     

Analytische Näherung für elastische Wellen in anisotropen kubischen Kristallen

It is shown that the frequencies ω_α(k) and the polarisation vectorse _α(k) (α=1, 2, 3) of the elastic waves in anisotropic cubic crystals can be described exactly as Taylor series in the parameter \(\delta = \frac{{c_{11} - c_{12} - 2c_{44} }}{{c_{12} + c_{44} }}\) for all wave number vectorsk. As the expansion functions of these series include no elastic constants, δ is taken as the proper anisotropy parameter. The series are converging very fast for almost all substances and may be broken off after the third expansion term.     

On the temperature behavior of second sound and Poiseuille flow

The linearized Peierls equation for the phonon densityN (k λ,r t) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants byk-dependent relaxation rates. For the normal process relaxation time the behaviorτ _N (k λ)∝|k|^?p for smallk is assumed. Taking into account thisk-dependence ofτ _N explicitly and avoiding an expansion with respect toΩτ _N (kλ) before performing the necessary integration overk yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments.     

Coordination preference and magnetic properties of FeII assemblies with a bis-azole bearing 1,2,4-triazole and tetrazole

With a new bis-azole molecular fragment (Htt) bearing 1,2,4-triazole and tetrazole, a mononuclear complex [Fe(tt)₂(H₂O)₄]·2H₂O (1), a trinuclear complex [Fe₃(tt)₆(H₂O)₆]·2H₂O (2) and a 1D coordination polymer [Fe(tt)(Htt)₂]BF₄·2CH₃OH (3) were obtained by varying reaction conditions. Htt acts either as an anionic or neutral ligand depending upon the reaction medium and pH. Thermal variation of spin states of 1–3 were investigated in the range 77–300?K by ⁵⁷Fe M?ssbauer spectroscopy. 1 totally remains in high-spin state over the entire temperature range whereas no spin crossover was evidenced in 2. Nearly 1:1 high-spin and low-spin population ratio is found in 3, which remains constant over the entire temperature range investigated.     

Influence of the degenerate d level and of the Jahn-Teller effect on the manganite electronic structure calculated in the tight-binding approximation

E(k) dispersion curves for the charge carriers in the LaMnO₃-like perovskites were calculated for the basic types of canted antiferromagnetic ordering of the Mn sublattice in the framework of the tight-binding approximation. The E(k) spectrum of the antiferromagnetic structures was calculated for the first time taking into account the degeneracy of the Mn e _g level and the Jahn-Teller distortion of the cubic perovskite structure. This calculation involved diagonalization of the 8×8 Hamiltonian matrix. Analytical expressions for the E(k) function at separate points and symmetry lines of the Brillouin zone were derived. The calculations showed that the properties of the La_1?x Ca_xMnO₃ system do not have electron-hole symmetry.     

Twinning and short-range order in ordered titanium monoxide

Electron diffraction was used to study the annealed titanium monoxide TiO_1.087 containing the monoclinic ordered phase Ti₅O₅. The diffraction pattern of titanium monoxide in the (112)* _B1 plane of the reciprocal lattice of the parent B1 cubic structure contains not only structural, superstructural, and additional reflections but also a system of planar diffuse strips. It has been established that part of the additional reflections are twins of the superstructure reflections of the monoclinic ordered phase; the twinning plane is the ( $\overline 1 \overline 1 1$ ) plane of the reciprocal lattice of the parent cubic phase. The diffuse scattering contours cover finite plane areas in the reciprocal space characterized by the wave vectors K ₁₀₀ ～ ± (h + 0.07)k ₁₀₀, K ₀₁₀ ～ ±(k + 0.07)k ₀₁₀, and K ₀₀₁ ～ ±(l + 0.07)k ₀₀₁ in the B1 structure. The diffuse scattering is caused by short-range displacement order. Short-range substitution order and the corresponding diffuse scattering are absent.     

Rotation of the plane of polarization and linear birefringence of sound in hematite below the morin point

The linear antiferromagnetic birefringence of sound in hematite (α-Fe₂O₃) residing in the collinear easy-axis phase (L ‖ C ₃) below the Morin point is experimentally studied. The plane of polarization of a linearly polarized transverse acoustic wave propagating along the trigonal axis C ₃ of a hematite crystal placed in a magnetic field H applied in the basal plane (H ⊥ C ₃, 3.5 ≤ H ≤ 15 kOe) is found to rotate after a temperature-driven orientational phase transition to the easy-axis state. The angle of rotation exhibits a 180° angular dependence on the direction of the magnetic field in the basal plane and varies from zero to ～π/2. Numerical estimates suggest that the conditions necessary for rotation of the plane of polarization through appreciable angles (～π/2) can be satisfied in the easy-axis phase at orientational phase transition temperatures close to the Morin point, which actually takes place in the fields employed. The results obtained are described sufficiently well by the theory of linear antiferromagnetic birefringence of sound (E.A. Turov) and confirm its main conclusions.     

Spatial dispersion of the lattice polarizability and the properties of the large polaron

The polaron states are studied in crystals with optical phonon dispersion of the type ω²(k) = ω ₀ ² + u ² k ². The appearance and propagation of a local polarization in such a medium is treated as the evolution of a wave packet having a nonzero group velocity. This approach enables one to construct a consistent theory of moving self-trapped electron. The total energy and the effective mass of a slowly moving polaron are found and are shown to be strongly dependent on the dispersion parameter σ = u/ω₀.     

Bis-Benzimidazolyl Diamide Based Fluorescent Probe for Copper(II): Synthesis, Structural and Fluorescence Studies

A new fluorescent probe based on a bis-benzimidazole diamide N ²,N ^2′-bis[(1-ethyl-benzimidazol-2-yl)methyl]biphenyl-2,2′-dicarboxamide ligand L ₁ with a biphenyl spacer group and a Copper(II) trinuclear metallacycle has been synthesized and characterized by X-ray single crystallography, elemental and spectral (FT-IR, ¹H & ¹³C NMR, UV-Visible) analysis. The fluorescence spectra of L ₁ in MeOH show an emission band centered at 300 nm. This band arises due to benzimidazolyl moiety in the ligating system. The diamide L ₁ in the presence of Cu²⁺ show the simultaneous ‘quenching’ of (300 nm) and ‘enhancement’ of (375 nm) emission band. Similar fluorescence behavior was found in water–methanol mixture (9:1). The new emission band at 375 nm is attributed to intra ligand π–π* transition of the biphenyl moiety. L ₁ exhibited high selectivity and sensitivity towards Cu²⁺ in both the medium over other common metal ions like Ni²⁺, Co²⁺, Mn²⁺, Mg²⁺, Zn²⁺, Pb²⁺ and Hg²⁺. The binding constant with Cu²⁺ was calculated by the Benesi-Hildebrand equation. Selective “off-on-off” behavior of L ₁ in methanol has also been studied. The fluorescent intensity of 375 nm bands in L ₁ enhances (turns-on) upon addition of Cu²⁺ and quenches (turn-off) upon addition of Na₂-EDTA.     

Dual-wavelength diode-pumped laser operation of N p-cut and N g-cut Tm:KLu(WO4)2 crystals

Simultaneous continuous-wave laser oscillation at two wavelengths has been observed and studied in a diode-pumped monoclinic N _p-cut Tm:KLu(WO₄)₂ for different transmission of the output coupler. The maximum output power reached 1.15 W with a slope efficiency of 20.4 % with respect to the absorbed power for polarization parallel to the N _m optical axis. In an analogous N _g-cut crystal, the dual-wavelength laser operation is accompanied by polarization switching with increasing pump power and the switching point depends on the output coupling. The thresholds are slightly higher, and the slope efficiency reached a maximum of 25.5 % for polarization parallel to N _m at low pump levels, but at high pump levels, the oscillating polarization is parallel to N _p, reaching maximum output power of 3.09 W. Simple modelling with rate equations taking into account reabsorption losses explains qualitatively the complex behavior observed in the continuous-wave laser experiments with this anisotropic biaxial laser crystal.