Contrasting routes to the Kostka coefficients of λ [boxvr] n (ln)-permutational module expansions for 6n8: Applications to NMR spin clusters under SU(mn)×Ln spin symmetries

Aspects of the higher-n λ( _n) permutational modules associated with Young subgroups of various highly-branched high-n fold algebras, which are pertinent to identical spin NMR clusters, are presented for λ [boxvr] _n (or λ [boxvR] n), aRota p-tuple or number partition; the method of optimal choice for deriving the Λ_[λ′] Kostka coefficients, found in {[λ′]} sets derived from λ permutational module expansions, rests on the ordering of the λ-(shape) to the self-associated diagram(s) in the dominance hierarchy. Hence, physical insight into these cage-cluster NMR systems is developed both from these properties and from the inter-related induced symmetries of GL(n, ) and _n groups. From these associated combinatorial, mapping or scalar invariant aspects of SU(mn)× _n symmetry, one may define the [A]_n( _n) systems of [AX]_n NMR problems in a general semi-topological limit. This corresponds to a high-n _n limit in which the individual spin cluster exhibits a lack of any (intracluster) ‘magnetic equivalence’ properties.     

Study of nuclear quadrupole interactions and quadrupole Raman processes of Ga and Ga in a β-Ga2O3:Cr single crystal

Nuclear magnetic resonance (NMR) data and the spin–lattice relaxation times, T₁, of ⁶⁹Ga and ⁷¹Ga nuclei in a β-Ga₂O₃:Cr³⁺ single crystal were obtained using FT NMR spectrometry. Four sets of NMR spectra for ⁶⁹Ga (I = 3/2) and ⁷¹Ga (I = 3/2) were obtained in the crystallographic planes. The ⁶⁹Ga and ⁷¹Ga nuclei each had two chemically inequivalent Ga_I and Ga_II centers. Each of the ⁶⁹Ga and ⁷¹Ga isotopes yielded two different central NMR resonance lines originating from Ga_I and Ga_II sites. The nuclear quadrupole coupling constants and asymmetry parameters of ⁶⁹Ga_I, ⁶⁹Ga_II, ⁷¹Ga_I, and ⁷¹Ga_II centers in a β-Ga₂O₃:Cr³⁺ crystal were obtained. Analysis of the EFG tensor principal axes (PAs) for Ga nuclei and the ZFS tensor PAs for the Cr³⁺ ion confirmed that the Cr³⁺ paramagnetic impurity ion substitutes for the Ga³⁺ ion in the oxygen octahedron. In addition, the temperature dependencies of the ⁶⁹Ga and ⁷¹Ga relaxation rates were consistent with Raman processes, as T₁⁻¹ ∝ T². Even though the Cr³⁺ impurities are paramagnetic, the relaxations were dominated by electric quadrupole interactions of the nuclear spins in the temperature range investigated.     

Multiple-Photon Dynamics in Molecules: A New Approach to High Resolution Spectroscopy of Highly Excited Vibrational States

Multi-photon transitions with two simultaneously interacting IR laser fields lead to final excited states with frequenciesnν = n₁ν₁+ n₂ν₂, withnthe total number of photons absorbed and (n,n₁,n₂) = (2, 1, 1), (3, 2, 1), (4, 1, 3), etc. The nature of the actual transition is determined by shift measurements, where the lasers are frequency-tuned by δν_iin opposite directions keeping the sum frequency,nν, resonant with the molecular transition. This technique opens a new spectral range for multi-photon transitions and a unique identification of the observed features. Forn₁andn₂both positive the excitation will lead to a “normal” up–up multi-photon transition. Many three- and four-photon transitions in the ν₃vibrational ladder of SF₆could be resolved with a resolution of 1 MHz, as well as four new two-photon transitions. As long asn₁+ n₂≥ 0, one of the twon_imay be negative resulting in an, e.g., up–down excitation pathway with its particular selection rules. The up–down excitations are demonstrated both for one- and two-photon transitions using the frequency shift technique. The different possible excitation schemes which meet the resonance condition for these transitions lead to interference effects and local couplings to highly excited states. Changes in resonance frequency for a one-photon transition (n= 1), due to these effects, are demonstrated. Evidently, the radiative coupling of participating levels to high-lying or quasi-continuum states may drastically change for different δν_ileading both to ac Stark shift and transition probability variations.     

Improved Estimation of Protein Rotational Correlation Times fromN Relaxation Measurements

In the study of protein backbone dynamics by¹⁵N relaxation measurements, an initial estimation of the isotropic global correlation time, τ_m, is usually obtained from the averageT₁/T₂ratio of nuclear spins that do not exhibit slow internal motion and withT₂values not significantly shortened by chemical or conformational exchange processes. Different methods have been used for identification of the rates of internal motion. However, the number of nuclear spins included in the τ_mestimation is often larger than the number that ultimately can be fitted to a single-order parameter,S², implying that some nuclear spins involved in the initial τ_mestimation actually have an effective internal correlation time, τ_e, not as fast as assumed. As a consequence, τ_mis underestimated, since internal motion reduces theT₁/T₂ratio. This situation becomes more obvious if the molecule has a large τ_mvalue because the reduction inT₁/T₂ratio arising from internal motion is more significant than for molecules with smaller τ_mand the same degree of internal motion. This Communication describes a more reliable method for identifying nuclear spins which should be excluded from the τ_mestimation because of insufficiently rapid internal motion. This results in an improved τ_mvalue, giving a much better agreement between the number of nuclear spins fitted successfully to a single-order parameter,S², and those used in the τ_mestimation.     

A new metallic state in two dimensions

We report the discovery of a new and unexpected kind of metal in two dimensions (2D), which exists in the presence of scattering by local magnetic moments. The experiment was carried out on a 2D electron system in silicon, where the local magnetic moments have been induced by disorder and their number was varied using substrate bias (V_sub). In the new metal, the conductivity decreases as σ(n_s,T)=σ(n_s,T=0)+A(n_s)T² (n_s – carrier density) to a non-zero value as temperature T→0. In three dimensions, this T² dependence is well known, and results from Kondo scattering by local magnetic moments. In 2D, however, the existence of a metal with dσ/dT>0 is very surprising. As the number of local moments is reduced, the range of temperatures [T<T_m(V_sub)] where they dominate transport becomes smaller. For T>T_m, we observe the usual 2D metallic behavior with dσ/dT<0.     

Integrable structure of melting crystal model with two -parameters

This paper explores integrable structures of a generalized melting crystal model that has two q-parameters q₁,q₂. This model, like the ordinary one with a single q-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions. The partition function is thereby a function of an infinite number of coupling constants t₁,t₂,… and an extra one Q. There is a compact expression of this partition function in the language of a 2D complex free fermion system, from which one can see the presence of a quantum torus algebra behind this model. The partition function turns out to be a tau function (times a simple factor) of two integrable structures simultaneously. The first integrable structure is the bigraded Toda hierarchy, which determines the dependence on t₁,t₂,…. This integrable structure emerges when the q-parameters q₁,q₂ take special values. The second integrable structure is a q-difference analogue of the 1D Toda equation. The partition function satisfies thisq-difference equation with respect to Q. Unlike the bigraded Toda hierarchy, this integrable structure exists for any values of q₁,q₂.     

Internal dynamics of hydroxymethyl rotation from CH2 cross-correlated dipolar relaxation in methyl-β- -glucopyranoside

Conventional relaxation parameters (T₁⁻¹, T₂⁻¹, and NOE), obtained at different temperatures and magnetic fields, are reported for the hydroxymethyl (C6) carbon in methyl-β- -glucopyranoside in a D₂O/DMSO cryosolvent. These data are interpreted with the Lipari–Szabo model. In addition, two-field measurements of longitudinal and spin-locked relaxation rates related to the cross-correlated carbon–proton dipole–dipole interactions for the same carbon are reported. The complete data set consisting the conventional and cross-correlated relaxation parameters is interpreted using a new “hybrid” approach, in which the Lipari–Szabo model for the auto-correlated spectral densities is combined with the two-site jump model for the cross-correlated spectral densities, with the global correlation time as a common parameter. The two-site jump rates thus obtained are in reasonable agreement with the ultrasonic relaxation measurements, and have reasonable temperature dependence.     

Dispersive optical constants of glassy AsSe1−xTex system

The compositional dependence of the optical constants, the refractive index n, and the absorption index k, of the AsSe_1−xTe_x thin films with 0<x<1.0 were determined in the spectral range of 400–2500 nm. The maximum value of the refractive index n, is shifted toward the long wavelength by increasing the Te content in the examined system. The values of the forbidden energy gap of the system have been determined and were correlated with the type and the amount of chemical bonds formed by the increasing Te content in the AsSe_1−xTe_x glassy system. The value of the dispersion energy E_d exhibits low value at the composition containing the same atomic percent of Se and Te.     

Electron heating in a submicron-size n GaAs wire

We have studied electron heating in a submicron-size GaAs wire from 4.2 K to 50 K. We find that the energy relaxation rate for the electrons is of the form τ_E⁻¹ = α + βT_eⁿ where α, β are constants and T_e is the electron temperature. We associate the temperature-independent term with a quasi-elastic surface scattering process in which an electron losses 1% of its energy at each collision. The temperature dependent term may be due to electron-phonon scattering. It is possible to fit the data to 2 < n < 3.     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Changes in Porcine Muscle Water Characteristics during Growth—An in Vitro Low-Field NMR Relaxation Study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field ¹H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T₂ relaxation data imparted the existence of three distinct water populations, T_2b, T₂₁, and T₂₂, with relaxation times of approximately 1–10, 45–120, and 200–500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T₂₁. It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T₂₁, during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T₂₁ time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

Spectroscopy and dynamics of the excited singlet and triplet states of 2,3-, 2,4- and 2,5-difluorobenzaldehyde vapors

Emission and absorption spectra have been measured for 2,3-, 2,4- and 2,5-difluorobenzaldehyde vapors at different temperatures. The observed emission consists of the T₁(n, π*) phosphorescence accompanied by the weak S₁(n, π*) delayed fluorescence for all the molecules. The vibrational analyses of the emission spectra based on the results of the DFT calculations indicate that the observed emission originates from only the stable (anti) conformer. It is inferred from the temperature dependence of the phosphorescence intensity that the T₁(n, π*) → T₂(π, π*) internal conversion and/or the reverse T₁(n, π*) → S₁(n, π*) intersystem crossing contribute to the decrease in the phosphorescence intensity upon increasing temperature. The obtained spectroscopic data include the Raman spectrum of 2,3-difluorobenzaldehyde.     

Sensitivity studies on certain optical techniques used to find n, k and relative thicknesses for thin films

The sensitivities of different combinations of three optical functions in the determination of n, k and relative thickness for absorbing thin films have been studied by computer plotting of error parallelepipeds. An abitrary standard of sensitivity was used to identify the regions of high sensitivity over ranges of n and k between 0.1 and 10.0 and of d/λ between 0.005 and 0.16. In general, few of the 12 combinations examined showed any extensive regions of high sensitivity unless the optical functions could be measured to high accuracy ( 0.1% ). The best combinations were T_pφ_tsφ_tp and T_sT_pφ_ts, using angles of incidence of about 75°.     

Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Flow propagators, used for the study of advective motion of brine solution in porous carbonate and sandstone rocks, have been obtained without the influence of Nuclear Magnetic Resonance (NMR) relaxation times, T₁ and T₂. These spin relaxation mechanisms normally result in a loss of signal that varies depending on the displacement ζ of the flowing spins, thereby preventing the acquisition of quantitative propagator data. The full relaxation behaviour of the system under flow needs to be characterised to enable the implementation of a true quantitative measurement. Two-dimensional NMR correlations of ζ − T₂ and T₁ − T₂ are used in combination to provide the flow propagators without relaxation weighting. T₁ − ζ correlations cannot be used due to the loss of T₁ information during the displacement observation time Δ. Here the moments of the propagators are extracted by statistical analysis of the full propagator shape. The measured displacements (first moments) are seen to correlate with the expected mean displacements for long observation times Δ. The higher order moments of the propagators determined by this method indicate those obtained previously using a correction were overestimated.     

Optical properties of AsSe1.5−xTex glassy system

Thin AsSe_1.5−xTe_x films with 0x<1.5 have been prepared by a thermal vacuum evaporation technique onto quartz and glass substrates kept at room temperature (300 K). The optical constants, the refractive index, n, and the absorption index, k, of the films were determined for the investigated compositions of different thickness values (100–300 nm) using spectrophotometric measurements of the transmittance, T, and the reflectance, R, at normal incidence in the spectral range 400–2500 nm. The obtained values of both n and k were found to be independent of the film thickness within the above mentioned thickness range. The estimated indirect and direct optical energy gap decreased as tellurium content increased in the parent sample AsSe_1.5. The values of dispersion energy, E_d, and lattice dielectric constant, _L, of the system have been determined and correlated with the type and amount of chemical bonds and the relative proportion of the constituent elements in the examined compositions.     

The calculated spectra of the azanaphthalenes

A modified INDO (intermediate neglect of differential overlap) method is used to calculate the electronic spectra of naphthalene and some mono-, di-, and tetraazanaphthalenes. The technique is capable of reproducing the better classified bands of this series within a rms error of 1000 cm⁻¹.The four lowest π-π^* bands of naphthalene are well represented; a fifth band reported at 52,600 cm⁻¹, and generally assigned ¹B_2u(π-π^*), may be ¹B_3g(π-π^*) borrowing intensity. The lowest excited singlet state calculated for quinoline is n → π^*, estimated nearly degenerate with the lowest π-π^*, while that for isoquinoline is calculated π-π^*; experimental evidence supports the π-π^* assignment in both cases, but the corresponding absorption in quinoline appears complex. Of the diazanaphthalenes examined (with two nitrogens in one benzenoid ring) all are calculated to have one n-π^* transition before the first π-π^* except phthalazine, in which two n-π^* transitions are calculated to be the lowest lying. This is in accord with experimental evidence to date, although the nature of the observation in phthalazine is reinterpreted as one ¹B₂(n-π). 1,4,5,8-tetrazanaphthalene is predicted to have a group theoretically forbidden n-π^* excited state as low as 21,000 cm⁻¹, and should prove interesting experimentally. Even though n-π^* excited states are often calculated to be the lowest lying, none of these compounds are predicted to have an “n” orbital as homo.Further interpretations of the spectra of the azanaphthalenes are made in view of the calculations. Theoretical limitations of the method employed for this study are discussed.     

Asymmetric phase diagram and phase separation in Pr0.5−δCa0.2+δSr0.3MnO3 (−0.04δ0.04)

We present electric and magnetic properties of polycrystalline Pr_0.5−δCa_0.2+δSr_0.3MnO₃, for δ between −0.04 and 0.04, where the hole concentration is n=0.5+δ. In this series, we study the effects of moving n away from 0.5 on both, the phase diagram and phase separated state. We found that the low temperature ferromagnetic fraction X_FM continuously decreases when n increases. As a result, the samples with n<0.5 (large X_FM) exhibit metallic resistivity at low T while for n>0.5 the insulating state predominates. We construct a detailed T–n phase diagram showing the asymmetries around half-doping.     

NMR study of proton transport in the inorganic ion-exchange compounds SnO2·nH2O and TiO2·nH2O

Proton NMR relaxation times (T₂, T₁, T_1? and T₁D) are reported for hydrous tin oxide (SnO₂·nH₂O) and hydrous titania (TiO₂·nH₂O) in the temperature range 135 K<T<336 K at 60 and 20 MHz. The data show proton transport including exchange between three environments: (1) surface hydroxyl groups, (2) “acid solution” in micropores (diameter <100 Å) and (3) “acid solution” in macropores (diameter>1000 Å). The NMR behaviour has many features in common with that of adsorbed water systems. A consistent interpretation of both NMR and conductivity data is presented.     

Prevention of spinning induced sample deterioration during long time solid state NMR experiments of quadrupolar spin systems

A simple solution is proposed to prevent a solid state polycrystalline sample from deterioration during long time high speed spinning experiments in solid state NMR. It is found that if a certain percentage (40% volume) of polyethylene glycol (PEG, (HO–CH₂–(CH₂–O–CH₂–)_n–CH₂–OH)_n) is mixed with the sample that are subject to deterioration, the quality of the sample can be maintained for a long time under high speed spinning for a few days or longer, sufficient for multi-dimensional and/or low-sensitivity experiments. Both 1D and 2D experimental results are shown to support this idea.     

Al satellite transition spectroscopy (SATRAS) of polycrystalline aluminium borate 9Al2O3 · 2B2O3

²⁷Al NMR spectra of polycrystalline aluminium borate 9Al₂O₃ · 2B₂O₃ have been measured at 104, 130 and 156 MHz. The parameters of the quadrupole interaction and the isotropic chemical shifts have been obtained by fitting the CT/MAS pattern and consideration of the inner satellite transitions m = 3/2 ↔ 1/2 and m = −1/2 ↔ −3/2. The gain in spectral resolution concerned with the observation of the MAS lines of the inner satellites leads to complete separation of the signals of AlO₆, AlO₅ and AlO₄ polyhedra. Also signals of structural groups of one and the same coordination number can be distinguished. Experimental and theoretical lineshape calculations are compared.