A simulation based method to assess inversion algorithms for transverse relaxation data

NMR relaxometry is a very useful tool for understanding various chemical and physical phenomena in complex multiphase systems. A Carr-Purcell-Meiboom-Gill (CPMG) [P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1991] experiment is an easy and quick way to obtain transverse relaxation constant (T₂) in low field. Most of the samples usually have a distribution of T₂ values. Extraction of this distribution of T₂s from the noisy decay data is essentially an ill-posed inverse problem. Various inversion approaches have been used to solve this problem, to date. A major issue in using an inversion algorithm is determining how accurate the computed distribution is. A systematic analysis of an inversion algorithm, UPEN [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data, Journal of Magnetic Resonance 132 (1998) 65–77; G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data II. Data spacing, T₂ data, systematic data errors, and diagnostics, Journal of Magnetic Resonance 147 (2000) 273–285] was performed by means of simulated CPMG data generation. Through our simulation technique and statistical analyses, the effects of various experimental parameters on the computed distribution were evaluated. We converged to the true distribution by matching up the inversion results from a series of true decay data and a noisy simulated data. In addition to simulation studies, the same approach was also applied on real experimental data to support the simulation results.     

29Si NMR in solid state with CPMG acquisition under MAS

A remarkable enhancement of sensitivity can be often achieved in ²⁹Si solid-state NMR by applying the well-known Carr–Purcell–Meiboom–Gill (CPMG) train of rotor-synchronized π pulses during the detection of silicon magnetization. Here, several one- and two-dimensional (1D and 2D) techniques are used to demonstrate the capabilities of this approach. Examples include 1D ²⁹Si{X} CPMAS spectra and 2D ²⁹Si{X} HETCOR spectra of mesoporous silicas, zeolites and minerals, where X = ¹H or ²⁷Al. Data processing methods, experimental strategies and sensitivity limits are discussed and illustrated by experiments. The mechanisms of transverse dephasing of ²⁹Si nuclei in solids are analyzed. Fast magic angle spinning, at rates between 25 and 40 kHz, is instrumental in achieving the highest sensitivity gain in some of these experiments. In the case of ²⁹Si–²⁹Si double-quantum techniques, CPMG detection can be exploited to measure homonuclear J-couplings.     

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG ¹H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T_2,short and 1/T_2,long were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T₁/T₂ ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T₂/T_2,eff is derived as a function of the T₁/T₂ ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T₁–T₂ correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T₁–T₂ experimental correlations maps were corrected for the T₁/T₂ effect using the derived T₂/T_2,eff correction factor.     

Self-broadening, self-shift and self-mixing in the ν2, 2ν2 and ν4 bands of NH3

Using Fourier-transform spectra (Bruker IFS 120 HR, resolution ≈0.004 cm⁻¹) of NH₃ in nine branches of the ν₂, 2ν₂ and ν₄ bands, self-broadening and self-shift as well as self-mixing coefficients have been determined at room temperature (T=295 K) for more than 350 rovibrational lines located in the spectral range 1000–1800 cm⁻¹. A non-linear least-squares multispectrum fitting procedure, including line mixing effects, has been used to retrieve successively the line parameters from 11 experimental spectra recorded at different pressures of pure NH₃. The accuracies of self-broadening coefficients are estimated to be better than 2% for most lines. The mean accuracies of line-mixing and line-shift data are estimated to be about 15% and 25%, respectively. The results are compared with previous measurements and with values calculated using a semiclassical model based upon the Robert–Bonamy formalism that reproduces rather well the systematic experimental J and K quantum number dependencies of the self-broadening coefficients.The results concerning line mixing demonstrate a large amount of coupling between the symmetric and asymmetric components of inversion doublets mainly in the ν₄ band. The line mixing parameters are both positive and negative. More than two thirds of the lines studied here have a positive shift coefficient. However, for most of them the shift coefficients are negative in the 2ν₂ band. They are positive for the R branch of the ν₂ band and for the ^PR and ^RP branches of the ν₄ band. For the other branches they are both positive and negative. Some components of inversion doublets illustrate a correlation between line mixing and shift phenomena demonstrated by a quadratic pressure dependence of line position.     

Radical-Recombination Luminescence of the Uranyl Nitrate Complex in the Adsorbed State

We have investigated the luminescence of uranyl nitrate molecules on the surface of powdery SiO₂ upon excitation by UV light (PhL) and hydrogen atoms (radical-recombination luminescence (RRL)). It has been found that the PhL and RRL spectra have a clearly defined vibrational structure. The luminescence peaks of the adsorbed UO₂ ^2– ion are characterized by a systematic longwave shift from the same peaks of crystalline uranyl nitrate (by 230–430 cm^–1 at 130 K). Moreover, in the adsorption centers the vibration frequencies of UO₂ ^2– are 20–80 cm smaller than in crystalline salt and the RRL bands are 150–350 cm^–1 (130 K) wider than the corresponding PhL bands.     

Generalized beam propagation factor of hard-edged circular apertured diffracted Bessel–Gaussian beams

Based on the truncated second-order moments method on the cylindrical coordinate systems and the incomplete gamma function, an analytical expression of the generalized beam propagation factor (M_G² factor) of hard-edged circular apertured diffracted Bessel–Gaussian beams is derived and illustrated numerically. It is shown that the M_G² factor of hard-edged diffracted BGBs mainly depends on the truncation parameter δ and the beam parameters m and η. The results can be reduced to that for the non-truncated Bessel–Gaussian beams case and that for the truncated fundamental Gaussian beams case under certain conditions, respectively. The power fraction is also discussed analytically and numerically.     

Investigation of the Fine Rotational Structure of the Fourth (500; A 1, E) Overtone of the AsH3 Molecule

The results of investigations into the high-resolution Fourier spectrum of the AsH₃ molecule first registered in the range 9720–9900 cm^–1 with a resolution of 0.015 cm^–1 are given in the present paper. Lines of (500; A ₁) and (500; E) bands are interpreted by the method of combination differences. The spectroscopic constants of the examined arsine bands are determined by solving the inverse problem. They have allowed 98 rotational energy levels (with J ^max = 6) to be reproduced with errors close to the experimental ones.     

The Mechanism of Magnetically Tuned Singlet–Triplet Avoided Crossings in the ÃA2– A1 40 Band of Thioformaldehyde H2C=S

Magnetically tuned singlet–triplet perturbations in the 4¹Ã¹A₂–2¹3¹ã³A₂ system of thioformaldehyde, found in ortho-rotational states (I = 1, the two hydrogen spins parallel) have been identified as being caused by vibronic spin–orbit coupling. This perturbation mechanism has been confirmed in several avoided crossings observed in this work for para states (I = 0, hydrogen spins antiparallel) which are much stronger. Parametrization of the theory has led to a quantitative understanding of the experimental frequency-field relations, and to an accurate prediction of the rovibrational energies of the triplet state. This in turn permitted the detection of about 100 Doppler-limited 2¹3¹ã³A₂–0^{0 1}A₁ rovibronic transitions which led into fine structure states. The combined data was then used to determine a set of rotational, fine, and hyperfine triplet-state parameters, the term value T₀(2¹3¹ã³A₂) = (16 685.385 ± 0.002) cm⁻¹, and the spin–orbit vibronic singlet–triplet coupling constant, W_ST = (0.0691 ± 0.0016) cm⁻¹. A large number of frequency perturbations observed in the crossings, ranging from 2 to 300 MHz, can be explained with this single parameter.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

Dynamic recrystallization of austenite during hot plastic deformation

The kinetics of dynamic recrystallization is dependent on the thermomechanical conditions in which plastic deformation is taking place. To determine the timet _p needed for the onset of dynamic recrystallization, experimental work was performed on low-carbon austenite to check the validity of the equationW= 2·1 × 10^–1 Z ^–0.94, whereW= t_pexp(–Q/RT),Z represents the Zener-Hollomon parameter, and Q=276 kJ mol^–1.     

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.     

Propagation parameters of the beam extracted from a diode pumped Nd:YAG ceramic slab laser with a hybrid stable–unstable resonator

We analyze the propagation properties of the beam extracted from a diode pumped ceramic Nd:YAG slab laser adopting a hybrid stable–unstable resonator. Such a resonator produces a beam characterized by an Hermite–Gauss mixture-like distribution in one transverse direction and a hard-edge diffracted distribution on the other transverse direction. The beam propagation parameters M_x² and M_y² are measured for different values of the diodes driving current. We obtain a beam parameter product smaller than 3 mm mrad in both transverse directions and in the whole range of powers, up to an extraction of 220 W in a QCW regime.     

Pitfalls in the Measurement of Metabolite Concentrations Using the One-Pulse Experiment in in Vivo NMR: Commentary on “On Neglecting Chemical Exchange Effects When Correcting in VivoP MRS Data for Partial Saturation”

In an article in a previous issue of the Journal of Magnetic Resonance, Ouwerkerk and Bottomley (J. Magn. Reson.148, pp. 425–435, 2001) show that even in the presence of chemical exchange, the dependence of saturation factors on repetition time in the one-pulse experiment is approximately monoexponential. They conclude from this fact that the effect of chemical exchange on the use of saturation factors when correcting for partial saturation is negligible. We take issue with this conclusion and demonstrate that because saturation factors in the presence of chemical exchange are strongly dependent upon all of the chemical parameters of the system, that is, upon all T₁'s and M₀'s of resonances in the exchange network and upon the reaction rates themselves, it is problematic to apply saturation factor corrections in situations in which any of these parameters may change. The error criterion we establish reflects actual errors in quantitation, rather than departures from monoexponentiality.     

Conformational Equilibria in Polypeptides. II. Dihedral-Angle Distribution in Antamanide Based on Three-Bond Coupling Information

The use of³Jcoupling information in deriving dihedral-angle restraints for polypeptide-structure determination in the presence of conformational equilibria is illustrated withantamanide,cyclo(–Val¹–Pro²– Pro³– Ala⁴– Phe⁵– Phe⁶– Pro⁷– Pro⁸– Phe⁹– Phe¹⁰–). The experimental basis comprises accurate three-bond coupling constants as obtained from both homonuclear [C. Griesinger, O. W. Sørensen, and R. R. Ernst,J. Magn. Reson.75,474 (1987)] and heteronuclear [J. M. Schmidt,J. Magn. Reson.124,298 (1997)] exclusive correlation spectroscopy (E.COSY). For the backbone and side-chain dihedral angles in the nonproline residues, φ and χ₁, respectively, probability-distribution functions are derived and evaluated on the basis of χ²statistics and significance estimates. Various motional models are considered in the quantitative compilation of molecular-geometry parameters from spin-system parameters. From the³Jcoupling analysis, antamanide is found to possess a very flexible structure which is consistent with the results previously obtained in homonuclear NOE and¹³C–T₁relaxation studies. To fully agree with experiment, rotamer equilibria must be assumed for almost all of the torsions investigated in the peptide.     

Supertransferred hyperfine interaction in magnetic insulators (II)

The important mechanisms of supertransferred hyperfine (STHF) interactions in N–O–M chains are briefly discussed: (i) spin polarization ofns states in the N-ion due to the s-d exchange interaction,H _STHF ^sd ; (ii) contributions of spin-polarized states of the intervening O-ion,H _STHF ^II ; (iii) transfer of d-electrons of the M-ion to emptyns states in the N-ion,H _STHF ^III . The dependence ofH _STHF upon the N–O–M bond configuration, electronic structure, and orbital state of the M-ion is presented in a convenient form. The STHF interactions in the chains Sn⁴⁺–O^2––Fe³⁺, Cr³⁺ in compounds with slightly distorted Perovskite structure are considered. The STHF field in the chain Sn⁴⁺–O^2––Cr³⁺ is shown to change the sign within the range of angles near 170°. This conclusion is in line with published data on the isoelectronic chain Sn⁴⁺–O²–Mn⁴⁺ in the compounds Ca_1–x Sr _x MnO₃. The results obtained for the N–O–Fe³⁺ chain are rationalized by the predicted angular dependence ofH _STHF=+ cos + cos². Features of the STHF interactions in N–O–M chains with an M-ion in an orbital degenerate state are examplified by a preliminary analysis of N–O^2––V³⁺ chains in orthovanadites.     

Magnetic and magnetotransport properties of Co-doped manganites with perovskite structure

A systematic study of the doping of the Mn-sites by cobalt in three series of manganites — La_0.76Ba_0.24(Mn_1−xCo_x)O₃ single crystals, La_2/3Ba_1/3(Mn_1−xCo_x)O₃ and La(Mn_1−xCo_x)O₃ ceramics has been performed. It was found that La(Mn_1−xCo_x)O₃ annealed at 800°C in the range 0.4x0.9 is a mixture of ferromagnetic domains with ordered Mn and Co ions and ionically disordered spin-glass domains. In the quenched samples the fraction of spin-glass-type component increases strongly. The La_2/3Ba_1/3(Mn_1−xCo_x)O₃ solid solutions exhibit also an evidence for phase separation in the range 0.5x0.8. All the La(Mn_1−xCo_x)O₃ samples show an insulating behavior, however, magnetoresistance reduces strongly when the cobalt content rises to x=0.5. The La_0.76Ba_0.24(Mn_1−xCo_x)O₃ single crystals show first-order phase transition below their Curie points associated with a change of ground state of the Co²⁺ ions. The magnetic phase diagrams are depicted. The results are discussed in terms of positive Mn³⁺–O–Mn⁴⁺, Mn³⁺–O–Mn³⁺, Mn⁴⁺–O–Co²⁺ and negative Mn⁴⁺–O–Mn⁴⁺, Co²⁺–O–Co²⁺, Co²⁺–O–Mn³⁺ superexchange interactions as well as Co²⁺ and Mn⁴⁺ ionic ordering.     

Effects of interactions and disorder on the compressibility of two-dimensional electron and hole systems

The compressibility χ of dilute two-dimensional electron and hole gases in GaAs semiconductor structures has been studied in the ranges of the interaction parameter r_s=1–2.5 and r_s=10–30 for the electron and hole system, respectively. Nonmonotonic dependence of χ^-1 with an upturn at low carrier densities is observed. Despite the large difference in r_s the behavior of χ^-1 in both systems can be accurately described by the theory of nonlinear screening of disorder by the carriers.     

Torsion-rotation far-infrared spectrum of O-18 methanol

High-resolution Fourier transform spectra have been recorded from 15–470 cm^–1 for the far-infrared trosion-rotation band of O-18 methanol in the vibrational ground state. So far, 57 subbands have been assigned in the 15–220 cm^–1 region for a wide range of rotational and torsional states, and their J-independent origins have been determined to an estimated accuracy of ±0.01 cm^–1. The observed origins were found to deviate in many cases by several tenths of a cm^–1 from the values calculated with the previous molecular parameters. Together with 4 known microwave origins, the new data have been fitted to a model torsion-rotation Hamiltonian in order to refine the set ofb-type molecular constants for the ground state. With the new parameter set, the experimental subband origins are reproduced with an rms error of ±0.02 cm^–1, representing a substantial improvement over the earlier situation. The spectroscopic results have also been of great assistance with our assignments of optically-pumped FIR laser emission in CH₃ ¹⁸OH, in providing FIR data for checking the identification of the IR-pump/FIR-laser transition systems through combination loop relations.     

Fluorescence studies and semiempirical calculations on alkali ion indicators

Two newly synthesized cryptands act as sensitive Na⁺- and K⁺-selective indicators for cation concentrations above 20 M. The fluorescence properties change markedly upon cation binding. In addition, the free ligands exhibit a pronounced sensitivity to pH, which is considerably lower for the cation complexes. Time resolved fluorescence is characterized by a decay time of about 5 ns that is attributed to the diprotonated protolytic state of the uncomplexed ligands. Semiempirical calculations show the systematic influence of the nitrogen lone pairs or the N–H bond on the stability of the system. The cause of the strong fluorescence intensity increase observed upon protonation of the fluorescent cryptands may be attributed to an increase in the S₁–T _x energy gap as a consequence of bridgehead nitrogen protonation.This is a peer-reviewed conference proceeding article from the Third Conference on Methods and Applications of Fluorescence Spectroscopy, Prague, Czech Republic, October 18–21, 1993.     

Positron annihilation study of spin-crossover in [Fe x Zn1−x (ptz)6](BF4)2 single crystals

Positron lifetime measurements were carried out on [Fe _x Zn_1–x (ptz)₆](BF₄)₂ single crystals in the temperature range of 72–300 K. Complementary Doppler broadening spectra were also recorded at room temperature. The probability of the formation of o-Ps (lifetime 500–1400 ps) was between 10–30%. Both the spin density and the lattice parameters of the sample affected the lifetime of o-Ps through the ortho-para conversion and the pick-off annihilation, respectively. The positron annihilation technique proved to be a sensitive detector of the spin-crossover⁵T₂ ¹A₁ and of the concomitant phase transformation.