H and K spin-lattice relaxation, ionic motion and Raman processes in the proton conducting KHSeO4 single crystal

The spin-lattice relaxation rates of ¹H and ³⁹K nuclei in KHSeO₄ crystals were studied in the temperature range 160-400 K. The spin-lattice relaxation recovery of ¹H nucleus in this crystal can be represented with a single exponential function, and the relaxation T₁⁻¹ curve of ¹H can be represented with the Bloembergen-Purcell-Pound (BPP) function. The relaxation process of ³⁹K with dominant quadrupole relaxation can be described by a linear combination of two exponential functions. T₁⁻¹ for the ³⁹K nucleus was found to have a very strong temperature dependence, T₁⁻¹=βT⁷. Rapid variations in relaxation rates are associated with critical fluctuations in the electronic spin system. The T⁷ temperature dependence of the Raman relaxation rate is shown here to be due to phonon-magnon coupling.     

A study of molecular motion and Raman processes in K3H(SO4)2 and KHSO4 single crystals by observation of H and K spin-lattice relaxation

The spin-lattice relaxation rates for ¹H and ³⁹K nuclei in K₃H(SO₄)₂ and KHSO₄ single crystals, which are potential candidate materials for use in fuel cells, were determined as a function of temperature. The spin-lattice relaxation recovery of ¹H can be represented for both crystals with a single exponential function, but cannot be represented by the Bloembergen-Purcell-Pound (BPP) function, so is not related to HSO₄ motion. The recovery traces of ³⁹K, which predominantly undergoes quadrupole relaxation, can be represented by a linear combination of two exponential functions. The temperature dependences of the relaxation rates for ³⁹K can be described with a simple power law T₁⁻¹=αT². The spin-lattice relaxation rates for the ³⁹K nucleus in K₃H(SO₄)₂ and KHSO₄ crystals are in accordance with a Raman process dominated by a phonon mechanism.     

Observation of an oscillatory behavior of the zero-field μ+ spin relaxation function in pure copper

High precision measurements were carried out on the zero field (ZF) spin relaxation function of μ⁺ in copper at 14.8 K, where μ⁺ is nearly localized. The time spectrum obtained shows an oscillatory deviation from the dynamical Kubo-Toyabe relaxation function. The deviation seems to come mainly from the distribution of local field different from a gaussian distribution.     

Proton relaxation times in 7LiCl and 6LiCl solutions

Measurements of the proton spin-lattice relaxation times have been made as a function of concentration and temperature in aqueous solutions of ⁷LiCl and ⁶LiCl. The difference in the relaxation times for two isotopic solutions of the same concentration and temperature is small, corresponding to a difference n reciprocal relaxation times of 0·004 sec^-1. c at 25°c, where c is the molarity of the solutions. This value decreases with increasing temperature. It is shown that the difference in relaxation times arises solely from the magnetic dipole interaction between the ⁷Li ion nucleus and water protons. The concept of a long-lived, rigid hydrated complex around the Li ion is shown to be inconsistent with the results.     

Non-secular part of nuclear dipolar broadening detected by zero-field spin relaxation of positive muon

The zero-field spin relaxation function of μ⁺ observed in ZrH₂ has revealed that the second moment of the nuclear dipolar broadening is five times larger than the high-field value. This experiment clearly demonstrates the recovery of the non-secular part of dipolar interaction between unlike spins. A general expression of zero-field relaxation function is presented to account for a slow modulation of random fields on μ⁺ found at room temperature.     

The optical conductivity of free carriers in GaAs

The optical conductivity of free electrons in polar semiconducting compounds has recently been calculated by use of a generalized Boltzmann equation derived from the equation of motion of the quantum density matrix. This reduces to the quasi-classical Boltzmann transport equation in the low frequency limit: the optical conductivity thus obtained spans a spectral range from around 30cm^?1 to 1.2 × 10⁴cm^?1 in GaAs. In this paper, the optical conductivity is calculated for GaAs as a function of carrier concentration in terms of a frequency dependent relaxation time which reduces to the usual relaxation time in the limit of low frequencies and an elastic scattering mechanism. The low frequency limit of the relaxation time is used to estimate the mobility as a function of carrier concentration. The frequency dependent relaxation time is given for GaAs at 298 K over the spectral region from 45 cm^?1 to 2.3 × 10³cm^?1 for carrier concentrations from 3.4 × 10¹⁵cm^?3 to 8.7 × 10¹⁸cm^?3.     

Vibrational relaxation of KrF* and XeCl* by rare gases

A steady-state, chemiluminescence technique has been used to measure effective rate constants for vibrational relaxation as a function of vibrational level for KrF^* in collisions with He, Ne, and Ar and XeCl^* with Ar. The effective rate constants reported include contributions to relaxation due to intersystem crossing between theB andC states, in addition to direct relaxation within theB state. The relevance of these results to the understanding of previous measurements in KrF and XeCl lasers is discussed.     

On the Brownian motion in a double-well potential in the overdamped limit

The Brownian motion of a particle in a double-well potential is considered and the position correlation function (excluding inertial effects) for the potential V(x)=ax²/2+bx⁴/4 is evaluated first by averaging the governing Langevin equation over its realizations. The exact solution is then obtained via matrix continued fractions by using a representation, which symmetrizes the recurrence relations for the observables generated by the averaging procedure leading to convergence of these recurrence relations unlike the previous approaches to the problem. A reliable approximate solution based on the exponential separation of the time scales of the fast intrawell and low overbarrier relaxation processes associated with the bistable potential is also given. It is shown that a knowledge of the three characteristic relaxation times (the integral, effective and the longest relaxation times) of the position correlation function allows one to accurately predict the relaxation behavior of the system in the overdamped limit for all time scales of interest.     

Paramagnetic relaxation of spin polarized 3He at coated glass walls

In this second in a series of three papers on wall relaxation of ³He-spins we discuss relaxation in metal-coated glass cells in terms of hyperfine coupling to paramagnetic conduction electrons at the Fermi surface. This scales with the square of the work function of the coating and thereby also with its He-adsorption energy. In this sense we investigate coatings with particularly low work function and adsorption energy, namely Cs and Cs-suboxides. Although we observe a suppression of relaxation rates by two orders of magnitude as compared to bare Pyrex and fused silica walls, their temperature dependence still shows the same Arrhenius dependence as observed for bare substrates, instead of a T ^3/2 dependence expected for a metallic surface. From this finding we conclude that, on one hand, the surface coverage is not complete and, on the other hand, the relaxation at the alkali surface itself is extremely slow. This finding is supported, too, by a semi-empirical estimate based on measured relaxation rates at ordinary metal surfaces, rescaled then with the respective dependence on adsorption energy.     

The T 1 and T 2 Relaxation Times Distribution for the 35Cl and 14N NQR in Micro-composites and in Porous Materials

The paper describes the results of an experimental study of the ³⁵Cl and ¹⁴N nuclear quadrupole resonance in composite and porous materials, the influence of the environment and the crystallite size of powder on the nuclear quadrupole resonance line widths, as well as on the spin–spin and spin–lattice relaxation times. It is established that the spin–lattice relaxation time has a unimodal distribution, and the spin–spin relaxation time—bimodal distributions for all the investigated samples. The idealized distribution function of the relaxation times is obtained on the assumption that the concentration of inhomogeneities and relaxativity decreases with an increasing distance from the surface into the interior of the crystallite exponentially. It is shown that the model with the spin diffusion explains the shortening of the decay signal with decreasing grain size, but this is not confirmed by the experimental distribution of relaxation times obtained by means of the inverse Laplace transformation.     

NMR proton relaxation and chemical exchange in the system H16 2O/H17 2O-[2H6]dimethylsulphoxide

NMR proton relaxation rates of normal and ¹⁷O enriched water in a mixture of 68 mol% water and 32 mol% [²H₆]dimethylsulphoxide were measured for temperatures between 298 K and 183 K. In the range between 240 K and 204 K the limit of fast proton-proton exchange between H¹⁶ ₂O and H¹⁷ ₂O is not obeyed, and relaxation curves deviate from mono-exponential behaviour. By fitting the relaxation curves to a model of NMR two-phase relaxation the proton-proton exchange rate within the aqueous component could be obtained. With decreasing temperature, proton-proton exchange slows down and a residence time of about 125 ms at 215 K is found, but it becomes faster again for still lower temperatures. From the phase-averaged relaxation rates of water in the ¹⁷O enriched mixtures, the ¹⁷O induced proton relaxation rate was derived as a function of temperature. This yields the rotational correlation times of the water molecule in the mixture and the dipolar spin-lattice coupling parameter. The latter is considerably lower than the one predicted from the geometry of water.     

NMR spin-lattice relaxation of the129Xe nucleus of xenon gas dissolved in various isotropic liquids

The spin-lattice relaxation time of the¹²⁹Xe nucleus of natural xenon gas dissolved in various isotropic liquids, acetonitrile, benzene, carbon tetrachloride and cyclohexane, was studied as a function of temperature at the magnetic fields of 9.4 and 4.7 T. The utilization of hydrogenated and deuterated benzene and cyclohexane reveals that the intermolecular¹²⁹Xe-¹H dipole-dipole interaction constitutes an important relaxation mechanism in hydrogenated solvents. According to this interpretation the interaction is rather strongly temperature-dependent, and increases with increasing temperature. An important observation of an experimental nature is also noted, namely convective flow present in non-spinning sample tubes at elevated temperatures disturbs inversion-recovery measurements and leads to erroneous and unreliable relaxation time values.     

NMR study of pure and doped β-LiAl

The NMR spin-lattice relaxation time, T_I, has been measured as a function of temperature for both ⁷Li and ²⁷Al in pure and doped β-LiAl alloys. Compositions with ⁷Li concentration in the range 48.3–54.5% and doping in the form Li₅₀Al_50?xM_x, where M = Ag or In, were studied. The relaxation rates T₁^?1 for the ²⁷Li and the ²⁷Al resonances were found to be peaked functions of temperature with the maxima for ⁷Li appearing at composition dependent temperatures. The ²⁷Al maxima always appeared at a lower temperature, independent of composition, and the ²⁷Al maximum relaxation rate was a strong function of composition in contrast with ⁷Li where the maximum rate was only weakly dependent on composition. The principle relaxation mechanisms are identified as dipole-dipole coupling in the ⁷Li and coupling of the ²⁷Al quadrupole moment to electric field gradients. The temperature dependence of these rates is attributed to the thermally activated diffusion of vacancies of a non-thermal origin in the Li sub-lattice. These vacancies are also responsible for the fluctuating electric field gradients. The results have been analyzed to give the Li diffusion coefficients with associated activation energies and estimates of the vacancy concentration as functions of alloy composition.     

Study of the paraelectric behavior of OH− ions in alkali halides with optical and caloric methods II.: Dynamics of the dipole alignment

The relaxation behavior of OH^? dipole centers in ten alkali halides was studied with electro-optical and electro-caloric methods as a function of applied field, temperature and host lattice system. The reorientation kinetics of the 〈100〉 oriented OH^? dipoles can be fitted successfully to a phonon-assisted (90°) orientational tunneling model. Below 5°K the observed time dependence of the optical dichroism and the T^?1 dependence of the relaxation time gives clear evidence for the predominance of one-phonon processes, while above 5°K the T^?4 dependence indicates multi-phonon processes. It could be demonstrated that in the one-phonon region of the dipole relaxation a population inversion among the dipole levels (with subsequent phonon emission) can be achieved after a fast reversal of the field polarity. An attempt is made to discuss the observed strong variation of the relaxation time (12 orders of magnitude) with the host lattice in terms of a tunneling matrix element renormalized due to the anisotropic lattice distortion around the defect.     

Analysis of the AC electrical data in the Davidson-Cole dielectric representation

The representation of the AC electrical data in the complex plane reveal two major classifications of the relaxation processes known as ideal (Debye) and non-ideal (non-Debye) types. The non-Debye relaxation has been empirically observed via Cole-Cole (C-C), Davidson-Cole (D-C), and Havriliak-Negami (H-N) responses. Each of these non-Debye relaxations is visualized with an equivalent circuit similar to the ideal relaxation. Both ideal and C-C relaxations reveal semicircular behavior in the complex plane while D-C and H-N relaxations deviate from the usual semicircular loci known as skewed behavior. The extracted equivalent circuit elements are essentially non-Debye for both D-C and H-N relaxations possessing complexity in the relaxation time. The analytical method of extracting these elements in conjunction with the empirical parameters of the D-C relaxation is described using conventional (real) domain and complex domain. The curve fitting procedure provided extremely small error for the complex domain analysis. The behavior of the D-C relaxation function and the depression parameter β are also discussed using ωτ=1 and ωτ≠1 corresponding to the maximum of the imaginary part of the impedance (Z^*) or permittivity (ε^*).     

Co2+ spin-lattice relaxation narrowing of 19F NMR in KCoF3

The temperature dependence of the ¹⁹F NMR linewidth ΔH in KCoF₃ has been measured over the entire paramagnetic solid state region. The dramatic decrease in the hyperfine-broadened, exchange narrowed ΔH that occurs above 200 K is interpreted as arising from fast Co²⁺ single-ion, spin-lattice relaxation. A model theory of the temperature dependence of ΔH is given which incorporates the interplay of exchange and spin lattice relaxation effects on the decay of the spin autocorrelation function.     

Nuclear spin-lattice relaxation in antiferromagnetic RbMnF3

The ⁸⁷Rb and ¹⁹F nuclear relaxation rates in antiferromagnetic RbMnF₃ are calculated as a function of temperature. The large difference in the relaxation rates of both nuclei as well as their temperature dependences are well accounted for over a considerable temperature range by a two-magnon process induced by the dipolar and “contact” parts of the hyperfine interaction.     

Influence of magnetic impurities on proton spin relaxation of water in clay

The¹H nuclear magnetic spin relaxation of water in slurry of kaolin clay was investigated in the presence of magnetite (black iron oxide, Fe₃O₄) at 0.2 T and room temperature. The water spectra at high magnetite contents showed two different resonances, presumably from surface-associated water and free interstitial water. The difference in observed resonance frequencies increased as much as 200 ppm with increasing magnetite content. The apparent nuclear magnetic resonance intensity decreased biexponentially as a function of magnetite added. The observedT ₂^* values at low magnetite contents were in accordance with the predicted values from the resonance intensities and the estimated magnetic susceptibilities. TheT ₁ relaxation was multiexponential in character, so a uniform penalty program was used for the analysis of distribution. At 0.2 T for¹H, kaolin slurry containing less than 5.5 ppm magnetite did not differ significantly from magnetite-free clay in the longitudinal relaxation rates of water. However, higher concentrations of magnetite produced features in theT ₁ distribution significantly different from those of magnetite-free clay. TheT ₂ could be approximated by monoexponential relaxation, probably because the fast-decaying components relaxed before they could be recorded. The apparent transverse relaxation ratesR ₂ increased linearly as a function of magnetite content. On the basis of the comparison of spin-echo and Carr-Purcell-Meiboom-Gill data, an empirical relation was derived to describe the signal loss due to diffusion. It can be expressed by a power function of magnetite amount, which is multiplied by the sum of volume-dependent and volume-independent terms.     

Temperature dependence of21Ne,83Kr,and131Xe quadrupole relaxation and of xenon diffusion in polyatomic solvents

The main aim of the present work is to contribute, by an extension of the experimental data base, to the understanding of quadrupole relaxation of nuclei of noble gases dissolved in molecular liquids. We have performed temperature dependent spin-lattice relaxation rate measurements of²¹Ne,⁸³Kr, and¹³¹Xe in various non-aqueous solvents (e.g. in methanol, ethanol, n-butanol, acetone, acetonitrile, benzene, carbon tetrachloride, N,N-dimethylformamide, dodecane, tetradecane, p-xylene, and hexafluorobenzene). In nine liquids we also measured translational diffusion coefficients of dissolved xenon as a function of temperature by the NMR spin-echo technique, obtaining partly the very first diffusion data for a number of systems. The comparison of the remarkable low activation energies for the noble gas nuclear quadrupole relaxation with that of the noble gas diffusion reveals that both seem to be closely connected. There are strong hints that the nuclear relaxation process follows an empirical “Dη ^γ =A correlation” found previously by Evans and co-workers for the tracer diffusion of noble gases in polyatomic liquids. For almost all solvents γ decreases from¹³¹Xe to²¹Ne parallel with a decrease of the corresponding activation energy for the quadrupolar relaxation. Possible physical reasons for this behavior are briefly discussed. Essential qualitative results in this paper were found to agree with two MD computer simulations for¹³¹Xe relaxation in benzene and methanol. Further MD simulations are proposed which are obviously required for the deeper understanding of the experimental results found in the present paper.     

Investigation of impurity diffusion in dilute alloys by nuclear magnetic resonance

The diffusion of Al in a Cu: 3.8 at % Al alloy has been investigated by observing the rotating-frame nuclear magnetic relaxation time T_1π of ²⁷Al as a function of temperature. It is shown that relaxation measurements of the solute atoms in a dilute alloy provide the correlation time of the diffusive motion of these atoms, if quadrupolar interactions form the main contribution to the relaxation time. From the correlation times the Al-diffusion coefficient in the alloy has been determined.