We studied deuteron NMR spectra and spin - lattice relaxation of deuterated acetone-d(6), adsorbed into zeolites NaX (1.3) and NaY(2.4) at 100% coverage of sodium cations. At temperatures roughly below 160 K the deuterons are localized and their NMR characteristics are determined by CD3 rotation and rotational oscillations of acetone molecules. In NaX the CD3 rotation and rotational oscillations about the twofold axis of acetone dominate the spectra below 100 K, while above it oscillations also about other axes become important. In NaY dominant features are related to methyl tunnelling and to a smaller extent to rigid acetones, before the rotational oscillations about twofold axis start to prevail above 40 K. The analysis of the strongly non-exponential magnetization recovery was done by applying the recently introduced method (Ylinen et al., 2015 [12]), improved here to take into account the limited fast recovery at the level crossings, 10% at omega(t) =omega(0) and 28% at omega(t) = 2 omega(0). At first the experimental recovery is fitted by three exponentials with adjustable weights and decay rates. Then these quantities are calculated from activation energy distributions and known expressions for the deuteron relaxation rate. In NaY two distinctly separate activation energy distributions were needed, the dominant one being very broad. The use of three distributions, two of them covering practically the same energies as the broad one, lead to a somewhat better agreement with experiment. In general the theoretical results agree with experiment within experimental scatter. As the final result the mean activation energies and widths are obtained for activation energy distributions.

Deuteron NMR spectra and spin-lattice relaxation were studied experimentally in zeolite NaY(2.4) samples containing 100% or 200% of CD3OH or CD3OD molecules of the total coverage of Na atoms in the temperature range 20-150K. The activation energies describing the methyl and hydroxyl motions show broad distributions. The relaxation data were interpreted by improving a recent model (Stoch et al., 2013 [16]) in which the nonexponential relaxation curves are at first described by a sum of three exponentials with adjustable relaxation rates and weights. Then a broad distribution of activation energies (the mean activation energy A0 and the width σ) was assumed for each essentially different methyl and hydroxyl position. The correlation times were calculated from the Arrhenius equation (containing the pre-exponential factor τ0), individual relaxation rates computed and classified into three classes, and finally initial relaxation rates and weights for each class formed. These were compared with experimental data, motional parameters changed slightly and new improved rates and weights for each class calculated, etc. This method was improved by deriving for the deuterons of the A and E species methyl groups relaxation rates, which depend explicitly on the tunnel frequency ωt. The temperature dependence of ωt and of the low-temperature correlation time were obtained by using the solutions of the Mathieu equation for a threefold potential. These dependencies were included in the simulations and as the result sets of A0, σ and τ0 obtained, which describe the methyl and hydroxyl motions in different positions in zeolite.

A new method is introduced for analyzing deuteron spin–lattice relaxation in molecular systems with a broad distribution of activation energies and correlation times. In such samples the magnetization recovery is strongly non-exponential but can be fitted quite accurately by three exponentials. The considered system may consist of molecular groups with different mobility. For each group a Gaussian distribution of the activation energy is introduced. By assuming for every subsystem three parameters: the mean activation energy E0, the distribution width σ and the pre-exponential factor τ0 for the Arrhenius equation defining the correlation time, the relaxation rate is calculated for every part of the distribution. Experiment-based limiting values allow the grouping of the rates into three classes. For each class the relaxation rate and weight is calculated and compared with experiment. The parameters E0, σ and τ0 are determined iteratively by repeating the whole cycle many times. The temperature dependence of the deuteron relaxation was observed in three samples containing CD3OH (200% and 100% loading) and CD3OD (200%) in NaX zeolite and analyzed by the described method between 20K and 170K. The obtained parameters, equal for all the three samples, characterize the methyl and hydroxyl mobilities of the methanol molecules at two different locations.

Nuclear magnetic resonance (NMR) provides means to investigate molecular dynamics at every state of matter. Features characteristic for the gas phase, liquid-like layers and immobilized methanol-d4 molecules in NaX and NaY zeolites were observed in the temperature range from 300 K down to 20 K. The NMR spectra at low temperature are consistent with the model in which molecules are bonded at two positions: horizontal (methanol oxygen bonded to sodium cation) and vertical (hydrogen bonding of hydroxyl deuteron to zeolite framework oxygen). Narrow lines were observed at high temperature indicating an isotropic reorientation of a fraction of molecules. Deuteron spin–lattice relaxation gives evidence for the formation of trimers, based on observation of different relaxation rates for methyl and hydroxyl deuterons undergoing isotropic reorientation. Internal rotation of methyl groups and fixed positions of hydrogen bonded hydroxyl deuterons in methyl trimers provide relaxation rates observed experimentally. A change in the slope of the temperature dependence of both relaxation rates indicates a transition from the relaxation dominated by translational motion to prevailing contribution of reorientation. Trimers undergoing isotropic reorientation disintegrate and separate molecules become localized on adsorption centers at 166.7 K and 153.8 K for NaX and NaY, respectively, as indicated by extreme broadening of deuteron NMR spectra. Molecules at vertical position remain localized up to high temperatures. That indicates the dominating role of the hydrogen bonding. Mobility of single molecules was observed for lower loading (86 molecules/uc) in NaX. A direct transition from translation to localization was observed at 190 K.

The nonlinear behavior of a phonon echo signal in high-temperature superconductors is studied experimentally. It is demonstrated that conventional consideration of anharmonic effects is insufficient for comprehensive explanation of the echo signal behavior. It is shown that the nonlinear properties of the phonon echo should be taken into account when the phonon echo is used as a means for studying superconductor parameters. An increase in the elastic nonlinearity in iron-doped yttrium ceramics is found.

Deuteron NMR spectra and relaxation were studied at the resonance frequency of 46MHz in polycrystalline fully and partly deuterated (NH(4))(2)ZnCl(4) between 300 and 5K. Spectral components confirm existence of ammonium positions with different potential symmetry, resulting in two- and threefold reorientation of ammonium ions. The temperature dependence of the spin-lattice relaxation rate discloses two time constants in the whole range. The fitting procedure allows the separation into contributions from subsystems of ions in respective potentials. Two relaxation rate maxima are attributed to ions performing threefold uniaxial reorientation at low temperatures. The lower-temperature maximum is observed at T36K. With increasing temperature reorientations about remaining axes start to contribute leading to the other maximum near 100K. The other category of ammonium ions gives rise to the maximum at about 50K. Below this temperature the dominant motion seems to be 180( composite function) reorientations about one twofold axis according to observed spectra. Consistent picture of ion mobility is accomplished for 5%, 30%, 70% and 100% deuterated compounds.

The phonon echo excited by radio-frequency pulses in superconducting MgB2 in external magnetic field was studied. Using the echo technique two contributions to ultrasound attenuation are observed: low-temperature relaxation, which depends on the magnetic field, and a decay connected to the superconducting energy gap at temperatures close to Tc. The value of about 7kBTc for the energy gap was extracted from the experimental data.

Deuteron spin-lattice relaxation via the motion-dependent part of the electric quadrupole interaction is discussed in partly and fully deuterated ammonium ions of ammonium hexachlorometallates. The dominant motion at temperatures T>50K is normally 120 degrees reorientations of the ammonium ions. In some hexachlorometallates the instantaneous equilibrium directions of the nitrogen-hydrogen vectors make a certain angle Delta with the metal-nitrogen vectors and they appear in groups of six near each metal-hydrogen vector. Each N-D vector jumps between the six directions of one group and this motion (called limited jumps) dominates the deuteron relaxation at lower temperatures. In some samples one direction of each group seems to become more populated than the others when the deuteration degree exceeds a certain value and the ammonium ions become ordered. A model is derived for the relaxation rate in the absence of tunnelling splittings, which includes the effects of reorientations and limited jumps also in the ordered structure, where the limited-jump rate of a N-D vector to the preferred direction, r(p), differs from that to the nonpreferred direction, r(n). The obtained relaxation rate depends, in addition to the angle Delta, also on the ratio d=r(n)/r(p). The effect of d is discussed and estimates for it are presented on the basis of earlier experiments. The recent model for the deuteron relaxation in NH(3)D(+) ions, including the effect of proton tunnelling, is shortly reviewed. At lowest temperatures the motional rates can be dominated by corresponding incoherent tunnelling and the rate of the incoherent tunnelling contributing to limited jumps is argued to be clearly larger than that of the incoherent tunnelling contributing to approximately 120 degrees rotations.

Deuteron NMR relaxation and spectra were studied at the resonance frequency of 46 MHz in polycrystalline (ND(4))(2)PtCl(6) between 300-5 K. The relaxation rate maximum near 50 K is about 53% smaller than the calculated maximum related to 120 degrees rotations about the threefold symmetry axes of the ammonium ion. The difference is explained by assuming for a N-D vector a total of 24 equilibrium directions, which in groups of six deviate from the nearest Pt-N vector by a certain angle Theta. So-called limited jumps between the directions of each group take place much more frequently than the large-angle rotations, thus rendering a fraction of the deuteron quadrupole coupling ineffective in relaxation. A motional model is presented, which takes into account both these motions simultaneously. A comparison with experimental data leads to Theta=26.0 degrees , in reasonable agreement with earlier neutron diffraction data. A sharp decrease found in the relaxation rate at the order-disorder phase transition temperature of 27.2 K is related to the fact that one of the six equilibrium directions becomes preferred. This leads to a formation of ordered domains, in which the active motion driving the relaxation is 120 degrees rotations. Two components in the spectra found below 55 K are related to domains (broad) and transition regions between domains (narrow). Reasons for the nonexponentiality observed below 20 K are discussed, the most likely explanation being that limited jumps dominate within transition regions and make the corresponding deuterons relax faster than those in domains.

Deuteron spin-lattice relaxation and spectra were studied in partially and fully deuterated (NH4)2PdCl6 in the temperature range 5–300K. The relaxation rate maximum was observed at 45K in (ND4)2PdCl6. Its value is reduced due to limited jumps by about 33% relative to the theoretical value expected for threefold reorientations. Limited jumps correspond to an N–D vector jumping between six directions on a cone around a Pd–N vector, the angle between the N–D and Pd–N vectors being denoted Δ. This motion makes a part of the quadrupole interaction ineffective in relaxation thus reducing the maximum rate at 45K. The observed reduction leads to the value Δ=21∘. Limited jumps are quenched to a large extent at the order–disorder phase transition and consequently a decrease is observed in the rate. Below the transition ND4+ ions reorient between the tetrahedral orientations of the ordered phase, therefore the quadrupole interaction has the full relaxing efficiency. In the 10% deuterated sample the temperature of the rate maximum is shifted to 35K and below 20K the rate itself is one order of magnitude larger than in (ND4)2PdCl6. The increase is related to (1) the absence of the order–disorder phase transition and (2) to the enhanced mobility of NH3D+ because of its electric dipole moment. Limited jumps are claimed to be the dominant relaxation mechanism below 20K. The relaxation in the disordered 30% deuterated sample is quite similar to that in 10% sample. The 50% and 70% deuterated samples undergo a transition to the ordered phase. The relaxation is biexponential with the characteristic rates somewhat smaller than those in (ND4)2PdCl6, but approaching them with increasing deuteration. This variation can be explained with different mobilities and varying relative numbers of the various isotopomers NH4-nDn+, n=1–4.

Deuteron spin-lattice relaxation is studied in 5% and 100% deuterated ammonium hexachlorostannate and perchlorate. The relaxation rate is observed to be independent of deuteration down to temperatures slightly lower than that of the maximum. At lower temperatures the rate of the 5% deuterated sample exceeds that of the 100% deuterated sample by four and two orders of magnitude in ammonium hexachlorostannate and perchlorate, respectively. The angular dependence of the deuteron relaxation rate in 5% deuterated ammonium hexachlorostannate at 6 K is explained in terms of existing models on quadrupolar relaxation. In 5% ammonium perchlorate one hydrogen equilibrium position, which lies on the preferred axis for 120 degrees rotations, has a larger probability to be occupied by the deuteron of NH3D+ ions. The deuterons at the other positions are still performing rotational jumps about the preferred C-3 axis and also about the other threefold axes, although at a slower rate. Such observations require a reconsideration of the relaxation process. A somewhat more general expression is derived for the relaxation rate, which agrees with the experimentally observed angular dependence for 5% deuterated ammonium perchlorate at 60 K. At lower temperatures the quadrupole coupling of the deuterons at the preferred axis may become practically time-independent. Then a significant contribution to the relaxation rate can be provided by the deuteron-proton magnetic dipolar interaction, which is still fluctuating fast via the rotation of the three protons about the axis through the stationary deuteron. (C) 2006 Elsevier B.V. All rights reserved.

Proton spin-lattice relaxation is studied in partly deuterated ammonium compounds at low temperatures. A model is proposed for the NH3D+ related contribution, which increases the relaxation rate many times larger than in nondeuterated samples. The model introduces two kinds of level-crossing minima in T1, where some tunnel frequency is equal to a separation between the proton Zeeman levels in the external magnetic field. One kind of minimum involves a CH3-type tunnel splitting of NH3D+, when the deuteron is stationary at anyone of the four threefold axes of the ammonium ion. The corresponding relaxation rate is expected to depend on the experimental pulse sequence. The other kind of minima (there could be six of them) result from the NH3D+ rotations moving the deuteron from one threefold axis to another and back, which make the otherwise motionally independent AA part of the magnetic dipolar interaction of NH3D+ time dependent. The involved tunnel splitting is equal to (2/3) times the difference between the CH3-type tunnel splittings. In a level-crossing transition the tunnel energy is changed by that splitting, but the resulting energy imbalance is transferred fast to the lattice by spin-state preserving reverse deuteron jumps, removing any coupling to the tunnel energy reservoir. Thereafter another level-crossing transition is possible. Experiments on polycrystalline 4% and 10% deuterated ammonium hexachlorotellurate samples reveal two additional level-crossing minima in T1 below 20K at the proton resonance frequencies 25MHz and about 28MHz, which are not found in the nondeuterated sample. The minima show different characteristics relative to the experimental pulse sequence and also agree otherwise well with the predictions of the model.

Proton magnetic resonance absorption spectra of yttrium dihydride (YH(2+x)), with x = 0.10, were recorded in the temperature ranges 4.2-310 K at 36.01 MHz and 150-400 K at 299.8 MHz. The evidence of proton self-diffusion follows from the changes of linewidth with temperature. The second moment of the resonance lines was determined from the experimental spectra and was compared with values calculated from the crystallographic data. The averaging effect of diffusion on the second moment was taken into account through Monte Carlo simulations of the diffusion process. The simulation was performed in a block of unit cells 5 x 5 x 5 with periodic boundary conditions. They compensated the effect of finite dimensions of the block. The calculated temperature dependence of the proton second moment values was fitted to the experimental ones. The fitting parameters were: the attempt frequency v0 and the activation energy Ea for hydrogen diffusion, assuming Arrhenius behavior of the jump frequencies vc = v0 exp(-Ea/k(B)T). In these preliminary studies, the Monte Carlo simulations were performed for tetrahedral-octahedral exchanges while direct tetrahedral-tetrahedral jumps were neglected for simplicity. Three models of hydrogen diffusion, differing in the maximum jump lengths allowed for a given model, were considered. These lengths were taken as the distances from the hydrogen attempting to jump to the first (1NN), second (2NN), and third (3NN) nearest neighbor position able to accept the jumping atom. Assuming the same attempt frequency v0 = 6.0 x 10(12)s(-1) for all three models, the activation energies giving the best fit to experimental data were 0.5, 0.54, and 0.55 eV for 1NN, 2NN, and 3NN models, respectively.

We studied the spin-lattice relaxation of the 13C magnetisation, M(C), in 13C-enriched single crystal of aspirin (only methyl carbons enriched to 99%) at the carbon resonance frequency of 54.5 MHz. After the carbon saturation the recovery appears exponential except below 30K, where it is biexponential due to the presence of the level crossing omega(t)=omega(C)+omega(H) (the symbols refer, respectively, to the tunnel frequency and the carbon and proton resonance frequencies in angular units). After the saturation of the proton magnetisation, M(H), the description of the M(C) recovery needs three exponentials. The evaluation of the time constants is easiest from the data in this case, since M(C) varies with time in an initial growth-subsequent decrease (or an initial decrease-subsequent growth depending on temperature) manner, instead of the monotonous growth after the carbon saturation. Experimental data agree semiquantitatively with the predictions of our recent model. According to the model the relaxation of M(C) is coupled to M(H) and the tunnel energy TE at temperatures below the minimum of the 13C relaxation time. Sufficiently above this minimum M(C) is coupled to M(H) and the rotational polarization (but not to TE) in agreement with experiment. Also the effect of torsional oscillations of a methyl group on the magnitude of various 13C-related transition rates was considered in detail. In aspirin the rates are reduced roughly by 10% and the reduction should become larger in samples with a larger tunnel splitting. The reduction also changes somewhat the angular dependence of these rates.

Nuclear spin–lattice relaxation of hydrogens in some ammonium hexachlorometallates at low temperatures is driven by small-angle or limited jumps of the NH4+ tetrahedra about the [111] equilibrium orientations of the high-temperature cubic phase. Usually, the low-temperature equilibrium orientations are not known and they vary most likely with the sample. Here they are defined by symmetry in such a way that each N–H bond of an NH4+ ion makes the same angle Δ with the nearest [111] direction. This assumption defines the six possible equilibrium orientations of NH4+ and also the directions of the intra-ion proton–proton vectors in terms of Δ. At low temperatures, when the rate of the 120° rotations about the threefold axes of ammonium groups (with the correlation time τc) has slowed down sufficiently, the limited jumps between the six equilibrium orientations dominate the proton spin–lattice relaxation. The time-dependent perturbation theory is used to calculate the transition rates, related to these limited jumps, between the various energy levels of the NH4+ rotational ground state, shifted by the rotational tunnelling and the interaction of the hydrogen atoms with the external magnetic field (the resonance frequency ω0). An expression is derived for the initial relaxation rate of the proton magnetization. A comparison with the relaxation rate at the normal minimum corresponding to ω0τc≈1 provides the angle Δ. The model is applied to the available experimental data on (NH4)2TeCl6 and the result Δ=5.3° is obtained.

The temperature dependences of the 127I nuclear quadrupole coupling in NH4IO4 and in ND4IO4 are reported. In each salt, the quadrupole coupling decreases to a very small value at low temperatures, and in the case of ND4IO4 passes through zero and changes sign at 87 K.

Spin-lattice relaxation processes in (CH3)-C-13 groups in methyl compounds are studied both theoretically and experimentally. The four spin-1/2 nuclei in such methyl groups give rise to 16 spin-rotational states, which are split by rotational tunnelling. From the corresponding populations (15 independent) five long lived combinations are formed: the C-13 magnetization M-C, proton magnetization M-H, tunnelling energy T E, rotational polarization RP and dipolar energy DE. Their spin-lattice relaxation via the transitions induced by the C-13-proton dipolar interaction is studied in detail. Direct relaxation rates and coupling terms between these combinations are derived. Predictions are compared with experimental data for C-13 spin-lattice relaxation at 75.4 MHz in 99% enriched (only methyl carbons enriched) single crystal of aspirin. Above 40 K, the M-C recovery is exponential and describable in terms of the direct relaxation transitions without couplings. The same is true for the initial relaxation in the region of non-exponential relaxation between 30 K and 40 K. The orientation dependence of the initial relaxation rate agrees with the theoretical calculations. The non-exponentiality is related to resonant level-crossing transitions with omega(t) + omega(C) = omega(H), where the angular frequencies represent rotational tunnelling and carbon and proton resonances, respectively. The resonant transitions produce couplings between M-C, M-H and T E that are described quite accurately by the present model.

We report on the first observation of the 89Y NMR signal in the hexagonal trideuteride phase YD2.98 at 14.7MHz (7.04T) and 302K. In this phase the 89Y nuclei are in an environment characterized by the shift tensor components δiso=361, δaniso=90ppm and ηs≈0.1. The spin–lattice relaxation time is estimated to be of the order of 7×103s at 302K. Magnetic measurements show that the magnetic susceptibility is small and diamagnetic in the temperature range 1.8–300K. For comparison, the 89Y NMR and susceptibility data for yttrium metal and its dideuteride phase YD1.99 are also given and discussed.

Proton spin-lattice relaxation time T1 was studied in a single crystal of (NH4)2S2O8 as a function of the orientation of the external magnetic field B0 in the crystalline a∗b plane. Angular dependence was observed at 100K at the proton frequency f0=8.7MHz and at 10K at the Zeeman-tunnel level-crossing frequencies 4.3 and 8.6MHz. At 8.7 and 4.3MHz the theoretically calculated angular dependence agrees satisfactorily with the experimental data but at 8.6MHz (10K) the theory fails. Various sources of the failure are discussed, the most likely one being the anisotropy of the ammonium motion.