M. Punkkinen

Zeeman spin-lattice relaxation of weakly hindered proton tetrahedra☆

A model is proposed to explain the additional minima and nonexponentiality of the proton Zeeman spin-lattice relaxation at low temperatures in certain samples containing tetrahedral four proton groups. A common Zeeman spin temperature is assumed for all nuclear spin isomers. Additional minima and nonexponentiality are expected to be observable in the region 0.5 ≦ωTω0 ≦ 3, where hω0 is the Zeeman splitting and hωT the average separation between the T and A species torsional ground states. For vanishing tunneling splittings the model agrees with the existing theories. A comparison with the experimental T1 data on (NH4)2PbCl6 suggests a temperature-dependent tunneling frequency ωT2π, increasing from 18 MHz at 44 K to 44 MHz at 20 K.

Spin-lattice relaxation in ammonium compounds with a complex molecular dynamics

Expressions are derived for the initial relaxation rate 1/T1 of protons and deuterons of nontunnelling NH4 and ND4 groups reorienting about various symmetry axes in solids. The reorientation rates are modified by a trigonal, tetragonal or monoclinic distortion of the predominantly cubic hindering potential. When the rates differ sufficiently from each other, two T1 minima are observed with a characteristic ratio. Experiments were performed in NH4VO3, (NH4)2S2O8, (NH4)2PtCl4, and their deuterated modifications, which all exhibit two T1 minima. In NH4VO3 and ND4VO3 the relaxation and spectral data agree rather well with the model of trigonal distortion. Also (NH4)2S2O8 has a preferred threefold axis but there, the large tunnel splitting of protons has to be taken into account before an agreement is reached. All the purely reorientational models fail with (NH4)2PtCl4, where, instead, the ammonium groups are proposed to be ordered into domains at low temperatures. The groups inside the domains and boundary regions give rise to the high- and low-temperature T1 minima, respectively. The boundaries are also believed to give rise to the narrow component in the deuteron spectrum at low temperatures. Evidence for a proton tunnelling frequency of 32 MHz is found in (NH4)2PtCl4.

Deuteron spin-lattice relaxation in (ND4)2SnCl6 below 60 K

Abstract Spin-lattice relaxation of deuterons in an (ND 4 ) 2 SnCl 6 single crystal, with B 0 |[100], was studied at the resonance frequencies 5.7, 14.5 and 43.9 MHz as a function of temperature. A reorientation-related minimum appears in the relaxation time T 1 near 60 K with activation energy 5.9 kJ/mol. A model is presented for the corresponding relaxation rate in the presence of librational tunneling. Below 30 K relaxation is clearly nonexponential and an additional minimum is observed near 15 K. This minimum is probably related to the fact that the equilibrium orientations of the ND bonds are not parallel to [111] and equivalent directions but they make a small angle with these directions. The ND 4 ion moves then as an entity amongst such orientations keeping always, at low temperatures when tunneling is ignored, each ND bond near a fixed [111] or equivalent direction. An expression is derived for the relaxation rate through this low-temperature motion. Results are compared with neutron diffraction experiments.

Hydrogen bond studies. 108. A nuclear magnetic relaxation study of molecular motion in solid trimethylammonium iodide, bromide, chloride, and hydrogen oxalate

Abstract Spin-lattice relaxation times in the laboratory frame at 60.16 and 20.00 MHz are reported for trimethylammonium iodide, bromide, chloride, and hydrogen oxalate in the temperature range 150–400 K. A model that makes it possible to analyze the experimental data on the basis of different assumptions regarding the reorientational motions of the methyl groups, the cations as a whole, and the correlations between these two types of motion is developed. No conclusions are drawn about the correlation since the two models investigated result in almost equally good fits with the experimental relaxation times. However, time factors, activation energies, and scale factors for the intramethyl relaxation constants could be determined from the refinements since the results were close for the two models, and thus apparently insensitive to reasonable assumptions about the correlations.

Rotational tunneling effects in 2H‐NMR spectra of polycrystalline (ND4)2SnCl6

Rotational tunneling effects are analyzed in 2H‐NMR spectra of deuterated ammonium ions in powders. The spectra are generally composed of a strong central line from A symmetry species and weaker T sidebands. At a high magnetic field (∼6.5 T) the central line contains well‐resolved doublets. Their separations supply a direct measure of the rotational tunneling frequency νt in the range 0.1<νt<6 MHz. At low magnetic fields the spectra depend both on νt and the Larmor frequency ν0. Level crossing related effects may be detected in a ±0.75 or ±0.35 MHz range around that Larmor frequency which is equal to νt or 1/2 νt, respectively. Generally, only the fitting of the theoretical spectra to those measured at different ν0 allows an estimation of the tunneling frequency. The measurement of νt up to about 20 MHz becomes thus possible. The theoretical predictions are verified by results on a (ND4)2SnCl6 powder sample. High and low field spectra lead to slightly different values for the tunneling frequency at 4.2 K ...

Ortho-para conversion in solid hydrogen, catalyzed by molecular oxygen impurities

Ortho-para conversion in solid hydrogen with small amounts of molecular oxygen as impurity (0.01–0.5%) was studied by NMR in the temperature range 4.2–7 K. The observed conversion rate was substantially greater than that of the natural conversion process in pure solid H2 and revealed a strong dependence on temperature and the oxygen content in the sample. Obviously, the conversion is catalyzed by the large paramagnetic moments of O2 impurities. Since the influence of O2 is of very short range, the overall rate of the catalyzed conversion in the sample is determined by the relative diffusion of ortho-H2 and the O2 impurities. The diffusion coefficient was found to obey an Arrhenius behavior D(T)=3(2). 10−11.exp[96(8)/T] cm2s−1. This temperature dependence is interpreted in terms of vacancy-particle exchange by quantum tunneling through the intervening barrier.

Spin-lattice relaxation in 13CH3 compounds: application to 13C enriched aspirin

Spin-lattice relaxation processes in 13CH3 groups in methyl compounds are studied both theoretically and experimentally. The four spin-½ 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 13C magnetization M C, proton magnetization M H, tunnelling energy TE, rotational polarization RP and dipolar energy DE. Their spin-lattice relaxation via the transitions induced by the 13C-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 13C 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 ωt, + ωC = ωH, where the angular frequencies represent rotational tunnelling and carbon and proton resonances, respectively. The resonant transitions produce couplings between M C, M H and TE that are described quite accurately by the present model.

The ortho-to-para conversion in solid hydrogen, catalyzed by hydrogen atoms

The combined techniques of ESR and NMR were used to investigate the process of ortho-para conversion in solid molecular hydrogen, containing small amounts (∼ 500 ppm) of hydrogen atoms as impurity. Although the impurity atoms catalyze the effective conversion of the neighboring ortho-H2, the total catalyzed conversion rate at temperatures from 2.2 K to 4.4 K is much less than expected from the rate of the H atoms recombination. A possible explanation is given in terms of the diffusion of H atoms, which is confined to some defects in the crystal.

Deuteron NMR spectrum of ND4VO3 and some other ammonium compounds

Abstract Deuteron NMR absorption line shape and its temperature dependence were studied in ND 4 VO 3 especially in the temperature range from 60 to 90 K, where the only molecular motion important for NMR is the reorientation about one threefold axis of ND 4 . Computer fits of the model by Lalowicz and Sagnowski to our experimental spectra gave the activation energy E a = 8.3 kJ/mol. Besides ND 4 VO 3 the low-symmetry samples (ND 4 ) 2 Cr 2 O 7 , (ND 4 ) 2 Ce(NO 3 ) 6 and ND 4 ClO 4 have, above the line-width transition region, a doublet as their absorption curve, which gradually narrows to a single line with a rising temperature. Various contributions to the magnitude of the doublet separation are discussed.

2H-NMR study of ammonium ion rotational tunneling and reorientation in (ND4)2SnCl6 single crystal: I. Tunneling frequency measurements

Theory of2H-NMR spectra is developed for a ND4+ ion. Quadrupole and dipole-dipole interactions for four deuterons of the tetrahedral ion as well as the rotational tunneling are taken into account. Features in the single crystal spectra at the high magnetic field of 6.7 T are analyzed. Their central doublets (±5 kHz range around the Larmor frequency) are attributed to theA symmetry species and exhibit sensitivity to theA−T tunneling frequencyvt. This allows the measurement ofvt in a wide rangevt <10 MHz. The shape of sidebands (±140 kHz range) is related to the T levels structure. Theoretical predictions are verified on a (ND4)2SnCl6 single crystal at 44 MHz. The tunneling frequency at temperatures below 10 K equals 7.5 MHz, which is about 100 times smaller than for (NH4)2SnCl6.vt was measured up to 40 K. At still higher temperatures motional narrowing effects were observed for theA spectral components preventing the determination ofvt.