L. P. Ingman

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.

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 ...

Proton relaxation and tunneling levels of NH4+ ions in an (NH4)2SnBr6 single crystal

Abstract Librational tunneling levels of NH4+ ions in an (NH4)2,SnBr6 single crystal were determined by studying the proton Zeeman relaxation. The relaxation rate speeds up when any of the tunnel frequencies vt equals nv0 (n = 1 2 , 1, 2), wherev0 is the proton resonance frequency. The energy separation between the A and T levels is about 33 MHz and the splitting of the 3T manifold is 4.6 MHz or less at 20 K. The temperature dependence of the splittings was also observed.

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.

Anisotropy of the nuclear dipolar relaxation in CF3COOAg

Abstract The spin-lattice relaxation time of the nuclear dipolar energy in a CF 3 COOAg single crystal was studied as functions of temperature and crystal orientation. The results were compared with the predictions of the density matrix theory.

2H-NMR study of ammonium ion rotational tunneling and reorientation in (ND4)2SnCl6 single crystal. II, T levels structure

In the preceding paper (Z. Phys. B — Condensed Matter66, 363 (1987)) we had shown that2H-NMR spectra of ND4+ in a cubic potential were separable into components originating fromA, E andT symmetry species. Separations of theA andE doublets supply currently an unique way to measure theA−T tunneling splitting up to about 10 MHz. Now we analyse tunneling effects and angular dependence ofT spectral components. Calculated spectra show angular dependence which varies withT levels structure. The spectra depend on theT−T splittings, allowing their evaluation up to about 1 MHz. The threeT levels of ND4+ in (ND4)2SnCl6 are found to be split asymmetrically by 91.5 kHz and 49.5 kHz at 4.2 K. The isotope reduction for theT level splittings amounts to about 670, in contrast to a factor 100 found for theA−T splitting.

2H-NMR study of ammonium ion rotational tunneling and reorientation in (ND4)2SnCl6 single crystal

Because of the quadrupole interaction, the2H-NMR spectra of a tunneling ND4+ ion depend on the Larmor frequencyv0 and the tunneling frequencyvt, when both frequencies are less than 20 MHz. Calculated single crystal spectra visualize features to be expected. Significant broadening and asymmetry are observed at level crossing regions aroundvt=v0 orvt=2v0. Angular, frequency and temperature dependences of the spectra are studied using an (ND4)2SnCl6 single crystal. Experimental spectra obtained for different frequencies at 4.2K are fitted withvt as a parameter. The tunneling frequency is also checked by measurements of the deuteron spin-lattice relaxation timeT1 as a fuction ofv0. Both methods give consistentlyvt=7.15±0.10 MHz.

Tunneling to Reorientation Transition Effects in High Field 2H-NMR Spectra of ND 4+ Ions

The high field 2H-NMR spectra of the tunneling ND 4 + ion are found to be separable into contributions of A, E and T symmetry species. Their temperature dependence as well as that of the tunneling frequency and spin-lattice relaxation are followed in an (ND4)2SnCl6 single crystal. A common correlation time scale exists.