Nuclear Pure Quadrupole Relaxation and Its Temperature Dependence in Solids
TL;DR: In this paper, the authors used a torsional molecular oscillator model to measure the T1 of the pure quadrupole T1 in cuprous oxide, paradichlorobenzene, 2,2-dichloropropane, t-butyl chloride, and methylene chloride at temperatures from 77°K to room temperature.
Abstract: The Cu63 and Cl35 pure quadrupole relaxation times have been measured by rf pulse techniques in cuprous oxide, paradichlorobenzene, 2,2‐dichloropropane, t‐butyl chloride, and methylene chloride at temperatures from 77°K to room temperature. The Cu63 T1 data agree with the ionic lattice model. The Cl35 T1 data for paradichlorobenzene agree with a torsional molecular‐oscillator model. For 2,2‐dichloropropane the Cl35 T1 values agree with a model based on field‐gradient fluctuations produced by reorienting CH3 groups. The more complicated T1 temperature dependences observed in t‐butyl chloride and methylene chloride appear to be the result of multiple thermal motions. The same can be said of our limited data on the Cl35 relaxation in 1,2‐dichloroethane. No discernible difference was found for the relaxation times of the two Cl35 resonance lines in methyl chloroform at 77°K.In general, the available proton T1 and linewidth data correlate well with our chlorine results; this agreement is discussed. The chlorine spin phase memory times are governed by the local magnetic fields except when decreased by spin—lattice lifetime broadening. The inverse linewidth parameters exhibit broadening by a distribution of field gradients. The fadeout of the Cl35 quadrupole resonance with increasing temperature in 2,2‐dichloropropane is the result of T1 broadening, while in t‐butyl chloride and methylene chloride it is produced by phase transitions.The Bayer model for spin—lattice relaxation by molecular torsional oscillations is treated in some detail, including a new approach which dispenses with some of his simplifying assumptions. A brief analysis is given of T1 for the case in which field‐gradient fluctuations are produced by random, large‐angle reorientations of groups near to the relaxed nucleus. The theory is presented for a null method of measuring the pure quadrupole T1. The method, which was used in most of our measurements, is similar to the Carr—Purcell 180°—90° pulse method for measuring nuclear magnetic T1's.The Cu63 and Cl35 pure quadrupole relaxation times have been measured by rf pulse techniques in cuprous oxide, paradichlorobenzene, 2,2‐dichloropropane, t‐butyl chloride, and methylene chloride at temperatures from 77°K to room temperature. The Cu63 T1 data agree with the ionic lattice model. The Cl35 T1 data for paradichlorobenzene agree with a torsional molecular‐oscillator model. For 2,2‐dichloropropane the Cl35 T1 values agree with a model based on field‐gradient fluctuations produced by reorienting CH3 groups. The more complicated T1 temperature dependences observed in t‐butyl chloride and methylene chloride appear to be the result of multiple thermal motions. The same can be said of our limited data on the Cl35 relaxation in 1,2‐dichloroethane. No discernible difference was found for the relaxation times of the two Cl35 resonance lines in methyl chloroform at 77°K.In general, the available proton T1 and linewidth data correlate well with our chlorine results; this agreement is discussed. The chlorin...
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TL;DR: The status of knowledge of the intermolecular potential, structural and thermodynamic properties, and lattice dynamics are discussed in detail and suggestions are made for further research as discussed by the authors.
285 citations
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TL;DR: In this paper, the authors derived the relaxation times of the deuterons in supercooled D2O at 225 MPa, measured at two frequencies: 55.54 and 39.14 MHz, under high hydrostatic pressure at temperatures below ∼220 K.
Abstract: Spin‐lattice (T1) and spin–spin (T2) relaxation times of the deuterons in supercooled D2O at 225 MPa, measured at two frequencies: 55.54 and 39.14 MHz down to 188 K are reported. The results show that T1 and T2 become frequency dependent in supercooled liquid water under high hydrostatic pressure at temperatures below ∼220 K. Theoretical expressions for the relaxation rates are deduced under the assumption that the orientational fluctuations of the water molecules are composed of fast librational oscillations and slower diffusional motions. The effect of the librations is to reduce the size of the deuterium quadrupole coupling constant. The diffusional motions are nearly isotropic and dominate the T dependence of the relaxation times. The autocorrelation function of the slow orientational fluctuations was assumed to be exponential at long times with a single time constant, the orientational correlation time τ2. The T dependence of the latter is well described by the VTF equation. The parameters obtained by least squares fitting the experimental spin‐lattice relaxation times to an isotropic motional model correctly predict the temperature and frequency dependence of the spin–spin relaxation times.
50 citations
TL;DR: In this paper, the far infrared and Raman spectra of solid (CH3)3CCl, (CD3), 3CCl and 3CBr have been obtained over a range of temperatures, and barriers to internal rotation of the methyl groups were calculated.
Abstract: The far‐infrared and Raman spectra of solid (CH3)3CCl, (CD3)3CCl, (CH33SiCl, (CH3)3GeCl, (CH3)3CBr, (CH3)3SiBr, and (CH3)3GeBr have been obtained over a range of temperatures. For (CH3)3CCl, (CD3)3CCl, (CH3)3SiCl, and (CH3)3CBr torsional vibrations were observed, and from the frequencies, barriers to internal rotation of the methyl groups were calculated. The barrier of 4.51 kcal/mole for tertiary‐butyl chloride (4.82 for the d9 compound) is consistent with that reported earlier for the fluoride. The 3.90‐kcal/mole barrier calculated for the tertiary‐butyl bromide is somewhat lower than expected. A barrier of 2.63 kcal/mole was found for the trimethylchlorosilane molecule. Intermolecular fundamentals were observed for all compounds in the series, and the higher‐frequency modes observed in the infrared spectra were assigned as librational fundamentals whereas the lower‐frequency Raman lines have been assigned as optical translations. The frequency shifts for these intermolecular fundamentals are discussed ...
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TL;DR: In this paper, the effect of diffusion on free precession in nuclear resonance has been studied, and a new scheme for measuring the transverse relaxation time is described, which largely circumvents the diffusion effect.
Abstract: Nuclear resonance techniques involving free precession are examined, and, in particular, a convenient variation of Hahn's spin-echo method is described. This variation employs a combination of pulses of different intensity or duration ("90-degree" and "180-degree" pulses). Measurements of the transverse relaxation time ${T}_{2}$ in fluids are often severely compromised by molecular diffusion. Hahn's analysis of the effect of diffusion is reformulated and extended, and a new scheme for measuring ${T}_{2}$ is described which, as predicted by the extended theory, largely circumvents the diffusion effect. On the other hand, the free precession technique, applied in a different way, permits a direct measurement of the molecular self-diffusion constant in suitable fluids. A measurement of the self-diffusion constant of water at 25\ifmmode^\circ\else\textdegree\fi{}C is described which yields $D=2.5(\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in good agreement with previous determinations. An analysis of the effect of convection on free precession is also given. A null method for measuring the longitudinal relaxation time ${T}_{1}$, based on the unequal-pulse technique, is described.
5,630 citations
TL;DR: In this article, the authors studied the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction in a rigid lattice and the line width of the absorption line.
Abstract: The exchange of energy between a system of nuclear spins immersed in a strong magnetic field, and the heat reservoir consisting of the other degrees of freedom (the "lattice") of the substance containing the magnetic nuclei, serves to bring the spin system into equilibrium at a finite temperature. In this condition the system can absorb energy from an applied radiofrequency field. With the absorption of energy, however, the spin temperature tends to rise and the rate of absorption to decrease. Through this "saturation" effect, and in some cases by a more direct method, the spin-lattice relaxation time ${T}_{1}$ can be measured. The interaction among the magnetic nuclei, with which a characteristic time $T_{2}^{}{}_{}{}^{\ensuremath{'}}$ is associated, contributes to the width of the absorption line. Both interactions have been studied in a variety of substances, but with the emphasis on liquids containing hydrogen.Magnetic resonance absorption is observed by means of a radiofrequency bridge; the magnetic field at the sample is modulated at a low frequency. A detailed analysis of the method by which ${T}_{1}$ is derived from saturation experiments is given. Relaxation times observed range from ${10}^{\ensuremath{-}4}$ to ${10}^{2}$ seconds. In liquids ${T}_{1}$ ordinarily decreases with increasing viscosity, in some cases reaching a minimum value after which it increases with further increase in viscosity. The line width meanwhile increases monotonically from an extremely small value toward a value determined by the spin-spin interaction in the rigid lattice. The effect of paramagnetic ions in solution upon the proton relaxation time and line width has been investigated. The relaxation time and line width in ice have been measured at various temperatures.The results can be explained by a theory which takes into account the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction. The local magnetic field produced at one nucleus by neighboring magnetic nuclei, or even by electronic magnetic moments of paramagnetic ions, is spread out into a spectrum extending to frequencies of the order of $\frac{1}{{\ensuremath{\tau}}_{c}}$, where ${\ensuremath{\tau}}_{c}$ is a correlation time associated with the local Brownian motion and closely related to the characteristic time which occurs in Debye's theory of polar liquids. If the nuclear Larmor frequency $\ensuremath{\omega}$ is much less than $\frac{1}{{\ensuremath{\tau}}_{c}}$, the perturbations caused by the local field nearly average out, ${T}_{1}$ is inversely proportional to ${\ensuremath{\tau}}_{c}$, and the width of the resonance line, in frequency, is about $\frac{1}{{T}_{1}}$. A similar situation is found in hydrogen gas where ${\ensuremath{\tau}}_{c}$ is the time between collisions. In very viscous liquids and in some solids where $\ensuremath{\omega}{\ensuremath{\tau}}_{c}g1$, a quite different behavior is predicted, and observed. Values of ${\ensuremath{\tau}}_{c}$ for ice, inferred from nuclear relaxation measurements, correlate well with dielectric dispersion data.Formulas useful in estimating the detectability of magnetic resonance absorption in various cases are derived in the appendix.
4,973 citations
TL;DR: The field of electric quadrupole interactions in nuclear magnetic resonance can be divided roughly into two areas according to the relative magnitude of the nuclear quadrupoles interactions as discussed by the authors, which can be classified into two categories according to their relative importance.
Abstract: Publisher Summary This chapter discusses quadrupole effects in nuclear magnetic resonance studies of solids. The first evidence that many nuclei possess magnetic moments came from the study of the hyperfine structure of atomic spectra in the visible region. The interaction of the nuclear magnetic moment with the magnetic field produced by the atomic electrons gives rise to a hyperfine spectrum that is relatively simple, being characterized by the well known “interval rule.” Marked departures from this interval rule do occur in a few cases, however, and some of the departures can definitely be attributed to the presence of a nuclear electric quadrupole interaction. The methods of radio-frequency spectroscopy are very well adapted for the investigation of the very small interaction energies to which nuclear moments give rise. They have led not only to much more precise determinations of nuclear magnetic moments, but also to a vastly increased knowledge of nuclear electric quadrupole effects. The first outstanding success along this line was the discovery, by the molecular beam resonance method, of the quadrupole moment of the deuteron. The field of electric quadrupole interactions in nuclear magnetic resonance can be divided roughly into two areas according to the relative magnitude of the nuclear quadrupole interactions.
651 citations
TL;DR: The experimental absorption line widths, for nuclei with spin 1/2, at nuclear magnetic resonance are given as a function of temperature for a number of molecular crystals.
Abstract: The experimental absorption line widths, for nuclei with spin 1/2, at nuclear magnetic resonance are given as a function of temperature for a number of molecular crystals. Temperatures ranged from 90°K to the melting points of the compounds. In some cases it has been possible to relate observed line structure and transitions in the line width to the existence and frequency of certain types of hindered rotational motion in the solid state. These deductions are based on mathematical considerations of the quantitative effect of such motions on the structure and second moment of an absorption line. It is emphasized that relatively low frequency motion of the order 105 cycles/second suffices to narrow the width of an absorption line from its value in the absence of that motion.1,2‐dichloroethane, 1,1,1‐trichloroethane, and perfluoroethane were found to have line‐width transitions coinciding with changes in crystal form and anomalies in the heat capacity. In 1,2‐dichloroethane and perfluoroethane these transiti...
577 citations