Contains research objectives and reports on three research projects

Macomber, J. D.

Mannis, F.

Riehl, J. W.

Thompson, D. S.

Wade, C. G.

Waugh, J. S.

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VIII. MAGNETIC RESONANCEProf. J. S. Waugh J. W. Riehl D. S. ThompsonJ. D. Macomber C. G. WadeRESEARCH OBJECTIVESThe activity of this group is centered on the study of the structure and atomic dynam-ics of solids and fluids through experiments on nuclear and electronic magnetism. Workis under way on six specific projects.1. Structure of Liquid DielectricsNuclear spin Hamiltonians of interest in magnetic-resonance experiments can beexpressed in terms of spherical tensors of rank 2, a circumstance that arises becausethe nuclear moments involved are magnetic dipole and electric quadrupole. The secularinteractions, which give rise to shifts and splittings of the nuclear Zeeman levels, thushave scalar parts and parts that depend on the orientation of molecules through Y m(0, ).In ordinary liquids, rapid molecular reorientation makes the anisotropic terms unob-servable, inasmuch as the average of Y m over a spherically symmetric probabilitydistribution vanishes. In a polar liquid subjected to an electric field, however, the prob-ability distribution is no longer exactly spherical, and one expects to see small pertur-bations of the nuclear-resonance spectrum which depend on electric field intensity Eand temperature T as (E/T)2 , and also on the local order in the liquid produced byintermolecular forces. For molecules of known properties it becomes possible to meas-ure such averages as Y20 through the nuclear-resonance spectrum. This information,together with a knowledge of Y10 obtained from dielectric studies, is expected - for thefirst time - to provide detailed information about the degree and type of local order pro-duced by molecular interaction in dielectric liquids. It is also expected that such exper-iments will throw light on the mechanism of electrical conduction in insulating liquids.The present state of our experiments is described in this report.J. D. Macomber, J. S. Waugh2. Magnetic Relaxation in GasesNuclear relaxation in monatomic gases such as helium is exceedingly slow, a factthat has suggested the use of He 3 nuclear moments in navigational gyroscopes. Weare studying the mechanisms responsible for such relaxation by performing tran-sient magnetic-resonance experiments on gases at high pressures for which the relaxa-tion is rapid enough to be measurable. We are even more actively studying nuclearrelaxation by similar methods in simple polyatomic gases, in which there are strongermechanisms arising from the anisotropy of the forces between colliding molecules. Weare at present attempting to get a detailed picture of these forces in the simple proto-type system of hydrogen deuteride gas at low temperatures. We hope, in collaborationwith Professor Irwin Oppenheim, to arrive at an exact theoretical connection betweennuclear relaxation times and intermolecular forces for simple systems.C. G. Wade, J. S. Waugh3. Transport Properties of Dense FluidsFor a long time, a great deal of theoretical attention has been devoted to the generalproblem of the nonequilibrium properties of liquids and dense gases. Despite the factthat diffusion, viscosity, thermal conductivity, and so forth, are among the most clas-sical subjects of experimental physical chemistry, almost none of the work that has beenQPR No. 72(VIII. MAGNETIC RESONANCE)done is of direct use in testing transport theory. This is because of the necessity oflow temperatures and/or high pressures for obtaining high densities of fluids composedof single atoms or small molecules. Also, one would like experimental values of trans-port coefficients over wide ranges of temperature and density, since one would expecttransport theories to do a better job of predicting the form of temperature and densitydependences than of giving numerical values of the transport coefficients. Fortunatelythe experimental difficulties of the classical methods are largely obviated, in the caseof diffusion, by the spin-echo technique of nuclear resonance. We have already usedthis method to study the temperature dependence of self-diffusion in liquid ethane overan extremely wide temperature range (see Quarterly Progress Report No. 64, pages 37-39). We have now completed and tested a system for extending the same type of meas-urements to high pressures. It will be used initially to study the experimentally con-venient liquids CH 4 and C2H 6, and will then be extended to monatomic and otherpolyatomic liquids.J. W. Riehl, J. S. Waugh4. Atomic Motion in SolidsThermal relaxation of nuclei in solids typically occurs through the agency of mag-netic dipole-dipole interactions, randomly modulated by the motions of nuclei withrespect to one another. In general, it is assumed that the time autocorrelation functionG(T) describing the statistical fluctuation of these interactions 3(t) is an exponential,described by a correlation time Tc:G(T) E <f(t) (t+T) (t)2 exp(-/Tc).This assumption, applied to solids whose atomic motions are thermally activated so thatTc = Tco exp(E/kT), has been very successful in identifying the atomic motions that occurand determining the energetic barriers E that hinder them. An example from our recentwork is described in this report.In general, where correlations exist between the motions of neighboring nuclei orwhere the motion is complex in character, the assumption that a single correlation timeexists is certainly not correct. The nuclear relaxation time is still a measure of thecorrelation function, being directly related to its Fourier transform evaluated at theexperimental resonance frequency. We are beginning a series of studies of relaxationin various solids with the object of mapping out the correlation function experimentallyand finding out what sorts of departures from exponential behavior do occur typically.Such work requires observing the relaxation of nuclear magnetization toward equilibriumin an applied magnetic field whose strength is variable from a few to many thousandoersteds. The usual procedure is to polarize the sample in a strong field and thenreduce the field quickly to the desired value. After a time, the field is restored to alarge value and the remaining magnetization is measured by means of a free-inductiondecay or an adiabatic fast passage. Alternatively, the desired low magnetic fields canbe obtained in the rotating frame by means of Solomon's "spin-locking" procedure.J. S. Waugh5. Electron-Spin ResonanceA good deal of interest exists in the properties of magnetically dilute solutions oftransition metal ions in diamagnetic crystals, partly because of the applications of suchsystems to optical masers. We are carrying out some optical and X-band electron spin-resonance studies on the d4 ion Cr + 2 in CaF 2 and SrF 2 single crystals. The object ofthis work is to obtain an analysis of the Jahn-Teller effect through its influence on theQPR No. 72(VIII. MAGNETIC RESONANCE)F 1 9 hyperfine interaction at low temperatures. We are also carrying on some electronspin-resonance work on solutions of rare-earth metals in liquid ammonia in the hope ofthrowing some further light on the structure of these peculiar conducting liquids (seethis report).D. S. Thompson, J. S. Waugh6. M6ssbauer EffectIsomer shifts and quadrupole splittings in recoilless gamma-ray spectra are knownto be related to the electronic structure of solids, but the theoretical interpretation ofthese quantities ab initio is very difficult. We have done some preliminary studies of anumber of solid monosubstituted ferrocyanides having a range of tetragonal crystal fieldstrengths in an attempt to establish semiempirical criteria for the discussion of chemicalbonding. This work is now dormant, but results obtained thus far are partially discussedin a paper that has been submitted to Applied Optics.F. Mannis, J. S. WaughSTATUS OF CURRENT PROJECTS1. NUCLEAR MAGNETIC RESONANCE OF POLAR LIQUIDS IN ELECTRIC FIELDSDetection of the small effects of dipolar interactions and anisotropy of chemical shifton the nuclear magnetic resonance (NMR) spectrum of a liquid subject to an electric fieldrequires the greatest possible spectral resolution. In sample cells of most practicaldesigns the applied magnetic field is made inhomogeneous by the presence of the cellstructure and the sample itself, both of which have magnetic susceptibilities differentfrom that of the surrounding air. Small currents flowing in the sample also produceinhomogeneous magnetic fields of their own. After much experimentation, we seem tohave solved the first of these problems by constructing long cylindrical cells containingthe sample liquid in a long cavity of rectangular cross section. The cell body is castfrom an epoxy resin that has been doped with rouge until its volume diamagnetic sus-ceptibility matches that of the sample. The electrodes are sufficiently thin that they donot appreciably distort the magnetic field. As far as the magnetostatic problem is con-cerned, the sample cell can then be treated as an infinite homogeneous cylinder, insidewhich the field is uniform. We have also tried long concentric glass cells in which thesample and electric field appear in a thin annulus. The glass is coated with a chemicallyinert semiconducting film (courtesy of Dr. D. W. Rice of the Corning Glass Company).Such a cell avoids, in principle, both sources of field inhomogeneity mentioned above.But it must be rapidly spun about its cylinder axis in order to average out the line broad-ening that arises because the relative directions of the electric and magnetic fields aredifferent in different parts of the cell. This averaging reduces the observable effectsof the electric field on the NMR spectrum by a factor of four. This, together with thecomplications inherent in making the necessary electrical connection to a rotating cell,have resulted in our preference for the, perhaps less elegant, parallel-plate geometry.QPR No. 72(VIII. MAGNETIC RESONANCE)The above-mentioned sorts of spurious line broadening, as well as other forms ofinterference, always occur to some degree when a strong electric field is applied to aliquid whose steady-state NMR spectrum is being examined. Rather than trying to dis-entangle the desired shifts and splittings from these adventitious effects by direct exam-ination of changes in the NMR line shape, we are now employing a sideband technique.Instead of a constant electric field, we apply an audiofrequency alternating field,E cos w t. Its effects are conveniently described with reference to the proton resonanceof CH3NOZ, on which much of our work has been done. In the alternating field the res-onance, previously a single line, splits into a triplet of intensity ratio 1:2:1 and spacing3DHH. At the same time, sideband resonances appear at ±2w e from the main resonance.These resonances have the form of doublets of spacing 6DHH. Their amplitudes containa component oscillating at the frequency 2we with intensity proportional to a product ofBessel functions: J (k) J (k), where the modulation index k is given by k =const. X Eo/ e . These sidebands are not present at all unless the desired electric-field splitting exists, and their intensities, suitably measured with a lock-in detectoroperating at the frequency 2we , measure DHH. Calibration is conveniently made by com-parison with a magnetic field modulation sideband of like frequency. In order to increasethe time during which the weak signals can be integrated, it is convenient to lock thespectrometer into resonance by means of still another magnetic sideband, after the fash-ion of Freeman and Anderson.1 The equipment for accomplishing this rather involvedsituation has now been built and successfully tested, although refinement still continues.A preliminary account of this work was given at the Eighth Jugoslav Summer Schoolof Physics, in Hercegnovi, September 1-7, 1963, and will be published in the Proceedingsof this conference.The polarization of a liquid by an electric field introduces into the spin Hamiltonian,among other things, a dipolar interaction for each pair of nuclei:0(i ) = D..(I. - I.- 31 I .),d 1 31 zi zjwhereij 2D. i 3 P 2 (cos ij)>.r..Here, 0. is the orientation of the internuclear vector r.. with respect to the magneticfield H. The average with respect to 8.. is related to the averaging of the moleculardipole moment ji in the electric field E (described by an angle L) as follows:<P 2 (cos 6ij)> = <Pz(cos ) P 2 (cos a) P 2 (cos Pij),QPR No. 72(VIII. MAGNETIC RESONANCE)where a is the angle between E and H, and i.. is that between 4 and r... Observationof dipolar splittings in the NMR spectrum of a molecule of known structure thus permitsa determination of <P 2 (cos )> . Both this quantity and < cos L >, which for highly polarliquids is approximately obtainable from the dielectric constant E:(E-1) E<cos >= 4 (v,are characteristic of the angular distribution of molecules in the electric field. For afluid without intermolecular forces, this distribution is proportional to exp(4E cos /kT),and leads to<cos > = T; P(cos) = E\In dense fluids, in which intermolecular forces are important, either of these may bemade consistent with experiment if E is replaced by an "effective field" F that is imag-ined to represent the effects of neighboring molecules. For this concept to be physicallymeaningful, the same value of F must be used in both of the above-mentioned averages,and leads to the requirementrP iP 2(cos )>/<cos >2  3The combination of the electric-field NMR experiment and measurements of dielec-tric constant thus provide a measure of the extent to which specific intermolecular forcescause the distribution function to depart from a basically independent-particle formdescribible by an effective field. Such departures may in fact be very large: The resultsobtained by Buckingham and McLauchlan on the molecule p-nitrotoluene, together withthe dielectric constant (estimated to be 20. 5 ± 0. 5 at the temperature of their NMRexperiment), give -r = 4.The absolute value sign on this result reflects the possibility that certain rather spe-cial types of local ordering in the liquid might lead to a negative value for PZ(cos 4). Sucha situation (considered very unlikely in this case) would require a reversal of the argu-ment by which the above-mentioned authors have determined the absolute sign of the indi-rect spin-spin coupling constant J...iJJ. D. Macomber, J. S. WaughReferences1. R. Freeman and W. A. Anderson, J. Chem. Phys. 37, 85; 2053 (1962).2. A. D. Buckingham and K. A. McLauchlan, J. Chem. Soc., p. .144, May 1963.QPR No. 72(VIII. MAGNETIC RESONANCE)2. NUCLEAR RELAXATION IN XENON TETRAFLUORIDEThe spin-lattice relaxation time TI of the F 1 9 nuclei in polycrystalline XeF 4 hasbeen measured between approximately 77°K and 400 0 K. (See Fig. VIII-1.) At low0--4.5 4.0 3.5 3.0 2.5I 0/ T (-K)-'Fig. VIII-1. Spin-lattice relaxation of F 1 9 in crystallineXeF 4 . The relaxation time, T 1 , is plottedon a logarithmic scale against the recipro-cal of the absolute temperature. Measure-ments were made at 30 mc. The straightline is drawn for an activation energy formolecular motion of 12. O0 kcal/mole.temperatures T 1 is roughly constant at approximately 103 sec, but at higher tempera-tures it drops proportionally to exp(E/RT). The activation energy is 12. 0± 1. 5 kcal/mole.The molecular motion responsible for relaxation is evidently an activated reorientationof XeF 4 molecules in situ. These results are consistent with a previously reported line-width transition in the neighborhood of 250 0 K. Details have been submitted for publica-tion to the Journal of Chemical Physics.C. G. Wade3. ELECTRON-SPIN RESONANCE OF METAL-AMMONIA SOLUTIONSThe well-known blue solutions of alkali metals in liquid ammonia exhibit a singlesharp paramagnetic resonance absorption. This single resonance has been attributedto "solvated free electrons" formed, for example, in the reaction:+Na + NH Na + e + NH(metal) 3 (liquid) (in liq. NH 3 ) (solvated) 3 (liquid)'There has been considerable speculation concerning the degree to which the metalions and the "solvated electrons" are associated. Knight Shifts of the Na 2 3 resonanceindicate an appreciable spin density of "solvated electrons" at the sodium nucleus inQPR No. 72(VIII. MAGNETIC RESONANCE)sodium-ammonia solutions. This has led to a model that considers the electrons to bevery closely associated with the sodium ions in solution - forming "expanded atoms."Indeed, concentrated solutions of metals in liquid ammonia have a metallic luster, andare very metallic in their electrical properties.We have prepared and measured the paramagnetic resonance spectra of solutions ofEuropium metal in liquid ammonia. It was predicted that this rare-earth metal-ammoniasystem, which is qualitatively similar to alkali metal-ammonia systems, might furtherelucidate the electronic structure of metal-ammonia solutions, in that the Europiumcations as well as the "solvated free electrons" might be expected to exhibit paramag-netic resonance absorption. This has been found to be the case.Work is now in progress to measure the line shapes and linewidths of these para-magnetic resonance spectra of Eu-NH3 as a function of concentration and temperature.Future work will include study of the absorption spectra of these solutions from the nearinfrared to the ultraviolet.Recent experiments indicate that Eu metal may also dissolve in very pure tetrahy-drofuran and dimethoxyethane, thereby giving blue solutions. It may also be possibleto study metal-ammonia solutions of other rare-earth metals.D. S. ThompsonQPR No. 72

Magnetic Resonance

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Magnetic Resonance

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