Contains research objectives and reports on one research project

Cochran, J. F.

Maxwell, E.

Waugh, J. S.

Whitney, W. M.

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IV. LOW TEMPERATURE PHYSICSProf. E. Maxwell W. A. Jeffers, Jr. A. A. ThieleProf. J. F. Cochran R. R. Oder R. C. WilliamsonProf. W. M. Whitney J. S. Rosenshein K. G. WitzkeM. Garber Y. Shapira R. P. WolfW. H. Glenn, Jr. M. YaqubRESEARCH OBJECTIVESThis group is interested in those phenomena in liquids and solids which can beadvantageously studied at very low temperatures. Some of these phenomena, princi-pally the superfluidity of liquid helium and superconductors, are peculiar to the low-temperature domain. There are other phenomena, such as those involving transportproperties, which are essentially temperature-dependent and whose behavior at lowtemperature is important. Current interests include relaxation processes in liquidhelium, magnetic properties and relaxation processes in superconductors, the studyof phase transitions and lambda points, and the improvement of techniques for attainingand using very low temperatures by adiabatic demagnetization.A brief description of the work that is being carried out by each member of thisgroup can be found in the Annual Research Report of the Laboratory of Chemical andSolid-State Physics, M.I.T., July 15, 1961.E. Maxwell, J. F. Cochran, W. M. WhitneyA. NUCLEAR MAGNETIC RESONANCE IN SOLID METHANEIn Quarterly Progress Report No. 62 (pages 97-98), we reported a determination ofthe proton magnetic resonance absorption line in solid methane (CH 4 ) at 4°K, from2which we obtained values of 7 gauss for the linewidth and 7 gauss for the secondmoment. During the past months we have tried to correlate these results with theo-retical predictions based on various models for the dynamical state of the moleculesin the methane lattice.Since a proton has a spin of 1/2, a free methane molecule will have states withtotal nuclear spin 0, 1, or 2. If transitions between states of different total spin wereas strongly prohibited for methane as they are for hydrogen, then at low temperaturesthere would be three distinct molecular species, or nuclear isomers, in approximatelytheir room-temperature proportions. In a gas of free molecules at sufficiently lowtemperatures, one would expect to find each molecule in the rotational ground stateconsistent with its nuclear spin.It has been shown that if one treats the methane molecules in the solid as a gasand assumes that there is no conversion between nuclear isomers, a value is obtainedfor the zero-point entropy of the crystal which does not agree with the experimentalvalue of R In 16. NagamiyaZ has determined the groups into which the rotationalenergy levels would be split by the crystalline field of the lattice, and has shown thatif the crystal symmetry is F43m, the zero-point entropy will be R In 16 whether ornot conversion takes place; a structure with this symmetry therefore serves as a goodstarting point for a second-moment calculation.(IV. LOW TEMPERATURE PHYSICS)Assuming that the molecules do not move, we obtain a value of 10 gauss2 for theintermolecular contribution to the second moment for the structure proposed byNagamiya. The intramolecular second moment for a stationary molecule is 33 gaussso the total rigid lattice second moment would be 43 gauss . The low experimentalvalue of 7 gauss 2 indicates that the molecules are in motion, and allowances must bemade for this motion in calculating theoretical second moments.Tomita 3 has calculated the shape of the absorption line in solid methane for theF43m structure under the assumption that the nuclear isomers do not readily convert atlow temperatures. His analysis leads to a linewidth of 7.5 gauss, which is attributableto intramolecular interactions alone. He estimates that the intermolecular second2moment will be 7. 3 gauss . While he does not state a value for the total second moment,he does plot a curve from which we obtain a value of 15 gauss 2 as an absolute lowerlimit. Tomita's results appear to be in good agreement with a line shape deduced byThomas, Alpert, and Torrey4 from pulse measurements of the spin-spin relaxationtime (T 2 ) in solid methane, but do not agree with our measurements, in which lineshape is measured directly.As we reported in Quarterly Progress Report No. 62, we tried to separate theintramolecular contribution to the second moment from the intermolecular one bydiluting the methane lattice with krypton. Preliminary results indicated that when thesecond moment was extrapolated to 100 per cent Kr, a value of 2 gauss 2 remained, but,since then, we have shown that our lines at 50 per cent Kr and at 90 per cent Kr wereinstrumentally broadened. For 90 per cent Kr we now obtain second moments in therange 0. 6-0. 9 gauss 2, and we conclude that the intramolecular second moment is prob-ably zero in dilute solutions. If the crystalline field had the same symmetry in thedilute solutions as in the pure crystal, we would have expected a large intramolecularcontribution from the molecules with nuclear spin 1, on the basis of Tomita's analysis.No one has established that nuclear isomers of the methane molecule do or do notconvert readily in the solid, and it is worth considering the consequences of the assump-tion that they do. If total nuclear spin were not a good molecular quantum number, eachmolecule would be free to drop into its lowest state. For the highly symmetrical meth-ane molecule in a cubic environment, this state would be very mych like the J = 0 stateof the free molecule, for which all angular orientations are equally probable. We havecalculated the intermolecular second moment for a face-centered cubic lattice of meth-ane molecules in J = 0 states, and obtain an upper limit of 4.4 gauss 2 . This numberlies below the experimental one, but it is clear that any attempts to make allowancesfor effects of the crystalline field or for cooperative motions of the molecules will makethe agreement better rather than worse.If one can treat the motions of the methane molecules without regard to the inhibi-tions imposed by their nuclear spins, it would be expected that the deuterated methanes(IV. LOW TEMPERATURE PHYSICS)should exhibit essentially the same behavior as CH 4 in their crystalline ground states.For CH 3 D, which has only three protons instead of four, the intermolecular proton second2moment should be simply three-fourths that of CH 4 , or approximately 5.3 gaussDuring the summer, A. Dammig, a senior thesis student, measured the second momentof CH3D at 4°K. The average value of the second moments obtained from the first runwas approximately 5.5 gauss . On each of two subsequent runs, however, the resultswere progressively higher, attaining values as high as 8 gauss2 . We believe that theupward trend of the data represents the effect of a leaking of large amounts of air(containing paramagnetic oxygen) into our ampoule during a run, and have redesignedour apparatus so that ampoules that are permanently sealed off can be used. Until theprecision of our CH3D measurements has been improved, we cannot claim support forour hypothesis. It is worth pointing out, however, that the second moment for a rigidCH 3 D lattice would be approximately 29 gauss2, and we feel confident in ruling out thepossibility that the lowest phase transition in CH3D represents a freezing-out of themolecular reorientation.W. M. Whitney, J. S. WaughReferences1. A. Frank and K. Clusius, Z. physik. Chem. B36, 291 (1937).2. T. Nagamiya, Progr. Theoret. Phys. (Kyoto) 6, 702 (1951).3. K. Tomita, Phys. Rev. 89, 429 (1953).4. J. T. Thomas, N. L. Alpert, and H. C. Torrey, J. Chem. Phys. 18, 1511 (1950).

Low Temperature Physics

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Low Temperature Physics

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