Waugh, J. S.

Whitney, W. M.

DSpace@MIT

III. LOW TEMPERATURE PHYSICSProf. E. Maxwell Dr. C. A. Shiffman A. A. ThieleProf. J. F. Cochran W. A. Jeffers K. G. WitzkeProf. W. M. Whitney C. Krischer R. P. WolfJ. S. RosensheinA. NUCLEAR MAGNETIC RESONANCE IN SOLID METHANEMeasurements of the nuclear magnetic resonance absorption spectrum in the tem-perat-ire range from 20K to 40K have been made for pure solid methane (CH 4 ) and forthree mixtures of methane with krypton. We obtain traces of the first derivative of theabsorption curve as a function of magnetic field, and our results can best be describedwith reference to two characteristics of these traces: (a) the linewidth, which we taketo be the difference between the values of magnetic field characterizing the maximumand minimum values of the first derivative, and (b) the second moment of the absorp-tion curve, or the average value of (H-Ho) 2, calculated by using the absorption at eachvalue of H as a weighting factor. (Ho is the field characterizing the center of the line.)The second moment can be calculated theoretically from an equation derived byVan Vleck. For a molecule such as methane which has several protons, the secondmoment is the sum of two contributions: an intramolecular part, arising from inter-actions among the four protons within a given molecule, and an intermolecular part,arising from interactions among the protons on one molecule and those on neighboringmolecules.Our experimental results for pure methane below 4°K give us 7. 1 gauss for thesecond moment, and 7. 1 gauss for the linewidth. We observe no changes in these quan-tities with temperature which are greater than ±5 per cent, our experimental uncer-tainty. For a methane molecule completely at rest, the intramolecular contribution tothe second moment alone is greater than 30 gauss , so it is clear that the methanemolecules cannot be standing still. It is known that the carbon atoms in methane forma face-centered cubic lattice in the solid. If one calculates the intermolecular contri-bution to the second moment, assuming that the four protons are smeared out uniformlyover a shell surrounding each carbon atom, a value of 10 gauss is obtained, which, ofcourse, is too large. A more realistic model would be one in which the molecules areassumed to have definite orientations with respect to various directions in the lattice,and to jump from one equivalent orientation to another. Calculations for the variouspossibilities are in progress.In order to study the intramolecular contribution to the second moment, we mademeasurements in krypton-methane mixtures. Both substances have face-centeredcubic lattices with approximately equal lattice constants, and are known to form solidsolutions at all concentrations. As the (almost) magnetically inert krypton atomsreplace methane molecules in the lattice, the second moment should decrease, falling(III. LOW TEMPERATURE PHYSICS)linearly with increasing krypton concentration either to zero or to some finite value,which would be interpreted as the intramolecular contribution to the second moment.Our measurements were made for methane lattices having 15 per cent, 50 per cent,and 90 per cent of their sites occupied by krypton atoms. The three second moments,together with the value for pure methane, lie on a straight line which extrapolates toa value of approximately 1. 8 gauss2 for isolated methane molecules. The linewidthdoes not fall linearly with increasing krypton concentration, but decreases in such away that it may become zero; however, further points are needed at higher kryptonconcentrations before a definite statement can be made. The indications are, never-theless, that the shape of the absorption curve is changing, and we believe that ourresults at high krypton concentrations may pose problems of interpretation which arenot necessarily related to those that arise in connection with pure methane.Our plans for the immediate future are to study the absorption spectra of methane-krypton mixtures at additional concentrations and to extend the measurements for allof our samples to temperatures in the range 4°K-770 K. Work has commenced onCH 3 D and will soon begin on CH 4 -CD 4 mixtures. These experiments are all part ofour long-range program to study the k-point in solid methane and in the various soliddeuterated methanes.Major contributions to the work reported here were made by Erlend H. Graf andHoward A. Rubin, senior thesis students, and by Robert Blinc, Alfred P. Sloan Foun-dation Foreign Postdoctoral Fellow.W. M. Whitney, J. S. Waugh

Low Temperature Physics

http://dspace.mit.edu/bitstream/1721.1/53593/1/RLE_QPR_062_III.pdf

Low Temperature Physics

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