Journal ArticleMagnetic resonance has been widely used to study phenomena such as atomic diffusion and molecular reorientation. It is applicable when the mean time, r, between atomic jumps is either  (a) sufficiently short to narrow the resonance  line width or (b) of the correct magnitude to produce spin-lattice relaxation. Case (a) occurs  when r is less than 1/Aco where Au> is the rigid lattice linewidth. Case (b) occurs when T is of the order of l/co0 , where oo0 is the Larmor  frequency. Typically, case (a) is found when  r < 100 /isec, case (b) when r ~ 10 ~ 8 sec. In this Letter we report a new, experimentally simple  technique which enables us to study motions of a much slower rate, the criterion being roughly T < T 1  where T1 is the spin-lattice relaxation time

Ailion, David Charles

Slichter, Charles P.

English

The University of Utah: J. Willard Marriott Digital Library

VOLUME 12, NUMBER 7 PHYSICAL REVIEW LETTERS 17 FEBRUARY 1964 about 5 at 2°K. It is expected that similar "giant oscillations" will occur also in the velocity of sound waves and that they can be used in a similar fashion to determine effective masses. Experiments designed to determine the line shape of the "giant oscillations" with greater pre-cision are now in progress. The results of such experiments should permit the use of Eq. (10) to determine the parameters {3 and QI. We wish to thank L. M. Foster for providing us with high-purity gallium, G. Trench for as-sistance in growing the samples, J. Zak, A. Gold-stein, L. Neuringer, and K. J. Button for useful discuSSions, and M. Kelly for technical assis-tance. *Kennecott Copper Predoctora1 Fellow. t Supported by the U. S. Air Force Office of Scientific Research. tOperated with support by the U. S. Army, Navy, and Air Force. IA. P. Korolyuk and T. A. Prushchak, Zh. Eksperim. i Teor. Fiz. 41, 1689 (1961) [translation: Soviet Phys.-JETP 14, 1201 (1962)]. 2J. G. Mavroides, B. Lax, K. J. Button, and Y. Shapira, Phys. Rev. Letters 9, 431 (1962). 3y. Shapira and B. Lax, Phys.-Letters 7, 133 (1963). 4V. L. Gurevich, V. G. Skobov, and Yu:- A. Firsov, Zh. Eksperim. i Teor. Fiz. 40, 786 (1961) [translation: Soviet Phys. -JETP 13, 552 (1961)]; J. J. Quinn and S. Rodriguez, Phys. Rev. 128, 2487 (1962). 5D. Shoenberg. Phil. Trans. Roy. Soc. London A245, 1 (1952). STUDY OF ULTRASLOW ATOMIC MOTIONS BY MAGNETIC RESONANCE* David Ailion t and Charles P. Slichter Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois (Received 13 January 1964) Magnetic resonance has been widely used to study phenomena such as atomic diffusion and molecular reorientation. It is applicable l when the mean time, 7, between atomic jumps is ei-ther (a) sufficiently short to narrow the reso-nance linewidth or (b) of the correct magnitude to produce spin-lattice relaxation. Case (a) oc-curs when 7 is less than 1 / ~w where ~w is the rigid lattice linewidth. Case (b) occurs when 7 is of the order of 1/ w o , where Wo is the Larmor frequency. Typically, case (a) is found when T<100 IJ.sec, case (b) when 7-10-8 sec. In this Letter we report a new, experimentally simple technique which enables us to study motions of a much slower rate, the criterion being roughly 7 < T l' where T 1 is the spin-lattice relaxation time. The method is in many ways equivalent to case (b) with Wo set equal to zero; however, by means of a trick we achieve this condition with the actual fieldHo at a large value (10000 gauss), thereby achieving important experimental advan-tages. An important problem in interpretation is understanding the effect of atomic motion on the relaxation time when the static field is com-parable to or less than the local field of the neigh-boring nuclei (wo "" ~w). The conventional theory of Bloembergen, Purcell, and Pound breaks down under these circumstances (in the limit of slow motion with which we are concerned). By gener-alizing the hlethods of Redfield et al. ,2,3 we have 168 been able to solve this problem. In this Letter we report the results of measure-ments of self-diffusion in lithium metal, a system chosen because the previous work of Holcomb and and Norberg4 gave information about T. Combin-ing their data with ours, we have measured 7 for this system over eight decades, from 2 x 10-9 second to 2 x 10-1 second, extending their data by nearly four decades. The experimental method is based on the tech-nique of adiabatic demagnetization. 3 If a spin system is demagnetized adiabatically from a high field to zero field, the order remains the same throughout the cycle. In the high field, the order consists of an excess of spins pointing along the applied field. In zero field the order consists of alignment of spins preferentially along the local fields due to their neighbors. Ordinarily, the order in zero field can be maintained for a time comparable to the spin-lattice relaxation time. If atomic jumps take place the situation is changed. When a spin jumps, its orientation does not change since the jumping time is very short compared to any precession period. But the local field in the new site is different from that at the old one, since the dipolar coupling falls off strongly with distance. To some degree, therefore, jumping randomizes the spin orientation in the local field and destroys the order. Clearly we can main-tain the order only for a time comparable to 7. We can therefore detect jumping by measuring VOLUME 12, NUMBER 7 PHYSICAL REVIEW LETTERS 17 FEBRUARY 1964 the rate of loss of order provided T satisfies the criterion T < T l' It is easiest to observe the loss of magnetic order by studying the strength of a magnetic res-onance. The use of a large H o' which gives the greatest sensitivity, makes demagnetization to zero field more complicated. We therefore use the trick of performing the adiabatic demagnet-ization in the rotating reference frame L that is, the frame which rotates at the frequency w of the alternating field H u and in the sense of the pre-cession. We describe the details below. The fact that one could achieve an effective Ho of zero in the rotating frame and thus study slow motion has been independently recognized by Lowe.s Since he has applied the conventional BPP theory to the problem, his results apply when HI is much bigger than the linewidth. The steps in our experiment are as follows s: At t = 0 we have HI = 0, and the static field H 0 set ex-actly on resonance. By means of extra coils placed in the magnet gap, we take Ho off resonance an amount ho, of the order of 15 gauss, and slowly conductIon electron contributIon Diffusion contribution(colculoted using Holcomb and Norberg data for r),---I if I I I ~ " return to resonance. By slowly we mean taking several milliseconds. We turn on an HI of about 1 gauss when the displacement of ho is at a max-imum. This value of HI is comparable to the local field, HL (JIL = 1. 2 gauss for lithium metal). This sequence of events brings the magnetization M parallel to HI in the rotating frame. Since HI ""HV M is less than Mo, the thermal equilib-rium magnetization, and a substantial amount of the order is in alignment of spins along their local fields. We keepHI on for a variable time T at the end of which we turn off HI suddenly. We measure the amplitude of the free induction de-cay immediately after turnoff. This signal is proportional to M, and decays exponentially with T. We call the time-constant (T 2)eff' the effective transverse relaxation time. As we have mentioned, calculation of (T 2)eff is complicated by the fact that HI ""H L' so that the quantum states of the spin system in the rotating frame are not known. By applying the concept of a spin temperature in the rotating frame,s,7 which is valid as long as T> 1 / ~w, and 'lH 12 > (~w / T 1),8 and --1----.-.-,-----1--. - J , ! ,-,2-!f-i f f I l '" ,mIW .. ,oo", 1 '"eff ~ 10 FIG. 1. In(T 2) ff vs (l03/e) for lithium metal. (H1 /HL )2 = 1.19. The conduction electrun contribution is ob-tained by fitting tlie low-temperature data to a (l/e) curve. The theor'Oltical diffusion contribution shown is ob-tained by Eq. (1) using data of Holcomb and Norberg extrapolated from (l03 / e) = 2.77 /"K, using their value of 13.2 ±0.4 kcal/mole for ED' the activation energy. The vertical bar on the theoretical curve at (103/e)=4.5/"K gives the diffusion contribution for the limits of error in ED' At this temperature, their data are extrapolated five orders of magnitude. 169 VOLUME 12, NUMBER 7 PHYSICAL REVIEW LETTERS 17 FEBRUARY 1964 by using the fact that spins do not reorient during an atomic jump, we find for lithium metal (T -1) 2 ,eff (1 ) where P is a quantity representing the extent to which the local field a spin sees after a jump is randomly oriented relative to the value seen be-fore a jump. (JJ can be calculated and is of order 1/10 to 1/2. For lithium metalp=O. 52.) (T)cond is the conduction-electron contribution to (T 2 )eff. 9 Figure 1 shows a plot of In(T2)eff vs l/fJ, where fJ is the absolute temperature, for W1 /H L)2 = 1. 19. At low temperatures T is very long and we find only the conduction-electron contribution. In the region 3. 8<103 /fJ<5. 4, (T2)eff is limited by dif-fusion. Note that for (103 / fJ) greater than about 4.0, 7 is so slow that neither the conventional linewidth nor spin-lattice relaxation time shows signs of diffusion. This is, however, the region in which the spin-temperature theory applies. A solid line extrapolating (T)cond from its low-temperature values using (T)cond a: (1/ fJ) is drawn. From the Torrey theory, the data of Holcomb and Norberg yield T = 5. 5 x 10 -8 second at the T1 minimum (103 /fJ=2. 77). Extrapolating using their activation energy of 13. 2±0. 4 kcal/ mole gives 7=5. 5x10-3 sec at (103 /fJ)=4. 50 with extremes of 8.0 msec or 3.8 msec for the range in activation energy. The experimental T at this temperature from our data is 3.2 msec. Alter-natively, use of our T together with Holcomb and Norberg's4 T at the T1 minimum gives an acti-vation energy of 12.6 kcal/mole. Figure 2 shows the H 1 variation of the dipolar contribution to (T 2)eff' Equation (1) predicts a straight-line dependence as a function of (H 1/ H L)2 intercepting the horizontal axis at -1. We have chosen the slope to give the best fit, although in principle the slope is given by Eq. (1). Such a line is shown and gives a good account of the data. For W1 /H L)2» 1, the spin-temperature theory breaks down8 since the dipolar and Zee-man systems cannot cross relax and a BPP theory applies. Then the slope of the graph should in-crease by a factor of 4/3. Literal application of the BPP theory to low H /s would give a straight line through the origin, clearly in disa-greement with the facts. A full account of the theory, the definition and calculation of p, the application to molecular reorientation, and details of the experimental technique will be published shortly. We wish to 170 DIffusion contribution 10 1.0 o 1.0 2.0 3.0 4.0 FIG. 2. The diffusion contribution to (T2)eff vs (H11 HL)2 for (l03 Ie) = 4. 571"1< (218.5"1<). Equation (1) predicts a straight line intercepting the horizontal axis at the (fictitious) (H /HL)2 = -1. The slope has been chosen to fit the data best, though in principle it is given when 7 is known. The BPP theory if used pre-dicts a straight line passing through the origin and clearly does not apply for these low HI's. thank Dr. F. M. Lurie for his able help with experimental aspects, and Dr. P. R. Moran, Mrs. Judith Franz, Dr. P. Mansfield, and Pro-fessor Leo Kadanoff for discussions of the theory. *This research was supported in part by a grant from the U. S. Atomic Energy Commission. tThis paper is based on the Ph. D. thesis to be pre-sented by David Ailion, at the University of Illinois, Urbana, Illinois (unpublished). tN. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev. 73, 679 (l948)-hereafter referred to as BPP 2 - . • 3A. G. Redfield, IBM J. Res. Develop. 1,19 (1957). A. G. Anderson and A. G. Redfield, Phys. Rev. 116, 583 (1959); L. C. Hebel and C. P. Slichter, Phys. Rev. ill, 1504 (1959). , D. F. Holcomb and R. E. Norberg, Phys. Rev. 98, 1074 (1955); H. C. Torrey, Phys. Rev. 92, 962 (1953); 96, 690 (1954); H. A. Resing and H. C. Torrey, Phys. Rev. 131, 1102 (1963). (We have corrected the results of Holcomb and Norberg for an error in BPP using new equations given by Resing and Torrey.) 5C. P. Slichter and W. C. Holton, Phys. Rev. 122, 1701 (1961); A. G. Anderson and S. R. Hartmann~hys. Rev. 128, 2023 (1962); F. M. Lurie and C. P. Slichter, Phys. Rev. (to be published); an excellent review of the spin-temperature concept is given by L. C. Hebel, in Solid State Physics, edited by F. Seitz and D. Turnbull (~cadem~c ::ress, Inc., New York, 1963), Vol. 15. A prehmmary report of experiments on glycerine and gypsum was presented by D. C. Look and I. J. Lowe at the Fourth Omnibus Conference on the EXperimental VOLUME 12, NUMBER 7 PHYSICAL REVIEW LETTERS 17 FEBRUARY 1964 Aspects of Nuclear-Magnetic-Resonance Spectroscopy, Mellon Institute, Pittsburgh, Pennsylvania, March 1963 (unpublished). We are indebted to Dr. P. Mansfield for calling our attention to the abstract of Look and Lowe's paper in the program of that meeting. They report a disagreement between the theory and experiment for the HI dependence. The difficulty may possibly arise from their application of a BPP-type theory to analyze the data. TA. G. Redfield, Phys. Rev. 98, 1787 (1955). BOur spin-temperature calculation assumes the dipolar and Zeeman energies can cross relax at a rate fast com-pared to (T2)eff' This condition fails when H12» HL2. 9A. G. Redfield and R. Blume, Phys. Rev. 129, 1545 (1963); 1. Solomon and J. Ezratty, Phys. Rev. 127, 78 (1962). DETERMINATION OF THE PROTON-PROTON 1So SHAPE PARAMETER· H. Pierre Noyes Stanford Linear Accelerator Center, Stanford University, Stanford, California (Received 10 January 1964) Modification of the effective-range expansion for the 1So nucleon-nucleon state to include the effect of the one-pion-exchange contribution (OPEC) by means of the partial-wave dispersion relation1 ,2 or the fixed-angle dispersion relationS leads to the prediction that the shape parameter, P, in the expansion q cotoo = -1 /a +!r eq2 - Pr /q4 + ..• is positive. This is also predicted by potential models which include the long-range one-pion-exchange potential (OPEP) and either an inter-mediate-range attraction plus repulsive core4 or energy-independent boundary condition at inter-mediate range5 whose parameters are adjusted to fit the effective range, re , and scattering length, a. A more quantitative prediction is provided by in-cluding the electrostatic repulsion in the partial-wave dispersion relation2 and using two additional parameters to fit observed phase shifts at 95 and 310 MeV as well as a and re; this calculation6 gives P = +0. 024. This prediction is of opposite sign to that made by an energy-independent bound-ary condition at intermediate range,7,8 an energy-dependent boundary condition9 which fits the high-energy (i. e., up to 310 MeV) 1So phase shifts/o,ll or hard-core potentials with intermediate-range attractive tails,12 which do not include the OPE effect. Since the OPE predictions have been quan-titatively confirmed in higher angular momentum states,13 and since the qualitative features of the phase shifts empirically determined in the 100-to 300-MeV range are in good agreement with models based on the exchange of known bosons and strongly interacting boson systems ("reso-nances") between the two nucleons (for a brief discussion of these qualitative features and ref-erences, see reference 11), it is important to test the consistency of these descriptions with the interaction in the S states as rigorously as possible. This is particularly true since the mod-els in best agreement with the high-energy scat-tering experiments predict only 2 MeV of the ob-served 8-MeV binding for the three-nucleon sys-tems,14 and the latter calculation is more sensi-tive to the details of the S-state interactions than the high-energy scattering. One of the few tests available is the prediction of the shape parameter. Since the effective-range expansion fails to con-verge above 10 MeV/ this test can only be made by means of very low-energy nucleon-nucleon ex-periments. Existing n-p data are not of sufficient precision to yield definite conclusions.ll In this Letter we show that the recently reported experi-ment on p-p scattering near the interference min-imum at 0.3825 MeV 15 and the p-p differential cross sections measured at 1. 397, 1. 855, 2.425, and 3.037 MeV 16 can be analyzed to yield a pre-cise value of the shape parameter. This analysiS is only possible because the latter experiments also yield a precise value for the J-weighted aver-age of the sp phase shifts, and because we claim to have a sufficiently quantitative understanding of the multirange character of the nucleon-nucleon interaction to use this value to predict the indi-vidual sPO,1,2 phase shifts. The energy at which the minimum in the p-p 90° cross section occurs is claimed by Brolley, Sea-grave, and Beeryl5 to have been determined to better than ±200 eV, and the energy at which the minimum occurs is given by Gursky and Heller17 as 0.3825 MeV. This value is preliminary, but even if the final result should differ by 200 or 300 eV, none of the conclusions drawn below would be affected. In the absence of vacuum polarization effectf:, this would imply a 1So phase shift of 0.25408 ± O. 00020 rad at precisely that energy; the uncertainty is assigned by assuming that the minimum actually was at 0.3823 (or 0.3827) MeV and then computing the phase shift to be expected 171 

Study of utraslow atomic motions by magnetic resonance

https://collections.lib.utah.edu/dl_files/07/75/07755d21435e25d37432fe89e931dd5b80f04d2c.pdf

Study of utraslow atomic motions by magnetic resonance

Abstract

Similar works

Full text

Available Versions

The University of Utah: J. Willard Marriott Digital Library