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Anomalous temperature dependence ofD andT 2 for dilute solutions of3He in solid4He

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Abstract

Results of measurements of the spin diffusion coefficientD and NMR relaxation timesT 1,T 2, and T1p are presented for a range of fractional3He concentrations 1 × 10−4x 3≤2.5 × 10−3 in solid4He at molar volumes 19.85≤V m≤21.0 cm3 and temperatures 0.4<T<2 K in both hcp and bcc phases. We observe a minimumD(T) atx 3=5×10−4, which is interpreted in terms of a transition from coherent impuriton motion to thermally activated diffusion. ForT<0.8 K, ∂(lnD)/∂(lnV m)=60±8. TheT 2 measurements show a minimum as a function of temperature forx 3≤10−3. TheT 2 (T) andT 1 (T) results yield values for activation energy and tunneling frequency of vacancies in these dilute solutions. Forx 3=5×10−4 andT ∼ 0.5 K,T 2 (V m) is anomalous.T measurements at the same concentration indicate there is an important contribution to the spectral density of dipole field fluctuations in the kHz region.

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References

  1. A. F. Andreev and I. M. Lifshitz,Zh. Eksp. Teor. Fiz. 56, 2057 (1969) [Sov. Phys.—JETP 29, 1107 (1969)].

    Google Scholar 

  2. R. A. Guyer, R. C. Richardson, and L. I. Zane,Rev. Mod. Phys. 43, 532 (1971).

    Google Scholar 

  3. W. Huang, H. A. Goldberg, and R. A. Guyer,Phys. Rev. B 11, 3374 (1975).

    Google Scholar 

  4. W. J. Mullin,Phys. Rev. Lett. 20, 254 (1968).

    Google Scholar 

  5. M. G. Richards, J. Pope, P. S. Tofts, and J. H. Smith,J. Low Temp. Phys. 24, 1 (1976).

    Google Scholar 

  6. M. G. Richards, J. H. Smith, P. S. Tofts, and W. J. Mullin,Phys. Rev. Lett. 34, 1545 (1975).

    Google Scholar 

  7. W. J. Mullin, R. A. Guyer, and H. A. Goldberg,Phys. Rev. Lett. 35, 1007 (1975).

    Google Scholar 

  8. J. E. Sacco, A. Widom, D. Locke, and M. G. Richards,Phys. Rev. Lett. 37, 760 (1976).

    Google Scholar 

  9. J. Schratter, A. R. Allen, and M. G. Richards, to be published.

  10. A. R. Allen and M. G. Richards,Phys. Lett. 65A, 36 (1978).

    Google Scholar 

  11. G. C. Straty and E. D. Adams,Rev. Sci. Instr. 40, 1393 (1969).

    Google Scholar 

  12. E. R. Grilly,J. Low Temp. Phys. 11, 33 (1973); E. R. Grilly and R. L. Mills,Ann. Phys. (NY) 8, 1 (1959).

    Google Scholar 

  13. H. Y. Carr and E. M. Purcell,Phys. Rev. 94, 630 (1954).

    Google Scholar 

  14. S. Meiboom and D. Gill,Rev. Sci. Instr. 29, 688 (1958).

    Google Scholar 

  15. E. L. Hahn,Phys. Rev. 80, 580 (1950); D. E. Woessner,J. Chem. Phys. 34, 2057 (1961).

    Google Scholar 

  16. A. G. Anderson and S. R. Hartmann,Phys. Rev. 128, 2023 (1962); D. C. Ailon, inAdvances in Magnetic Resonance, Vol. 5 (Academic Press, New York, 1971).

    Google Scholar 

  17. A. R. Allen, PhD Thesis, University of Sussex (1978), unpublished.

  18. J. E. Sacco and A. Widom,Phys. Rev. B 17, 204 (1978).

    Google Scholar 

  19. A. Landesman,Phys. Lett. 54A, 137 (1975).

    Google Scholar 

  20. A. F. Andreev,Usp. Fiz. Nauk 118, 251 (1976) [Sov. Phys.—Usp. 19, 137 (1976)].

    Google Scholar 

  21. D. I. Pushkarov,Pisma Zh. Eksp. Teor. Fiz. 19, 751 (1974) [JETP Lett. 19, 386 (1974)];Fiz. Nizk. Temp. 1, 586 (1975).

    Google Scholar 

  22. T. McMullen,J. Low Temp. Phys. 38, 619 (1980).

    Google Scholar 

  23. A. Landesman,J. Low Temp. Phys. 30, 117 (1978).

    Google Scholar 

  24. E. H. Kennard,The Kinetic Theory of Gases (McGraw-Hill, New York, 1938), p. 113.

    Google Scholar 

  25. Y. Yamashita,J. Phys. Soc. Japan 37, 1210 (1974).

    Google Scholar 

  26. J. Wilks,The Properties of Liquid and Solid Helium (Oxford University Press, 1967).

  27. V. N. Grigorev, B. N. Esel'son, and V. A. Mikheev,Zh. Eksp. Teor. Fiz. 66, 321 (1974) [Sov. Phys.—JETP 39, 153 (1974)].

    Google Scholar 

  28. A. R. Allen, M. G. Richards, and J. Schratter,J. Phys. (Paris)39 (Coll. C6), C6–113 (1978).

    Google Scholar 

  29. V. A. Mikheev, B. N. Esel'son, V. N. Grigorev, and N. P. Mikhin,Fiz. Nizk. Temp. 3, 385 (1977) [Sov. J. Low Temp. Phys. 3, 385 (1977)].

    Google Scholar 

  30. V. N. Grigorev, B. N. Esel'son, and V. A. Mikheev,Zh. Eksp. Teor. Fiz. 64, 608 (1973) [Sov. Phys.—JETP 37, 309 (1973)].

    Google Scholar 

  31. J. K. Hoffer, W. R. Gardner, C. G. Waterfield, and N. E. Phillips,J. Low Temp. Phys. 23, 63 (1976).

    Google Scholar 

  32. H. A. Goldberg and R. A. Guyer,J. Low Temp. Phys. 28, 449 (1977)

    Google Scholar 

  33. D. J. Sanders, J. Kwun, A. Hikata, and C. Elbaum,Phys. Rev. Lett. 39, 815 (1977);40, 458 (1978).

    Google Scholar 

  34. R. C. Richardson, E. Hunt, and H. Meyer,Phys. Rev. 138, A1326 (1965).

    Google Scholar 

  35. D. S. Miyoshi, R. M. Cotts, A. S. Greenberg, and R. C. Richardson,Phys. Rev. A 2, 870 (1970).

    Google Scholar 

  36. A. S. Greenberg, W. C. Thomlinson, and R. C. Richardson,J. Low Temp. Phys. 8, 3 (1972).

    Google Scholar 

  37. N. Sullivan, G. Deville, and A. Landesman,Phys. Rev. B 11, 1858 (1975).

    Google Scholar 

  38. R. Balzer and R. O. Simmons, inLow Temperature Physics—LT13 (Plenum Press, New York, 1974), Vol. 2, p. 115.

    Google Scholar 

  39. B. A. Fraass, S. M. Heald, and R. O. Simmons, inProc. Int. Quantum Crystals Conf., Fort Collins, Colorado, 1977 (unpublished), p. C-73.

  40. H. H. Sample and C. A. Swenson,Phys. Rev. 158, 188 (1967).

    Google Scholar 

  41. D. S. Greywall,Phys. Rev. B 15, 2604 (1977).

    Google Scholar 

  42. A. Widom, J. B. Sokoloff, and J. E. Sacco,Phys. Rev. B 18, 3293 (1978).

    Google Scholar 

  43. H. Reich,Phys. Rev. 129, 630 (1963).

    Google Scholar 

  44. R. L. Garwin and A. Landesman,Phys. Rev. 133, A1503 (1972).

    Google Scholar 

  45. Y. Hirayoshi, T. Mizusaki, S. Maegawa, and A. Hirai,J. Low Temp. Phys. 30, 137 (1978).

    Google Scholar 

  46. A. Landesman,Ann. Phys. (Paris)8, 53 (1973).

    Google Scholar 

  47. R. C. Richardson, A. Landesman, E. Hunt, and H. Meyer,Phys. Rev. 146, 244 (1966).

    Google Scholar 

  48. D. C. Look and I. J. Lowe,J. Chem. Phys. 44, 2995, 3437 (1965).

    Google Scholar 

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Financial support provided for apparatus, materials, and a research studentship (ARA) by the Science Research Council.

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Allen, A.R., Richards, M.G. & Schratter, J. Anomalous temperature dependence ofD andT 2 for dilute solutions of3He in solid4He. J Low Temp Phys 47, 289–320 (1982). https://doi.org/10.1007/BF00683732

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