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Splitting of NMR spectrum of solid hydrogen
Volume 39A, number 1
PHYSICS LETTERS
10 April 1972
SPLITTING OF NMR SPECTRUM OF SOLID HYDROGEN* N.S. SULLIVAN and R.V. POUND
Lyman Laboratory of Physics, Harvard University, Cambridge, USA Received 11 February 1972 We report a hitherto unobserved dependence of the splitting of the NMR spectrum on the ortho content of solid hydrogen at very low temperatures.
The NMR spectrum of f.c.c, solid hydrogen has a fine structure arising from the intramolecular dipoledipole interaction [ 1,2]. This results from the partial lifting of the rotational degeneracy of the ortho molecules by their collective quadrupolar interactions, the states J z = +- 1 being separated from the ground state Jz = 0 by an energy cap A. The line shape of the powdered sample [3] has a width between cusps of 3 2 VDD = 3 d ( 1 - -~ ( J z ) T ) (1)
where ( j 2 ) T is the orientational order parameter [4] at temperature T. The statistical average ( J 2 ) r is taken over the spectrum of rotational states. These have been studied theoretically by several investigators [5-8] using models of librational excitations for which A ~ 12 (2.06X-1)°K and the bandwidth is ~ 0.8A. (X is the fractional ortho content.) We have observed that the splitting is reduced as the sample ages at constant temperature. Samples of normal hydrogen (75% ortho) were condensed into a resonant cavity and maintained below 90 m°K by a 3He-4He dilution refrigerator. The NMR spectra were observed with a bridge spectrometer at 311 mHz using
*Work supported by a grant from the National Science Foundation NSF-GP-24736 and, formerly, under Contract Nonr1866 (56) from the Office of Naval Research.
178
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150
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Fig. 1. Observation of the dependence of NMR splitting UDD on the ortho content of ordered solid hydrogen. 23
Volume 39A, number 1
PHYSICS LETTERS
low rf levels to avoid saturation. The results for several different samples at 85 -+ 5 m°K are shown in fig. 1 where the separation in frequency of the points of maximum slope taken from derivative line spectra are plotted against the ages of the samples. The ortho contents of the samples were estimated from the published ortho-para conversion rates [9]. The NMR intensities were consistent with this assumption. No sudden transition to a disordered state ( J z2 = 2 , PDD - 0) is observed as the samples age toward J( ~ 0.56 for which previous studies report no ordering [10,11]. We attribute this to an effective crystal field [5] arising from anisotropic Van der Waal's forces and leading to an energy gap A c. Van Kranendonk and Sears [ 12] have estimated A c ~ --0. 15°K, while experiments [13] suggest Ac ~ +0.35°K. For these values, Ac has negligible effect for the relatively high temperature experiments previously reported, but in this case the crystal field effectively removes the rotational degeneracy. The solid curve shown in fig. 1 illustrates the variation of PDD with ortho concentration for the energy gap A = 11 ( 1 . 8 X - 1) + 0.24°K for X > 0.555, and A c = 0.24°K for X < 0.55. A contribution due to the dipole-dipole broadening has been included as well as the correction to be made for the zero point rotational motion [141. The value o f A c was consistent with the fact no fine structure was observed on thermally cycling an aged sample with X < 0.56 unless T < 0.3°K. (The temperature dependence of PDD was observed to be less than but in qualitative agreement with that
24
10 April 1972
estimated from the order parameter calculated by Ueyama and Matsubara [8] .) The accuracy of the results has been limited by the inability to operate the 75 kG superconductive magnet in the persistent mode. These results and related data on the spin relaxation times will be described in greater detail elsewhere.
References [1 } J. ltatton and B.V. Rollin, Proc. Roy. Soc. A199 (1949) 222. 12l I:, Reif and E.M. Purcell, Phys. Rev. 91 (1953) 631. 13J A, Abragam, The principles of nuclear magnetism (Oxford University Press, London, 1961) p. 223. [4] J.C. Raich and R.D. Etters, Phys. Rev. 155 (1967) 457; 161 (1967)493. [51 J.C. Raich and R.D. Etters, Phys. Rev. 168 (1968)425. [61 S. ttomma, K. Okada and 11. Matsuda, Prog. Theoret. Phys. (Kyoto) 38 (1967) 767. [71 H. Ueyama and T. Matsubara, Prog. Theoreh Phys. (Kyoto) 38 (1967) 784. [8] I:.G. Mertens, W, Biem and H. Hahn, Z. Physik 213 (1968) 33. [9] S.A. Dickson and H.M. Meyer, Phys. Rev. 138 (1965) A1293. [10] L.I. Amstutz, H. Meyer, S.M. Meyers and D.C. Rorer, Phys. Rev. 181 (1969) 589. [11] R.L. Mills, A.F. Schuch and D.A. Depatie, Phys. Rev. Lett. 17 (1966) 1131. [12] J. van Kranendonk and V.t:. Sears, Can. ,1. Phys. 44 (19661 313. ]13] A.B. ttarris and E. Hunt, Phys. Rev. Lett. 16 (1966) 845. [14] A.B, Harris, Phys. Rev. BI (1970) 1881.
PHYSICS LETTERS
10 April 1972
SPLITTING OF NMR SPECTRUM OF SOLID HYDROGEN* N.S. SULLIVAN and R.V. POUND
Lyman Laboratory of Physics, Harvard University, Cambridge, USA Received 11 February 1972 We report a hitherto unobserved dependence of the splitting of the NMR spectrum on the ortho content of solid hydrogen at very low temperatures.
The NMR spectrum of f.c.c, solid hydrogen has a fine structure arising from the intramolecular dipoledipole interaction [ 1,2]. This results from the partial lifting of the rotational degeneracy of the ortho molecules by their collective quadrupolar interactions, the states J z = +- 1 being separated from the ground state Jz = 0 by an energy cap A. The line shape of the powdered sample [3] has a width between cusps of 3 2 VDD = 3 d ( 1 - -~ ( J z ) T ) (1)
where ( j 2 ) T is the orientational order parameter [4] at temperature T. The statistical average ( J 2 ) r is taken over the spectrum of rotational states. These have been studied theoretically by several investigators [5-8] using models of librational excitations for which A ~ 12 (2.06X-1)°K and the bandwidth is ~ 0.8A. (X is the fractional ortho content.) We have observed that the splitting is reduced as the sample ages at constant temperature. Samples of normal hydrogen (75% ortho) were condensed into a resonant cavity and maintained below 90 m°K by a 3He-4He dilution refrigerator. The NMR spectra were observed with a bridge spectrometer at 311 mHz using
*Work supported by a grant from the National Science Foundation NSF-GP-24736 and, formerly, under Contract Nonr1866 (56) from the Office of Naval Research.
178
174 - -
o o
170 - -
co o o~oo ooo
o o
166
162
QI58 o 154 o
150
o
o
--
oooom
146 0.70
~
I,
( F R A C T I O N A L ORTHO C O N T E N T ) 0.50 0.40
0.60
,
:J lo
,:
I
: , zo
:l
!
!
30
~L 40
~'
t 50
I,
) 60
AGE (hrs)
Fig. 1. Observation of the dependence of NMR splitting UDD on the ortho content of ordered solid hydrogen. 23
Volume 39A, number 1
PHYSICS LETTERS
low rf levels to avoid saturation. The results for several different samples at 85 -+ 5 m°K are shown in fig. 1 where the separation in frequency of the points of maximum slope taken from derivative line spectra are plotted against the ages of the samples. The ortho contents of the samples were estimated from the published ortho-para conversion rates [9]. The NMR intensities were consistent with this assumption. No sudden transition to a disordered state ( J z2 = 2 , PDD - 0) is observed as the samples age toward J( ~ 0.56 for which previous studies report no ordering [10,11]. We attribute this to an effective crystal field [5] arising from anisotropic Van der Waal's forces and leading to an energy gap A c. Van Kranendonk and Sears [ 12] have estimated A c ~ --0. 15°K, while experiments [13] suggest Ac ~ +0.35°K. For these values, Ac has negligible effect for the relatively high temperature experiments previously reported, but in this case the crystal field effectively removes the rotational degeneracy. The solid curve shown in fig. 1 illustrates the variation of PDD with ortho concentration for the energy gap A = 11 ( 1 . 8 X - 1) + 0.24°K for X > 0.555, and A c = 0.24°K for X < 0.55. A contribution due to the dipole-dipole broadening has been included as well as the correction to be made for the zero point rotational motion [141. The value o f A c was consistent with the fact no fine structure was observed on thermally cycling an aged sample with X < 0.56 unless T < 0.3°K. (The temperature dependence of PDD was observed to be less than but in qualitative agreement with that
24
10 April 1972
estimated from the order parameter calculated by Ueyama and Matsubara [8] .) The accuracy of the results has been limited by the inability to operate the 75 kG superconductive magnet in the persistent mode. These results and related data on the spin relaxation times will be described in greater detail elsewhere.
References [1 } J. ltatton and B.V. Rollin, Proc. Roy. Soc. A199 (1949) 222. 12l I:, Reif and E.M. Purcell, Phys. Rev. 91 (1953) 631. 13J A, Abragam, The principles of nuclear magnetism (Oxford University Press, London, 1961) p. 223. [4] J.C. Raich and R.D. Etters, Phys. Rev. 155 (1967) 457; 161 (1967)493. [51 J.C. Raich and R.D. Etters, Phys. Rev. 168 (1968)425. [61 S. ttomma, K. Okada and 11. Matsuda, Prog. Theoret. Phys. (Kyoto) 38 (1967) 767. [71 H. Ueyama and T. Matsubara, Prog. Theoreh Phys. (Kyoto) 38 (1967) 784. [8] I:.G. Mertens, W, Biem and H. Hahn, Z. Physik 213 (1968) 33. [9] S.A. Dickson and H.M. Meyer, Phys. Rev. 138 (1965) A1293. [10] L.I. Amstutz, H. Meyer, S.M. Meyers and D.C. Rorer, Phys. Rev. 181 (1969) 589. [11] R.L. Mills, A.F. Schuch and D.A. Depatie, Phys. Rev. Lett. 17 (1966) 1131. [12] J. van Kranendonk and V.t:. Sears, Can. ,1. Phys. 44 (19661 313. ]13] A.B. ttarris and E. Hunt, Phys. Rev. Lett. 16 (1966) 845. [14] A.B, Harris, Phys. Rev. BI (1970) 1881.