Journal of Low Temperature Physics, Vol. 111, Nos. 3/4, I99S

The Orientational Ordering in Dilute Solid N2-Ar Mixtures J. A. Hamida, S. Pilla, and N. S. Sullivan Department of Physics, University of Florida, Gainesville, FL 32611-8440, USA

NMR studies have been carried out to determine the nature of the orientational ordering of N2 in dilute solid N2-Ar mixtures. The orientational ordering for cubic lattices (x(N2) = 50%) was compared to that observed for the hexagonal lattice structures for 57 < x(N 2 ) < 75%. The NMR line shapes for the cubic structures were found to be sharply defined and could only be explained in terms of a narrow distribution of order parameters. This is in contrast to the quadrupolar glass state with a very broad order parameter distribution observed for the hexagonal structures. PACS numbers: 76.60-k, 64.70Kb, 75.50Lk

1. INTRODUCTION There is strong interest in mixed molecular solids (such as N 2 -Ar and ortho — para H2 mixtures) because of the quadrupolar glass states that have been observed.1-3 These glass systems are characterized by a random freezing of the orientational degrees of freedom of the molecules, resulting from the combined effects of disorder and frustration. The interactions are short ranged and well known, and the substitutional disorder results from replacement of molecules having electric quadrupole charge distributions by molecules with spherical charge distributions. The interest in these systems is that one can systematically study the effects of both the frustration and the disorder on the orientational ordering and thereby probe the underlying physics of glass formers for which frustration and disorder appear to be universal features.4 The N 2 -Ar mixtures form a system of interacting electric quadrupoles in which the Ar serves as a random dilutant. Pure N2 and mixtures dilute 365 0022-2291/98/0500-0365$15.00/0 © 1998 Plenum Publishing Corporation

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Fig. 1. Phase diagram for solid N2-Ar mixtures. Phase III ( f c c ) is the periodic Pa3 structure and phase IB is the new phase reported here. Phase II (hcp) is the quadrupolar glass state.

in Ar, undergo phase transitions to a long range periodic (Pa3) orientationally ordered phase with a cubic lattice structure for T < 35.6 K.5 This structure is determined by the highly anisotropic interactions (principally electrostatic quadrupole-quadrupole) between the molecules and it is highly frustrated. The frustration arises from the geometrical impossibility of realizing the minimum possible energy configuration (a mutually orthogonal tee alignment) for all pairs of neighboring molecular quadrupoles in close packed 3D lattices. The long range order is fragile with respect to disorder, and for N2-Ar mixtures with x(Ar) > 23%, quadrupolar glass states have been observed.2,3,6-12 In the quadrupolar glasses,1,2 both the principal axes for the molecular quadrupoles and the local order parameters evaluated with respect to those axes vary at random throughout the sample. The quadrupolar glasses have only been observed when the lattice structure is hcp. In view of the geometrical nature of the frustration it is important to explore the effect of lattice geometry on the local ordering. The N2-Ar solid mixtures offer a unique opportunity for studying the effect of lattice geometry on the ordering because both hcp and fcc structures

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exist for high substitutional disorder, namely fcc for x(N2) < 57% and hcp for 57 < x(N 2 ) < 77%. (Fig. 1)7 We studied samples with x(N 2 ) = 50% because this concentration is sufficiently close to the fcc/hcp phase boundary that the effects of quenched disorder should be comparable for the two structures. The NMR line shapes in this fcc phase were found to be very different from the broad line shapes of the hcp quadrupolar glass state.13

2. NMR STUDIES NMR studies were carried out using the isotope 15N with nuclear spin (I = 1/2) because the common isotope 14N has a nuclear quadrupole moment and would result in very broad resonance lines if there is an appreciable distribution of local order parameters. If a given molecule has a well defined mean orientation, the intramolecular nuclear dipole-dipole interaction and the asymmetric chemical shifts do not average to zero. These interactions determine the width and shape of the NMR absorption spectrum and can be used to determine the local orientational order parameters. For a magnetic field applied along the z-axis, the intramolecular nuclear spin-spin Hamiltonian for the ith ortho molecule (/ = 1) whose molecular axis makes an angle 0i with the z-axis is given by

D/27T — 1.38 kHz is the intramolecular dipole interaction strength, P 2 (9i) — 1/2 (3 cos2 B( — 1) and K = (4x 10 -4 )wo is the asymmetric chemical shift which is proportional to the Larmor frequency w0. The NMR spectrum for the ith molecule is the superposition of two lines shifted from w0 by <5wf = (K ± D)P 2 (O i ), where P 2 (9 i ) — P2(on)Xi. a is the angle between the molecular symmetry axis and the z-axis, and Xi —

with a = 1,2 and K1 = 1/2(K + D), K2 = 1/2(K - D), respectively. 0 is the step function. The observed NMR absorption spectrum S(w) is a broadened asymmetric Pake doublet 14 given by the sum over the distribution P ( X ) of

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the order parameters.

where g ( w ) is a broadening function that takes into account the intermolecular dipolar interactions and local field inhomogeneities.

Fig. 2. Comparison of the experimental line shape (solid line) with the theoretically calculated NMR line shape (dotted line) for a 50-50% N2-Ar solid mixture at 4.2 K. The inset shows the distribution P(x) of order parameters used for the calculated line shape.

Homogeneous samples were prepared by rapidly condensing and solidifying a 50% N2-Ar gas mixture inside the NMR cell. This was followed by rapid heating to generate the internal strains that are believed to be necessatry to nucleate and stabilize the fcc lattice structure. 7,15 The sample was then warmed and annealed for several hours at 59 K just below the melting point (60.5 K). The low temperature NMR line shapes did not vary as a function of different annealing times.

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3. RESULTS The experimentally observed NMR line shape for the 50% (N 2 -Ar) solid mixture at 4.2 K is shown in Fig. 2. The existence of the sharp secondary peak for T < 6.0 K is a strong indication of a very narrow order parameter distribution.

Fig. 3. The NMR line shapes observed for different N2 concentrations and the corresponding quadrupolar order parameter distribution function P(X). The line shapes varied smoothly with temperature with no evidence of a sharp phase transition. Measurements of the cooling rates with a weak thermal coupling to the sample were also carried out to obtain a qualitative measure of the heat capacities and these also showed a continuous evolution with temperature, consistent with previous studies.6 The best fit to the experimental line shape was obtained using a very narrow distribution of order parameters P ( X ) . This fit is shown by the dotted line in Fig. 2, and the distribution P(X) is shown in the inset. A comparison of the line shapes observed for different N2 concentrations and the associated order parameter distributions is shown in Fig. 3. The spectra for x < 40% are very broad and very similar to the NMR spectra seen for x(N 2 ) = 67%, and they are attributed to a quadrupolar glass ordering. The excellent reproducibility of

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the line shapes for several samples and different mixtures for 40 < x < 50% prepared with different annealing times shows that this cannot be attributed to a phase separation or strained crystal growth. 4. CONCLUSION Measurements of the NMR line shapes of N 2 -Ar solid mixtures for a 50% N2 concentration where the crystal structure is fcc have shown that contrary to expectations, the orientational order parameter has a very sharp distribution of values. Long range ordering is not expected for this dilute concentration of N2 and experimentally no discontinuites or abrupt changes in the thermodynamic properties have been reported for this concentration. The NMR observations therefore imply that the local orientational ordering is very different from that of the familiar quadrupolar glass phase. In this new orientational glass state the molecular axes are distributed at random but the mean order parameters evlauated with respect to those local axes have only a very narrow distribution. ACKNOWLEDGEMENTS The work was supported by a grant from the National Science Foundation — DMR-9216785. REFERENCES 1. N. S. Sullivan, M. Devoret, B. P. Cowan, and C. Urbina, Phys. Rev. B 17, 5016 (1978). 2. D. Esteve, N. S. Sullivan, and M. Devoret, J. Phys.(Paris) Lett. 43, 793 (1982). 3. K. Binder and J. D. Reger, Adv. Phys. 41, 547 (1992). 4. D. Chowdhury, Spin Glasses and Other Frustrated Systems, Princeton Univ. Press, Princeton, NJ (1986). 5. T. A. Scott, Phys. Rep. 27, 89 (1976), 6. L. G. Ward, A. M. Saleh, and D. G. Haase, Phys. Rev.B 27, 1832 (1983). 7. C. S. Barret and L. Meyer, J. Chem. Phys. 42, 107 (1965). 8. W. Press, B. Janik, and H. Grimm, Z. Phys. B 49, 9 (1982). 9. U.T. Hochli, K. Knorr, and A. Loidl, Adv. Phys. 39, 405 (1990). 10. K.H. Michel and J.M. Rowe, Phys. Rev.B 22, 1417 (1988). 11. P. Wochner, E. Burkel, J. Peik, and A. Eckold, Europhys. Lett. 17, 703 (1992). 12. N.S. Sullivan, Can. J. Chem. 66, 908 (1988). 13. J. Hamida, N.S. Sullivan, and M.D. Evans, Phys. Rev. Lett. 73, 2720 (1994). 14. L. M. Ishol and T. A. Scott, Magn. Res. 27, 23 (1977). 15. L. D. Yantsevich, A. I. Prokhvatilov, I. N. Krupski, and A. S. Baryl'nik, Sov. J.Low Temp. Phys. 12, 335 (1986).