NH3 reorientation in phases I, 11, and I11 of Ni(NH3)6(N03)2

GORDON J. KEARLEY AND HERMA BLANK Institut Mar von Laue - Paul Langevin 156X, 38042 Grenoble CEDEX, France

Received September 28, 1987 This paper is dedicated to Professor Jarnes A. Morrison

GORDON J. KEARLEY and HERMA BLANK. Can. J . Chem. 66 ,692 (1988). The inelastic neutron scattering (INS) spectra of rotational tunnelling and librations of NH3 ligands in phase 111 of

Ni(NH3)6(N03)2 are not consistent with a rotational hindrance potential containing only cos ( 3 4 ) terms owing to strong interaction between neighboring cations. This type of interaction, and motion of the whole cation, also influences the classical reorienta$onal motions involving displacement of the H atoms, where the overall radius of rotation is consistently greater than the 0.9 A expected for isolated NH3 rotors. Quasielastic neutron scattering (QNS) suggests that in phase 111 there are two sublattices of cations, one of which becomes completely disordered (with respect to the NH3 rotors) at the 111-11 phase transition. Disorder of the second sublattice marks the 11-1 transformation where only a single type of rotational motion is found.

GORDON J. KEARLEY et HERMA BLANK. Can. J . Chem. 66, 692 (1988). Les spectres de diffusion des neutrons inklastiques (DNI) de l'effet tunnel de rotation et des librations des ligands NH3 dans le

Ni(NH3)6(N03)2 de phase 111 ne sont pas en accord avec un potentiel d'em@chement la rotation ne contenant que des termes cos ( 3 ~ 4 ) provenant d'une interaction forte entre les cations voisins. Ce type d'interaction, ainsi que le mouvement du cation dans son ensemble, influencent aussi les mouvements classiques de rkori5ntation impliquant le dkplacement des atomes H dans lesquels le rayon global de la rotation est toujours plus grand que le 0 ,9 A attendu pour des rotors NH3 isolCs. La diffusion des neutrons quasi-dastiques (DNQ) suggkre que, dans la phase 111, il existe deux sous-rkseaux de cations dont I'un devient complete- ment dCsordonnk (par rapport aux rotors NH3) lors de la transition phase 111 + 11. Le dtsordre du deuxi5me sous-rCseau marque la transformation I1 + I dans laquelle on ne trouve qu'un seul type de mouvement de rotation.

[Traduit par la revue]

Introduction The role played by disorder and reorientations of the ammine

ligands in transition-metal hexammine salts has attracted the attention of several groups over the course of a number of years (see ref. 1 and references therein). The overall picture of six ammine groups, which undergo rotational diffusion at high temperature and then freeze into fixed orientations in the lowest-temperature phase transition, is generally accepted, but the details of the NH3 orientations, particularly in the low- temperature phases, are largely unknown (2-5). In the present study we are concerned with motions not only of the NH3 groups but also of the entire hexammine ion in three phases of nickel hexammine nitrate.

The sequence of phase transitions has been studied by ir (6), Raman (7), epr (8), and INS (9) spectroscopies, and by specific heat measurements (10, 1 1). For Ni(NH3)6(N03)2, the transi- tions between the phases are usually quoted as (9):

Marked thermal hysteresis of the low-temperature transition is now well established for the nitrates, although it may well have been the source of confusion in the past (10) regarding the presence of an "extra" phase transformation at around 80 K. In the present work all temperature changes were made on heating to avoid ambiguity due to hysteresis. The 111-11 transition is usually attributed to disorder of the NH3 ligands (6 ,7 ,9 ) , while the onset of NO3- ion disorder is responsible for the 11-1 transformation (7).

Recently, neutron scattering spectroscopies have been used to study motions of the NH3 groups in metal hexammine salts and have given a new insight into the potential energy surface of the NH3 groups in the lowest-temperature phases (1, 12). Although the situation that emerges is complex, there is qualitative agreement with the idea that all NH3 groups are essentially identical but that there is a disorder due to at least two energetically equivalent orientations (per cation) available to

the ligands (13). The effect of this disorder on the NH3 rotational potential seems to increase as the cation-cation separation decreases (12). In the present paper, we examine the rotational-tunnelling spectrum of the NH3 ligands in the nitrate analogue, where the small anion leads to a reduced tunnel splitting and a greater sensitivity to the orientations of NH3 groups on neighbouring cations compared with the iodide (12) or hexafluorophosphate (1) derivatives.

In many cases the tunnel splitting of the librational ground state can be compared with the energies of the librational modes, to deduce the form of the rotational hindrance potential and the bamer height (1, 12, 14-16). For phase 111 of Ni(NH3)6(N03)2, however, the energy of the librational transi- tions of the NH3 groups is too high to correlate with the tunnel splitting using a simple cosine potential form. Further, a multiplet of peaks has been reported in the librational region of the INS spectrum (9), which has been tentatively assigned to the presence of rather different barriers to rotation for the various NH3 groups. This assignment gained support from the results of QNS spectra, which were interpreted as two of the six NH3 groups on each cation undergoing reorientation on the time scale of this spectroscopy, while the remaining four groups are "stationary" (9). Tunnel splitting varies almost exponentially with the height of the barrier to reorientation, and if the above interpretation were valid, the effects of inequivalent NH3 groups would be more manifest in the tunnelling spectrum.

In the present study we attempt to clarify the situation by a careful comparison of the tunnelling and librational INS spectra. We then present, and analyse, QNS spectra as a function of temperature in phases I, 11, and 111, going out to considerably higher momentum transfers than were previously available, to obtain a more accurate description of the reorien- tational processes.

Experimental Samples were prepared by dissolving Ni(H20)6(0H)2 in concen-

trated ammonia solution, forming Ni(NH3)6(0H):. The nitrate ana-

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KEARLEY AND BLANK 693

Results Rotational tunnelling

When the tunnel splitting of rotational ground states is sufficiently large, INS provides a sensitive probe of the environments of the rotors, the subject having been reviewed by Press (17). Probably the most thoroughly studied example is that of methane, in which the spectra of protonated, deuterated, and partially deuterated species have been used to achieve'a very complete description of the partially disordered structure of phase I1 of this compound (1 8). A similar situation appears to exist for the metal hexammines, and in the present case our concern is to distinguish the effects of disorder from those of crystal-field distortions.

Inspection of the tunnelling spectrum shown in Fig. 1 reveals the presence of at least two peaks in energy loss and in energy gain. These peaks arise from rotational tunnelling of the NH3 ligands. Their positions provide information about the rotation- al hindrance potential while, in the simplest case, their intensities reflect the number of NH3 groups experiencing these potentials, and hence provide a stringent test of the differing barrier heights alluded to above.

logue was precipitated by the addition of ammonium nitrate solution, I I

transfers of 5.5 and 18.9 peV, respectively, the low intpsities being due to the small momentum transfer, only 0.64A-'. A comparison of the intensity of the 18.9-peV peak, at higher momentum transfer, with the tunnelling spectrum of Ni(NH3)J2 (12) reveals that the total tunnelling intensity is very similar for the two salts, from which we conclude that for both salts the intensity accounts for essentially all NH3 ligands.

The intensity ratio of the two tunnelling peaks in the present case, ca. 1:4, is not readily reconciled with crystallographic inequivalences of six NH3 groups. While it could be argued that there may be a further unresolved peak of unit intensity that is missed due to inaccuracies in our intensity estimates, it is more likely that the observation of more than one peak is due to interaction between ligands, as described for the iodide analogue (12), and that static crystallographic inequivalences play only a minor part. In fact, a comparison of the librational spectrum (below) with the tunnelling spectrum suggests that, as expected, the NH3-NH3 interaction is stronger in the nitrate salt than in the iodide, vide infra. A study of the temperature dependence of the tunnelling spectrum would help clarify this point.

I I

Peak positions and intensities, collected in Table 1, were Librational motions estimated by fitting the spectrum with Gaussian functions For Ni(NH3)6(N03)2 at temperatures below ca. 5 K, the convoluted with the instrumental resolution function, with the rotational motions are best described by tunnelling and libra- constraint that the spectrum be symmetric about the elastic tions rather than by almost free rotation. In principle, we may peak. The fitted function is represented by the solid line in Fig. use the energy transfers of NH3 tunnelling in this salt (above) to 1, with the component peaks below. Peak intensities, relative to derive the energy transfers of the NH3 librational modes if we the elastic peak, are 0.023 and 0.008 for the peaks at energy ignore the effects of cation-cation interactions. Assuming that

filtered, and recrystallized from dilute ammonia solution. The nitrate 5 - I i -

derivatives in particular lose ammonia rapidly and were handled and dried in an atmosphere with a small partial pressure of ammonia. Deuterated samples were prepared by the use of D20 and deuterated 4 - - ammonia solution. x -

Tunnelling spectra were collected using the IN5 multichopper . -

time-of-flight spectrometer at the Institut Laue-Langevin (ILL), g 3 - -

France. An incident neutron wavelength of 16 A was used, giving an - I-

energ resolution (FWHM) of 3.3 peV with a momentum transfer of " 2 I I I ~ : -

0.64 1-1. For the tunnelling spectrum detectors were grouped together at scattering angles between 90 and 130 degrees, with the final spectrum being obtained from the sum of these detectors. The IN5 spectrometer was also used for the quasielastic scattering experiments, using an incident neutron wavelength of 2.69 A with detectors grotped ---....,:::-

to give a useful momentum-transfer range between 0.5 and 4.2 A-I. The resolution lost by the use of such short wavelengths was partly recovered by "squeezing" the neutron pulse length via a careful energy (yeV)

de~hasing of the last two choppers. f ie measured energy resolution was FIG. 1. Tunnelling spectrum of Ni(NH3)6(N03)2 (1.8 K) obtained 410 P ~ V in place of 700 P ~ V normally associated with awavelengthof using the IN5 spec&ometer. The solid line represents the fitted function, 2.69 A. Spectra collected at different Scattering angles Were normal- while the broken line shows the individual Gaussian components. The ized by comparison with a standard vanadium sample. Individual sloping background arises from the use of a high neutron pulse rate detector columns containing Bragg peaks were identified by inspection and fitted using a single parameter, and removed from the data-treatment procedure.

High energy transfer sf)ectra were using the IN4 TABLE 1 . Positions and intensities of the INS peaks in the tunnelling rotating-crystal time-of-flight Spectrometer at the ILL. An incident and librational spectra regions. The intensities are quoted relative to the neutron wavelength of 1.28 A was used, giving anenergy resolution of elastic peak intensity being unity ca. 2.5 meV. Spectra recorded in all detectors between 100 and 140 degrees were summed together to produce the final spectrum. Standard liquid helium cryostats were used for all experiments, and changes to Relative intensity

the sample temperature between quasielastic scattering measurements Assignment Energy transfer EPP = 1.000)

were made on heating. Data-treatment routines were written locally using standard neutron- ( p e w

scattering algorithms. The fitting procedures, to extract peak positions NH3 tunnelling 5.56 0.008

and intensities, used a numerical convolution of the experimental NH3 tunnelling 18.94 0.023

resolution function with the calculated scattering functions. The (mew calculated functions were then refined to minimize the difference NH3 librations 20.5-37.9 between the observed and calculated spectra. ND3 librations 15.7-32.0

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694 CAN. J . CHEM. VOL. 66, 1988

energy (rneV)

FIG. 2. INS spectra of Ni(NH3)6(N03)2 and Ni(ND3)6(N03)2 (5.0 K) in the librational spectral region obtained using the IN4 spectrometer. The low intensity of the peaks in the latter spectrum is due to the small incoherent scattering cross section of deuterium.

the NH3 groups retain their molecular C3,, symmetry, but occupy a site that has no symmetry on the time scale of the rotation, the hindrance potential, V, has the form cos (34). This potential can be included in the Schrodinger equation for a one-dimensional rotor:

to obtain the eigenvalues. Attributing the tunnelling energies at 5.5 and 18.9 peV to J =

O+ J = 1 transitions gives rotational barrier heights of 38.0 and 27.5 meV, respectively. The corresponding librations ( J = 0 + J = 2) are calculated at 13.7 and 1 1.2 meV, respectively.

The INS spectra of Ni(NH3)6(N03)2 and Ni(ND3)6(N03)2 in the 5-40 meV region are shown in Fig. 2. The large amplitude of the librations, alongside the high scattering cross section of H atoms, strongly suggests that the dominant features, between 20 and 35 meV (Table l ) , arise from librational modes, as proposed by ref. 9. This assignment is supported by the approximate 1 /~ shift of these peaks and loss of intensity in the spectrum of the deuterated analogue. These librational features occur at energies more than twice the values calculated on the basis of a simple cos (34) potential using the barrier height calculated from the tunnel splitting. Cosine potentials of higher symmetry, cos (3n4) or combinations of such potentials including phase angles (16, 19), cannot reproduce the large separation between the tunnel-split ground state and the other librational levels. A detailed discussion of the ~otential form is beyond the scope of the present paper, since we have only two observations on which to base our arguments. We note, however, that the observed separation between the tunnel-split ground state and the librational levels can be produced by the use of a coupled potential ( 15).

The evidence for a coupled system is quite strong on the basis of both the tunnelling spectrum and the librational spectrum. It is conceivable that in such a coupled system, the multiplet peaks observed in the librational spectral region arise from a group of closely spaced energy levels, since it is clear that they do stem from crystallographically distinct ligands.

FIG. 3. Example of a QNS spectrum of phase I1 Ni(NH&(N03)? recorded at a scattering angle of 82.5 degrees (Q = 3.1 kl). The solid line represents the calculated function and the broken lines represent the Lorentzian components.

EISF

X X

0 I I I I

0 1 2 3 Q (2") 4

FIG. 4. Total EISFs of Ni(NH3)6(N03)2 obtained by fitting the QNS spectra with one Lorentzian function (phase I, 250 K: phase 111, 50-140 K) and two Lorentzians (phase 11, 180-230 K). Broken lines show the best-fit calculated EISF using eq. [2] allowing only the radius, r, and the fraction, F, to refine. The number of sites on the circle, m, was set to 20.

complexity, but this spectroscopy is particularly useful for investigating the radius of rotational motions and the number density of species performing this rotation. For these purposes the most reliable measured quantity in QNS is the experimental elastic incoherent struture factor (EISF), which is the ratioof the

Quasielastic neutron scattering elastic intensity to the elastic plus quasielastic intensity (see Direct deduction of molecular motions from QNS spectro- review article by Leadbetter and Lechner (20)). For the moment

scopy of powdered samples is rarely feasible for systems of any we will consider only the calculated EISF for motion on a circle,

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KEARLEY AND BLANK 695

FIG.. 5. Separated EISFs for the two Lorentzians fitted to the quasielastic spectra of phase I1 Ni(NH&,(NO&. Calculated EISFs were obtained as described for Fig. 2.

E lSF maximize the significance of the fitted parameters, spectra

which is given by: - ,,I: I tn

[2] 1 - F/n x m-' 1 jo(2 Qr sin .srk/m) cos (2.srlklm) I= 1 k= 1

collected at nine different scattering angles were refined :I80 K simultaneously. Preliminary analyses revealed that the

Lorentzian peak widths are Q dependent, from which we ; 200K conclude that the overall process is of a diffusive nature, rather

than jumps between a small number of sites. This conclusion is in good agreement with the mode of NH3 motion reported for : 230K the iodide analogue (3) but in conflict with the instantaneous-

08-

0

where jo is the zero-order Bessel function, m is the number of sites on the circle of radius, r , and Q is the momentum transfer. F is the fraction of protons in the system undergoing reorienta- tion. If the elastic peak is readily separable from the quasi- elastic components, the overall experimental EISF is virtually independent of the detailed fitting of the quasielastic components.

\ \, xx - : mi&---3-- = jump process reported in previous studies of the nitrate and . - . _ _ * _ - - - _ _ perchlorate salts (9, 21, 22). The Q dependence of the 0 4 - t - - quasielastic width fordiffusion on a circle was taken to be that of

I + the sum of m Lorentzians with widths, T , proportional to (23):

I 0 T 7 - > . 1 I I I . - - .- e -- -. - - - - - - - - -. -.- .

$'$, A. .:$, , e

\ - - : : , _ - 8 - - - - - - - _ - - x A

\ \\ - tx - - $ - - - + - - - - + - - -

\ :i\ x 8\\?,m

6 - + \k\, A

-

In the present case, it transpired that elastic and quasielastic contributions are separable by fitting a single Lorentzian to the quasielastic scattering at sample temperatures below 180 K (phase 111), and above 245 K (phase I). Between these temperatures (phase 11), two Lorentzian functions were required to fit the data adequately. An example of a single spectrum with two fitted Lorentzian components is illustrated in Fig. 3. To

weighted according to eq. [2]. Use of eqs. [2] and [3] with m, the number of sites on the circle, set to 20 gives a very close approxim!tion to rotational diffusion. For motions on a radius of ca. 1 A the quasiela~tic~ width is almost constant below a momentum transfer of 2.5 A-I.

In the event, spectra at nine scattering angles were refined using nine quasielastic intensity factors, an overall scale factor, and two width factors, for each of either one or two quasielastic components. The broken lines in Figs. 4 and 5 represent the best-fit calculated EISFs obtained using eq. [2] with m = 20, and allowing only the radius of rotation, r, and the fraction of protons in the system undergoing reorientation, F , to refine. We emphasize that the fitted EISFs are calculated using only rotation on a circle and, clearly, the actual reorientation process is more complicated than this, as evidence! by the systematic misfit of the calculated EISFs at around 1 A-' (Figs. 4 and 5). We have obtained almost perfect fits to the EISFs by allowing two processes to occur: diffusion on a circle and spherical diffusion, refining the populations and radii of both processes. There is, however, a danger of overinterpretation of the results (the average error on the points of the EISFs (not shown) is about 12%) and we prefer to restrict our discussion to a more approximate overall process using only diffusion on a circle.

Two important results are derived from these EISFs. Firstly, on the timescale of this spectroscopy, the total fraction of

FIG. 6. Variation of the fraction of protons in the system contributing to the EISF with temperature. The filled circles represent the total occupancy; the left-filled and right-filled circles denote occupancies associated with peaks 1 and 2 , respectively (Table 2). The dotted line is a guide to the continuity of peak 1 through the 111-11 phase transition.

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CAN. J. CHEM. VOL. 66, 1988

TABLE 2. Radii and fraction of protons involved in motion (occupancy) for the overall reorientation processes (on the timescale of the spectroscopy) in Ni(NH3)6(N03)2 at various temperatures in various phases. These values give

the calculated EISFs shown in Figs. 4 and 5

Peak 1 Peak 2 Temperature

Phase (K) Radius (A) Occupancy Radius (A) Occupancy

FIG. 7. Variation of peak width (diffusion constant) derived from the quasielastic components. The proportionality between the diffusion constant (HWHM) and temperature is consistent with Einstein behavior.

protons undergoing reorientation increases almost linearly with temperature up to the 11-1 transition, and is not simply related to crystallographically distinct NH3 groups. This trend is shown graphically in Fig. 6. Secondly, the radius of rotation at all tempetatures, including the two components akove 180 K , is >1 .O A (Table 2). A radius of rotation of ca. 1.5 A resulted from the refinement of quasielastic peak widths (eq. [3]), and these radiioare to be compared with simple NH3 rotation (radius ca. 0.9 A). A similar result has been obtained for NH3 motions in Ca(NH3)6 (24) for which it was suggested that the NH3 rotation occurs about a fluctuating axis. Clearly, in the present case there is some motion of the whole cation, but there is no unique interpretation of our results, and we must admit the possibility of tumbling motions, rotations of the octahedral cation around several axes, and simple precession of the Ni-N vectors.

Discussion The spectra of both tunnelling and librational motions of the

NH3 ligands in this salt support the idea that the rotational

potential is very sensitive to the orientation of the NH3 ligands on the neighboring cation. This effect was predicted by Bates and Stevens (13) on the basis of a simple point-charge model. These authors also calculated that there are two energetically equivalent orientations of the NH3 ligands on an isolated hexammine cluster, related by 60-degree rotation of all ligands. We denote these orientations A and B. For the isolated hexammine ion, a very low barrier separates the concerted interchange between A and B. The strong interaction between the cations, however, militates against the concerted process, and we are left with a situation in which various arrangements of A and B cations within the lattice must be considered.

It is interesting to note that at the 111-11 phase transition the population of H atoms involved in the reorientational processes giving the quasielastic scattering is around 50% (see Fig. 6). Further, comparison of the temperature dependence of the diffusion constants (Fig. 7) with the population of H atoms involved reveals that the 111-11 transition is marked by the onset of a second process rather than any stepwise change in the diffusion constant of the phase 111 process. This behavior suggests that there are two sublattices of cations (or groups of cations), one of which is ordered in phase 111. This behavior could arise from the A and B orientations discussed above, and a crystallographic investigation of phases I1 and I11 would be most enlightening.

The trend of the total EISFs shown in Fig. 4 summarizes the nature of the phase transitions rather well. At a sample temperature of 250 K (phase I), the quasielastic scattering was fitted well with a single Lorentzian, as would be expected for the known crystallographic space group, Fm3m, of this phase. As with all the EISFs shown in the figures, the falloff with increasing Q is too rapid for simple reorientation of the NH3 groups. The normal crystallographic description of the NH3 groups in the cubic phases of these salts is that the three H atoms are disordered between 24 positions (3) (effectively rotational diffusion on a radius of ca. 0.9 A). More recently, a phenomen- ological Frenkel model has been applied to describe the X-ray and neutron scattering from the NH3 groups (25) but the physi- cal meaning of this model is not clear.

Our results suggest that in all phases of Ni(NH3)6(N03)2, NH3 reorientations between neighboring cations are coupled to each other and to some form of whole-body "cation libration". The involvement of softening of the librational lattice mode in the phase transitions of these salts has already been suggested (5) and certainly merits further investigation.

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KEARLEY AND BLANK 697

Acknowledgments W e are grateful t o S. Clarke for his help with the sample

preparation and to A. Murani for his assistance with the experiments using the IN4 spectrometer.

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