Combined translationrotation jumps in solid carbon dioxide
ShangBin Liu, Montee A. Doverspike, and Mark S. Conradi
Citation: J. Chem. Phys. 81, 6064 (1984); doi: 10.1063/1.447610
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Combined translation-rotation jumps in solid carbon dioxide
Shang-Bin Liu, Montee A. Doverspike, and Mark S. Conradi
Department ofPhysics, The Col/ege of William and Mary, Williamsburg, Virginia 23185
(Received 24 May 1984; accepted 10 August 1984)
Combination translation-rotation jumps in solid CO2 have been measured using 13C NMR
techniques previously applied to a-CO. In the Pa3 structure of CO 2, a molecule which jumps to a
neighboring (presumably vacant) site will also reorient, due to the orientationally ordered
structure. The rates of translation and rotation have been measured independently by using low
and high field NMR. The two rates agree, indicating that one combined motion occurs, as
expected. The jump rate obeys the thermal activation expression with activation energy E /
k = 6600 K and frequency prefactorwo = 2X 10 17 S-I. The activation energy in CO2 agrees with
that found previously for the same motion in N 20 and a-CO, after scaling by the latent heats of
sublimation. All three molecular solids belong to the family of solids composed of small, linear
molecules with the Pa3 crystal structure. Unusually high frequency prefactors are seen in all three
solids. The shift anisotropy of 13C02 has been measured as 325 ppm.
I. INTRODUCTION
The linear molecules N z, CO, N 2 0, and CO2 form a
family of similar molecular solids. I ,2 N2 and CO and N 2 0
and CO 2 are isoelectronic pairs. All of the molecules are
linear with end-for-end symmetry (or nearly so; the dipole
moments ofN 20 and CO are so small as to be unimportant
to the properties of the solids3 ). The anisotropic molecular
interactions in all the systems are the electric quadrupolequadrupole and the anisotropic parts of the molecular repulsion and dispersion (van der Waals attraction).4.5 Solid N 20 6
and solid C0 2 7 exist in only one phase at all temperatures
under equilibrium vapor pressure. Stevenson found no other
phases of CO 2 up to 10 kbar at temperatures above 77 K. 8
Solid N2 and CO, on the other hand, crystallize in two stable
phases (a andp ) at equilibrium vapor pressure. 9-11 The crystal structure of the low temperature solids a-N 2 and a-CO
are the same as those of solids N 20 and CO 2, The solids are
all primitive cubic in structure belonging to space group Pa3
(an orientationally ordered fcc lattice).2 One expects from
the similarities of molecular properties and crystal structures that the solids obey some kind of corresponding states
relation. I
Carbon dioxide, the subject of this study, is known 7,12 to
melt at 216.56 K with a high vapor pressure (5.112 atm). The
CO 2 molecule is linear and symmetric about its center. Thus
the questions 13 of head-tail orientation present in solids aCO and N 20 are absent in CO 2 , The Pa3 structure of solid
C0 2 14 has four molecules per unit cell and the lattice is composed of four interpenetrating simple cubic sublattices. All
molecules on anyone sublattice are parallel to each other,
lying along one of the four body-diagonals of the cube. A
given molecule has 12 nearest neighbors, all belonging to
different sublattices than the given one. A molecule jumping
onto a previously vacant neighboring site finds itself on a
new sublattice and will reorient accordingly through a tetrahedral angle. Our recent NMR experiments on solid a-CO I5
confirmed that a molecular jump translation is accompanied
by a jump rotation. Because of their similar crystal structures and molecular shapes, the combined translation-rotationjumps observed in solid a-CO should also occur in solid
CO 2 , We report here a l3C NMR study of the jumps in COz'
6064
J. Chem. Phys. 81 (12). Pt. II. 15 Dec. 1984
The NMR techniques used to study a-CO have been
used here for CO 2 ; the techniques and their analyses have
been described. 15 The rates of translation and rotation were
separately determined. The rotations were detected at high
field by their effect on the chemical shift anisotropy, as observed with NMR line shapes, spin echoes, and stimulated
echoes. The translation jump rate was determined at low
field and high i3C enrichment from the modulation of the
intermolecular dipole-dipole interactions, observed by line
narrowing and the Slichter-Ailion slow motion experiment 16.17 (T lD)' It will be shown that the two jump rates
separately measured in this way are essentially equal, as expected for the combined motion.
II. EXPERIMENTAL
The gases used in the experiments are from either of two
cylinders. One contained 99% l3C enriched CO2 (Prochem,
Summit, New Jersey) the other contained natural abundance
CO2 (Matheson, research purity 99.995%). Some of the experiments require samples with 15% l3C enrichment. These
samples were mixed in the gas phase by assuming the additivity of partial pressures and ideal gas behavior. Since the
spin-lattice relaxation time T I of solid CO 2 is too long for
signal averaging (on the order of hours), a small amount of
O 2 gas was usually added to the sample. The resultant paramagnetic relaxation reduced T I to = 100 s at 150 K.
The samples were first condensed from the stainless
steel mixing bottle into a 1.5 cc nylon sample cell. The sample cell was cooled by a stream of thermostatted, flowing N2
gas in a research Dewar. After the sample was transferred to
the cell at 120 K (where the vapor pressure is essentially
zero 7), approximately 2 atm of O 2 were added on top ofthe
solid CO 2 , The sample was then warmed above its melting
temperature and was allowed to stand for typically 2 h. During this time O 2 gas dissolved into the liquid CO2 reducing
the l3C T I in the liquid from - 50 s to - 2 s. The sample was
then frozen: in order to form good polycrystalline powders,
the sample was frozen quickly by immersing the cell into
liquid N2 in a separate vessel. Next, the probe was returned
to the research Dewar at - 130 K: the residual O 2 gas in the
fill line of the probe was pumped out. The O 2 gas dissolved in
0021-9606/84/246064-05$02.10
@ 1984 American Institute of Physics
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6065
Liu, Doverspike, and Conradi: Translation-rotation jumps in solid CO,
the solid CO 2 stayed in solution, except near T melt where T I
was observed to lengthen over a period of many hours.
The temperature was measured with a platinum resistance thermometer; the temperature reading was confirmed
by a copper-constantan thermocouple. The temperatures so
determined are accurate to ± 0.2 K. All data reported here
are believed accurate to ± 0.5 K due to small temperature
drifts in the course of each experiment (typical laboratory
time per data point was 5-12 h).
The NMR apparatus for this experiment is that described previously. 15
10'
00
o
00
0
FWHM
(Hz)
10'
,,
,,
Tme1t
III. RESULTS AND DISCUSSION
10'
A. Spin interactions
L.L._ _' - - _ - ' - _ - - '_ _- - ' - _ - - '
5
Similar to a-CO solid, two line broadening mechanisms
are effective in solid 13C02: the chemical shift anisotropy
and the intermolecular dipole-dipole interactions. 18 The
shift anisotropy is proportional to the external field Ho and is
independent of the 13C concentration, whereas the dipolar
interaction is independent of Ho and increases with increasing 13C concentration.
The jump rotations between the body-diagonals modulate the chemical shift anisotropy; however, rotations do not
modulate the intermolecular dipole interactions because the
13C spin is at the molecular center. On the other hand, translation jumps alone will not modulate the chemical shift anisotropy but will modulate the dipolar interaction. Either
interaction can be made to dominate by appropriate choice
of field and 13C enrichment. Since the two interactions are
separately sensitive to rotations and translations, their rates
may be measured independently.
B. High field experiments
The 13C line shapes at high field (14.7 MHz) have been
investigated in both 15% and 99% enriched samples. At
high field, chemical shift anisotropy is the dominant source
of broadening. Below 200 K, the resonance lines are uniaxial
powder patterns with a shift anisotropy of 325 ± 15 ppm;
the parallel orientation is shifted to low frequency. This
agrees very well with a reported 318 ± 18 ppm anisotropy
for 13C02 adsorbed onto sodium mordenite at 30 .c. 19 The
only difference between the 15% and 99% powder patterns
in solid CO 2is the rounding of the sharp features for the 99%
sample, from the dipolar couplings.
As temperature is increased towards the melt, the sharp
features of the powder pattern become rounded and eventually (above 208 K) the line narrows (Fig. 1). As the line
narrows it loses its asymmetric shape. This sequence of
rounding and then narrowing is just that expected from theories of motional averaging, such as chemical exchange
broadening/narrowing. 2o,21 Narrowing should occur when
the rotation jump rate Wj exceeds the rigid lattice powder
pattern linewidth ..::!WRL (21TX4780 S-I). The linewidth decreased to about 1000 Hz FWHM near the melt, but the
extent of narrowing is too small to allow an activation energy
to be determined. The narrowing in CO2 should be contrasted with the behavior in a-CO: the sample transforms to the
plastic /loCO phase before narrowing occurs. 15
6
7
10'/T(K-')
FIG. 1. Linewidth FWHM of CO 2 at low field and 99% l3C enrichment
(circles); this is almost entirely dipolar Iinewidth. The line through the circles was chosen to have a slope corresponding to the activation energy of
6600 K (determined from data in Fig. 2.). High field Iinewidths reflect
chemical shift anisotropy and appear as squares (15% l3C) and triangles
(99%). The horizontal line is the width of the rigid high field powder pattern.
A 90~-'7'-180: pulse sequence was used to measure T2
from the echo envelope in a 15% 13Cenriched sample at 14.7
MHz. The signal-to-noise ratio was improved by averaging
typically 20 echoes at each 7 value. The phase of the first
pulse was alternatedy/y to allow for add/subtract averaging
and the elimination of coherent noise. The pulse sequence
generates a spin echo at time 27. For Wj too small to produce
line narrowing (the slow motion regime, T < 208 K) only
those spins which have remained at the same frequency (and
hence orientation) during the entire 27 interval contribute to
the echo. 15,20,21 Therefore jump rotations cause the echo amplitude to decay as exp( - 27hj ) where 7j =Wj - 1 is the mean
time between rotation jumps. The weaker dipolar coupling
between the 13C spins is a like-spin term and is not refocused
by the 180· pulse. Hence, the echo envelope should also decay due to dipolar effects (temperature independent) with an
approximately Gaussian envelope.
Experimentally, at high temperatures the echo envelopes are exponential and temperature dependent. At low
temperatures the envelopes are nearly Gaussian and are temperature independent. The decay times T2 were obtained by
fitting the data to the more appropriate function (exponential or Gaussian). The resulting T2 values are displayed in
Fig. 2 as open circles. Clearly, only at high temperatures
(T> 185 K) do the T2 values reflect jump rotations, with
T2 = 7j. Below 185 K T2 is only a measure of the dipolar
interactions. The minimum in T2 at 210 K occurs near the
onset of motional narrowing, as expected. Hence T2 is essentially equal to 7 j (a slow motion regime result) only between
185 and 210 K.
A 90~1Y-'7'-90~-T-90~ pulse sequence was used to generate stimulated echoes 22 at 14.7 MHz from two 15% enriched CO 2 samples. Data was obtained by averaging typically 30 echoes at each T value.
The advantage of the stimulated echo is that slower motions can be studied than with the ordinary spin echo. 23- 25 A
J. Chern. Phys., Vol. 81, No. 12, Pt. II, 15 December 1984
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6066
Liu, Doverspike, and Conradi: Translation-rotation jumps in solid CO,
T(K)
225K 200K
175K
of the stimulated echo data over three decades to the thermal
activation expression
I50K
1"j- I = Wj = Wo exp( -
10'
00
o
TID
o
echo T2
10'
T (s)
(2)
C. Low field experiments
Tme't
00 0
00
0
0
~
I
I
4
E /kT)
The activation energy is 6600 ± 300 K and the frequency
prefactor Wo is 2 X 10 17 S - I (factor of 7 uncertainty in either
direction). At the lowest temperatures the stimulated echo
data appear to be leveling off, perhaps because of spectral
diffusion.
" stimulated echo
I
10 4~~~~5---L---6L-~--~7
103/T (K-')
FIG. 2. Relaxation times T in solid CO2 as functions of reciprocal temperature. The squares are TID taken at low field and 99% 13C enrichment. The
other data are from high field measurements on 15% enriched CO 2, The
circles are T2 from spin echoes; T2 becomes temperature independent below
185 K because of dipolar coupling. Stimulated echo data from two 15%
samples are shown as open and filled triangles. The line drawn is fit to the
data and corresponds to an activation energy of 6600 K.
discussion of the technique as applied here has appeared. IS
For the pulse spacing 1"<1"j (as always used here,
1" = 6x 10- 4 s) the orientation of the molecules and hence
the frequency of the spins may be considered constant during the intervals t = 0 to 1" and t = 1" + T to 21" + T. The
second pulse serves to store information about the initial
molecular orientation as z magnetization. During the waiting interval T molecular rotations can occur. A stimulated
echo forms at time 1" after the third pulse: only those spins
with no net frequency change during the interval Twill refocus and contribute to the echo. In any crystallite only four
orientations are available to a molecule, so there is a 1/4
probability of a molecule having its initial orientation, even
at T = 00. As derived in Ref. 15, the stimulated echo envelope becomes
(1)
All of the experimental stimulated echo envelopes decay to a
relative baseline between 0.2 and 0.3. The baseline determination was hampered by low signal to noise. Besides molecular rotations, spin-lattice relaxation and spectral diffusion
may contribute to the observed decay rate. However, the
level of O 2 doping used here resulted in TI~150 s, much
larger than the longest 1"j measured.
The observed values of 1"j from stimulated echoes using
Eq. (1) are shown in Fig. 2 as triangles. The data extend to
motions as slow as 1"j = 12 s. Although the stimulated echo
data agree reasonably with the T2 data, there is an offset
(factor of - 2) between them. The offset is like that in aCO, IS but is not understood. The straight line in Fig. 2 is a fit
The line shape of a 99% l3C enriched CO 2 sample has
been studied at 1.256 MHz. At such a low field and high l3C
concentration the dipolar interactions are expected to be
larger than the chemical shift anisotropy. The experimental
linewidths are shown in Fig. 1 as circles. The rigid lattice
linewidth (T < 185 K) is 1120 ± 50 Hz FWHM and the rigid
line shape is very nearly symmetric. At the low field, the shift
anisotropy scales to 410 Hz overalllinewidth. Because different sources of broadening generally add as squares, the
shift anisotropy is seen to be unimportant here. The symmetric lineshape also indicates that the dipolar interactions are
dominant.
The Van Vleck expression for the like-spin dipolar second moment in a powder isiS
M2 = ~ ~filI (l
+ 1)/2]1: 6,
(3)
k
where / is the fractional concentration of the magnetic nuclei. The lattice sum for the fcc lattice of l3C spins is 14.45
d 0- 6, where do is the nearest neighbor distance (0.399 nm at
150 K 26 ). The resulting second moment with f = 0.99 is
M2 = 3.63 X 106 rad 2/s 2 • Analysis of both time domain and
frequency domain data yields M2 = 5.0 ± 0.5 X 106 rad 2/s2 •
The agreement with the Van Vleck calculation is fair, given
that the chemical shift anisotropy has been ignored.
The line narrows above 195 K, becoming as narrow as
68 Hz FWHM near the melt (Fig. 1). This is much smaller
than the dipolar and shift anisotropy contributions (individually) to the rigid lattice linewidth. Hence, at the high temperatures both rapid translations and rotations occur in this
orientationally ordered solid.
The
Jeener-Broekaert
pulse
sequence
90~rx --1"- 45~ - T-45~ was used to measure the spin-lattice
relaxation time TID of the nuclear spin dipolar-ordered
state. 27 Typically 40 Jeener echoes were averaged at each T
value, using a 99% enriched CO2 sample at 1.256 MHz. The
TID results appear as squares in Fig. 2. As expected for a
system with only one dipolar spin temperature, the Jeener
echoes decay exponentially with time (T). The rate of motion
(1"j~TID) was followed over three decades. Above 155 K,
the temperature dependences of TID and 7) from stimulated
echoes are the same, indicating that the translations responsible for TID and the rotations that damp the stimulated
echoes are two aspects of one combined motion. The temperature independence of TID below 155 K is not understood: T 1 was typically 150 s, much greater than TID'
The TID data may be treated with the strong collision,
slow motion theory of Slichter and Ailion. 16•17 They show
that
J. Chern. Phys., Vol. 81, No. 12, Pt.II, 15 December 1984
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Liu, Doverspike, and Conradi: Translation-rotation jumps in solid CO,
T 11/
= 1'j- 12(1
(4)
- p),
where 1 - p is a geometrical factor characterizing the fractional change in dipolar energy resulting from a diffusion
jump. Calculated values of2( 1 - p) are of order unity (0.882~,
1.5 29 ). The experimental offset between T 1D and 1'j from stImulated echoes indicates 2( 1 - p) = 1.8. In a-CO, the quantity 2(1 - p) was 2.0/ 5 close to the value found here. The
presence of shift anisotropy prevents a comparison of the
theoretical 2(1 - p) values with the CO2 data. However, to
within a factor of 2 uncertainty in the correct value of
2( 1 - p), the translation and rotation jump rates are seen to
be equal.
D.Analysls
As described in the Introduction, CO2, N 20, and a-CO
belong to the family of orientationally ordered solids with
Pa3 structure and composed of linear molecules. Previous
NMR experiments IS measured the rate of combined translation-rotation jumps in a-CO. Dielectric spectroscopy13 followed the rate of some reorientation in solid N 20; preliminary NMR results indicate30 that the motion seen
dielectrically in N 20 is the same as that seen with NMR in
CO2 and a-CO.
The anisotropic intermolecular potential of the molecules cannot be described by a single "strength" parameter.
Hence, a strict law of corresponding states is not expected to
hold. Indeed, the phase diagrams of the solids are different
(see the Introduction). Nevertheless, because of the similarities of the solids, certain scaling relations are expected to
apply. In Table I the activation energies for the combined
translation-rotation jumps are compared to the latent heats
of sublimation (essentially the cohesive energies of the solids). The ratios E act 1iiHsubl are all very nearly equal to 2.15.
We feel the agreement is surprising, given that the comparison includes a diatomic and two triatomic molecules.
Diffusion in the rare gas solids is known to proceed via
monovacancies. 31 The ratio EactliiHsubl is 1.9 in the classical rare gas solids32.33 : Ar, Ke, and Xe (see Ref. 33 for more
accurate Ke 83 NMR data). Neon should not be included in
this comparison because of its substantial quantum effects. 32
TABLE I. Comparison of activation energies and heats of sublimation in aCO, N 20, and CO2 ,
a-CO
Ttriple (Kl
Tap (Kl
JiH,.bl/k (K)
Eac.lk (Kl
E act I JiH,.bl
liIo (S-I)
2
Do(cm /s)
68.09"
61.55"
988d
21()()8
2.13
2X 10 18•
SxIO'
N 20
CO2
I 82.4b
216.56c
2773"
602ct
2.17
6XlO 19h
1.6X 10"'
• From Ref. II.
bFrom Ref. 33.
cFrom Ref. 12.
dFromRef.ll,a-COatTap.
e From Ref. 33, at triple point.
(From Ref. 7, at normal sublimation 194.67 K.
I From Ref. IS.
h From Ref. 13.
iThiswork.
3035 f
6600'
2.17
2X lO 17i
5XlO l
6067
Diffusion in the plastic (f3 ) phase of CO also is described by
this value of the ratio. 34 A review of diffusion in molecular
solids (mostly rotor phases) indicates that the ratio Eactl
£iHsubl is generally near two. 3S In short, the value of the ratio
in the Pa3 solids is typical of molecular solids and the rare
gas solids.
Heat capacity measurements of CO 2 and N 20 show a
concave upwards rise at high temperatures. 36.37 The rise has
been interpreted as originating in orientational defects in the
Pa3 structure with energy E·. In CO 2, E· /k is found to be
1000 ± 100 K,36 while in N 20 the energy is 1200 K.37 The
agreement of these independent analyses is striking. The
heat capacity analyses indicate that -2% of the molecules
have defective orientations near the melt. The energies E·
are much smaller than the activation energies listed in Table
I. It is not clear whether orientational defects are involved in
the combined translation-rotation jumps. It should be noted
that such heat capacity analyses are quite uncertain because
of the difficulty in estimating the background (no defects)
heat capacity. In the rare gas solids, this technique is not
regarded as reliable. 31
In the CO2 and a-CO NMR measurements, the jump
rate Wj was fit only to the stimulated echo data. We believe
this procedure reduces the possibility of obtaining incorrect
Wo values. For example, if Wj data from stimulated echoes
and from line narrowing were used, the data would clearly
extend over a wider range of temperature. But the activation
energy obtained would be sensitive to multiplicative factors
in the interpretation of each kind of data. Resulting small
errors in the activation energy, while not serious in themselves, would produce large errors in the frequency prefactor. Fitting to just one kind of data makes the activation
energy insensitive to numerical factors [like 4/3 in Eq. (1)].
As a result, the Wo value is almost insensitive to any such
numerical factors. The Wo values should be correct even if
the detailed model of the motion is not.
Combined translation-rotations have been followed in
solid NH3 using the proton Tip as a probe. 38.39 In ammonia,
translation should be accompanied by a reorientation of the
molecular triad axis. It also seems probable39 that a reorientation of the hexad axis occurs during translations in solid
benzene, as measured by proton T 1D and Tip experiments. 40,41 However, Tip and T 1D measurements cannot determine the details of the motion step. The existence of rotations during the translational steps in ammonia and benzene
has only been inferred 39 from the orientationally ordered
crystal structures. A reexamination of diffusion in benzene
would be useful because of the large discrepancy (three orders of magnitude at 273 K) between the NMR41 and tracer42 diffusion measurements. Since ammonia and benzene
are both orientationally ordered, they are interesting to compare to CO 2 , a-CO, and N 20. In benzene the ratio of E act
from NMR41 to £iB.ubl 42 is 2.08 while in ammonia the ratio
is 1.57. 35
A surprising result in all the members of the Pa3 family
is the high value of the preexponential frequency WO' For
comparison to other data, the Wo values have been converted
to Do values in Table, I using the reiation 3S
Do
= l;a2wo,
J. Chern. Phys., Vol. 81, No. 12, Pt. II. 15 December 1984
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(5)
6068
Liu, Doverspike, and Conradi: Translation-rotation jumps in solid CO2
where a is the nearest neighbor distance. It does not matter
that this formula neglects the effects of correlated jumps,
since these are factors of 2 while the UJo values are only accurate to a factor of 10. Probably the best Do value in the classical rare gas solids is from Xe 129 NMR data,43,44 Do = 10
cm 2/s. The simplest theories 35 predict
Do = lzvD a2 ,
fred P. Sloan Fellow. We appreciate helpful conversations
with J. Schaefer, E. Fukushima, and A. A. V. Gibson. The
magnet system used for the experiments is a gift of E. 1.
DuPont de Nemours and Co., Inc.
(6)
wherezis the number of nearest neighbors (12) and VD is the
Debye frequency. For CO 2 , N 2 0, a-CO, and the rare gases
Ar, Kr, and Xe this formula predicts Do = 7 ± 3 X 10- 3
cm 2/s. Clearly, in all three Pa3 solids and Xe, the experimental Do is three to six orders of magnitude faster that the prediction of simple theories.
The multiplicative offset between the experimental Do
and f,zv D a 2 is commonly treated as arising from an entropy
of diffusion, a sum of a defect formation entropy Sf and a
defect migration entropy Sm' That is,
2
(7)
D o =e (5[+ 5 m )lk,jizvDa.
In the rare gas solids31 s/k is - 2. Glyde has calculated31 ,45
a linear and negative temperature dependence of the defect
migration energy which is the origin of a relatively large S m /
k - 8. Hence, the rare gas Do values are in reasonable accord
with theory. No calculations are available for CO 2 , a-CO, or
N 20; it is not clear whether a calculation similar to Glyde's
can explain the very large UJo and Do values in these solids.
IV. CONCLUSIONS
Molecules of CO 2 in the solid perform combined translation-rotationjumps. This motion has also been found in aCO and N 20. The translation and rotation jump rates have
been separately determined. The rate of translation was obtained with a 99% 13C enriched sample at low field. The
rotation jump rate was studied at high field using small 13C
enrichment. The two rates agree as expected in an orientationally ordered solid.
The rate of the combined jumps follows the thermal
activation expresion over three decades with E /k = 6600 K
and UJ o = 2 X 10 17 S -1. The activation energies in CO 2 , N 20,
and a-CO (all members of the family of linear molecular
solids with Pa3 structure) agree well when scaled by their
latent heats of sublimation. Unusually large frequency prefactors UJo have also been observed for this motion in all three
solids. We plan to study these systems under pressure to
determine the volume dependence of the reorientation rates.
The anisotropy of the 13C02 chemical shift has been
found to be 325 ± 15 ppm (parallel orientation to lower frequency) in the solid. No temperature dependence from librations was detected from 190 K down to the lowest temperature studied, 145 K.
ACKNOWLEDGMENTS
This work was supported in part by the Jeffress Memorial Trust; one of us (MSC) was supported in part as an AI-
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