J. Phys. Chem. 1995,99, 14167-14173
14167
Calorimetric, Dielectric, and Neutron Diffraction Studies on Phase Transitions in Ordinary and Deuterated Acetone Crystals' R. M. Ibberson and W. I. F. David ISIS Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX, England 0. Yamamuro, Y. Miyoshi? T. Matsuo,* and H. Suga8 Department of Chemistry and Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan Received: April 14, 1995; In Final Form: July 7, 1995@
Heat capacities of acetone (CH3)2CO and its deuterated analogue (CD3)zCO have been measured with an adiabatic calorimeter in the temperature range 13-300 K. A broad peak in the heat capacity attributable to a phase transition was observed at 127 K in (CH3)2CO and at 132 K in (CD3)2CO. The accompanying excess entropy ((CH3)zCO 2.04 J K-' mol-', (CD3)2CO 2.08 J K-' mol-') was small, suggesting that the transition is not of the order-disorder type. In both samples, the magnitude and shape of the heat capacity peaks were affected not by cooling rates but rather by the temperature to which the samples were cooled before the measurements. From these data, hysteresis loops (the extent of the transition vs temperature) were determined for the cooling and heating processes. The dielectric permittivity of (CH3)2CO has also been measured in the frequency range 100 Hz to 1 MHz over the temperature range 87-270 K. Both high- and low-temperature phases exhibit small permittivities and no dielectric dispersion, indicating that the dipole moments of the acetone molecules are ordered in both phases. A hysteresis effect quite similar to that in the calorimetric measurement was observed. The transition properties are similar to those of a martensitic transition more typically observed in metals. Preliminary neutron powder diffraction data have been recorded for (CD3)2CO as a function of temperature and c o n f i i unusual structural behavior. Both high- and low-temperature structures are orthorhombic (at 5 K V, = 1469.45 A3 and at 140 K V, = 1535.47 A3). There is no evidence to suggest a change of space group between the phases.
Introduction Acetone (CH3)2CO is a well-known organic liquid. It is the simplest member of the ketone family and because of this role as a basic structural unit has been widely studied. Its physical properties in the solid state have, however, been determined by only a limited number of studies. In 1929, Kelley' measured the heat capacity of acetone in the temperature range 13-300 K and determined the thermodynamic quantities of the solid and liquid phases. He noted a small heat capacity peak below the melting point but could not specify its origin. hecise normal-mode analysis was carried out following IR and Raman spectroscopic studies,2 and the rotational motion of the CH3 group has been investigated using NMR.3*4 The gas-phase molecular structure of acetone has been determined by electron diffra~tion.~ The purpose of the present study is to examine in detail the heat capacity peak below the melting point using a highly purified sample and to investigate the nature of the phase transition. The heat capacities of (CH3)2CO and (CD3)2CO were measured over the temperature range 13-300 K. The dielectric permittivity of (CH3)zCO was also measured over the frequency range 100 Hz to 1 MHz and the temperature range 87-270 K. Acetone is one of the last simple organic molecules that has an unknown crystal structure. Preliminary powder neutron difContribution no. 114 from the Microcalorimetry Research Center. Matsushita Electric Industrial Co., Ltd., Kadoma, Osaka 57 1, Japan. * To whom correspondence should be addressed. 9 Present address: Research Institute for Science and Technology, Kinki University, Kowakae, Higashi-Osaka, Osaka 577, Japan. Abstract published in Advance ACS Abstracts, September 1, 1995.
* Present address:
@
0022-3654/95/2099-14167$09.00/0
fraction data were thus recorded with the initial intention of providing structural information relating to the nature of the phase transition and the final objective of solving the crystal structure.
Experimental Section Sample Preparation. Commercial reagents of acetone (CH3)2CO (purity 99.5%) and (CD&CO (D atom % 100%) were purchased from Tokyo Kasei Kogyo Inc. and Aldrich Chemical Co., respectively. The samples were first dehydrated with molecular sieves (3A 1/16, Wako Pure Chemical Ind., Ltd.). (CH3)zCO was fractionally distilled with a concentrictype rectifier (HC-5500-F, Shibata Kagakukikai Kogyo Co., Ltd.). The main distillate of (CH3)zCO and dehydrated (CD3)2CO were degassed and distilled in vacuo with a homemade vacuum line. Both samples subsequently showed no trace of organic impurity as detected by gas chromatography (PerkinElmer F21). A Karl-Fischer test was also carried out for (CD3)2CO, and the amount of water contained was found to be negligible (0.0055 mol %). The purities of (CH3)2CO and (CD3)2CO were determined to be 99.86% and 99.94%, respectively, using a fractional-meltingmethod and measured in the course of the heat capacity determination. Heat Capacity Measurement. Some 3.5004 g (0.060 268 mol) of (CH3)2CO and 4.1727 g (0.065 066 mol) of (CD3)zCO were loaded into a sample cell. The remaining volume of the cell (about 1 cm3 for both samples) was filled with helium gas at room temperature and atmospheric pressure in order to enhance thermal equilibration at low temperatures. The heat capacities of (CH3)zCO and (CD3)2CO were measured using an adiabatic calorimeter with an in-built 0 1995 American Chemical Society
Ibberson et al.
14168 J. Phys. Chem., Vol. 99, No. 38, 1995 TABLE 1: Experimental Molar Heat Capacities of Acetone (CH&CO (M = 58.080 g mol-') 'T 13.37 13.84 14.34 14.88 15.46 16.06 16.68 17.30 17.96 18.66 19.38 20.12 20.88 21.64 22.42 22.56 23.35 24.14 24.94 25.75 26.58 27.44 28.30 29.17 30.03 30.89 31.76 32.63 33.49 34.36 35.22 36.09 36.95 37.81
Cp/J
K-' mol-] 3.8692 4.2343 4.6440 5.0774 5.5586 6.0923 6.6449 7.2151 7.8285 8.5093 9.2138 9.9489 10.713 11.504 12.299 12.440 13.251 14.068 14.906 15.724 16.628 17.492 18.420 19.381 20.268 21.107 21.997 22.890 23.793 24.660 25.536 26.362 27.192 28.005
T/K 38.68 39.56 40.5 1 41.52 42.52 43.53 44.53 45.54 46.54 47.55 48.56 49.56 50.57 5 1.58 52.59 53.60 54.61 55.63 56.64 57.66 58.68 59.71 60.73 61.76 62.79 63.83 64.87 65.91 66.95 68.00 69.05 70.1 1 71.17 72.23
CdJ
K-I mol-' 28.799 29.576 30.425 31.303 32.196 33.065 33.918 34.727 35.549 36.361 37.154 37.945 38.710 39.474 40.234 40.957 41.669 42.391 43.088 43.763 44.446 45.095 45.745 46.390 47.008 47.622 48.249 48.833 49.432 50.037 50.594 51.179 5 1.769 52.308
T/K 73.30 74.37 75.45 76.53 77.61 78.70 79.79 80.89 81.99 83.10 84.21 85.32 86.44 87.72 89.15 90.57 91.99 93.42 94.84 96.26 97.68 99.10 100.52 101.95 102.30 103.72 105.15 106.57 108.00 109.47 110.99 112.51 114.03 115.54
CdJ
K-' mol-' 52.869 53.444 53.983 54.55 1 55.084 55.620 56.179 56.690 57.216 57.738 58.227 58.762 59.276 59.808 60.521 61.192 61.878 62.501 63.151 63.788 64.428 65.104 65.687 66.343 66.591 67.23 1 67.903 68.61 1 69.249 70.086 70.831 71.594 72.501 73.401
T/K 117.06 118.57 120.08 121.58 123.07 124.54 125.98 127.39 128.80 130.24 131.71 133.22 134.73 136.26 137.79 139.33 140.88 142.44 144.01 145.58 147.16 148.75 150.34 151.94 153.55 155.16 156.78 158.40 160.03 161.66 163.30 164.94 166.58 168.22
CdJ
K-' mol-' 74.442 75.584 76.849 78.501 80.730 84.236 90.592 94.952 92.391 88.365 85.808 84.424 83.732 83.420 83.299 83.290 83.388 83.525 83.500 83.750 83.897 84.043 84.256 84.554 84.880 85.131 85.513 85.983 86.433 86.867 87.484 88.148 88.951 89.951
T/K 169.86 171.59 173.57 175.41 176.81 177.63 178.00 178.11 178.17 178.20 178.22 178.23 178.24 178.25 179.07 180.73 182.43 184.15 186.06 188.19 190.35 192.65 194.96 197.28 199.62 201.96 204.32 206.69 209.07 211.46 213.86 216.28 218.71 221.15
CLJJ K-' mol-' 91.571 94.256 102.43 131.25 430.97 875.08 3557.2 8094.3 14175 24986 37523 51766 58247 465 11 245.87 115.43 115.42 115.44 115.51 115.48 115.50 115.59 115.64 115.61 115.63 115.76 115.85 115.81 115.90 116.01 116.15 116.11 116.26 116.43
CdJ
T/K 223.61 226.07 228.55 230.97 233.35 235.74 238.15 240.57 243.00 245.45 247.90 250.36 252.83 255.32 257.84 260.37 262.92 265.48 268.06 270.65 273.26 275.88 278.51 281.16 283.82 286.49 289.18 291.88 294.58 297.3 1 300.04
K-' mol-' 116.58 116.60 116.75 116.99 117.16 117.31 117.38 117.58 117.81 118.09 118.17 118.39 118.65 118.92 119.24 119.40 119.67 119.99 120.32 120.69 120.95 121.27 121.68 122.13 122.59 123.02 123.30 123.82 124.31 124.76 125.24
T/K 217.52 219.92 222.33 224.75 227.18 229.62 232.08 234.54 237.02 239.5 1 242.01 244.51 247.01 249.53 252.06 254.61 257.17 259.74 262.32 264.92 267.53 270.15 272.79 275.44 278.10 280.78 283.46 286.15 288.86 291.58 294.30 297.04 299.79 302.54
CdJ K-' mol-' 125.34 125.62 125.87 126.12 126.31 126.60 126.94 127.29 127.44 127.71 128.11 128.49 128.80 129.08 129.43 129.82 130.23 130.52 130.85 131.32 131.77 132.26 132.69 133.05 133.62 134.14 134.69 135.29 135.63 136.17 136.82 137.34 137.94 138.16
TABLE 2: Experimental Molar Heat Capacities of Acetone (CD&CO (M = 64.121 g mol-') T/K 13.91 14.18 14.57 15.03 15.52 16.04 16.59 17.18 17.81 18.47 19.15 19.84 20.55 21.31 22.10 22.90 23.70 24.50 25.29 26.09 26.88 27.70 28.56 29.42 30.27 31.12 3 1.97 32.82 33.66 34.50 35.34 36.18 37.02 37.85 38.68
Cp/J
K-I mol-] 5.0411 5.3025 5.6691 6.0920 6.5815 7.1151 7.7113 8.3408 9.0268 9.7810 10.575 11.394 12.243 13.147 14.113 15.089 16.085 17.062 18.040 19.019 19.974 20.997 22.072 23.221 24.135 25.127 26.154 27.119 28.085 29.060 29.981 30.889 3 1.786 32.639 33.483
T/K 39.51 40.35 41.23 42.15 43.07 44.02 45.00 45.98 46.96 47.95 48.93 49.91 50.90 5 1.88 52.87 53.86 54.85 55.84 56.84 57.83 58.83 59.84 60.84 61.85 62.86 63.88 64.89 65.94 67.00 68.06 69.12 70.20 71.27 72.35 73.42
CdJ
K-I mol-' 34.306 35.092 35.932 36.800 37.676 38.489 39.364 40.214 41.043 41.851 42.65 1 43.433 44.174 44.934 45.668 46.363 47.063 47.762 48.423 49.069 49.721 50.336 50.960 51.569 52.159 52.734 53.331 53.891 54.461 55.045 55.581 56.161 56.715 57.247 57.832
T/K 74.51 75.59 76.68 77.77 78.87 79.97 81.07 82.18 83.29 84.41 85.53 86.65 87.78 88.91 89.96 91.37 92.78 94.18 95.59 96.99 98.40 99.80 101.20 102.61 104.01 105.42 106.82 108.23 109.63 111.08 112.57 114.05 115.54 117.02 118.50
CdJ
K-I mol-' 58.363 58.894 59.436 59.933 60.486 6 1.024 61.530 62.082 62.591 63.090 63.632 64.156 64.663 65.178 65.594 66.287 66.939 67.541 68.202 68.782 69.440 70.057 70.676 71.328 71.906 72.561 73.299 73.859 74.572 75.256 75.980 76.739 77.758 78.404 79.304
refrigeratold in the temperature range 13-300 K. The heat capacity - measurement was carried out using - a standard intermittent heating method, i.e., repetition of equilibration and energiz-
T/K 119.99 121.47 122.95 124.42 125.89 127.35 128.80 130.23 131.64 133.04 134.45 135.89 137.35 138.82 140.30 141.80 143.30 144.82 146.35 147.88 149.42 150.97 152.52 154.08 155.64 157.21 158.78 160.36 161.94 163.74 165.71 167.68 169.65 171.61 173.55
CdJ
K-' mol-' 80.197 8 1.242 82.397 83.629 86.01 1 86.641 90.625 92.702 97.327 97.303 95.75 1 94.168 92.990 92.130 91.623 9 1.270 90.943 90.863 90.886 91.001 91.081 91.300 9 1.649 91.982 92.242 92.601 92.946 93.247 93.635 93.741 94.714 95.183 96.341 98.743 102.87
T/K 175.44 177.12 178.16 178.52 178.62 178.67 178.69 178.71 178.72 178.73 178.73 178.74 178.74 178.75 178.76 178.76 179.67 181.55 183.48 185.42 187.37 189.32 191.29 193.26 195.24 196.29 198.35 200.43 202.5 1 204.61 206.72 208.83 2 10.96 213.10 215.25
Cp/J
K-' mol-' 111.32 161.98 581.35 2559.5 6603.6 12445 2046 1 32496 50975 61573 64064 71356 65241 65510 77347 439960 136.05 123.07 123.00 123.25 123.36 123.38 123.47 123.61 123.75 123.84 123.88 124.06 124.21 124.41 124.44 124.60 124.83 125.06 125.17
ing intervals. The temperature increment for each measurement was between 1 and 2.5 K. It took about 1 min to reach thermal equilibrium in the cell after each energy input around 13 K and
Ordinary and Deuterated Acetone Crystals
20
I 0.6
T I K Figure 1. Experimental molar heat capacities of (CH3)zCO (closed
circles) and (CD3)zCO (open circles).
--.. 100
i
-
0
I
I
I
1.o
0.8
T I
1.2
Ttrs
Figure 3. Excess molar heat capacities due to the transitions of (CH3)ZCO (open circles) and (CD3)zCO (closed circles).
' 1
-
jc
0. 8
1.0
.
0
. 0
\
0.0 I
T I K Figure 2. Experimental molar heat capacity of (CD3)zCO (open circles) and the contributions from the vibrational degrees of freedom determined from the least-squares fitting (see text for the details). (A) intramolecular vibration; (B) methyl rotation; (C) lattice vibration; (D) libration; (E) C, - C , correction.
about 5 min around 300 K. Single-step heating experiments were performed separately to determine the enthalpy of fusion precisely. The accuracy of the heat capacity measurement was better than 1% at T 20 K, 0.3% at 20 < T < 30 K, and 0.1% at T > 30 K. The effect of the vaporization enthalpy on the heat capacity data was estimated to be less than 0.1% even at 300 K. This favorable situation resulted because the dead space inside the cell was small (ca. 1 cm3). In the present calorimetry work, the temperature was measured using Rh-Fe resistance thermometers (27 B at 273 K, purchased from Oxford Instruments Co.) calibrated on the temperature scale E n 7 6 (T < 30 K) and IPTS68 (T > 30 K). The heat capacity difference caused by the conversion to the new temperature scale ITS907was estimated to be smaller than 0.05% over the 13-300 K temperature range. Dielectric Measurement. The dielectric permittivity of (CH3)2CO was measured using a three-electrode cell described elsewhere.8 The cell was mounted in a doubly thermostated environment in a cryostat. The sample temperature was stabilized to f0.03 K with an accuracy of f O . l K. The capacitance and the loss were measured with a LCR meter (HP4284A, Hewlett-Packard). The temperature and frequency ranges observed were 87-270 K and 100 Hz to 1 MHz, respectively. The measurement was performed both in cooling and heating directions.
0.6
I
0.8
I
1.o
1.2
I
T I Tms Figure 4. Excess molar entropies due to the transitions of (CH3)2CO (open circles) and (CD3)zCO (closed circles).
Neutron Powder Diffraction. A powder sample of (CD3)zCO was prepared by hand-grinding 5 g of material using a liquid nitrogen cooled stainless steel mortar under a cold nitrogen gas atmosphere. The resulting fine powder was loaded into a 15 mm diameter V sample can and transferred to a standard cryostat? Time-of-flight diffraction data were recorded on the high resolution powder diffractometer (HRF'D)'O at the ISIS spallation neutron source. Data were recorded in both phases at 140 and 5 K over a time-of-flight range of 30-230 ms corresponding to a d-spacing range of 0.6-4.6 A. A series of rapid measurements were also taken over a restricted d-spacing range on cooling. Results and Discussion Heat Capacity. (CH3)zCO and (CD&CO liquid samples were cooled from room temperature to about 100 K and then heated to just below their respective fusion points (ca. 170 K). The samples were subsequently annealed for about 1 day to ensure complete crystallization prior to the heat capacity measurements. The annealed samples were cooled to the base temperature (ca. 13 K) prior to starting the heat capacity measurements. The molar heat capacities of (CH3)zCO and (CD3)zCO are collated in Tables 1 and 2, respectively, and shown in Figure 1. An endothermic effect due to fusion appears at (178.32 f 0.02) K in (CH3)zCO and at (178.78 f 0.02) K in (CD3)zCO. The enthalpies of fusion of (CH3)zCO and (CD&CO determined
Ibberson et al.
14170 J. Phys. Chem., Vol. 99, No. 38, 1995 110
-
'
1
100
m
3
90
i4
i-r \
80
c? 70
lot d o ;
60
1
I
I
I
100
120
140
160
T I K Figure 5. Molar heat capacities of (CD&CO around the transition in the samples prepared by the different manner before the measurements. Open circles: cooled slowly (0.06 K min-I), closed circles: annealed at 100 K for 1 day, triangles: cooled rapidly (10 K min-I).
3.2 8
00
3.1 100 "
'
I
1 3.0
'
2.9
2.8
2.7 I I
1
120
T I K Figure 6. Molar heat capacities of (CD3)?COin the runs with different
starting temperatures around the transition.
110
130
I
140
11
Figure 9. Dielectric permittivities of (CH&CO measured at 10 kHz around the transition in the heating (open circles) and cooling (closed
circles) directions. at 127 K in (CH3)2CO, in agreement with the work of Kelley (126 K), and 132 K in (CD3)zCO. Comparable deuteriuminduced shift of the transition temperature is reported for cyclohexanone." In the following sections, this peak is shown to be an intrinsic feature of acetone resulting from a rather unusual phase transition. Baseline Determination. To evaluate the excess heat capacity caused by the transition, a model function (eq 1) was
50 0 90
I
120
T I K
160
140
1
100
150
170
T I K Figure 7. Excess molar enthalpies due to the transition of (CD&CO gained in the heating (open circles) and cooling directions (see text for the details). are (5.612 f 0.002) kJ mol-' and (5.665 f 0.002) kJ mol-', respectively. The present fusion temperature and enthalpy of fusion of (CH3)2CO were slightly different from those reported by Kelley in 1929 (176.62 K, (5.715 f 0.008) kJ mol-'). In addition to the fusion peak, a broad peak in the heat capacity was observed for both samples. The peak maximum occurred
cp = c,a,(3) + Clib(3) + cMe(2) + cvib(22) + Acto, (l) first fitted to the experimental heat capacities over a range considered to be free from the effects of the phase transition itself. clat, Cllb, C Mand ~ Cvlb are the heat capacities due to the lattice vibration, rotational vibration (libration), methyl-group rotation, and intramolecular vibration, respectively. The numbers in parentheses denote the degrees of freedom included in each term. The last term in eq 1 gives the correction for the difference between C, and C,, which is given by
AC,,, = AC;T (2) where A is a constant and T the temperature. Cia[ was approximated by a Debye function and CrOlby an Einstein function, each having three degrees of freedom. Cvib due to intramolecular vibrations was represented by the combination of 22 Einstein functions. C Mwas ~ evaluated from the energy levels calculated using the Mathieu function as a potential energy
Ordinary and Deuterated Acetone Crystals
J. Phys. Chem., Vol. 99, No. 38, 1995 14171
0.2
1 .a
1.6
1.4
d-spacing
-
2.5
(A)
3.5
3 d-spacing
I
2
I1
'
I
4
(A)
I
7
Figure 10. Observed (+) and calculated (Pawley refinement) powder diffraction profiles for (CD&CO at 5 K. The integrated intensity refinement was carried out using space group Pbcm and shows evidence for anisotropic peak widths.
in a 3-fold hindered rotation. All of the frequencies of the intramolecular vibrations (for (CH3)zCO and (CD3)zCO) and the potential barrier for the methyl-group rotation (for (CH3)zCO) were known from the Raman and infrared spectroscopy2 and NMR,334respectively. The potential barrier of (CD3)zCO was assumed to be the same as that of (CH3)zCO (4.6kJ mol-'). A Debye temperature &(3) for the lattice vibration, two Einstein temperatures &(2) and OE(1) for the libration, and the correction coefficient A were determined by a least-squares fitting method to the experimental heat capacities in the temperature ranges 13-90 and 157-165 K for (CH3)zCO and 13-100 K and 160167 K for (CD3)zCO. The optimum values were &(3) = 106.3 K, &(2) = 199.4 K, &(I) = 101.5 K and A = 1.24 x mol J-' for (CH3)2CO and &(3) = 98.1 K, &(2) = 195.7K, &(1) = 123.2K,andA = 1.21 x mol J-' for (CD3)$2O. The baseline fitting was satisfactory for both samples and is illustrated in Figure 2 for (CD3)zCO. The contribution from each part is also shown by A (intramolecular vibration), B
(methyl rotation), C (lattice vibration), D (libration), and E (Cp - C, correction). Excess Heat Capacity and Entropy. Figures 3 and 4 show the excess heat capacities and excess entropies from the transitions. These were calculated using baselines determined as described in the previous section. Note that the abscissa of each figure is reduced by the respective transition temperature T,,,. The shape of the excess heat capacity is broad and symmetrical. The isotope effect on the excess heat capacity and entropy is small. This result suggests that the transition is not associated with the methyl-group rotation. The saturated value of the excess entropy (transition entropy) is 2.04 J K-' mol-' in (CH3)2CO and 2.08 J K-' mol-' in (CD&CO, indicating that the transition is not of order-disorder type in which transition entropy is usually larger than R In 2 (4.7J K-' mol-'). However, it is also possible that only a fraction (e.g., l/3) of the molecules are disordered in the high temperature phase, while the other molecules are ordered in both the high-
Ibberson et al.
14172 J. Phys. Chem., Vol. 99, No. 38, 1995
O
I
7.8
21.6 n
s
s 21.4
21.2L 0
I
I
50
I
100
150
I
I
T(K) I
I
1540
n
sn
nn
s>" 1500
8.9
I
0
I
I
50
100
I 150
1460 I 0
I
I
50
100
I 150
T(K)
Figure 11. Variation of lattice parameters and unit cell volume of (CD&CO as function of temperature. The lines are a guide to the eye and are calculated following a least-squares fit to the data below 100 K using a second-order polynomial function.
and low-temperature phases. If this is the case, the entropy values are compatible with an order-disorder mechanism. The large unit cell (see below) is consistent with this interpretation, however, it is not the only possibility. Kinetics of the Transition. To investigate the kinetic aspect of the transition, the heat capacities of three different runs were compared. In these runs the samples were cooled to 80 K at different rates (0.06 or 10 K min-I) or annealed at just below the transition (100 K) for 1 day and then cooled to 80 K. All data in this sequence give the same heat capacities, as shown for (CD&CO in Figure 5. This result indicates that the transition takes place very rapidly on cooling. Hysteresis Effect of the Transition. Hysteresis effects have been investigated by comparing several runs in which the samples were cooled down to different temperatures over the region of the transition (1 10- 140 K) and annealed for about 1 day before measurement. Figure 6 clearly shows the different heat capacity curves of (CD3)zCO depending on the starting temperatures. This elaborate procedure had to be taken because, in adiabatic calorimetry, one can measure the heat capacity only in the heating direction. To evaluate the extent of the transition as a function of temperature T, the excess enthalpy AH was calculated using eqs 3 and 4 for the heating and cooling directions, respectively.
(3) (4) In eq 3, Tis the final temperature of a cycle of C, measurements
in the normal run shown in Figure 1. In eq 4, T represents the starting temperature of the runs shown in Figure 6. Figure 7 contains the plots of AH in the cooling (closed circles) and heating (open circles) directions, showing a hysteresis effect of between 2 and 3 K. Dielectric Permittivity. Figure 8 shows the dielectric permittivity of (CH3)2CO observed at 10 kHz in the heating direction. A large jump of permittivity at Tf,,indicates that the polar molecular axis of (CH3)2CO is ordered in the crystalline phases. No dielectric dispersion was observed over the whole temperature (87-270 K) and frequency (100 Hz to 1 MHz) regions studied. Figure 9 gives an enlarged plot of the dielectric permittivity of crystalline (CH&CO at 10 kHz. Open and closed circles denote the data in the heating and cooling directions, respectively. A hysteresis loop, which is very similar to that of the excess enthalpy, was observed. This suggests that the extent of the transition corresponds to the change of some property associated with dielectric permittivity. Typically, in orientationally ordered organic crystals, this corresponds to changes in the unit-cell dimensions of the crystal. Neutron Powder Diffraction. The neutron powder diffraction profile for (CD3)zCO in the low-temperature phase at 5 K is shown in Figure 10. Preliminary analysis suggests an orthorhombic structure with the space group tentatively assigned as Pbcm: a = 21.24622(6); b = 9.16625(5); c = 7.53201(4) A; V, = 1466.9 A3.Surprisingly, there is no evidence to suggest a change in space group in the high-temperature phase as measured at 140 K: a = 21.74376(6); b = 8.93622(5); c = 7.89144(4) A; V, = 1533.4 A3. Consideration of the molecular
Ordinary and Deuterated Acetone Crystals
J. Phys. Chem., Vol. 99, No. 38, 1995 14173
TABLE 3: Molar Thermodynamic Functions of Acetone (CH&CO (M= 58.080 g mol-', R = 8.31451 J K-' mol-', A,'s'_ - A~I-P-IT) TIK 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300
cQp,,i~
0.1958 1.190 2.43 1 3.593 4.604 5.451 6.162 6.772 7.312 7.874 8.461 9.235 10.71 10.02 10.13 10.39 11.04 13.88 13.90 13.91 13.95 13.99 14.06 14.14 14.24 14.36 14.50 14.55 14.67 14.86 15.02 15.06
A,THOJRT
A;Y,IR
Q",,,lR
0.04894 0.3440 0.8331 1.380 1.927 2.446 2.927 3.371 3.779 4.162 4.525 4.882 5.302 5.649 5.943 6.212 6.472 10.51 10.69 10.85 10.99 11.13 11.25 11.37 11.49 11.59 11.70 11.73 11.80 11.90 11.99 12.01
0.06526 0.4686 1.186 2.048 2.961 3.878 4.773 5.636 6.466 7.266 8.044 8.810 9.636 10.39 11.08 11.74 12.39 16.84 17.59 18.31 18.99 19.64 20.26 20.86 2 1.44 22.00 22.54 22.71 23.07 23.59 24.01 24.10
0.01632 0.1246 0.3529 0.6671 1.034 1.432 1.846 2.266 2.687 3.105 3.519 3.927 4.334 4.740 5.140 5.532 5.917 6.336 6.909 7.461 7.994 8.509 9.006 9.488 9.954 10.41 10.85 10.98 11.27 11.69 12.02 12.09
density and cell volume suggest 16 moleculeshit cell, implying at least two independent molecular sites in the crystal structure. The powder diffraction profiles of both phases exhibit anisotropic line broadening which hinders the complete structural description of the phases. The variation of lattice parameters with temperature is shown in Figure 11. A discontinuity is clearly observed above ca. 120 K and there is a pronounced anisotropic behavior of the lattice parameters as a function of temperature. Note in particular, the negative b-axis thermal expansion.
Conclusions Transition Mechanism. From the investigations described above, the thermodynamic properties of the transition may be summarized as follows: (i) very broad temperature dependence, (ii) small transition entropy, (iii) small isotope effect, (iv) rapid transition rate, (v) hysteresis effect. These properties are very similar to those of martensitic transitionsI2 where shear deformation of the lattice occurs as a function of temperature. However, in contradiction of normal martensitic behavior, there appears to be no change in space group. The crystallographic information, although limited, suggests a complex phase transition behavior that may be fully understood only on completion of the full structural description of both the observed phases. Acknowledgment. The authors would like to thank the Daiwa Anglo-Japanese Foundation for financial support for this work.
TABLE 4: Molar Thermodynamic Functions of (CD3)2C0 (M= 64.121 g mol-', R = 8.31451 J K-' mol-', @Om = GS", - A@,JT) T/K 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 273.15 280 290 298.15 300
C a p,IR
AIWmIRT
A$',IR
0.2421 1.394 2.872 4.173 5.221 6.063 6.761 7.362 7.895 8.437 8.990 9.647 11.11 11.03 10.96 11.21 11.64 14.81 14.85 14.92 15.00 15.11 15.24 15.38 15.53 15.70 15.90 15.96 16.12 16.35 16.54 16.58
0.06 139 0.4077 0.9842 1.624 2.243 2.812 3.327 3.795 4.221 4.616 4.988 5.348 5.724 6.127 6.449 6.139 7.01 1 11.08 11.28 11.46 11.62 11.78 11.93 12.07 12.20 12.33 12.46 12.50 12.59 12.72 12.82 12.84
0.08197 0.5589 1.405 2.416 3.464 4.493 5.481 6.424 7.323 8.183 9.012 9.822 10.64 11.48 12.24 12.95 13.64 18.14 18.95 19.71 20.44 21.14 21.82 22.47 23.10 23.71 24.31 24.49 24.89 25.46 25.92 26.02
Q0JR
0.02058 0.1512 0.4210 0.7916 1.221 1.681 2.154 2.629 3.101 3.567 4.024 4.474 4.916 5.356 5.790 6.215 6.632 7.069 7.674 8.257 8.820 9.364 9.891 0.40 0.90 1.38 1.85 1.99 2.30 2.75 13.10 13.18
Appendix Standard Thermodynamic Functions. The molar heat capacities, enthalpies, entropies, and Giauque functions of (CH3)2CO and (CD3)zCO were calculated from the smoothed heat capacity data and summarized in Tables 3 and 4, respectively. Extrapolation of the heat capacity down to 0 K was performed by using the baseline functions described above. References and Notes (1) Kelley, K. K. J. Am. Chem. SOC. 1929, 51, 1145. (2) Dellepiane, G.; Overend, J. Spedrochim. Acta 1966, 22, 593. (3) Allen, P. S.; Branson, P.; Punkkinen, M.; Taylor, D. G. J. Phys. C 1976, 9, 4453. (4) Clough, S.; Horsewill, A. J.; McDonald, P. J. J. Phys. C 1984, 17, 1115. ( 5 ) Kato, C.; Konaka, S.; Iijima, T.; Kimura, M. Bull Chem. SOC.Jpn. 1969, 42, 2148. ( 6 ) Moriya, K.; Matsuo T.; Suga, H. J. Chem. Thermodyn. 1982, 14, 1143. ( 7 ) Goldberg, R. N.; Weir, R. D. Pure Appl. Chem. 1992, 64, 1545. (8) Yamamuro, 0.;Matsuo, T.; Suga, H. J. I n c h Phenom. 1990, 8, 33. (9) The cryostat is vanadium-tailed and of the I.L.L. (orange) design with a 100 mm bore. Institute Laue-Langevin, BP 156X 38042, Grenoble, France. (10) Ibberson, R. M.; David, W. I. F.; Knight, K. S., The High Resolution Powder Diffractometer (HRPD) at ISIS-A User Guide. Rutherford Appleton Laboratory Report (1992), RAL-92-031. (11) Huang, Y.; Gilson, D. F. R.; Butler, I. S. J. P hys. Chem., 1993, 97, 1998. (12) Rao, C. N. R.; Rao, K. J. Phase Transitions in Solids; McGrawHill: New York, 1978. JP95 1066X
