J. Phys. Chem. 1984,88, 3877-3880 imide formation can be schematically written
H 1
J
H
Where again H and H’ represent the inequivalent protons in the distorted ammonia molecule. Such a transition state would correspond to a saddle point on the total energy surface. In this case the surface is six dimensional, since the Ca-N distance, the tilt angle, and two different N-H distances and H-N-H bond angles must be specified. This problem can only be tackled by a full C I approach, including a t least all single and double excitations with a multiparameter geometry search.95 Moreover, the basis set for such a calculation needs to be very flexible (up to g and perhaps h function on N), and triple and possibly quadrupole excitations could well make an important contribution to the total energy. This amounts to a 30-electron problem for CaNH3, and the computational cost would be exhorbitant. A more limited C I calculation could be attempted in which the N 1s and Ca Is, 2s, and 2p populations are frozen and all single excitations and perhaps 30000 to 50000 double excitations are included. This should retrieve about 70-75% of the correlation energy, which should be sufficient to outline the semiquantitative form of the energy ~urface.9~ Nevertheless, such a calculation would still be very expensive (~20-30 Cray h). Initially, it would be much more economical to examine the energy surface for a limited number of parameters. The simplest approach would be to use a multiconfiguration self-consistent-field calculation, since a H F calculation is not adequate to describe a saddle point.96 However, caution must be exercised because the energy surface may well (96) The HF approach uses a single determinantal Slater function, whereas a saddle point can only be described in terms of a linear combination of the Slater determinants for all minima on the energy surface.
3877
be a multiminimum surface. We highly recommend that such theoretical calculations be undertaken in order to better understand the novel ammonia geometry in M-NH, compounds, but in someone else’s laboratory!
IV. Conclusions Research on M-NH, compounds over the past 15 years has revealed that these expanded metals have a rich variety of structures, molecular motions, and electronic properties. During the latter half of this period an impressive and growing body of evidence indicates that the ammonia molecules in these compounds adopt a highly distorted geometry, but it is perhaps still premature to say that the precise molecular shape has been established unambiguously. Although the distortion can be made plausible on the basis of an elementary treatment of excess electrons on ammonia, it is very unlikely that the observed structure represents the ground state of the molecule. Rather, it appears that the structural parameters and electronic structure of M-NH, compounds stabilizes a transition state of this molecule on the decomposition pathway. It has also occurred to us that such a distorted ammonia structure could also exist in M-NH3 solutions, especially on the metallic side of the metal-nonmetal transition. Research on confined M-NH, systems by techniques such as matrix isolation and intercalation into layered compounds would be very helpful in further elucidating the nature of the novel ammonia geometry in M-NH, compounds, and such studies are currently underway in our laboratories. Acknowledgment. The authors gratefully acknowledge the valuable contributions of the following students, collaborators, and technical personnel to the research described in this paper: T. R. White, M. J. Mobley, K. B. Rawlings, F. Y. Robb, R. J. Peck, D. A. Gordon, P. Hsu, J. Newsome, G. Weeks, K. Burton, J. L. Yarnell, A. L. Bowman, J. C. Thompson, A. K. Cheetham, J. K. Burdett, M. J. Sienko, J. Witschel, M. Wheeler, and R. Taylor. We also thank the Departments of Chemistry and Physics and the Center for Solid State Science at Arizona State University for use of their excellent research facilities. This work was supported by Grants DMR 75-09215, DMR 79-21069, and DMR 82-153 15.
Heat Capacity of Calcium Hexaammlne and Strontium Hexaammine D. A. Jacobs, T. J. Majors,? and W. D. McCormick* Department of Physics, The University of Texas at Austin, Austin, Texas 7871 2 (Received: August 25, 1983; In Final Form: March 1, 1984)
The heat capacities of the metallic compounds calcium hexaammine (Ca(NH&) and strontium hexaammine (Sr(NH,),) were measured in the temperature range 1.8-150 K by conventional heat pulse calorimetry. No sharp anomalies indicative of a phase transition were found in the calcium compound over the temperature range of the experiment, but there was a rapid change in slope of the Cpvs. T curve near 40 K. The strontium compound exhibited a single sharp anomaly at 38.6 f 0.2 K. The specific heat of the calcium hexaammine samples was not measured at low enough temperatures to detemine a Debye characteristic temperature, OD The Debye temperature of strontium hexaammine was found to be 24 f 2 K, where the uncertainty comes from extrapolation to 0 K. The molar heat capacities of these metal hexaammines are already about 15R, where 3R is from the Debye modes, by 40 K, indicating the existence of many low-energy rotational and vibrational modes. These modes have been seen in inelastic neutron scattering experiments by Leclercq, Damay, and Chieux.
Introduction Recent on the earth hexammines have clearly exhibit& their unusual and anomalous behavior,l Powder neutron diffraction (PND) studies2J on fully deuterated samples of metal hexammines have shown that the metal atoms Permanent address: Diasonics, Inc., San Francisco, CA.
0022-3654/84/2088-3877$01.50/0
are arranged in a body-centered-cubic structure. The ammonia ligands, which are greatly distorted, are octahedrally coordinated about the metal atoms in the cubic directions. The F”D studies (1) F. Leclercq, P. Damay, and P. Chieux, J . Phys. Chern., this issue. (2) R. B. Von Dreele, W. S. Glaunsinger, A. L. Bowman, and .I. L. Yarnell, J . Phys. Chem., 79, 2992 (1975). (3) W. S . Glaunsinger, J . Phys. Chem. 84, 1163, (1980).
0 1984 American Chemical Society
3878 The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 have also demonstrated the existence of a low-temperature phase in deuterated Sr(ND&, first thought to be rhombohedral below 45 K. Recent P N D work by Glaunsinger4 indicates that the low-temperature phase of Sr(ND3), is tetragonal and the transition temperature is 61 K. Ca(",),, on the other hand, remains body centered cubic down to the lowest temperature measured, 4 K. The magnetic susceptibilities of the alkaline earth hexammines have been measured by Mobley and Glaunsinger.5 The susceptibility of Ca(",), is strongly temperature dependent and exhibits a peak near 10 K. There is a very sharp transition a t susceptibility and perhaps a less pronounced 61 K in the Sr(",), feature at 20 K. Mobley and Glausinger associate the hightemperature transition in the strontium compound with the structural transition observed in Sr(ND3)6by neutron diffra~tion.~ The magnetic susceptibility results for Ca(NH3), and ST(",), are especially interesting when compared to the electrical resistivity measurements made by Mobley, Glaunsinger, and Thompson.6 There is a cusp in the resistivity vs. temperature curve for Ca(NH,), at 37 K. Slight inflections are suggested in the strontium data at 23 and 69 K. Mobley et al. again associate the hightemperature anomaly in the resistivity of Sr(NH& with the structural transition in the deuterated compound. They also predict a low Debye temperature for Sr(NH3), and state that the resistivity in the regions close to the anomalies can be described by a Bloch-Grueneisen formula if the Debye temperature is less than 30 K. The multiplicity of observed anomalies in the alkaline earth metal hexammines prompted our investigation of their heat capacities. We report here new measurements of the heat capacity of Ca("3)6 and Sr("3)6 from 1.8 to 140 K.
Experimental Section Samples were prepared by first removing the surface tarnish from an alkaline earth metal rod (99.9% pure, CERAC) with 500-grit emory paper and an X-acto knife in an argon atmosphere glovebox. Metal was shaved from the rod and cut into thin pieces measuring approximately 2 mm square. The metals were handled on a clean glass plate to prevent contamination from the floor of the glovebox. The metal pieces were weighed and transferred to the reaction vessel, which was then evacuated to lo-, Pa. The reaction vessels for the calcium samples were pyrex, while the strontium was prepared in both pyrex and quartz. The reaction vessel was transferred from the glovebox to the ammonia still and a stoichiometric volume of ammonia was distilled onto the metal in the reaction vessel by using a liquid nitrogen bath. The ammonia used was Matheson (99.998%), which had been previously dried over sodium with any residual gases pumped away. The reaction vessels were sealed under vacuum, minimizing the amount of excess glass as much as possible, and the ampoule containing the sample was then placed in a dry ice-ethanol bath at 200 K overnight to complete the reaction. The metal hexammine sample did not appear to contain any unreacted constituents and there was no visible decomposition. The accuracy of the sample composition was about f2% and was determined by the ammonia distillation process. There were two calcium hexammine samples (sample A = 0.003 989 mol, sample B = 0.002 759 mol) and two strontium hexammine samples (sample A = 0.003 612 mol, sample B = 0.003321 mol). The calorimeter was of conventional design,' used in the isothermal mode. Temperature control of the sample environment was accomplished by using an Allen-Bradley carbon resistor on the adiabatic shield as a temperature sensor. A sensitive ac bridge circuit was used to monitor the resistance; the bridge output was input to a conventional three-term temperature controller. The (4) W. S. Glaunsinger, J. Phys. Chem., this issue. ( 5 ) M. J. Mobley and W. S. Glaunsinger, Solid State Commun., 40, 357 (1981). (6) M. J. Mobley, W. S. Glaunsinger,and J. C. Thompson, J. Phys. Chem. 84, 1168 (1980).
( 7 ) Guy K. White, "Experimental Techniques in Low-Temperature Physics", Clarendon Press, Oxford, 1979.
Jacobs et al. I
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temperature of the shield could be held constant to within hO.1 mK at all temperatures. Once the sample and the shield were in thermal equilibrium, as indicated by the same constant temperature for at least 20 min, a pulse of heat was applied to the sample. The temperature change AT, of the sample, was measured by employing the conventional method of observing the long time decay of the sample temperature back toward that of the shield. Immediately after the heat pulse there were fast temperature variations due to the internal time constants of the sample and ampoule; these altered the shape of the temperature relaxation curve, so it could not be described by a simple exponential. The internal time constants were short compared to that for the equilibrium between the sample and shield. The standard practice in this case is to fit the temperature decay curve at times beyond where the internal equilibrium had been attained and to extrapolate the resultant exponential curve back in time to the middle of the heat pulse. Subjective evaluation of the computer fit to the temperature relaxation curve was the greatest source of error. The magnitudes of A T s were 0.6% of the temperature for T > 20 K and 1% of the temperature for T I20 K. The sample thermometer was a 1/10 W Allen-Bradley carbon composition resistor, which was cemented in a tightly fitting indentation in the bottom of the ampoule. The sample thermometer resistance was measured with an ac ratio transformer bridge and calibrated at each data point against a primary thermometer located on the adiabatic shield. The primary thermometer was a Lake Shore Cryotronics carbon glass resistor or silicon diode whose calibration was traceable to the Bureau of Standards. A table was made of the sample resistor values and the corresponding temperature as known from the primary thermometer. These data were fitted to a polynomial employing a least-squares technique.
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Heat Capacity of Ca(”3)6
and Sr(”3)6
Results and Discussion The observed temperature dependencies for the heat capacities of Ca(NH3)6 and are presented in Figures 1 and 2. These figures show the molar heat capacities for the two samples of each compound, obtained by substracting the heat capacities of the empty calorimeters from the raw data. The heat capacities of the empty calorimeter are always less than half the total heat capacities and at temperatures below 10 K the contribution from the calorimeters is 10% of the total. The calorimeter for the calcium hexammine sample plotted as triangles was destroyed before it could be measured. It was very close to the same size as that for the other calcium sample, however, so the same calorimeter values were substracted from both samples. For this reason, the calcium data plotted as triangles should be examined for its qualitative, not quantitative, behavior. The magnitudes of the heat capacities of the metal hexammines are quite large as to be expected for a complex molecule and the accuracy of the determined heat capacities is approximately 3~3%. There was some difference between the measured heat capacities of the two samples of each compound, especially at high temperatures. Coulter* has recently found a first-order solidsolid transition in at about 185 K and a similar transition in the calcium compound near this temperature. Since low-temperature structural phase transitions are often sluggish, we suggest that the variation in the data between the two samples of the same compound was due to different amounts of the metastable, supercooled high-temperature phase in the samples. This could have been caused by different rates of cooling through the phase transition and different amounts of time spent below the phase transition, but at high enough temperature so that annealing could take place. The strontium sample plotted as circles was always kept below 80 K, after initial annealing until the high-temperature data were taken. Other investigators had indicated that their measurements were more reproducible when this procedure was followed. The strontium sample plotted as triangles was cycled up near 200 K for several hours 5 or 6 times during the course of the experiment. This sample would probably be more fully converted to the low-temperature phase since it had been kept near the transition temperature over longer time spans. The calcium hexammine samples also had different thermal histories and this similarly may account for the differences at the high temperatures. Coulter’s heat capacity from 80 to 150 K lies between the curves of our two samples of strontium hexammine. No comparison has been made for the calcium hexammine, as the high-temperature data are not yet available. The heat capacity of calcium hexammine exhibits no sharp anomalies indicative of a thermodynamic phase transition. Within the scatter of the data there is no clear evidence for a feature in the heat capacity corresponding to the peak in the magnetic susceptibility a t about 10 K. Although the electrical resistivity measurements show a cusplike anomaly at 37 K indicative of a phase transition, the heat capacity data do not show a sharp transition in this temperature region. The slope of the C, vs. T curve does change rapidly at about 40 K and the two phenomena could certainly have a common origin. Our heat capacity data for strontium hexammine show a sharp break in slope at 38.6 f 0.2 K. If this anomaly is indeed an equilibrium phase transition then in the Eherenfest scheme it would be classified as third order. Other workers have seen anomalies in the magnetic susceptibility of strontium hexammine at 61 K5 and in the resistivity at 69 K.6 It is possible that all these anomalies have a common origin, the diverse temperatures being explained by differences in sample preparation, stoichiometry, or thermal history. These anomalies may also be associated with the structural transition from a high-temperature body-centered-cubic phase to a low-temperature tetragonal phase at about 61 K observed in P N D studies on Sr(ND3)6.4 N o low-temperature anomaly is visible in the heat capacity which would correspond to those observed in the magnetic susceptibility’ and resistivity6 (8) L. V. Coulter, private communication.
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3879 I
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Figure 3. C,/T vs.
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at 20 and 23 K, respectively. These may be purely electronic phenomena as no low-temperature transition has been observed in the structural studies. from 1.8 to about 3 K is shown in Figure The data for 3 as a graph of C p / Tvs. p. A value of OD(0),the characteristic Debye temperature, was obtained by extrapolating the curve to 0 K. A value of BD(0) = 24 2 K was obtained for Sr(”,), where the uncertainty is an estimate of the error due to a subjective choice of extrapolation. The data are not in the true T3 region, which is less than 1 K. We have ignored any possible electronic contribution to the heat capacity which, in view of the low electron density of the metal hexammines, is expected to be negligibly small with respect to other contributions at these temperatures. We calculated the ideal electrical resistivity from our value of OD and the p ( 6 ~ )reported by Mobley et aL6 using BlochGrueneisen theory. We did not find that the data of Mobley et aL6could be described by a Bloch-Grueneisen equation if our value of OD was used. In fact, we were unable to choose any Debye temperature for which the Bloch-Grueneisen formula would describe the resistivity. The heat capacity of calcium hexammine was only measured down to 5.5 K, which was not low enough to determine a Debye temperature. Ca(NH& melts near room temperature, so the Debye temperature would be low (
