8939
J . Phys. Chem. 1991, 95, 8939-8941
Molecular Dynamics Examination of an Anomalous Phase of TeF, Lawrence S.Bartell* and Shimin Xu Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: March 7, 1991)
At intermediate temperatures very large crystalline clusters of TeFs exhibit a monoclinic phase that is unusual by several criteria. This phase is also generated in molecular dynamics computations designed to investigate phase transitions in clusters during cooling and heating cycles. The computer simulations place the problem into a coherent perspective by showing that the monoclinic phase is metastable, not thermodynamically stable, and is formed only by virtue of the kinetics of phase change. Results also clarify the relationship between the nonmetal and metal hexafluorides.
Introduction Because the hexahalides (AX6) are arguably the simplest and most symmetrical of all polyatomic molecules, it is reasonable to expect to be able to understand their solid-state structures in some detail. Despite their quasispherical shape, however, their intermolecular interactions are sufficiently anisotropic to give them a complex crystal chemistry. They have been found to pack in at least five distinctly different crystal structures at atmospheric pressure, including body-centered cubic, rhombohedral, trigonal, monoclinic, and orthorhombic.l-1° It is the purpose of the present paper to seek to clarify properties of a subgroup of the octahedral substances, the rather rigid hexafluorides of the main-group and transition metals. Crystallographic evidence is incomplete, and most of it is based on powder patterns. Some of the investigations have been on bulk matter and some only on large molecular clusters (of -lo4 molecules) generated in supersonic flow. Because structures of clusters have been virtually indistinguishable from those of the bulk when common phases have been compared, both sources of information will be considered in the following. Just below their freezing points, the hexafluorides of the chalcogens (A = S,Se, Te) and the transition metals (A Mo-Rh and W-Pt) behave similarly. They all pack in a plastically crystalline bcc lattice.’+ On cooling, however, the metal hexafluorides all transform to an orthorhombic structure,ll while all three of the chalcogenides have been observed to adopt a monoclinic structure in large clusters5 (and in the bulk for SF6).6.7 At sufficiently low temperatures, however, tellurium hexafluoride does convert to an orthorhombic str~cture,~f’in clusters as well as in bulk. Puzzling aspects of the tellurium compound are as follows. First, molecules of TeF6are so nearly identical in size, shape, and flexibility with those of the transition-metal hexafluorides that it is difficult to see why TeF, should behave differently. Differences in bond lengths among the compounds are far less than the amplitudes of vibration of the bonds.” Another curious feature of TeF6 is the fact that its lowest temperature crystal structure, orthorhombic, has a higher symmetry than that of the ( I ) Siegel, S.;Northnip. D. A. Inorg. Chem. 1966,5, 2187. Taylor, J. C.; Wilson, P. W.; Kelly, J. W. Acta Crystallogr. 1973,829, 7. Levy, J. H.: Taylor, J. C.;Wilson, P. W. Actu Crystallogr. 1974.1931,398. Levy, J. H.: Sanger, P. L.; Taylor, J. C.; Wilson, P. W. Acta Crystallogr. 1974,B31, 1065. Taylor, J. C.; Wilson, P. W. J . Solid State Chem. 1975,14, 378. Levy, J. H.:Taylor, J. C.; Wilson, P. W. J . Solid State Chem. 1975,15, 360. Levy, J. H.; Taylor, J. C.; Wilson, P. W. J . Less-Common Mer. 1976,45, 155. (2) Taylor, J. C. Coord. Chem. Rev. 1976,20, 197. (3) Michel. J.; Drifford, M.; Rigny. P. J . Chim. Phys. 1970,67, 31. (4) Raynerd, G.; Tatlock, G. J.; Venables, J. A. Acta Crystallogr. 1982, 838. 1896. (5) Bartell, L. S.;Valente, E. J.; Caillat, J. C. J . Phys. Chem. 1987,91, 2498. (6) Dove, M. T.; Powell, B. M.; Pawley, G. S.;Bartell, L. S. Mol. Phys. 1988.65, 353. (7) Cockcroft, J. K.; Fitch, A. N. Z . Kristallogr. 1988, 184, 123. (8) Bartell, L. S.;Powell, B. M. Moi. Phys., in press. (9) Ketelaar, J. A. A.; Van Oosterhout, G. W. Recl. Trau. Chim. Pays-Bas 1943,62, 197. (IO) Taylor. J . C.; Wilson, P. W. Acta Crystallogr. 1974,830, 1216. ( I I ) For a complete citation of references on bond lengths, see ref 8.
0022-3654/91/2095-8939$02.50/0
TABLE I: k”rd-Jones Parameters for Seven-Site Intermolecular Potential Function for TeF‘ Molecules atom pair ~
‘4 e, kJ/mol eff bond length, A Q,
FF
TeTe
TeF
2.940 0.2049
4.294 1.376
3.553 0.531 1.8148
intermediate phase, monoclinic. This is opposite to the direction generally found. Finally, monoclinic TeF6 has never been seen in bulk* even though its occurrence is plainly evident in large
cluster^.^ To gain some insight into the observed behavior, a molecular dynamics investigation was undertaken. Results significantly elucidated the relationships between the metal and nonmetal hexafluorides and suggested a convincing interpretation of observations. Computational details are described in the next section. Procedure Molecular dynamics computations were carried out on clusters of TeF6 with a modified version of the Daresbury program MDMPOL. Pairwise-additive atomatom intermolecular interaction potentials were adapted from Buckingham functions of Caillat” that had successfully accounted for the monoclinic phase of TeF6 seen in clusters.’ In the process of simplifying Caillat’s functions to the Lennard-Jones form for expedience in computation, it was found that a slightly better representation could be obtained with an unconventional combining law which made both u and t for Te-F the geometric means of the Te-Te and F-F interactions. Parameters were then refined to make Monte Carlo computations on bulk TeF6 (128 molecules, with periodic boundar conditions) yield the experimental bcc lattice constant (6.293 at 223 K8) and energy of sublimation (taken as 27.7 kJ/mol at 217.5 K13). Final parameters are listed in Table I. No cutoffs of the potential functions were applied in calculations on clusters. Computations were carried out on clusters of 128 and 250 molecules constructed to be as spherical as possible starting with a tellurium atom a t the center. Several other configurations to be described were also tried. Molecules were initially arranged in an idealized packing to be tested. At each temperature to be examined an initial bath temperature was maintained by rescaling after each of the first lo00 time steps (always of 10 fs each). After this period of equilibration, the temperature rescaling was switched off and constant-energy MD trajectories were followed for 4000 time steps during which thermodynamic averages were calculated. Cluster structure was monitored during heating and cooling cycles to detect phase changes. These were recognized by viewing the molecular arrangement with the aid of the program MACSPIN, by noting changes in the slope of mean potential energy vs temperature, by examining Pawley-Fuchs projections“ of orientational
l
(12) Bartell, L. S.;Caillat, J. C.; Powell, B. M. Science 1987,236, 1463. (13) The energy of sublimation is uncetain by perhaps IO%. A plausible value was deduced from information in: Kubaschewski 0.;Evans, E. L.; Alcock, C. B. Metallurgical Thermochemistry; Oxford University Press: London, 1967; Vol. 4. Yost, D. M.: Clauuen, W. H. J. Am. Chem. Soc. 1933, 55, 885. OHare, P. A. G. ANL Report 7315, 1968.
0 1991 American Chemical Society
Bartell and Xu
8940 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
. 2 1 =
-18 .19
L
c
-.w a
.22
L
-23
2 50
100
150
.21
L
E
0
.20
.24
200
50
T (K)
figure 1. Variation of configurationalenergy of a 250-molecule cluster of TeF, with change in temperature. (Triangles and circles) Two different cooling curves beginning with a bcc cluster. Clusters transformed to a monoclinic structure. (Diamonds) Warming of the monoclinic cluster. The warming curves corresponding to the two different cooling curves were indistinguishable. (Dashed curves) are added to make the transitions more conspicuous.
distributions, by studying distributions of angles between neighboring tellurium atoms,I5 and, in some cases, by inspecting velocity autocorrelation curves.
Results A spherical cluster with 250 molecules in a bcc structure was equilibrated at 190 K and then cooled in steps of 10 degrees every 50 ps. It retained its packing arrangement until it reached 110 K, whereupon it began to undergo a transition to the monoclinic structure. The transformation to this structure, the structure seen experimentally in clusters at intermediate temperatures, was complete by about 90 K. The failure to transform sharply is, of course, due partly to the very rapid cooling rate and partly to the small size of the cluster. Upon further cooling, the cluster remained monoclinic all the way to the lowest temperature investigated (10 K). For curiosity, a bcc cluster with a nearly cubic shape was cooled from 190 K. Initially its potential energy was appreciably higher than that of the sphere, but after about 250 ps of cooling and annealing, its corners became round and its potential energy became indistinguishable from that of the cluster which had been spherical from the beginning. After the monoclinic cluster had been cooled to 10 K, it was heated in ]@degree steps every 50 ps. It retained its monoclinic structure until, at about 90 K, it began to transform smoothly back to bcc. The change was complete by 140 K. Figure 1 illustrates the influence of temperature changes on the configurational energy. In one run a physically unrealistic bcc cluster of 54 molecules was constructed by placing 27 unit cells into a cubic array. As this unfavorable cluster was cooled from 200 K it last one molecule by evaporation and became amorphous and liquid-like in velocity autocorrelation after several hundred picoseconds. Why it is of interest to report the results for such a physically meaningless starting configuration is that the amorphous cluster began to crystallize to a monoclinic structure at 95 K and completed the change by 50 K. A few of the surface molecules had orientations deviating from those characteristic of the monoclinic structure, but the molecular centers of mass packed into the proper sites. That a transition could proceed from bcc to monoclinic facilely through a disordered intermediate is worth noting. It is possible that some critical nucleus with a suitable configuration remained intact, but it was not obvious in visual inspections of molecular distribution. The kind of reorganization required for the change from bcc to monoclinic will be discussed presently. What emerges from these runs, among other things, is a confirmation that the higher temperature modeling of TeF, sucH.;Pawley, G. S.J . Phys (Paris) 1988, 49, 41. (15) Haymet, A. D. J. Chem. Phys. Lett. 1984, 107, 77. Quirke, N.; Shcng, P. Chem. Phys. Leu. 1984, 110, 63. (14) Fuchs, A.
100
150
200
T (K)
Figure 2. Variation of configurational energy of 128-moleculeclusters of TeF, as they are heated. (Triangles) Monoclinic cluster. (Diamonds) Orthorhombic cluster. Both clusters transformed to bcc. Dashed curves are added to make the transitions more conspicuous.
cessfully simulates experiment. Thermally agitated TeFs octahedra preferentially adopt a bcc structure, even in submicroscopic crystals. Also illustrated is the natural tendency for bcc aggregates to reorganize quickly to a monoclinic structure when cooled. That the monoclinic structure is retained down to the lowest temperature does not, however, indicate that it is the thermodynamically stable low-temperature phase. Even if the modeling were perfect, the subnanosecond times of the simulations are too brief to ensure that true thermodynamic equilibrium is established. Therefore, spherical clusters with 128 molecules were constructed to oompare the two most likely low-temperature structures. One of them was the monoclinic form already discussed. The other was the orthorhombic packing arrangement possessed by all of the transition-metal and recently found for the low-temperature phase of bulk TeF6.* Runs were begun a t 50 K, and clusters were warmed in 10-degree steps every 50 ps. The monoclinic cluster behaved just as the larger 250-molecule cluster did, except that its transformation to bcc occurred a t a temperature lower by about 15 degrees. While a lower transition temperature is to be expected, the magnitude of the shift with cluster size was not accurately established in the comparatively brief time scale of the run. Of greater significance is the fact that the orthorhombic cluster retained its structure as it was heated until it transformed to bcc over the range from 90 to 135 K. The transformation occurred at a temperature approximately 10 degrees warmer than that at which monoclinic changed to bcc. Moreover, over its range of stability, the orthorhombic cluster possessed a potential energy 0.3% lower than that of the monoclinic cluster. Results of the run are plotted in Figure 2.
Discussion Results of the MD computations parallel experimental observations of bcc, monoclinic, and orthorhombic forms of TeF, a t successively lower temperatures. More than that, however, they suggest a satisfactory resolution of the seemingly anomalous behavior of TeF6 noted under Introduction. To make the reasoning clearer, it is helpful briefly to review the packing arrangements in the different structures. in the bcc structure, the space group Imjm, 2 = 2, implies a symmetry with TeF bond axes parallel to the cubic axes. In fact, when the molecules pack together as closely as they do, they manage to avoid excessively short fluorinefluorine contacts only by a substantial disordering of their orientations.I6 The structure is plastically crystalline. How SF6 molecules reorder in transitions from bcc to monoclinic through a trigonal intermediate has been shown graphically by Raynerd et a1.4 and Pawley and Dove." (In the latter reference and in ref 5 a different convention was adopted for unit cells and the monoclinic lattice was identified as triclinic.) If just one-third of the quasispherical molecules in the bcc crystal (16) Powell, B. M.;Dolling, G. Can. J. Chem. 1988, 66, 897. (17) Pawley, G. S.;Dove, M.T. Chem. Phys. Lett. 1983, 99, 45.
J . Phys. Chem. 1991, 95, 8941-8944 reorient by 60°, fluorines of one molecule then fit nicely into hollows of a neighbor, leading to a nominally hexagonal closest packing of fluorines when the lattice readjusts to the monoclinic form. Although this more compact structure has a lower energy than the bcc, the bcc has a higher entropy (accounting for its greater stability at higher temperatures). Especially to be noted, then, is the close similarity of the monoclinic structure to that of the bcc. If s F 6 (or TeF,) molecules were somehow to transform smoothly into spheres, the monoclinic structure would transform smoothly to body-centered cubic. If, on the other hand, molecules in the orthorhombic structure were gradually to become spherical, the lattice would smoothly transform to hexagonal closest packed. Because the coordination in this structure is markedly different from that in bcc, it can be seen that a transition from bcc or monoclinic to orthorhombic requires a major reorganization, and one which would be expected to be comparatively slow. The present MD computations are entirely consistent with this picture. They indicate that throughout the range of temperatures over which the monoclinic TeF, clusters were encountered they were metastable with respect to the orthorhombic. That they were seen at all, then, is due to the kinetics of the transition, not to the thermodynamics. It is no longer strange that the lower symmetry monoclinic form is seen at a higher temperature than the orthorhombic form. Neither is it surprising that the monoclinic clusters of TeF, were seen even though the monoclinic phase had never been found for bulk TeF6 or for the transition-metal hexafluorides whose molecules so closely match TeF, in size and shape. Observations of monoclinic clusters were made only microseconds after rather warm microcrystals had condensed from the vapor in a cooling flow. Orthorhombic clusters seem to be generated only if they are grown in flow that is already very cold. That TeF6 is closer in its crystal chemistry to the metal hexafluorides than to its smaller homologues SF6and SeF, is indicated
8941
by the lack of a thermodynamically stable monoclinic phase of TeF6. These and the above considerations prompted us to propose a study of clusters of the metal hexafluorides. Removing all doubts about the close kinship between the hexafluorides of tellurium and the transition metals was the outcome of the suggested investigation. Clusters of WF6 produced in supersonic flow were found to behave almost identically with those of TeF6.'* When nucleated in very cold flow, they displayed orthorhombic diffraction patterns. When formed in warmer flow conditions, however, their diffraction patterns were unmistakably those of monoclinic crystals. Certain details remain to be settled before the hexafluoride story is complete. Whether an elusive trigonal form of SF6 reported to exist at temperatures between those of bcc and monoclinic4J9 is stable or metastable and whether it can occur in the heavier hexafluorides is uncertain. It is a t least a likely intermediate in the transition from bcc to monoclinic. Neither is it entirely substantiated that the lighter hexafluorides cannot exist as orthorhombic crystals at sufficiently low temperatures. Nevertheless, the present research appreciably clarifies the relationship between the chalcogen and metal hexafluorides.
Acknowledgment. This research was supported by a grant from the National Science Foundation. We thank Messrs. T. S.Dibble, J. W. Hovick, and P. J. Lennon for permission to cite their unpublished results for clusters of tungsten hexafluoride. We are indebted to Mr. F. Dulles for considerable help in computations and to Dr. W. Smith of the Daresbury Laboratory for the program MDMPOL. Registry No. TeF6, 7783-80-4. (18) Bartell, L. S.;Hovick, J. W.; Dibble, T. S.;Lennon, P. J. Unpublished research. (19) Bartell, L. S.;French, R. J. Rev. Sd. Instrum. 1989,60, 1223.
Calculated Equillbrlum Yields of Csofrom Hydrocarbon Pyrolysis and Combustion J. Thomas McKinnon TDA Research, Inc., Wheat Ridge, Colorado 80033 (Received: January 22, 1991; In Final Form: May 17, 1991)
The equilibrium yield of Buckminsterfullerene, Cso, has been computed for the pyrolysis and oxidation of a hydrocarbon source using a free-energy-minimization computer code as a function of temperature, pressure, and element ratios. High Cm yields are favored by low pressure and high C/H ratios and low oxygen concentrations. A temperature window exists in which fullerene yields are favored between 2200 and 2600 K. The computed yields are extremely sensitive to the value used for the Cso heat of formation and are fairly sensitive to the vibrational frequencies of the molecule.
Introduction In 1985, Kroto et a1.l proposed the existence of a class of closed-cage carbon molecules with aromatic structure. The most abundant of these molecules, c60, was speculated to have a structure resembling a soccer ball and was given the name Buckminsterfullerene in honor of Buckminster Fuller's work on geodesic domes. The other molecules in this class, such as C,,,. have come to be known as fullerenes. Interest in this area has increased greatly with the discovery by Kratschmer et a1.2 of a simple method to produce large quantities (ca. 100 mg) of fullerenes. In the Krsitschmer et al. process, fullerenes are formed by vaporizing carbon rods in an electric arc.
fullerenes could be extracted from combustion soot4 led us to conduct an investigation on the thermodynamic limits to fullerene production. We have shown that Cm and C70can be extracted from combustion soot produced in a premixed benzene/oxygen/ argon flame a t a C/O ratio of 0.96 and a pressure of 40 Torr. The yield of fullerenes from the soot is about 1% (grams of Cso + C70 per gram of soot) and the yield of soot from fuel carbon is about 3%. The overall yield of fullerenes from fuel carbon, 0.0396,is quite low compared to the yields of fullerenes from
(I)Kroto, H. W.;Heath, J. R.;OBrien, S. C.; Curl, R. F.;Smalley, R. E. Nature 1985,318, 162-163. (2)Kratschmer, W.;Lamb, L. D.; Fostiropulos, K.;Huffman, D. R.
137, 306-3 10. (4) McKinnon, J. T.; Bell, W. L.; Barkley, R . M. Combusr. Flame, sub-
Nature 1990. 347, 354-358.
Gerhardt et al. reported in 1987 that microscopic quantities
of Cm and C70 were produced in sooting benzene and acetylene flame^.^ Our recent discovery that macroscopic quantities of
(3)Gerhardt, Ph.; Loffler, S.;Homann, K. H. Chem. Phys. Lerr. 1987, mitted for publication.
0022-3654/91/2095-8941%02.50/0 0 1991 American Chemical Society
