2498
J. Phys. Chem. 1987, 91, 2498-2503
acetone partial pressures were then used to generate a two-parameter Redlich-Kister correlation for the liquid activity coefficients. These expressions are In y, = x2(B - C(4x - 3)) In y2 = (1
- X ) ~ ( B+ C( 1 - 4x))
where B = 1.68 and C = -0.20. Higher order fits are not justified with this procedure. The results appear to be satisfactory, but without actual data there is no quantitative way to assess their accuracy. Surface tension data of Teitelbaum et al.,27as reported
by Timmermans20 (p 45), were fit as In u vs. the variable 1l x / ( l + lox) by using a cubic spline routine. All points were given unit weight. Surface tension values at x = 0.054, 0.141, and 0.365 were reduced from their measured values by 1, 1.5, and 1.2 dyn/cm, respectively, for use as input data to the spline fitting routine. A fictitious point (28.0 dyn/cm) at x = 0.6 was included in the data set. The fitted curve is shown in Figure 11. Average molar volumes, computed from the density data of Sapozhnikov28 as reported in Timmermans2' (p 40), were fitted to a third-order polynomial in x. Registry No. CHBOH,67-56-1;H3CCH20H,64-17-5;H3C(CH2),OH, 71-23-8; CHSCOCH3, 67-64-1.
(27) Teitelbaum, B. Y.; Ganelina, S. S.; Gortalova, T. A. Zh. Fiz. Khim. 1951, 25, 1044.
(28) Sapozhnikov, A. J . Russ. Phys.-Chem. SOC.1896, 28, 223.
Electron Dlffraction Studies of Supersonic Jets. 8. Nucleation of Various Phases of SF,, SeF,, and TeF, Lawrence S. Bartell,* Edward J. Valente,? and Jacques C. Caillat Department of Chemistry, University of Michigan, Ann Arbor, Michigan 481 09 (Received: June 17, 1986)
Cold ~crocrystalsof SF,, %F6, and TeF6are condensed when the gaseous hexafluorides in monatomic carriers flow supersonically through a miniature Laval nozzle. Electron diffraction records of the condensates display strong Debye-Scherrer rings. The diffraction patterns depend markedly upon.the carrier gas and expansion conditions. For the hexafluorides of sulfur and selenium the well-known body-centered plastic cubic phase forms if the molecular weight of the carrier gas is low and the subject mole fraction exceeds several percent. A phase I1 of lower symmetry begins to appear only at low mole fractions o f s F 6 and requires a carrier at least as heavy as argon. Phase I1 appears for SeF, with argon carrier under all conditions examined and with neon under extreme conditions. It appears readily even with helium in the case of TeF,, provided the subject mole fraction is comparatively high. At lower mole fractions and total pressures another, as yet unidentified, phase 111 of TeF6 is produced. Patterns of phase I1 are well accounted for by the triclinic lattice Pi,Z = 3, predicted in a molecular dynamics simulation of SF6 at low temperature by Pawley and Thomson. Refinements based on this space group, for the two compounds yielding nearly pure phase 11, led to the following cell constants (30): SeF6 (T < 140 K), a = 14.51 (8) A, b = 8.22 (3) A, c = 4.92 (3) A, a = 85.6 (3)', p = 93.7 (4)', y = 88.14 (4)'; TeF6 (T< 160 K?), a = 14.99 (7) A, b = 8.53 (3) A, c = 5.06 (3) A, a = 85.6 (3)', p = 93.5 (3)', y = 88.9 (3)'. Low temperature patterns of SF6 were highly contaminated by bcc rings but matched the 75 K neutron patterns of Powell to within the appreciable experimental error. Contrary to some previous reports, phase I1 is denser than the bcc phase.
Introduction Studies of nucleation in nozzle flow by the late Gilbert D. Stein played an important role in the design of the present research program. Preliminary investigations'q2 showed that supersonic nucleation affords a versatile means of generating clusters whose structure can be controlled, within limits, by the flow conditions imposed. Therefore, it appeared worthwhile to explore in more detail clusters formed from the hexafluorides of sulfur, selenium, and tellurium. These compounds are stable, adequately volatile, and known to crystallize in more than one form. Furthermore, because the molecules are simple and symmetrical, their packing arrangements should be particularly amenable to theoretical analysis. Most metal hexafluorides form plastic crystalline body-centered cubic phases on freezing3 and undergo a transition to an ordered orthorhombic phase isomorphous with U F t at lower temperatures. The nonmetallic group VI (group 16)39hexafluorides SF6,SeF6, and TeF, resemble the metal compounds insofar as the bcc structure of their warmest solid phase is ~ o n c e m e d . ~They * ~ have also been observed to exhibit phase transitions at lower temperatures.@ Although a final mncensus on the structure of the lower temperature phases had not been reached in prior published work, 'Present address: Department of Chemistry, Mississippi College, Clinton, MS 39058.
0022-3654/87/2091-2498$01.50/0
it is certain that they are distinctly different from those of the metal hexafluorides. In a previous paper of this series,' it was shown that crystalline clusters of SF,, SeF,, and TeF6 of lower symmetry than the bcc form can be produced by homogeneous nucleation under certain conditions of expansion through a Laval nozzle. Microcrystals are characterized by electron diffraction within microseconds of the time they issue from the nozzle. It was found that the diffraction patterns of the noncubic form resembled the X-ray pattem reported for SeF6 at 153 K by Michel et ale6and tentatively identified as orthorhombic. This identification is herein shown to be incorrect by a new procedure of analysis. Neither could (1) Valente, E. J.; Bartell, L. S. J. Chem. Phys. 1983, 79, 2683. (2) Valente, E. J.; Bartell, L. S. J . Chem. Phys. 1984, 80, 1458. (3) Siegel, S.; Northrup, D. A. Inorg. Chem. 1966,5, 2187. (4) Hoard, J. L.; Stroupe, J. D. Chemistry of Uranium-Collected Papers, Katz, J. J., Rabinowitch, E., Eds.; US.Atomic Energy Commission: 1958;
Paper 45. ( 5 ) Taylor, J. C.; Waugh, A. B. J. Solid State Chem. 1976, 18, 241. (6) Michel, J.; Drifford, M.; Rigny, P. J . Chim. Physicochim. Biol. 1970, 67, 31. (7) Salvi, P. R.; Schettino, V. Chem. Phys. 1979, 40, 413. (8) Raynerd, G.; Tatlock, G. J.; Venables, J. A. Acta Crystallogr., Sect. B 1982, 38, 1896. (9) Powell, B. M. private communication.
0 1987 American Chemical Society
SF6, SeF6, and TeF6 Nucleation the patterns be accounted for by the hexagonal structure reported for SF6 a t intermediate temperature by Raynerd et al.8 The patterns did, however, closely match those found for SF6by Powell9 a t 75 and 19 K by neutron diffraction and probably correspond to the phase observed by Raynerd et aL8 below 50 K. In the following we investigate the conditions under which the various forms of the group VI (group 16) hexafluorides are nucleated. We also determine the lattice constants of the cubic and one of the lower temperature phases observed.
Experimental Section The electron diffraction apparatus used has been previously described'O as has the modification for studies of supersonic nucleation.l' Helium, neon, argon (99.999%), and SF6 (>99.95%) from Air Products, Ltd., SeF6 and TeF, (99.8%) from N O A H Chemical Division, and krypton (grade 3.5) from Airco Industrial Gases were used as received. Well-mixed samples with hexafluoride mole fractions between 0.01 and 0.12 in the monatomic carriers were prepared. A consensate beam, formed by the expansion of the gas mixture through our Lava1 nozzle no. 6,' was passed through a skimmerI1-l3transmitting much of the condensate while skimming away the bulk of the uncondensed gases. Sectored diffraction patterns of 40-keV electrons (A = 0.06015 A) were recorded on Kodak 4 in. X 5 in. medium projector slides located about 215 nm below the region of scattering. Relative scattered intensities are expressed in the following as a function of s ( = 4 ~ sin O/X; 0 is the Bragg angle). Ranges of the sectors are 0.8 < s < 4.0 A-' (r' sector) and 2.2 < s < 12 A-1 (r2 sector). The camera height was established by recording gas diffraction of pure CCI, and standardizing against the 1.769-w"g: length.le" Conditions of the expansions for representative experiments are given in Table I. Raw intensities from microdensitometry were sampled at intervals of As = 0.015 A-1and corrected for nonlinear emulsion response, sectoring attenuation, and background scattering. A modified, leveled molecular intensity was then obtained by dividing the data by the theoretical atomic scattering for the monomer. An analytical fit to the monomer and carrier scattering was then subtracted to give a modified intensity due to crystals. Mean sizes of the cubic crystals obtained were estimated from the breadths of the diffraction ring^,^^**^ and temperatures for cubic phases were inferred from the cubic cell parameters by taking into consideration the estimated linear coefficients of expansion for SF6 (3.0 X 104/deg)14.20 and SeF6(3.6 X 104/deg).6-20 The fwhm of the electron beam in these experiments is less than about 0.025 mm, contributing only a small instrumental broadening to the profiles of the peaks for which the fwhm is 0.125 mm for l00-A crystallites. For patterns of cubic crystals, peak profiles above an adjustable background were fitted by Gaussian functions which served to characterize intensities, breadths, and positions. Patterns of the lower temperature phase were much more complex. While the major diffraction peaks could be explained in terms of reflections from an orthorhombic lattice, as previously reported,'V6 the implied crystal densities were improbably small, (10) Bartell, L. S. In Physical Methods of Chemistry, Vol. I, Part IIID; Weissberger, A., Rossiter, B. W., Eds.; Wiley: New York, 1972. (1 1) Bartell, L.S.; Heenan, R. K.;Nagashima, M . J. Chem. Phys. 1983, 78, 236. (1 2) Anderson, J. B. In Molecular Beams and Low Density Gasdynamics, Wegener, P. P., Ed.; Marcel Dekker: New York, 1974. (13) DeBoer, B. G.; Kim, S. S.; Stein, G. D. Rarified Gas Dynamics (Eleventh Symposium), Campargue, R., Ed.; Commissariat a L'Energie Atomique: Paris, 1979. (14) Bartell, L. S.;Brockway, L. 0.; Schwcndeman, R. H. J. Chem. Phys. 1955, 23, 1854. (15) Morino, Y.; Nakamura, Y.; Iijima, T. J . Chem. Phys. 1960, 32,643. (16) Haase, J.; Zeil, W. Z . Phys. Chem. 1965, 45, 202. (17) Shibata, S.; Iijima, K.; Taui, R.; Nakamura, J. Rep. Fac. Sci. Chizuoka Uniu. 1974, 9, 33. (18) Guinier, A. X-ray Diffraction; Freeman: San Francisco, 1963; p 121. (19) Bartell, L. S.; Caillat, J. C., unpublished research. (20) Because the coefficient of thermal expansion of the denser, lower temperature phase appears to be larger, according to neutron diffraction studies by Powell, ref 9, than the coefficients estimated in ref 6 and 13, it is likely that the values cited are underestimated.
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2499 TABLE I: Selected Results of Supersonic Expansions through Nozzle 6 subj mole subiect carrier fraction
solid
P,,,# Dhaseb
lattice constC
diamC ~~
He Ne
Ar
Ne
Ar
0.125 0.11 0.11 0.11 0.06 0.03 0.015 0.12 0.06 0.03 0.015
6.1 6.8 4.8 3.4 4.8 4.8 4.8 4.8 4.8 4.8 4.8
0.12 0.06 0.06 0.03 0.015 0.12 0.06 0.03 0.015
4.8 .4.8 5.4
I I I I I I I I I I + I1 I + I1 + Ar(s)
I I I 4.8 I + I1 4.8 I1 4.8 3.4 3.7 4.8
5.812 5.798 5.799 5.800 5.802 5.794 5.790 5.791 5.789
(3)-(3) (3) (4) (3) (4) (4) (4) (22)
180 (25) 180 (25) 112 (10) 100 (6) 114 (11) 98 (7) 85 (3) 79 (5) 99 (7)
5.975 (5)
97 (7)
5.960 (4) 5.960 (17)
94 (6) 75 (7)
I1
I1 I1 I1
+ Ar(s)
He Ne
Ar
Kr
0.20 0.06 0.03 0.12 0.12 0.067 0.067 0.03 0.10 0.10 0.039 0.10 0.05
6.1 5.4 5.4 7.1 6.9 7.1 6.4 5.4 4.1 3.1 5.8 4.8 4.8
I1 111 111
I1 I1 I1 111
I11
I1 111 111
I1 111 +
Ws) 'Stagnation pressure, in bar. bPhase I, bcc; phase 11, triclinic; phase 111, unknown structure; rare gas, fcc. cIn angstroms.
and several weak, reproducible features could not be accounted for. At this juncture, neutron diffraction powder patterns of sF6 from much larger crystals were obtained by P ~ w e l l .It~was clear that they corresponded closely to the cold SeF6 and intermediate TeF6patterns, but the much narrower neutron diffraction peaks exhibited additional splitting. Because standard least-squares procedures for fitting such patterns lead to a multitude of local minima, a new, robust procedure, described elsewhere,19 was devised to reduce the possibility of entrapment in false minima. Briefly sketched, this procedure attempts to fit the profile of scattered intensity by a sum of calculated peaks. N o explicit assignment of Miller indices of experimental peaks ever need be made. Initial estimates of atomic positions for structure factors are generated by packing calculations.21 At the beginning, only the inner part of the pattern is included in refinement, and experimental and calculated peaks are both deliberately broadened by a simple prescription. This enhances the overlap of experimental and calculated peaks and thereby allows the design matrix to steer the refinement in an appropriate direction. Gradually, the angular range is increased, the structure factors are updated, if necessary, to be consistent with changing lattice parameters in PCK6 computations,21and peaks are relaxed to their natural breadths until the entire pattern is fitted well. By such a procedure, the distinct local minima obtained in conventional fits of powder data have all, so far, refined to a common, presumably global, minimum. (21) Williams, D. E.; Starr, T. L. Compur. Chem. 1977.1, 173. Williams, D. E.; PCKS/PCK~ (Quantum Chemistry Program Exchange) Indiana University: Bloomington, IN.
2500 The Journal of Physical Chemistry, Vol, 91, No. 10, 1987
Bartell et al.
SeFG
r-
r 0
1
2
3
4
0
1
2
S Figure 1. Leveled intensities of electrons diffracted by a jet of SF, recorded with r1 sector, stagnation pressure P = 4.8 bar. Upper trace, subject mole fraction, X , = 0.06 in neon, bcc clusters. Lower trace, clusters nucleated at lower temperature in argon, X, = 0.03, predomi-
4
S Figure 2. Leveled intensities for SeF,, P = 4.8 bar, X , = 0.06. Upper trace, bcc clusters in neon carrier. Lower trace, triclinic clusters in argon
carrier.
nantly bcc pattern displaying some triclinic lines (phase 11).
I
Results Cubic SF, (referred to as phase I) formed in all of our nozzle experiments with this substance for which a condensate appeared. Crystal temperatures, as inferred from the lattice constants, varied as the expansion conditions were varied. When the carrier gas was helium or neon, expansions produced only cubic SF6 with temperatures in the range 100-130 K. In argon, temperatures near the 94 K transition value* were achieved even at relatively high mole fractions. Lower mole fractions of hexafluoride led to lower nucleation temperatures because low partial pressure delays condensation in the nozzle. At the lowest mole fractions in argon such low temperatures were reached that even crystals of the argon carrier appeared in the nozzle effluent. Carrier crystals had the normal face-centered cubic lattice with a re eat distance of about 5.35 A. They were approximately 50 in diameter and, at 45-70 K, colder than the SF6 crystals they coexisted with. The cubic crystals of SF6 had diameters of about 50-180 A, the larger sizes occurring at higher mole fractions and stagnation pressures. Although very small crystals may have cell parameters diminished in comparison with bulk values, the observed crystals were probably large enough to reduce this Laplacian pressure effect2*qZ3below our experimental error. The three hexafluorides behaved quite differently in nozzle flow. In order to obtain the low temperature phase of SF6, phase 11, it was necessary both to go to a low mole fraction and to use the heavy carrier gas argon. Even under these conditions the cubic pattern dominated as shown in Figure 1. For SeF6, whose transition temperature is higher than that of SF,, the low temperature phase appeared under milder conditions (Figure 2). It could be obtained with neon carrier, if the mole fraction of SeF, were low and the stagnation pressure, high, and with argon at all mole fractions and pressures studied. All of the phase I1 patterns of SeF6obtained with neon and most of the patterns obtained with argon showed small amounts of phase I, as well. The pure cubic phase of SeFs was produced in expansions with neon at subject mole fractions from 0.12 to 0.01 5 and pressures up to 3.4 bar. At the lowest concentrations the lattice constant decreased to 5.96 (2) A. Although the implied temperature of 155 K appears to be somewhat below the equilibrium temperature
3
I
I
1
(22) Torchet, G.; Bouchier, H.; Farges, J.; de Feraudy, M . F.; Raoult, B. J . Chem. Phys. 1984,81, 2137. (23) Yokozeki, A. J . Chem. Phys. 1978, 68, 3766.
0
1
2
3 4 S Figure 3. Leveled intensities for TeF6in neon, P = 6.4bar. Upper trace, X, = 0.12, triclinic clusters. Lower trace, X , = 0.067, clusters of unidentified lower temperature phase 111. for transition to phase 11, it is probable that the crystals nucleated and grew at higher temperatures, and then cooled in the expanding carrier. Expansions of TeF, at lower mole fractions in all carrier gases from helium to krypton at total pressures below 7 bar yielded a condensate consisting of a new and, as yet, unidentified phase giving a pattern quite unlike those of SF6 and SeF,. We will hereafter refer to this phase as phase 111. This result led us to try expansion conditions that would produce warmer nucleation conditions. At higher mole fractions of TeF, and suitable pressures a second phase appeared corresponding to phase 11 of SF6 and SeF, (Figure 3). Diffraction patterns of phase I1 were found to be well accounted for by a triclinic lattice, as discussed in the next section. Triclinic clusters of SeF, and TeF6 appear to be comparable in size to those of the cubic phases nucleated at higher mole fractions. Even though the diffraction peaks in the triclinic patterns are often broader, they are composites of many overlapping lines, the envelopes of which are well represented by crystal diameters of about 100-120 h;. Temperatures for the low symmetry forms are unknown but are probably somewhat below (for SF,) and appreciably below (for SeF,) the temperatures of the transitions from the cubic to triclinic phases. The present phase I1 lattice constants for SeF,
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 0
0
0.i0 Z
I
0 I- 0.051 0
-0-0
o-o-o-
I
,
Figure 4. Approximate representation of flow conditions through nozzle no. 6 corresponding to the production of clusters of phase I, phase 11, or phase 111. (a) SeF, in neon carrier; argon carrier yielded phase I1 over the entire range plotted for neon. (b) TeF6 in carriers from helium
through krypton. TABLE II: Unit Cells of Triclinic Clusters" comDd a b C ff B Y S=b, 14.51 (8) 8.22 (3) 4.92 (3) 85.6 (3) 93.7 (4) 88.1 (4) TeF,' 14.99 (7) 8.53 (3) 5.06 (3) 85.6 (3) 93.5 (3) 88.9 (3)
Lengths, A; angles, degrees; uncertainties, 3u. Nucleated from mole fraction 0.03 in argon carrier, stagnation pressure 4.8 bar, cluster temperature believed to be 140 K or less. CNucleatedfrom mole fraction 0.12in neon carrier, stagnation pressure 6.4 bar, cluster temperature believed to be less than 180 K. correspond to crystal temperatures perhaps a dozen or more degrees cooler than the 153 K temperature of the X-ray study by Michel et aL6 Unfortunately, the listing of the X-ray pattern was too incomplete to make the full identification of the pattern certain. Listed in Table I are representative results for experiments, including phases nucleated and, where analyzed, cluster sizes and (for cubic crystals) lattice constants for various flow conditions. A complete list of experiments is given in the supplementary material. (See paragraph at end of text regarding material.) Figure 4 maps the phases encountered for SeF6 and TeF, with various flow conditions and camer gases. Lattice constants derived for SeF6 and TeF6 by our new refinement procedure are listed in Table 11. Diffraction patterns of triclinic SF6were too badly obscured by strong lines from the cubic phase to warrant a comparable analysis. In due course refinements of Powell's neutron data9 will appear.
Discussion Cubic Phases. The cubic phase of sulfur hexafluoride is well characterized. It has been studied by neutron diffraction at 193 K,5 and clusters of it generated by supersonic flow have been reported by three l a b o r a t o r i e ~ . ' ~In ~ ~common * ~ ~ with the cubic metal hexafl~orides,~ it exhibits plastic crystalline behavior. Molecules display a considerable degree of librational freedom, a freedom which persists even when the temperature is lowered to near the transition temperature.% At this point, the cell repeat distance is 5.78 (1) A. Plastic crystalline behavior of comparatively spherical molecules such as SF6 can be accounted for by the (24) Abraham, 0.; Kim, S.S.;Stein, G. D. J. Chem. Phys. 1981, 75,402. ( 2 5 ) Farges, J.; de Feraudy, M. F.;Raoult, B.; Torchet, G. Surf. Sci. 1985, 156, 444. (26) Dolling, G.; Powell, B. M.; Sears, V. F. Mol. Phys. 1979, 37, 1859.
2501
shallowness of their surface indentations and, hence, the weakness of their ability to interlock, as gauged by a simple c r i t e r i ~ n . ~ ' Clusters are produced much more easily in flow through Lava1 nozzles than in free-jet expansions. In the present investigation, pressures less than 3 bar through a nozzle at room temperature readily yielded clusters. By contrast, free-jet expansions at Orsay with gas precooled to 220 K were carried out at 20-40 bar to generate clusters of SF6.25These clusters were small, ranging from 40 A in diameter, temperature 113 K (neat gas) to 30 A, 70 K (mole fraction 0.01 in Ne). Here, again, as noted above for SeF,, the cubic phase is seen supercooled below its bulk equilibrium transition temperature to phase XI. The triclinic phase was not observed in the free-jet expansion^.^^ Selenium hexafluoride also crystallizes as a plastic crystalline body-centered cubic material, and its freezing point, 226.6 K,6 is only 4 K above that of SF6. On the other hand, its transition to the lower symmetry form takes place at 170 K,6 almost 80 K above the corresponding transition for SF6. Even below the transition to phase 11, rotational motion, detected by nuclear magnetic resonance,6 remains substantial in the bulk until the temperature falls below 110 K. While tellurium hexafluoride freezes to a body-centered cubic crystal at 238 K,6 a temperature little warmer than the freezing points of its lighter homologues, its range of stability in this form is small. It undergoes a transition at 233 K to a form of lower symmetry.6 Whether this form is an intermediate phase or phase I1 observed in the present study is unknown. In none of the patterns we have obtained to date has evidence been found for the presence of the cubic form, even when butane was added to slow considerably the cooling rate during expansion. Finding the narrow window of stability of bcc might be difficult, for one thing. Even if the cubic form had been generated, however, its microcrystals would have been extremely unlikely to survive during the lo2ps between nucleation and the probing by the electron beam, unless severe supercooling had taken place. The vapor pressure near the transition temperature, approximately 1 atm,28is simply too high. Application of the kinetic theory suggests an intrinsic rate of evaporation into a vacuum of thousands of angstrom units per microsecond. Even cubic SeF6 at its transition temperature of 170 K is doubtful. Lower temperature phases are of greater interest because much less is known about them. They are discussed in the next section. Low Temperature Phases. A complete resolution of the lower symmetry forms of the group VI (group 16) hexafluorides has not been achieved. Information about their behavior was provided by a nuclear magnetic resonance study of Michel et aL6 in which decreasing molecular reorientation rates at lower temperatures paralleled transitions from plastic to more ordered phases. An X-ray powder diffraction pattern of SeF6, obtained at 153 K by the same workers, was provisionally (and it now appears, incorrectly) indexed in an orthorhombic lattice consistent with space group Pnma known to apply to metal hexafluorides. Spectroscopic evidence for the low temperature phase of SF6 also suggested an orthorhombic structure.' Raynerd et a1.* were able to obtain single-crystal electron diffraction patterns of SF6 by selected area diffraction in an electron microscope. A hexagonal lattice was found, between 94 and 50 K, that was believed to be isostructural with UC16.29 This distorted, at lower temperatures, to a lattice identified as monoclinic, or of lower symmetry. Concurrently with this work some remarkable molecular dynamics computations were carried out by Pawley and co-workers on a sample of 4096 SF6 molecules, with periodic boundary conditions imposed. These successfully simulated the plastic body-centered cubic phase at higher t e m p e r a t ~ r e a, ~partially ~ ordered trigonal phase at intermediate temperature^,^^ and a triclinic phase at 25 K.30 Subsequent neutron diffraction studies by Powellg at 19 and 75 (27) Postel, M.; Riess, J. G. J . Phys. Chem. 1977, 81, 2634. (28) Stull, D. R.Ind. Eng. Chem. 1947, 39, 517. (29) Zachariasen, W. H. Acta Crystallogr. 1948, 1 , 285. (30) Pawley, G. S.; Thomas, G. W. Phys. Rev.Lett. 1982, 48, 410. (31) Pawley, G. S.;Dove, M. T. Chem. Phys. Letf. 1983, 99, 45.
2502 The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
Bartell et al.
TABLE III: Positional Parameters in Unit Cells from Minimization of Packing Energy"
atom
X
S
0.00000 0.034 04 0.098 82 -0.098 82 -0.034 04 0.035 25 -0.035 25 0.334 60 0.427 42 0.292 47 0.292 47 0.376 72 0.376 72 0.241 71 0.665 33 0.758 22 0.623 27 0.623 27 0.707 52 0.707 52 0.572 51
F F F F F F S F F F F F F S F F F F F F LI
SF6 Y 0.000 00 0.16328 -0.023 52 0.023 52 -0.163 28 -0.101 43 0.101 43 -0.003 47 -0.014 13 0.12529 -0.147 80 -0.132 22 0.140 87 0.007 20 0.003 55 -0.007 11 0.13230 -0.140 79 -0.12521 0.147 76 0.01421
z
atom
X
SeF, Y
z
0.000 00 0.12306 -0.124 02 0.124 02 -0.12306 0.275 64 -0.275 64 0.576 63 0.764 95 0.764 95 0.764 95 0.388 11 0.388 1 I 0.388 11 0.421 54 0.61006 0.610 06 0.610 06 0.233 23 0.233 23 0.233 23
Se
0.000 00 0.032 86 0.10509 -0.10509 -0.032 86 0.037 86 -0.037 86 0.334 55 0.433 89 0.291 65 0.291 65 0.377 44 0.377 44 0.235 21 0.665 26 0.764 61 0.622 37 0.622 37 0.708 16 0.708 16 0.0565 92
0.000 00 0.17583 -0.026 49 0.026 49 -0. I75 83 -0.103 28 0.103 28 -0.003 68 -0.018 60 0.134 63 -0.15507 -0.14200 0.147 70 0.01 1 23 0.003 04 -0.01 1 88 0.141 35 -0.148 35 -0.135 28 0.15442 0.017 95
0.000 00 0.12478 -0.1 20 36 0.120 36 -0.1 24 78 0.297 38 -0.297 38 0.574 8 1 0.773 73 0.773 73 0.77373 0.37590 0.375 90 0.375 90 0.425 22 0.624 13 0.624 13 0.624 13 0.226 30 0.22630 0.226 30
atom
X
TeFn Y
z
~
F F F F F
F Se
F F F F F F Se F F F
F F F
Te
F F F F
F F
Te F F F
F F F Te
F F F F F F
0.00000 0.036 13 0.10797 -0.10797 -0.036 13 0.040 53 -0.040 53 0.334 54 0.437 70 0.290 02 0.290 02 0.379 12 0.379 12 0.231 37 0.665 57 0.768 75 0.621 06 0.621 06 0.710 16 0.710 16 0.562 47
0.00000 0.17995 -0.021 44 0.021 44 -0.17995 -0.11292 0,11292 -0.003 I O -0.014 15 0.139 11 -0.16206 -0.145 19 0.155 86 0.008 07 0.002 80 -0.008 38 0.14488 -0.1 56 17 -0.13929 0.161 76 0.01396
0.000 00 0.14304 -0.135 19 0.135 19 -0.14304 0.30557 -0.30557 0.568 15 0.77798 0.77798 0.777 98 0.35833 0.358 33 0.358 33 0.430 64 0.640 67 0.64067 0.640 67 0.22081 0.22081 0.22081
Lattice parameters constrained to the experimental values
K found no evidence for the intermediate temperature trigonal form. Debye-Scherrer patterns at the two temperatures were identical, except for small thermal effects. According to our new procedure of analysis, the neutron intensities are well accounted for by a triclinic lattice closely resembling that of the 25 K simulation of Pawley and Thomas.30 Although the triclinic lattice is pseudo-orthorhombic, it is unrelated to the orthorhombic lattice tentatively assigned previously by Michel et aL6 and ourselves.' Why the hexagonal pattern seen by Raynerd has not been reproduced in later studies is uncertain. A disorder of molecules in the triclinic lattice, possibly induced by the high incident flux of electrons, might lead to a hexagonal pattern, as discussed by Pawley and Dove. N o structural information about the low temperature forms of TeF6 has been published. When nucleation conditions produce nearly pure triclinic clusters of SeF6 or TeF6, the electron diffraction patterns bear a close resemblance to the neutron patterns of cold SF6.9 The most conspicuous difference is that the diffraction rings from the microcrystals generated supersonically are so broad that the principal features are superpositions of many overlapping Bragg reflections. While this overlapping impedes somewhat a highly precise determination of lattice parameters, it does not prevent a refinement that is quite satisfactory. Observable intensity features considerably exceed, in number, the six lattice parameters to be deduced, as shown in Figure 3. All phase I1 patterns are well accounted for by the triclinic lattice, Pi,Z = 3, with ratios a:b:cand angles cy, p, and y that are very close to those obtained in our refinement of Powell's neutron data. Results are given in Table 11. Atomic coordinates from the packing calculations (via Williams algorithm PCK62') are listed in Table 111. Moreover, parameters for SF6 agree closely enough with those predicted by Pawley and Thomas on the basis of their molecular dynamics simulation to suggest that a fair understanding of phase I1 is at hand. Presumably, a modest adjustment of molecular interaction functions would lead to even more accurate results. An extension of such calculations to the low temperature phase of TeF6 would be highly desirable. Molecules of this substance attract each other more strongly than those of SF,, and their greater deviation from a spherical shape should be manifested in packing at low temperatures. Supersonic Nucleation. Several aspects of the generation of microcrystals in supersonic expansions are noteworthy, including the control that can be exercised over the temperature, size, and internal organization of the clusters produced. While our understanding of the processes involved is fragmentary at best, plausible rationalizations of some features can be advanced. General principles of nozzle flow, outlined in several reviews24,32-34
of homogeneous nucleation and cluster formation, will not be repeated here. First, the striking role of the carrier gas upon the phase nucleated and the crystal temperature attained deserves comment. Profiles of temperature as a function of distance of flow along the nozzle are nominally the same for all rare gas carriers in the absence of nucleation. Nevertheless, argon is conspicuously more effective than neon in generating the low temperature phases of SF6 and SeF,. Any distinction in the case of TeF6 seems to be small, possibly because the temperature associated with the transition between the two low symmetry phases of this substance lies within the easy reach of all carriers. Helium was less effective in cooling clusters than were neon or argon. Krypton was not tested in enough experiments to detect a difference from argon. One factor favoring argon over the lighter carriers is its higher thermal accommodation coefficient35and, consequently, its greater efficiency in removing the heat of condensation from the clusters. Augmenting this effect is a substantial fractionation of lighter species away from the nozzle axis and heavy species, particularly clusters, toward the Argon, suffering less fractionation, is depleted less severely from the region where cooling is needed than are the lighter carriers. Another possible factor is that the flow is slower, the greater the carrier molecular weight. This increases the number of collisions of hexafluoride molecules with clusters during flow through the nozzle. Even though clusters are sometimes observed to cool below 100 K before they encounter the electron beam, they are nevertheless much warmer than predicted according to conventional computer simulations of nucleation and cluster g r o ~ t h . ~ Such ~ , ~ sim~,~~ ulations correctly account for trends in fraction condensed and cluster size with changes in flow conditions and yield nucleation temperatures approximately consistent with the phases seen experimentally. They are based, however, on a one-dimensional flow model assuming little lag in cluster temperature behind the temperature of the rapidly cooling carrier. This assumption seems well justified for such minute clusters.32 The flow model, however, neglects fractionation and impoverishment of carrier from the region of the clusters. One piece of evidence that the argon carrier (32) Wegener, P. P. In Nonequilibrium Flows, Wegener, P. P., Ed.; Marcel Dekker: New York, 1969. (33) Abraham, 0.;Binn, J. A,; DeBoer, B. G.; Stein, G. D. Phys. Fluids 1981, 24, 1017. (34) Bartell, L. S . Chem. Reu. 1986, 86, 491. (35) Menzel, D.; Kouptsidis, J. In Fundamentals of Gas-Surface Interactions, Saltsburg, M. Smith, J. N. Rogers, M., Eds.; Academic: New York, 1967; p 439. (36) Valente, E. J.; Bartell, L. S . J . Chem. Phys. 1984, 80, 1451.
SF6, SeF6, and TeF6 Nucleation temperature, at least, does indeed drop well below the cluster temperature in some regions of flow is the appearance of clusters of Ar when hexafluoride concentrations are low enough. As noted in a previous section, these clusters, which presumably are formed away from the jet axis, are substantially colder than the hexafluoride clusters they coexist with. The fact that the low temperature phase of SF6 is produced in argon but not neon can be rationalized as discussed above. That it also requires a low mole fraction of SF6 is readily explained, as well. A higher concentration would reach critical supersaturation earlier in the flow, hence at a higher temperature, and the higher temperature phase would result. Although the structural details of the lowest temperature phase of TeF6 are unresolved, the flow conditions associated with the onset of nucleation of phase I11 instead of phase 11 are fairly straightforward. As shown in Figure 4b, phase I11 appears when the mole fraction is dropped or the stagnation pressure is decreased. In either case, critical supersaturation is delayed in the flow until a lower temperature is reached. Why the differences in carrier gas appear to be unimportant is unclear. Selenium hexafluoride, on the other hand, emphasizes the difference between argon and neon. Argon carrier nucleated the low temperature phase under all pressures and concentrations tested. Neon carrier yielded this phase only when SeF6 mole fraction was low and pressure was high. As can be seen in Figure 4a, the phase boundary mapped is different in character from that for TeF6. Why this is so if temperature is the main consideration is uncertain. The fact that clusters can be seen in the cubic phase at temperatures appreciably below the bulk transition temperature is of some interest. Solid-state transitions in small clusters are probably slow in comparison with flow times in the supersonic experiment. This suggests that the structure of the clusters at an early stage of condensation may play a definitive role in guiding the final structure of clusters formed. Since the surface stress of these minute nuclei must be considerable, the phase transition temperature of a given nascent crystal nucleus may deviate appreciably from that for a bulk crystal. According to classical nucleation t h e ~ r y , ~ ’critical , ~ * nuclei are often only three or four (37) Wu, B. J. C. NTIS report AD-775 257, 1974. (38) Bartell, L. S., unpublished research. (39) In this paper the periodic group notation in parentheses is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups I A and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111 3 and 13.)
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The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2503 molecules in diameter. Moreover, once crystal growth is initiated, the heat of condensation not only warms the cluster but it quite appreciably warms the surrounding medium, including carrier gas, before the expansion reverses the trend and the temperature falls, again. Temperature increases are readily calculated in computer simulations and have been observed in some experimental studies.32 They depend strongly, of course, on carrier concentration. In typical cases they may be 10 to 50 degrees or more. When nucleation temperatures are close to transition temperatures it is not known whether a colder form nucleated will continue to grow, epitaxially, as the colder phase or whether it will continue as the warmer phase when the temperature rises through the transition threshold. Clearly, much remains to be learned before supersonic nucleation can be considered to be well understood.
Concluding Remarks Significant gaps remain in our knowledge of the complex ways the present hexafluoride molecules manage to organize themselves in the solid phase. The lowest temperature phase of TeF, has not yet been elucidated. Whether new low temperature phases of SF6 or SeF6 will be found cannot be predicted with confidence. Packing c a l ~ u l a t i o n sreveal ~ ~ a variety of structures of comparable energy and a not insignificant sensitivity of results to assumed intermolecular potentials. Until the low temperature behavior of these extremely simple molecules is resolved, our understanding of the principles of crystal structures will remain demonstratively imperfect. Meanwhile, the novel supersonic technique affords a versatile means of studying such systems. Acknowledgment. This research was supported by a grant from the National Science Foundation. We thank Mr. John Shanahan and Mr. Anding Jin for assistance in experimental work and data processing. We are deeply indebted to Dr. Brian Powell for making available the neutron diffraction data and to Professor G. Stuart Pawley for advice and helpful cooperation in refinements. We gratefully acknowledge a generous allocation of computing time from the Michigan Computing Center. Registry No. SF6, 255 1-62-4; SeF6, 7783-79-1; TeF,, 7783-80-4.
Supplementary Material Available: Tables containing experimental conditions and species nucleated in all supersonic expansions carried out in this research as well as intensity data for representative diffraction patterns (19 pages). Ordering information is given on any current masthead page. (40) Nore added in proof. In recent reanalyses, the Orsay workers have concluded that their coldest clusters of SF6possess the triclinic structure first identified in the present research. Farges, J. et al. Fifteenth Symposium on Rarified Gas Dynamics; Grado, Italy; June 18, 1986.
