J . Phys. Chem. 1984, 88, 4466-4414
4466
Progress in Overexpanded Supersonic Jets and Skimmed Molecular Beams in Free-Jet Zones of Sllence
R. Campargue Laboratoire des Jets Mollculaires, DZpartment de Physico- Chimie, Centre d’Etudes NuclPaires de Saclay, France (Received: December 22, 1983)
Various improvements are described for producing free jets and nozzle beams without complex formation. It is shown that our approach, based on the creation of a free-jet zone of silence unaffected by the background gas at relatively high pressure (PIN lo-’ to 1 torr), is very efficient for improving the practical performance limited by the pumping means in the conventional method (PI5 torr). The skimmer interference problem is found to be relatively simple at low ambient pressure but very difficult under our usual conditions where the free-jet shock wave structure is well formed. However, this difficulty is now conveniently solved and the zone of silence appears as an ideal medium for supercooling pure or seeded light gases expanded through miniature capillary nozzles (10-100 pm in diameter) operated at very high pressure (up to 200 bar) even at low temperature (down to 80 K). The limitations due to condensation, for most of the gases, are avoided by using high-temperature, high-pressure sources. Furthermore, skimming is greatly simplified by increasing the particle energy by heating and/or seeding, as also observed with clustering. The most interesting characteristics obtained for a He beam are as follows: speed ratios SI, N 350, corresponding to velocity spreads of OS%, energy resolutions of 0.6 meV, and translational K. The kinetic energy range from lo-’ to about 40 eV can be covered by the heating and seeding temperatures Til N 6 X techniques. Results obtained for He-Ar and He-Xe mixtures in time-of-flight experiments are well confirmed theoretically by the method of moments of the Boltzmann equation. Finally, fluorescencemeasurements on heated CO free-jets find more or less complete rotational relaxation and vibrational freezing close to the nozzle throat, for instance at 2000 K with the source operated at 2500 K.
Introduction The description of molecular beams from nozzle sources1cannot be separated from free-jet behavior, since the properties of jets are skimmed and reflected in those of beams. Moreover, free jets and nozzle beams are often encountered in the same fields of basic and applied research: studies of translational, rovibrational, and even electronic relaxation, atomic and molecular spectroscopy, scattering processes in gas-gas, gas-photon, or gas-surface interactions, gas or isotope separation by aerodynamic or laser methods, gas dynamic or chemical lasers, condensation phenomena, physics and chemistry of van der Waals complexes or clusters, nuclear fusion, molecular beam epitaxy, flow phenomena, aerospace studies, etc. In most of these important applications, it is of interest to obtain, as much as possible, narrow velocity spreads (or very low temperatures) in the jet or the beam, high density or intensity in the molecular beam, and a variable kinetic energy from the thermal to the electronvolt range. All these jet and beam characteristics can be improved by increasing the quantity P@* where Po is the nozzle stagnation pressure and D* is the nozzle diameter. This product represents the total number of two-body collisions undergone by a given molecule during the expansion process and, consequently, characterizes the degree of cooling. The extent of this flow cooling may also be limited by the formation of unwanted van der Waals complexes determined by the number of three-body collisions scaling roughly as Po2D*. Also the nozzle stagnation temperature To and the nozzle shape, governing together with D* the expansion rate, allow one to control the condensation process. In this paper are presented and discussed various possibilities for improving the supersonic jet and beam techniques without producing van der Waals complexes. It is shown that important progress can be achieved by minimizing the interaction of the free jet with the background gas, in particular in a zone of silence where the supersonic expansion operates as if it entered a perfect vacuum, also by optimizing the nozzle and skimmer geometries, and finally by cooling or heating the gas source. Optimization of the Nozzle Size and Shape For a given nozzle flow rate (fi cc = constant) which can be handled by the pumping system connected to the expansion (1) A. Kantrowitz and J. Grey, Rev. Sci. Instrum., 22, 328 (1951).
0022-3654/84/2088-4466$01.50/0
chamber, an enhancement of cooling is attainable by reducing D* since, in this case, P@* a l / D * . Thus, as shown experimentally in our early nozzle beam work,2 it is of major interest to operate with a miniature nozzle. The most efficient one2 is not a Lava1 nozzle,3 nor a short converging nozzle, nor a sharpedged orifice with length to diameter ratio LID* 1) because the nozzleskimmer distance may be increased without inducing large losses due to the background gas at low pressure or molecules reflected from the skimmer. On the contrary, skimming in a free-jet zone of silence is a real aerodynamic problem for transforming the normal shock in an oblique shock wave "swallowed" in its centerline part facing the orifice and attached to the external skimmer edge as shown in Figures 2 and 3. Furthermore, the nozzle-skimmer distance must be adjusted carefully in order to avoid, or to minimize, scattering taking place either in front of (23) R. Campargue, Bntropie, 30, 15 (1969). (24) U. Bossel, Thesis, Berkeley, 1970; U. Bossel, F. C. Hurlbut, and F. S . Sherman, "Rarefied Gas Dynamics", 6th Symposium, Vol. 11, L. Trilling and H. Y. Wachman, Eds., Academic Press, New York, 1969. (25) G. Brusdeylins, H. D. Meyer, J. P. Toennies, and K. Winkelmann, "Rarefied Gas Dynamics", 10th Symposium, Vol. 11, J. L. Potter, Ed., AIAA, New York, 1977.
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 I
I
I
I
D'= 29 5 pm
I
100
I
200
I 300
Po D'
I
I
0 005
D=50pm
I
400
I 500
I 600
I 700
torr cm
Figure 6. Effects of skimmer diameter 0,on speed ratio S,,. The data show that optimization of the skimmer design leads to large deviations ,~' Quantum mechanical from predictions of classical t h e ~ r y ~(CM). predictions agree more closely with experiments using the optimized skimmer design when it is assumed the expansion is into a skimmerless perfect vacuum29 (new QM) rather than with the assumption of an expansion frozen at the skimmer entrance2s(original QM).
the skimmer (at X , > (X,),,,, Le., after the limit of the zone of silence) or within the skimmer (if Kn, becomes too small at X, < (X,),ax). The postskimmer effect, observed by varying Kn,by different skimmer diameters D,, appears to be the most important from the experiments reported below. Effect of Skimmer Diameter D, and Length Lex,on Parallel Speed Ratio SI,. The very high H e speed ratios Sll plotted in Figure 6 have been obtained with the same molecular beam TOF system (Figure 4 and ref 14) as those reported for different skimmer angles (Figure 5 ) . These experiments have been performed also at room temperature and only by skimming in a zone of silence (Roots pump) because, as previously, the detection of the low-density beams (Booster pump) was not possible at 4.5 m from the nozzle. The effect of skimmer diameter D, on the parallel speed ratio SIIhas been investigated with six different skimmers attached to a sliding support which allows direct comparisons on the same free jet, with the same TOF system. As indicated in Figure 6, these skimmers have identical parameters aint,cyext, Lext, and 6 but different diameters increasing from D, = 0.25 to 1.5 mm. Finally, the range of POD*, which is limited to about 400 torr cm with D* = 29.5 pm (due to the maximum pressure of Po = 190 bar available, as in the experiments reported in Figure 5 ) has been extended up to about 700 torr cm by using a nozzle diameter of D* = 50 pm. Two kinds of skimmer jet interaction appear in these experimental data which are reported with open or filled points for D* = 29.5 or 50 pm, respectively. First, an end wall effect, initially observed at Berkeleyz4and later at S a ~ l a y ,seems ~ ~ , ~to~occur at high POD*. This explains the measured speed ratios lower than expected and also the leveling off of the three curves obtained with D* = 50 pm (filled points). In fact, our recent investigations have shown that the length Lext of the skimmer has to be increased with P$* nearly in a linear way in order to avoid disturbances due to the standoff shock wave produced by the support of the skimmer. This end wall effect is expected to be present in the experiments performed with D* = 50 pm since the length used, Le,, = 19 mm, is only sufficient for P$* 5 400 torr cm. Second, as shown in Figure 6 , the skimmer diameter effect is strong enough to reduce S,, by a factor of about three, as D,
Campargue increases from 0.25 to 1.5 mm. This occurs apparently without the superimposed endtwall effect, at least for the jets produced with D* = 29.5 pm (open points). Such losses are attributed to skimming at too small Knudsen number (Kn,< 1) and, consequently, with excessive flux and density within the skimmer; both increased by a factor of 36 by going from D, = 0.25 to 1.5 mm. The losses result from very complicated scattering phenomena6 within the cone which may be due to self-scattering in the skimmed stream tube, reflected molecules from the internal surface, diffuse oblique shock waves extending from the skimmer lip to the axis,3 a thick boundary layer along the inner wall, or a combination of these different possibilities. Discussion of Skimmer Interference Problems. From the effects observed by varying the skimmer angles (Figure 5 ) , diameter (Figure 6), and also the other parameters 6 and Lext,skimming in the overexpansion of a free-jet zone of silence is a difficult problem encountered both in front of and within the skimmer. In spite of such difficulties, the achievement of very high Mach numbers, or extremely low temperatures, in helium free jets (as predictedgand obtained effectively, but not yet measured, in 1968), has been done in our laboratory in 1974 by using this skimming a p p r o a ~ h . 'At ~ this time, the helium Mach numbers Mall2 140) measured at Saclay, even with a TOF system having insufficient resolution, were about one order of magnitude above those obtained previously and also much higher than the best values (MallN 45) achieved simultaneously with the conventional method.26 Furthermore, these Mach numbers were found to be higher than expected from classical theory prediction^^,^' (CM in Figure 6). These deviations were attributed by Miller et alez6to quantum effects in He free jets. Finally, our experimental findings seem to have stimulated Toennies and Winkelmann to go further in the development of a quantum theory at first by stopping the expansion at the skimmer entrance2*(original Q M in Figure 6) and later by expanding the free jet into a skimmerless perfect vacuum29(new Q M in Figure 6). This theoretical analysis from Gottingen is of great interest for knowing the regime of the flow through the skimmer. As a matter of fact, it appears clearly in our experimental data (Figure 6) that the optimization of the skimmer shape and size leads to speed ratios much higher than the original Q M predictions and even close to the new QM predictions. Consequently, it is shown that the expansion process is going on within the skimmer and even the measured speed ratios SIlcan be nearly twice as high as those attainable theoretically in a continuum flow at the skimmer orifice. This is due to a great enhancement of the He-He quantum mechanical cross sections with decreasing relative velocity down to g 5 10 m/s.26 If these large cross sections are taken into account, the skimmer Knudsen number Kn, is in the range of lo-' to In spite of this nearly continuum flow through the skimmer, it has been possible to produce room temperature He beams with speed ratios as high as 350 (ref 14 and present paper), corresponding to velocity spreads as narrow as 0.5%, or translational temperatures TIIas low as 6 X K. Such performance seems to indicate that the problem of skimming in a free-jet zone of silence has been finally solved. Also, it is worth mentioned that the possibility of achieving very high speed ratios in He free jets, as expected in 19689 and found in 197413 at Saclay, has been confirmed in G ~ t t i n g e nwith ~ ~ ?conventional ~~ molecular beam sources operated with miniature nozzles at room temperature (D* 14.5 pm), long, slender, conical skimmers (L.,,, = 25 mm and cyext/aint = 32O/25O), and very large diffusion pumps (8,= 12000 to 50000 L/s). Thus, with POD*lower than that at Saclay, the beam characteristics SI,N 225 and TI1N 1.5 X K have been obtained in 1976. (26) D. R. Miller, J. P. Toennies, and K. Winkelmann, "Rarefied Gas Dynamics", 9th Symposium, Vol. 11, M. Becker and M. Fiebig, Eds., DFVLR Press, Porz-Wahn, West Germany, 1974. (27) J. B. Anderson and J. B. Fenn, Phys. Fluids,8,780 (1965). (28) R. Campargue, A. Lebehot, J. C. Lemonnier, D. Marette, and J. Pebay, "Proceedings of the 5th International Symposium on Molecular Beams", Nice, France, 1975. (29) J. P. Toennies and K. Winkelmann, J . Chem. Phys., 66,3965 (1977).
Supersonic Free Jets and Molecular Beams
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984
4471
By considering the beam intensity (in addition to the skimmed speed ratios) and also other gases (instead of only He which is very special due to quantum effect^^^,^^) it is found generally that the skimmer interference problem cannot be avoided except at very low density a t the skimmer entrance: as shown in Figure 5. In conventional nozzle beam sources, the highest beam intensities and speed ratios are achieved at the highest P&* attainable with diffusion pumps operated at Pl close to or even higher than 10” torr. Under these conditions, as indicated by Knuth30 and also observed by the skimmer Knudsen number (calculated by letting the collision cross section vary as the negative one-third power of the temperature) is found to have nearly the same value (Kn, 5 1) as obtained by skimming in the overexpansion of a free-jet zone of silence. Consequently, similar losses are expected within the skimmer, as found by determining the ratio Zexp/Zth of measured intensities to ideal theoretical intensities. This intensity ratio appears to vary in the range from 1 to 0.01 in the Fenn beams5s6as well as in the Campargue beams.31
is of scientific interest and/or technical importance in the range of 1-10 eV (activation and chemical bond energies) and even up to 24.5 eV (first ionization potential of He). The heated nozzles operated as conventional sources of seeded beams33(P@* 5 10 torr cm) with hydrogen as carrier gas provide kinetic energies ( 5 7 eV for Xe) which are limited by the very incomplete rotational relaxation of Hz and the velocity slip between the heavy and light species. With increasing P@*, both of these effects can be reduced simultaneously, by use of a very large diffusion pump,34or nearly eliminated by means of Roots pumps, following the nozzle beam technique developed in our laboratory.13335 a. General Principles and Advantages of a High- Temperature, High-pressure Nozzle Beam Source. This source previously described36 is provided as a special component of the molecular beam generators constructed at Saclay for a number of laboratories. Heating is obtained by the Joule effect through small concentric tungsten tubes surrounded by concentric heat shields and finally a cooling jacket. A stream of gas is circulated, at very high pressure, successively outside and inside the thermal screens Improvements Obtained by Cooling or Heating the Gas Source and then the heating elements, up to the exit of the inner tungsten Cooled or heated sources are of great interest for producing tube located in the upstream vicinity of the nozzle orifice. As special jets and beams or obtaining special characteristics by means the entire enclosure including the nozzle throat is water cooled, of continuously variable parameters (temperature, kinetic or invery high source pressures can be used at very high temperature ternal energy, de Broglie wavelength, etc.). Furthermore, imup to about 3000 K.13 Also worth mentioning are other advantages portant improvements in the beam performance (intensity and resulting from such a special conception: the absence of alignment density; wavelength, velocity, and energy resolutions) are attainable problems usually due to thermal expansion of heated walls, the by cooling or heating the gas source. Finally, the adjustment of trapping of nearly all the photons emitted from the heated elethe nozzle stagnation temperature To allows one to prevent or to ments, the possibilities of changing or cleaning easily the nozzle control condensation. throat and of replacing broken tubes or other construction material, Cooled Sources. The cooled nozzles constructed at Saclay can etc. The high-temperature, high-pressure source, constructed be operated either at To N 80 K with liquid nitrogen as a coolant recently in F r e i b ~ r g , ~is’ also based on the principles developed or at any temperature in the range from 300 to about 120 K, with at Saclay. gaseous nitrogen evaporated from liquid nitrogen. This makes Much effort has been devoted in our laboratory to improving available in particular an helium monochromator which is a this heated source for the purpose of achieving, for a number of powerful tool used in a number of European laboratories in crossed gases, jet and beam performance similar to those obtained for beam experiments (energy resolution -0.5 meV) and gassurface helium at room t e m p e r a t ~ r e . ’ ~ As , ’ ~ a matter of fact, heating studies (de Broglie wavelength from 0.56 to about 1 A, with 0.5% makes it possible to operate the nozzle at very high P&*, without resolution). condensation. This is feasible not only for the other noble gases Finally, our cooled nozzles, with or without special ~ h a p e , ~ . ~ , but also the polyatomic gases such as Ha, D2, N,, CO, CH,, etc., which can be operated over a wide pressure range, are very useful which are, particularly at high pressure, both stable thermally for producing van der Waals complexes and also large clusters, and inert with respect to the heating elements (tungsten or other as used in particular in the field of plasma physics and thermoresistive materials which have a high melting point, such as, Ta, nuclear fusion. We have shown recently3, that skimming cluster Mo, graphite, may also be used36). Furthermore, the combination beams in a high-density free jet is not a difficult problem due of heating and seeding in this system makes available an interesting to the relatively high energies of the particles. monochromator with variable kinetic energy in the electronvolt Heated Sources. Heating the nozzle is obviously the only range, up to about 40 eV.13,35Finally, there is the possibility (see possibility for producing jets and beams of particles which are below) of freezing in the jet and the beam a large part of the not in the gas state at room temperature. Furthermore, for most vibrational energy produced by thermal excitation prior to exof the gases and vapors, this allows one to enhance POD*,and pansion. consequently the jet and beam performance, without complex Generation of a nozzle beam, by skimming in a zone of silence formation. Finally, the variation of the stagnation temperature of such free jets, is a relatively simple operation for three main To provides a very simple means for controlling the kinetic and reasons. First, since the nozzle throughput is even the internal energies of the molecules. By combining heating
and one can produce kinetic energies in the electronvolt range to study inelastic collision processes with exchange of energy, charge, or atoms (reactive scattering). This (30) E. L. Knuth, Appl. Mech. Rev., 17, 751 (1964). (31) H. C. W. Beijerinck, R. J. F. van Gerwen, and J. F. M. Martens, “Book of Abstracts”, 9th International Symposium on Molecular Beams, Freiburg, F.R.G., 1983, pp 172-4. (32) R. Campargue, Discussion Meeting on “Experiments on Clusters”, Deutsche Bunsengesellschaft fur Physikalische Chemie, Konigstein, F.R.G., 1983. (33) N. Abuaf, J. B. Anderson, R. P. Andres, and J. B. Fenn, “Rarefied Gas Dynamics”, 5th Symposium, Vol. 11, C. L.Brundin, Ed., Academic Press, New York, 1967; N. Abuaf, J. B. Anderson, R. P. Andres, J. B. Fenn, and D. G. H. Marsden, Science, 155, 997 (1967). (34) U.Buck, L. Mattera, D. Pust, and D. Haaks, ‘Book of Abstracts”, 7th International Symposium on Molecular Beams, Riva del Garda, Italy, 1979, pp 181-3. (35) R. Campargue, A. Lebehot, J. C. Lemonnier, and D. Marette, “Rarefied Gas Dynamics”, 12th Symposium, Vol. 11, S . S . Fisher, Ed., AIAA, New York, 1981.
N
E
P,D*~/T,~/~
the volumetric pumping speed at the pressure P1 in the expansion chamber is (7)
Thus, the length X M of the shock barrel increases with To, a t constant value of S1. For example this increase is about 80% for the temperature range 300-3000 K. Second, the problem of the background gas in the expansion chamber is simplified also by increasing Tosince this makes it possible to operate the heated nozzle-skimmer system even at P1 as high as 1 torr. Third, the skimmer-jet interaction appears to be reduced by an increase of (36) R. Campargue, J. Bouffenie, and A. Recule, Patent 2279045, July 1974 (France) and foreign patents; R. Campargue, M. A. Gaveau, A. Lebehot, J. C. Lemonnier, and D. Marette, “Book of Abstracts”, 7th International Symposium on Molecular Beams, Riva del Garda, Italy, 1979. (37) B. Brutschy and H. Haberland, J. Phys. E., 13, 150 (1980).
4412
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984
0.3 % Xe in He isotope 129 P0=50bars Do=0.23 mm Tn=600K
FWHM = 2 2 . 7 ~ s s//,120 t,=1657 FS
Campargue is particularly realistic and acceptable for simplifying moment method calculations. Also the flow on the centerline of an axisymmetric free jet can be modeled by a spherically symmetric source flow. Consequently, as shown by Willi~,~O the equation describing the flow field can be reduced from a set of 13 equations for each species to a set of four equations with four unknown quantities: number density ni, mean velocity ui, and parallel and perpendicular temperatures, Ti and TLt,respectively. After such simplifications, the nonzero collision terms are formulated for Maxwell molecules, i.e., an R4potential. This greatly simplifies the problem and avoids the need to specify the velocity distribution. which represents long Afterward, an attractive potential (-C6R6) distance interactions is introduced in the calculation of collision integrals. Finally, the solutions are obtained numerically by means of a fourth-order Runge-Kutta integration scheme, starting from isentropic values (close to the nozzle) and neglecting the velocity slip (51% from e~perirnent’~).In Figures 9 and 10, the scaled temperature t’and scaled distance r’ from the nozzle throat have been derived from Willi~:~O I
2 ps/channel
tzo
Figure 7. Highest speed ratio, SI, N 120, achieved for Xe deluted in He. A tail appears in the TOF curve compared to a single Maxwellian dis-
tribution. the particle energy, as obtained by heating and/or seeding (and also observed by clustering as mentioned above). b. Molecular Beam Characteristics f o r Pure Gases and Gas Mixtures. The beam intensities, measured for a variety of pure common gases, appear to increase with Toin the range of 1019 to loz1mol steradian-I s-l. The heavy species, diluted and accelerated in H e or H2 free jets, are so concentrated on the flow axis that their partial fluxes in the seeded beams are nearly the same as obtained from jets of pure heavy gases.1° Also, the velocity distributions in molecular beams have been extensively measured by the TOF technique in order to determine beam characteristics such as the speed ratio SII, temperature Til, and kinetic energies. In spite of the relatively large diameters used, D* N 0.2 mm, with the heated source (in order to avoid clogging problems depending on Toand gas purity), the speed ratios obtained, for example, for pure Ar and H2 are as high as SI,= 40-50 and 70-80, respectively. In seeded beams, when He was used as a carrier gas, it was found for Xe, for example, that Si, = 60 at To N 1650 K (ref 35) and SI, 7 120 at ToN 600 K (Figure 7). In all these cases, the velocity slip between Xe isotopes and He is negligible ( A U / o 5 1%) due to the values of P$* up to about 10’ torr cm. As expected, the highest kinetic energies have been achieved with the H2 carrier gas.13-35This is due both to the high mass ratio (largest value attainable) and to the rotational relaxation of H2 which appears to be very significant in our high-density free jets. Nevertheless, since the specific heat ratio y is unknown and not even constant during the expansion, the source temperature To cannot be obtained from the energy balance equation, as done easily with He.35 An example of a high-energy monokinetic Xe beam ( E = 34.2 eV, S,, = 43.6) is shown in Figure 8, together with the TOF curve for the H2carrier gas. The velocity slip, A U / o =4%, is higher than with He, but very much lower than in conventional nozzle beams produced with the same H2-Xe mixture (see Figure 8 in ref 33). Also, it is found that both Slland TIIare higher for the heavy than the light species; this is a general result.35 Finally, for the heavy species, a tail appears in the TOF curves (Figures 7 and 8) when compared to a single Maxwellian distribution. This effect, also observed by Miller et aL4 for 16% C 0 2 in He, is not understood at present. In addition to these measurements by the TOF technique, calculations have been recently p e r f ~ r m e d ,by ~ ~the , ~method ~ of moments of the Boltzmann equation, for heated free jets of binary mixtures: He-Ar and He-Xe with heavy gas mole fraction from 0.3 to 10%. For the experimental conditions used with these mixtures (P$* up to 500 torr cm), the assumption that hypersonic flow is established before significant nonequilibrium effects occur ~~
~~
(38) A. Chesneau and R. Campargue, “Proceedings of the 13th International Symposium on Rarefied Gas Dynamics”, Novosibirsk, USSR, 1982, Plenum, New York, 1984. (39) A. Chesneau, A. Lebehot, and R. Campargue, “Proceedings of the Euromech Colloquium 169, The Boltzmann Equation in Gas Dynamics”, Trondheim, Norway, 1983.
Here F = 0.63, E = 1.755, and r* = 0.7D* is the radius of the apparent source sphere (Ma = 1); C,HeHeis the potential coefficient for the R6 part of the He-He interaction. The theoretical results (Figures 9 and 10) appear to be in good agreement with the TOF data if the expansion is assumed to be arrested by the skimming process, in the expected absence of quantum effects as encountered in room temperature He jets (Figure 6). Finally, the following main characteristics have been found: (i) Til > T , = Tisentropic, which is consistent with all the known previous results; (ii) Tilheavy > Tillight, in qualitative agreement with most of the published theoretical and experimental findings; (iii) Tilheavy decreases with increasing heavy gas mole fraction, as predicted before by Andemon6 and w i k 4 O also Tillight decreases similarly to TI,heavy. c. Rovibrational State Population Distributions in Heated Free Jets of Polyatomic Molecules. It is well established that the translational energy and the internal energies of molecules are not in equilibrium in free jets, due to the successive freezings of temperatures associated with each degree of freedom, Tvib>> Trot> as far as Boltzmann distributions can describe the populations of the rovibrational states. The spatial distributions of these populations have been measured previously in free jet expansions, for a variety of gases, with different spectroscopic technique^.^^^^^ The discrepancies appearing between the existing experimental data may be due to the model used for relating the measured intensities (for example, in the fluorescence spectra) to the state populations and also to unavoidable superimposed effects associated with self-absorption, quenching, secondary electrons in the electron beam technique, background gas, etc. In our laboratory, Gaveau et aL41 have obtained results on CO-N2 and CO-Ar mixtures and recently on pure C0.42 The heated free jets are produced through sonic nozzles (D* = 0.22 or 0.275 mm) from very high stagnation enthalpy (To5 2500 K, Po 5 30 bar) in a relatively high-pressure environment (P15 0.15 torr). The rovibrational population distributions of CO are obtained from measurements of the infrared fundamental (Av = 1) spontaneous fluorescence emission of the CO jet molecules. The total intensity of the radiation results from the superposition of
T,, , ,
(40) D. R. Willis, Sandia Laboratories Energy Report, SAND 78-8216, Part I, 1978. (41) M. A. Gaveau, J. Rousseau, A. Lebehot, R. Campargue, and J. P. Martin, “Proceedings of the 13th International Symposium on Rarefied Gas Dynamics”, Novosibirsk, USSR, 1982, Plenum, New York, 1984. M. A. Gaveau, J. Rousseau, A. Lebehot, and R. Campargue, “Proceedings of the 4th International Symposium on Gas Flow and Chemical Lasers”, Stresa, Italy, 1982, Plenum, New York, 1984. (42) M. A. Gaveau, Thesis, Paris XI-Orsay, 1984.
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4473
Supersonic Free Jets and Molecular Beams
H, in 0.1%Xe in H, tm=563 P S Si/= 25.8 FWHM = 36.3 US TI,= 9.9 K Xe in 0.1% Xe in H2 (without
mass
t,=586
HS
discrimination)
Si/=43.6 208 K
FWHM= 22.4 PS E = 34.2 eV
Figure 8. Typical TOF curves for X e H e beams, with Xe energy in the range of 30-40 eV. A tail appears in the Xe TOF curve cornpared to a single Maxwellian distribution.
method1 Experiment T,,
Il%Ar inHel
0.1
-
IA ,
1
*I
present work I
10
100
r'
200
Figure 9. Variation of scaled temperature with scaled distance from the nozzle, for heated free jets of He-Ar mixtures. The references for previous work are listed in ref 35 and 38.
400
J'(J'+l)
Figure 11. Measured and calculated fluorescence line intensities vs. J'(J' 1) for the spontaneous emission of a pure CO free jet generated at 1800 K (Gaveau, ref 42).
+
Moment method Experiment T,, A
0.5%Xein He
present 0 work 0 Anderson A
TABLE I: Rotational and Vibrational Temperatures in Free-Jet and Background Gas, Measured for 20% CO in N, or Ar, and
for Pure COa T!!
20%COinN,
t' 10 20%COinAr pure CO a
1
0.1
1 ri
10
Figure 10. Variation of scaled temperature with scaled distance from the nozzle, for heated free jets of He-Xe mixtures. The reference for Anderson is in ref 35 and 38.
both emission and absorption due to the jet and also to the bachround gas. Consequently, the intensity of the radiation has been integrated over the successive media encountered by the optical path, using absorption and emission constants deduced from Einstein coefficients for each transition. Also refinements taking into account Doppler shifts and broadenings have been introduced
30 30 30 6
1800 1800 2500 1800
18
70
36
45 15 80
18 18
.
1600 1500
2000 1600
300 380 450 420
1000 1000 1200
1000
Reference 42.
in the calculations. Then, as shown previously41 for C O in N 2 or Ar, and in Figure 11 for pure CO, the experimental data are well interpreted by the theory with a flow model which assumes a Boltzmann distribution for each internal mode (in the jet and the background gas) and vibrational freezing at the nozzle throat." Finally, the main features for pure CO are essentially the same as those obtained for 20% C O in nitrogen or argon: (i) the fluorescence of the background gas is dominant at low u and high J' quantum numbers, with rotational and vibrational temperatures TiGand GG, respectively, as reported in Table I; (ii) the radiation is more and more due to pure free jet emission (i.e., without background gas contribution) at high u and low J'numbers, with Boltzmann equilibrium at vibrational temperature T:J independent of the distance from the nozzle and rotational temperature GJ depending on X/D* (Table I). Contrary to the experiments with
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J. Phys. Chem. 1984,88, 4414-4418
gas mixtures, the detection sensitivity with pure CO now is sufficient for observing rotational freezing in the final stages of the expansion.42 Departures from rotational equilibrium have been observed in previous measurements of spontaneous fluorescence in C 0 2 P or fluorescence induced by electron impact in N2,44*45 but apparent deviations could be due to the model sed,^^*^^ to neglecting the emission of the background or to effects of the skimmer.45 The Raman scattering data have shown only Boltzmann rotational distributions for N2, COz, CH4, and SF6,’” but not for H2 and D t 8 due to their relatively large rotational collision numbers. In any case, the departures are found to appear and increase with increasing J’ and/or the rarefaction (low collision frequency at (43) S. P. Venkateshan, S. B. Ryali, and J. B. Fenn, J. Chem. Phys., 77, 2599 (1982). (44) F. Robben and L. Talbot, Phys. Fluids, 10, 521 (1967); R. G. Sharafutdinov, A. E. Belikov, N. V. Karelov, and A. E. Zarvin, “Proceedings of the 13th International Symposium on Rarefied Gas Dynamics”, Novosibirsk, USSR, 1982, Plenum, New York, 1984. (45) P. B. Scott and T. R. Mincer, “Rarefied Gas Dynamics”, 7th Symposium, Vol. I, D. Dini, Ed., Editrice Technic0 Scientifica, Pisa, Italy, 1971; B. M. Dekoven, D. H. Levy, H. H.Harris, B. R. Zegarski, and T. A. Miller, J. Chem. Phys., 74,5659 (1981); M. Faubel and E. R. Weiner, ibid., 75,641 (1981); S. P. Hernandez, P. J. Dagdigian, and J. P. Doering, Chem. Phys. Lett., 91, 409 (1982). (46) E. P. Muntz, Phys. Fluids, 5, 80 (1962); D. Coe, F. Robben, L. Talbot, and R. Cattolica, “Rarefied Gas Dynamics”, 11th Symposium, R. Campargue, Ed., C.E.A., Paris, 1979; A. K. Rebrov, G. I. Sukhinin, R. G. Sharafutdinov, and J. C. Lengrand, Sou. Phys. Tech. Phys., 26, 1062 (1981). (47) I. F. Silvera and F. Tomasini, Phys. Reu. Lett., 37, 136 (1976); G. Luijks, S. Stolte, and J. Reuss, Chem. Phys., 62, 317 (1981). (48) H. P. Gcdfried, I. F. Silvera, and J. van Straaten, “Rarefied Gas Dynamics”, 12th Symposium, Vol. 11, S. S. Fisher, Ed., AIAA, New York, 1981.
low P a * and largeX/D*). Consequently, it is not surprising to find Boltzmann distributions in our measurements performed only for J ’ S 10, with X / D * 5 36, and POD* 5 500 torr cm. New techniques such as multiphoton ionization (MPI) and laser-induced fluorescence (LIF) will soon be included in our free-jet and nozzle beam diagnostics. Conclusion The zone of silence, as obtained mainly in He free jets, appears as an ideal cooling medium. This possibility is now largely used for simplifying the laser spectroscopy of polyatomic molecules.21~22 The great selectivity of excitation attainable by this technique may augment the potential of the molecular process in laser isotope ~ e p a r a t i o n . ~Nozzle ~ beam generators operated by skimming carefully in such a zone of silence provide in particular an He beam monochromator now exploited in a number of European laboratories in gas-surface interaction studies (with de Broglie wavelength close to 1 .&) and crossed beam experiments (with energy resolution of 0.6 meV). Molecular beams in the electronvolt energy range have important applications in gas-phase scattering with exchange of energy, charge, or atoms (chemical reactions). Finally, the frozen internal energy can produce a great enhancement of the cross sections for these processes. Thus a difficult problem of diagnostics is encountered, requiring determination of the rovibrational state population distributions in the beams entering the collision. This must be solved by laser methods, which also allow detection of unwanted van der Waals complexes. ~~
(49) R. Campargue, “Flow Cooling as Applied to Laser Induced Separation”, von Karman Institute Lecture Series, Rhode-St GenBse, Belgium, 1978.
Effects of Nozzle Geometry on Kinetics in Free-Jet Expansions Hylton R. Murphy and David R. Miller* Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, California 92093 (Received: April 28, 1983)
Numerical analysis of the free-jet expansion from three types of subsonic nozzles shows significant differences in the flow fields only in the early stages of the expansion. Kinetic processes are examined, theoretically and experimentally, which demonstrate the effects of these different flows.
Introduction The supersonic free-jet expansion’ of a gas into a vacuum has provided a useful flow field in which to study fast kinetic processes, such as rotational relaxation and condensation, and also provides a cold bath for spectroscopic studies. The flow begins from some reservoir where the velocity is small compared to the speed of sound; properties in this region are referred to as the stagnation temperature, pressure, etc. The flow is then accelerated up to the speed of sound, Mach number Ma = 1, in a subsonic nozzle (e.g., a simple aperture, short converging nozzle, or tube). The free-jet supersonic expansion then begins from the sonic ( M a = 1) surface. The location and shape of the sonic surface plays an important role for the subsequent free-jet expansion. The flow field properties, such as temperature, density, and velocity, are routinely calculated from a knowledge of the Mach number variation in the free-jet expansion. The most widely used Mach number calculations are the ideal, isentropic calcu(1) J. B. Anderson in “Molecular Beams and Low Density Gas Dynamics,” P. Wegener, Ed., Marcel Dekker, New York, 1974, p 1.
lations obtained by the numerical method of characteristicx2 This isentropic solution for the free-jet expansion normally uses as an initial condition uniform exit conditions at Ma = 1 with the sonic surface in the vertical plane of the subsonic nozzle exit. Many of the processes for which the free jet is being used depend strongly on the flow field near the nozzle exit, where the supersonic flow begins, and where the gradients of thermodynamic properties are the largest. We have been interested in obtaining accurate calculations for this region both for the ideal isentropic exit conditions and for free-jet expansions starting from nozzles which do not provide the ideal sonic surface. We have examined the limiting cases, which are the sharp-edged orifice and a long tube source, both experimentally and theoretically. In this paper we wish to show the type of behavior that may occur and the effect that it may have on subsequent physical p h e n ~ m e n a . ~ (2) H. Ashkenas and F. S. Sherman, “Rarefield Gas Dynamics,” Vol. 2, J. deleeuw, Ed., Academic Press, New York, 1966, p 84. (3) Some preliminary experimental data with different sized sources were presented by D. Miller, M. Fineman, and H. Murphy at the 13th International Symposium on Rarefied Gas Dynamics, July 5-9, 1982, Novosibirsk, USSR.
0022-365418412088-4414$01.50/00 1984 American Chemical Societv
