Abstract.
We describe a theoretical model which treats the effects of evaporation-induced recoil on the mass and temperature distributions of a collimated beam of small neutral clusters emitted by a hot-nozzle source. The model incorporates two important consequences of in-flight cluster fragmentation processes. One is the well-known statistical evaporation of atoms and dimers accompanied by cluster size redistribution and cooling, and the other is the accompanying mechanical recoil of the fragments. We predict that the filtering effect introduced by cluster recoil can be used to an advantage by separating out the off-axis cluster population. This fraction will have a significantly narrower and colder distribution of internal temperatures than the on-axis ensemble.
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References
H. Haberland, in Metal Clusters, edited by W. Ekardt (Wiley, New York, 1999)
T. Bergen, X. Biquard, A. Brenac, F. Chandezon, B.A. Huber, D. Jalabert, H. Lebius, M. Maurel, E. Monnand, J. Opitz, A. Pesnelle, B. Pras, C. Ristori, J.C. Rocco, Rev. Sci. Instrum. 70, 3244 (1999)
J. Borggreen, K. Hansen, F. Chandezon, T. Døssing, M. Elhajal, O. Echt, Phys. Rev. A 62, 013202 (2000)
M.L. Homer, J.L. Persson, E.C. Honea, R.L. Whetten, Z. Phys. D 22, 441 (1991)
S. Vongehr, A.A. Scheidemann, C. Wittig, V.V. Kresin, Chem. Phys. Lett. 353, 89 (2002)
C.P. Schulz, P. Claas, D. Schumacher, F. Stienkemeier, Phys. Rev. Lett. 92, 013401 (2004)
S. Vongehr, V.V. Kresin, J. Chem. Phys. 119, 11124 (2003)
W. de Heer, W. Knight, M.Y. Chou, M.L. Cohen, in Solid State Physics, edited by H. Ehrenreich, D. Turnbull (Academic, New York, 1987), Vol. 40
K. Hansen, J. Falk, Z. Phys. D 34, 251 (1995)
P. Brockhaus, K. Wong, K. Hansen, V. Kasperovich, G. Tikhonov, V.V. Kresin, Phys. Rev. A. 59, 495 (1999)
C. Lifshitz, Int. J. Mass Spec. 198, 1 (2000)
C. Bréchignac, Ph. Cahuzac, B. Concina, J. Leygnier, B. Villard, P. Parneix, Ph. Bréchignac, Chem. Phys. Lett. 335, 34 (2001)
K. Głuch, S. Matt-Leubner, O. Echt, R. Deng, J.U. Andersen, P. Scheier, T.D. Märk, Chem. Phys. Lett. 385, 449 (2004)
This signal includes unevaporated clusters from the original population, as well as all those daughters which recoil in the forward direction. And although the fraction of such daughters quickly falls off with the distance from the detector plane (i.e., for evaporation at early flight times), the evaporation rate at the early time is significantly higher. To a significant extent, the two effects cancel each other and turn the energy contents of the on-axis beam into a rather broad mixture
J.U. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics (Wiley, New York, 1952)
T. Ericson, Adv. Phys. 9, 425 (1960)
G.F. Bertsch, N. Oberhofer, S. Stringari, Z. Phys. D 20, 123 (1991)
S. Frauendorf, Z. Phys. D 35, 191 (1995)
P.A. Hervieux, D.H.E. Gross, Z. Phys. D 33, 295 (1995)
P. Fröbrich, Ann. Physik (Leipzig) 6, 403 (1997)
P. Engelking, J. Chem. Phys. 87, 936 (1987)
P.J. Robinson, K.A. Holbrook, Unimolecular reactions (Wiley, London, 1972)
N.W. Ascroft, N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976)
C. Bréchignac, Ph. Cahuzac, J. Leygnier, J. Weiner, J. Chem. Phys. 90, 1492 (1989)
C. Walther, G. Dietrich, W. Dostal, K. Hansen, S. Krückeberg, K. Lützenkirchen, L. Schweikhard, Phys. Rev. Lett. 83, 3816 (1999)
M. Schmidt, J. Donges, Th. Hippler, H. Haberland, Phys. Rev. Lett. 90, 103401 (2003)
K. Hansen, Philos. Mag. B 79, 1413 (1999)
M.M. Kappes, M. Schär, E. Schumacher, A. Vayloyan, Z. Phys. D 5, 359 (1987)
Ph. Dugourd, D. Rayane, R. Antoine, M. Broyer, Chem. Phys. 218, 163 (1997)
The energy-temperature relation for a microcanonical ensemble is better represented if (3n-6) is replaced by (3n-7) andersen:01 but this point has only a minor influence on the recoil calculation
J.U. Andersen, E. Bonderup, K. Hansen, J. Chem. Phys. 114, 6518 (2001)
Handbook of Mathematical Functions, edited by M. Abramowitz, I.A. Stegun (Dover, New York, 1965)
M. Kappes, S. Leutwyler, in Atomic and Molecular Beam Methods, edited by G. Scoles (Oxford, New York, 1988)
G.D. Stein, Surf. Sci. 156, 44 (1985)
S.B. Ryali, J.B. Fenn, Ber. Bunsenges. Phys. Chem. 88, 245 (1984)
H. Pauly, Atom, Molecule, and Cluster Beams (Springer, Berlin, 2000)
O.F. Hagena, Surf. Sci. 106, 101 (1981); O.F. Hagena, Z. Phys. D 4, 291 (1987)
C.E. Klots, J. Chem. Phys. 83, 5954 (1985); C.E. Klots, J. Phys. Chem. 92, 5864 (1988); C.E. Klots, Z. Phys. D 21, 335 (1991)
U. Näher, K. Hansen, J. Chem. Phys. 101, 5367 (1994)
K. Hansen, U. Näher, Phys. Rev. A 60, 1240 (1999)
G. Tikhonov, K. Wong, V. Kasperovich, V.V. Kresin, Rev. Sci. Instrum. 73, 1204 (2002)
H. Beijerinck, N. Verster, Physica 111C, 327 (1981)
The free-flight trajectories of cluster parents and daughters may, in principle, be deflected by collisions with background gas in the vacuum chambers and with the carrier gas atoms. As mentioned in the text, the primary contribution to the off-axis signal comes from clusters evaporating after Aperture 2, so the concern is whether scattering in this region may distort the pattern created by evaporative recoil. Such scattering will be dominantly of the elastic van der Waals type, and the relevant cross sections have been studied in reference kresin:93. From the data in this reference, it follows that the “extinction length” for scattering a fraction 1/e of the clusters into an angle of 4 mrad (the angle subtended by the radius r0 in the detector plane as seen from Aperture 2) by a pressure P of Ar or N2 is ≈\(5~{\rm mm} / P(10^{-3}~{\rm mbar})\). This means that with chamber pressures of \(\gtrsim\)10-8 mbar following Aperture 2, only a fraction of one percent of the parent clusters will be scattered beyond r0 by the background gas. Note that the carrier gas which accompanies the beam will not scatter the par- ents, as they travel at close speeds. This carrier gas can, in principle, scatter the deflecting daughters, but an estimate of its pressure remaining in the beam at this point pauly yields ~10-5 mbar. Only a negligible fraction of the daughter clusters will be deflected after traversing the ~1 mm radius of this beam. Thus we see that background and carrier gas scattering will not alter the calculated off-axis populations by more than a few percent
V.V. Kresin, A. Scheidemann, J. Chem. Phys. 98, 6982 (1993)
W.D. Knight, K. Clemenger, W.A. de Heer, W.A. Saunders, M.Y. Chou, M.L. Cohen, Phys. Rev. Lett. 52, 2141 (1984)
The dissociation energies of neutral clusters are obviously somewhat different from the ionic cluster data used in our calculations. This is well illustrated by taking the example of the Na21 cluster. In the experimental mass spectra, this unit has an abundance of about 10% of Na20, but in the simulation it does not appear at all. This is due to the dissociation energies assigned to the Na22 cluster. For the reaction Na22 →Na20+ Na2, the value inferred from Nan+ data in reference brechignac:89 is D=0.65 eV, whereas monomer dissociation is not quoted at all, thus not allowing the reaction Na22 →Na21+Na. Consequently, the simulation leaves no signal in the n=21 channel. It would be interesting to reevaluate the dissociation energies of neutral clusters by combining experimentally measured mass spectra (corrected for ionization efficiency effects) and the evaporation model (cf. adjustments of Lin+ separation energies described in Ref. bjornholm:96)
S. Bjørnholm, J. Borggreen, H. Busch, F. Chandezon, in Large Clusters of Atoms and Molecules, edited by T.P. Martin (Kluwer, Dordrecht, 1996)
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Hansen, K., Wong, K. & Kresin, V. Obtaining colder ensembles of free clusters by using evaporation and recoil. Eur. Phys. J. D 32, 339–345 (2005). https://doi.org/10.1140/epjd/e2004-00188-9
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DOI: https://doi.org/10.1140/epjd/e2004-00188-9