Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T09:06:45.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition-State Model for Entropy-Limited Freezing

Published online by Cambridge University Press:  28 February 2011

J. Y. Tsao,
M. J. Aziz,
P. S. Peercy and
M. O. Thompson
J. Y. Tsao
Affiliation:
Device Research Dept., Sandia National Labs, Albuquerque, NM 87185
M. J. Aziz
Affiliation:
Div. of Applied Sciences, Harvard University, Cambridge, MA 02138
P. S. Peercy
Affiliation:
Device Research Dept., Sandia National Labs, Albuquerque, NM 87185
M. O. Thompson
Affiliation:
Dept. of Materials Science, Cornell University, Ithaca, NY 14853
Get access

Abstract

A brief review is given of transition-state theory, both for the case of unimolecular reactions in the gas phase, and for reactions in condensed phases. An argument is made that, within the context of this theory, heterogeneous freezing in Si is limited to rates much lower than collision rates by the difference between the entropies of the solid and the liquid.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Glasstone, S., Laidler, K.J. and Eyring, H., Theory of Rate Processes (McGraw-Hill, New York, 1966); and H. Eyring, S.H. Lin and S.M. Lin, Basic Chemical Kinetics (Wiley-Interscience, New York, 1980).Google Scholar
[2] Forst, W., Theory of Unimolecular Reactions (Academic Press, New York, 1973).Google Scholar
[3] Christian, J.W., The Theory of Transformations in Metals and Alloys, 2nd Ed. (Pergamon Press, Oxford, 1975), Chap. 3.Google Scholar
[4] Tsao, J.Y., Aziz, M.J., Thompson, M.O. and Peercy, P.S., Phys. Rev. Lett. 56, 2712 (1986); and manuscript submitted to Phys. Rev. B.Google Scholar
[5] Larson, B.C., Tischler, J.Z. and Mills, D.M., J. Mater. Res. 1, 144 (1986).CrossRefGoogle Scholar
[6] Tsao, J.Y., Peercy, P.S. and Thompson, M.O., J. Mater. Res., to be published.Google Scholar
[7] Tsao, J.Y., Peercy, P.S. and Thompson, M.O., unpublished.Google Scholar
[8] It is also possible that transition-state theory alone is inadequate, and that other theories (or combinations of theories), such as those suggested by Bucksbaum, P.H. and Thompson, M.O. (to be published), and by Richards, P.M. (to be published), may be necessary.Google Scholar
[9] This is an asymmetry additional to that which might already be present due to an activation enthalpy.Google Scholar
[10] Lindemann, F.A., Trans. Faraday Soc. 17, 598 (1922).CrossRefGoogle Scholar
[11] In step 1, especially at high pressures, the strong-collision approximation (one-step activation) is usually made: a thermal population distribution is assumed to be established after each collision.Google Scholar
[12] The collisional energization rate into transition states is independent of whether the system is in equilibrium or not, and so is given by the equilibrium rate (which must exactly equal the collisional de-energization rate out of the transition states [2]).Google Scholar
[13] We assume that, in condensed phases under normal atmospheric pressure conditions, enthalpies are approximately equal to energies.Google Scholar
[14] These two assumptions represent important differences between the ideas presented here and those of Bucksbaum, P.H. and Thompson, M.O. [8]Google Scholar
[15] Spaepen, F. and Turnbull, D., in Laser Annealing of Semiconductors, Poate, J.M. and Mayer, J.W., eds. (Academic, New York, 1982), pp. 15–42.Google Scholar
[16] Since ks+ = and k1+ = where ps+ (E) and ps+ (E) are the densities of transition states, and Note that the two sets of transition states are not the same; microscopic reversibility implies a relation governing transition rates between states, rather than equality of states.Google Scholar
[17] See, e.g., Eq. (9) in Jackson, K.A., in Crystal Growth and Characterization, Ueda, R. and Mullin, J.B., eds. (North-Holland, Amsterdam, 1975), pp. 21–32.Google Scholar