Transition-State Model for Entropy-Limited Freezing
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TRANSITION-STATE MODEL FOR ENTROPY-LIMITED FREEZING J.Y. Tsao*, M.J. Aziz**, P.S. Peercy* and M.O. Thompson*** SDevice Research Dept., Sandia National Labs, Albuquerque, * Div. of Applied Sciences, Harvard University, Cambridge, • Dept. of Materials Science, Cornell University, Ithaca,
NM87185 MA02138 NY 14853
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. INTRODUCTION Since its formulation in the 1930's [1], transition-state and its variants have been successful in accounting for a large body of experimental reaction-rate data. For example, for unimolecular reactions in the gas phase, the theory is known to chemical kineticists as the highly successful RRKM theory [2]. For condensed-phase reactions and transformations transition-state theory has also yielded useful results [3], although in these cases it is difficult to deduce from first principles the exact nature of the transition state. Recently, we compared the predictions of transition-state theory with constraints, both experimentally measured as well as derived from first principles, on the kinetics of heterogeneous melting and freezing of Si [4]. Our conclusion was that if transition-state theory were valid, and if a single mechanism were operative at all temperatures, then the constraints enumerated were only consistent with an "entropy-limited" freezing model, in which the transition state has an enthalpy greater than or equal to that of the liquid, and an entropy less than or equal to that of the solid. In effect, not all collisions of liquid atoms onto the solid/liquid interface result in freezing, but only those which bring the liquid atom into special configurations closely approximating the solid. More recently, measurements indicate that there may be multiple mechanisms for melting and freezing, each of which may be dominant in a different temperature regime [5-7]. A single theory for the kinetics of melting and freezing across the entire temperature range may therefore be inappropriate. Nevertheless, if the mechanisms are independent, it may be possible (and it seems reasonable to attempt) to describe the rates of each mechanism individually using some form of transition-state theory [8]. In the first part of this paper, we review briefly the structure and assumptions of transition-state theory. We begin with the simpler case of unimolecular reactions in the gas phase, and then turn to reactions in condensed phases. In the second part, we argue that for reversible transitions between states having very different enthalpies and entropies, e.g., the solid-liquid transformation in Si, transition-state theory is naturally asymmetric, i.e., successful forward and backward "hopping" rates are very different [9].
Mat. Res. Soc. Sym
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