Computer Science
Scientific paper
Apr 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994e%26psl.122..373y&link_type=abstract
Earth and Planetary Science Letters, Volume 122, Issue 3-4, p. 373-391.
Computer Science
7
Scientific paper
This paper explores the application of homogeneous reaction kinetics to geospeedometry and to structural relaxation theory. Numerical simulations of reaction kinetics during cooling for some first- and second-order elementary reactions have been carried out to systematically examine the effects of kinetic parameters and cooling histories on the final speciation. An analytical solution for a special case of first-order reaction A <==> B has also been obtained. On the basis of both the analytical solution and the numerical simulation, the cooling rate (-dT/dt) at the apparent equilibrium temperature (Tae, obtained by measuring `quenched' speciation) and the relaxation time scale (τr, the time for the departure from equilibrium to decrease to 1/e of the initial departure) at Tae can be approximately related as follows: (-dT/dt)T=Tae ~ 2RTae/max( Ef, Eb) where R is the gas constant, and max(Ef, Eb) is the greater of Ef and Eb, which are the activation energies of the forward and backward reactions. This approximation works well when the initial temperature (T0) is high such that τr(T0) is small compared to the cooling time scale. Using the above relation, the cooling rate at Tae can be estimated easily and the cooling history of a natural assemblage can be inferred if enough homogeneous reactions are characterized.
Relaxation of homogeneous reactions during the quench of a silicate melt into a glass can be studied quantitatively using the above method if the kinetic parameters are known. Melt-glass transitions probably involve the quenching of many homogeneous reactions that may have different Tae for a given quench rate, and are thus complicated. Authors have previously discussed relaxation of a reaction during cooling using the idea of a melt-glass transition. Because glass relaxation is complicated and the theory is still in its infancy, whereas reaction kinetics can be understood and quantified, it may be more productive to study the relaxation of homogeneous reactions directly and to study glass relaxation using the concept of reaction kinetics instead.
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