An empirical modification of Dodson's equation for closure temperature in binary systems

Details An empirical modification of Dodson's equation for closure temperature in binary systems An empirical modification of Dodson's equation for closure temperature in binary systems

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994gecoa..58..241e&link_type=abstract

Geochimica et Cosmochimica Acta, vol. 58, Issue 1, pp.241-248

Mathematics

Logic

6

Scientific paper

Closure temperature is defined as the temperature given by the compositions of the minerals, once they have ceased changing during cooling, on substitution of the compositions into a geothermometer. Consider a cooling one dimensional system involving two minerals, A and B , of which B is the slower diffusing mineral, with two diffusing components, and denote with l A and l B the half widths of mineral A and B , and with C A and C B the core concentrations of mineral A and B . Then Dodson's equation to model the closure temperature given by the core concentrations of A and B is appropriate if r is very large (or A is much larger than B ), and if k is very large (or C B is near 0 or 1). For smaller r and/or smaller k , a new empirical extension to Dodson's equation, involving a term in rk , has been devised on the basis of numerous numerical experiments: , in which T c is the closure temperature, D 0 the pre-exponential factor of mineral B , Q the activation energy of mineral B , s the cooling rate, R the gas constant, and and are two adjustable parameters. This equation gives T c within 5-10 K for rk > 0.1, with = 2.56 and = 1.72. It is therefore useful in the prediction of closure temperatures for exchange thermometers in petrological systems. On the other hand, the equation can be used to calculate the cooling rate if the closure temperature can be estimated independently.

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