DIFFUSION MODELING OF METAMORPHIC LAYERED CORONAS WITH STABILITY-CRITERION AND CONSIDERATION OF AFFINITY

Layered coronas between two reactant minerals can, in many cases, be a ttributed to diffusion-controlled growth with local equilibrium. This paper clarifies and unifies the previous approaches of various authors to the simplest form of modelling, which uses no assumed values for t hermochemical quantities. A realistic overall reaction must be estimat ed from measured overall proportions of minerals and their major eleme nt compositions. Modelling is not restricted to a particular number of components S, relative to the number of phases Phi. If Phi > S + 1, t he overall reaction is a combination of simultaneous reactions. The st epwise method, solving for the local reaction at each boundary in turn , is extended to allow for recurrence of a mineral (its presence in tw o parts of the layer structure separated by a gap). The equations are also given in matrix form. A thermodynamic stability criterion is deri ved, determining which layer sequence is truly stable if several are c omputable from the same inputs. A layer structure satisfying the stabi lity criterion has greater growth rate (and greater rate of entropy pr oduction) than the other computable layer sequences. This criterion of greatest entropy production is distinct from Prigogine's theorem of m inimum entropy production, which distinguishes the stationary or quasi -stationary state from other states of the same layer sequence. The cr iterion leads to modification of previous results for coronas comprisi ng hornblende, spinel. and orthopyroxene between olivine (Ol) and plag ioclase (Pi). The outcome supports the previous inference that Si, and particularly Al, commonly behave as immobile relative to other cation -forming major elements. The affinity (-Delta G) of a corona-forming r eaction is estimated, using previous estimates of diffusion coefficien t and the duration t of reaction, together with a new model quantity ( -Delta G). For an example of the Ol + Pl reaction, a rough calculatio n gives (-Delta G) > 1.7RT (per mole of Pl consumed, based on a 24-oxy gen formula for Pi). At 600-700 degrees C, this represents (-ac) > 10 kJ mol-l and departure from equilibrium temperature by at least simila r to 100 degrees C. The lower end of this range is petrologically reas onable and, for t < 100 Ma, corresponds to a Fick's-law diffusion coef ficient for Al, D-Al > 10(-25) m(2) s(-1), larger than expected for la ttice diffusion but consistent with fluid-absent grain-boundary diffus ion and small concentration gradients. Copyright (C) 1997 Elsevier Sci ence Ltd.