The rocky road to equilibrium. Spear, F. S.

The rocky road to equilibrium
Spear, F. S.
Metamorphic reactions cannot proceed without a driving force, but it is often assumed that deviation from equilibrium is sufficiently small that little error is introduced by assuming that rocks evolve through a sequence of equilibrium steps. A growing body of recent work, however, suggests that deviations from equilibrium may be significant. The two main approaches that we have used are quartz-in-garnet (QuiG) barometry and zirconium-in-rutile (ZiR) thermometry. Rutile inclusions are common in garnet and the temperature recorded by ZiR thermometry places a lower limit on the temperature of garnet formation. QuiG barometry, which is independent of assumptions of chemical equilibrium, provides an estimate of the pressure of garnet formation. Comparison of the estimate of P–T conditions of garnet formation with calculations of the garnet-in reaction reveals significant degrees of overstepping with calculated affinities ranging from several hundred to several thousand J/mol-O.
For example, comparison of rocks with a “normal” density of garnet crystals (1–20 crystals/cm3 = LoCD) with rocks with a high density of garnet crystals (tens of thousands to many millions of crystals/cm3 = HiCD) reveals that LoCD samples have calculated affinities at conditions of garnet growth of only several hundred J/mol-O whereas HiCD samples have calculated affinities of several thousand J/mol-O. Application of homogeneous nucleation theory to these data supports the hypothesis that the variation in nucleation rates between the LoCD and HiCD samples is consistent with differences in the thermodynamic affinity and permits an estimate of the surface energy of the nucleus. The question then arises as to what kinetic controls dominate the recrystallization process when reactions are significantly overstepped. Possibilities include surface kinetics of the reactants and/or the products, grain boundary diffusion or lattice diffusion. Carmichael [1] argued that grain boundary diffusion, and especially the immobility of Al and relatively high mobility of K, played a dominant role in impacting the evolution of reaction textures.
To better quantify the processes controlling metamorphic recrystallization, numerical models are being developed to explore the various possible rate-limiting steps. The model utilizes a 2-dimensional grid consisting of minerals typical of pelites linked together by grain boundaries. Local equilibrium is assumed such that reactions are only permitted between adjacent phases and the grain boundary medium. Reactions are balanced by conserving oxygen and only proceed until local equilibrium is established at each grid point. For example, where garnet is in contact with quartz the reaction is:
Si1/2O + 1/6Al + 𝝂1Fe + 𝝂2Mg + 𝝂3Mn + 𝝂4Ca = (Fe𝝂1,Mg𝝂2,Mn𝝂3,Ca𝝂4)Al1/6Si1/4O + 1/4Si
where the composition of the garnet is governed by the Maximum Driving Force (MFD) method. These local reactions change the composition of the grain boundary setting up chemical gradients which then drive grain boundary diffusion. The grain boundary composition is thus modified in the vicinity of reactant phases, which renders them out of equilibrium and drives local reactions at those grid points. The process is repeated through successive iterations by which garnet grows at the expense of chlorite, quartz, and plagioclase.
The model predicts local variation in the growth and consumption of phases. For example, muscovite is consumed at some localities whereas elsewhere in the rock it grows, depending on the adjacent phases. Most importantly, the growth rate and compositional evolution of garnet is locally variable —not all garnet grows at the same rate and at any point in time not all garnet has the same composition.