Oxygen isotope exchange kinetics of mineral pairs in closed and open systems: Applications to problems of hydrothermal alteration of igneous rocks and Precambrian iron formations

Abstract

The systematics of stable-isotope exchange between minerals and fluids are examined in the context of modal mineralogical variations and mass-balance considerations, both in closed and in open systems. On mineral-pair δ^(18)O plots, samples from terranes that have exchanged with large amounts of fluid typically map out steep positively-sloped non-equilibrium arrays. Analytical models are derived to explain these effects; these models allow for different exchange rates between the various minerals and the external fluids, as well as different fluid fluxes. The steep arrays are adequately modelled by calculated isochron lines that involve the whole family of possible exchange trajectories. These isochrons have initially-steep near-vertical positive slopes that rotate toward a 45° equilibrium slope as the exchange process proceeds to completion. The actual data-point array is thus analogous to the hand of an “isotopic clock” that measures the duration of the hydrothermal episode. The dimensionless ratio of the volumetric fluid flux to the kinetic rate parameter (u/k) determines the shape of each individual exchange trajectory. In a fluid-buffered system (u/k ≫ 1), the solutions to the equations: (1) are independent of the mole fractions of the solid phases; (2) correspond to Taylor's open-system water/rock equation; and (3) yield straight-line isochrons that have slopes that approach 1/f, where f is the fraction reacted of the more sluggishly exchanging mineral. The isochrons for this simple exchange model are closely congruent with the isochrons calculated for all of the more complex models, thereby simplifying the application of theory to actual hydrothermal systems in nature. In all of the models an order of magnitude of time (in units of kt) separates steep non-equilibrium arrays (e.g., slope ≈ 10) from arrays approaching an equilibrium slope of unity on a δ-δ diagram. Because we know the approximate lifetimes of many hydrothermal systems from geologic and heat-balance constraints, we can utilize the ^(18)O/^(16)O data on natural mineral assemblages to calculate the kinetic rate constants (k's) and the effective diffusion constants (D's) for mineral-H_2O exchange: these calculated values (k_(qtz) ≈ 10^(−14), k_(feld) ≈ 10^(−13)–10^(−12)) agree with experimental determinations of such constants. In nature, once the driving force or energy source for the external infiltrating fluid phase is removed, the disequilibrium mineral-pair arrays will either: (1) remain “frozen” in their existing state, if the temperatures are low enough, or (2) re-equilibrate along specific closed-system exchange vectors determined solely by the temperature path and the mineral modal proportions. Thus, modal mineralogical information is a particularly important parameter in both the open- and closed-system scenarios, and should in general always be reported in stable-isotopic studies of mineral assemblages. These concepts are applied to an analysis of ^(18)O/^(16)O systematics of gabbros (Plagioclase-clinopyroxene and plagioclase-amphibole pairs), granitic plutons (quartz-feldspar pairs), and Precambrian siliceous iron formations (quartz-magnetite pairs). In all these examples, striking regularities are observed on δ-δ and δ-Δ plots, but we point out that δ-δ plots have many advantages over their equivalent δ-Δ diagrams, as the latter are more susceptible to misinterpretation. Using the equations developed in this study, these regularities can be interpreted to give semiquantitative information on the exchange histories of these rocks subsequent to their formation. In particular, we present a new interpretation indicating that Precambrian cherty iron formations have in general undergone a complex fluid exchange history in which the iron oxide (magnetite precursor?) has exchanged much faster with low-temperature (< 400°C) fluids than has the relatively inert quartz.