NON-EQUILIBRIUM EFFECTS IN CRYSTAL-FLUID PARTITIONING OF TRACE ELEMENTS AT LOW- TO INTERMEDIATE TEMPERATURES

The trace-element compositions of minerals provide key insights into the conditions of mineral growth in systems ranging from magmas to ancient oceans. In general, our ability to extract "environmental" information from trace-element concentrations of minerals hinges on laboratory or natural-system calibrations of equilibrium crystal-fluid partitioning as a function of the system variables of interest (T, P, f_O2, etc.). In some instances, there is reason to be cautious in our assumptions about equilibrium. It is well known, for example, that rapid crystal growth can result in significant deviations from equilibrium between a crystal and its fluid growth medium. "Rapid" is a relative term, however, and we need more quantitative criteria to assess non-equilibrium effects; the potential causes do not necessarily require growth that is rapid in an absolute sense. Broadly speaking, non-equilibrium growth is attributable to dynamical phenomena occurring on one side or the other of the crystal/fluid interface—i.e., in the growth medium or in the near-surface of the advancing crystal lattice itself. Two specific conditions leading to non-equilibrium element uptake at geologically relevant growth rates will be discussed: 1) the rate of crystal growth outpaces the ability of diffusion in the growth medium to supply strongly compatible components or disperse incompatible ones (diffusive boundary layer effects - "DBL"); and 2) the thermodynamic properties of the near-surface of the crystal differ significantly from those of the bulk lattice, and the “anomalous” near-surface composition may be trapped within the bulk lattice if growth is fast relative to diffusion in the crystal (the growth-entrapment model - "GEM"). These phenomena are revisited with an updated perspective that includes realistic "stirring" of the crystal/fluid system in circumstances conducive to DBL effects. Broadly speaking, stirring has the effect of diminishing the magnitude of non-equilibrium effects attributable to a diffusive boundary layer, but such effects may nevertheless be non-negligible. A quantitative application of the GEM to Ti uptake in quartz will also be presented to show that—although the effect does operate for plausible assumed growth rates—the consequences for Ti-in-quartz thermobarometry are minor.