Diffusion coupling between trace and major elements and a model for calculation of magma residence times using plagioclase

Residence times of plagioclase crystals in magma reservoirs can be determined by modeling the compositional zoning of trace elements in these crystals. We present a formulation to model diffusion of trace elements in plagioclase paying special attention to certain thermodynamic and kinetic aspects. In particular, we account for the compositional dependence on anorthite content of the chemical potential and diffusion coefficients of trace elements (e.g., Mg), the choice of suitable boundary conditions and potential effects of diffusion in more than one dimension. We show that contrary to intuition, diffusive fluxes of trace elements may be coupled to major element concentration gradients, and ignoring such coupling can lead to incorrect estimates of timescales. We illustrate application of the model using plagioclase crystals from a suite of gabbroic xenoliths from a Holocene dacitic lava flow of Volcán San Pedro (Chilean Andes, 36°S). The inferred timescale for metasomatism of the xenoliths by evolved liquids is on the order of 100 (30 to 148) yr and serves to illustrate how trace element zoning in plagioclase provides a window into timescales of magmatic processes inaccessible by isotopic or other methods.