Magmatic residence times of zoned phenocrysts: introduction and application of the binary element diffusion modelling (BEDM) technique

This paper describes a general technique, binary element diffusion modelling (BEDM), for determining single-crystal residence times in magmas that relies on modelling the diffusion of two or more elements in the crystal. BEDM has the advantage over other diffusion-based models in that it does not need a precisely defined initial compositional profile for the crystal at “zero time”, and instead requires that the concentrations of the two elements are correlated during crystallisation. Any differences subsequently observed between the two elements are caused by intracrystalline diffusion during residence in hot magma. These differences are removed by artificially ageing the slower-diffusing of the two elements, and the amount of time taken to “undo” the difference between the elements is simply related to the crystal residence time (=decoupling time) at high temperatures. The BEDM principle is demonstrated using artificial data and is then applied to literature data for Sr and Ba in a zoned sanidine crystal from the Bishop Tuff (Anderson et al., in J. Petrol 41(3):449–473, 2000). For this crystal, the method gives a residence time estimate of 114 ka at 800°C, which is then compared with estimates from other methods. In theory, the method can be further expanded for use as a geothermometer as well as geochronometer. However, this is not easily possible with the diffusivity data currently available.