A quantitative model of trace element and isotopic behavior during simultaneous assimilation and imperfect fractional crystallization

Coupled assimilation and fractional crystallization (AFC) process is one of the most popular concepts of open-system magmatic evolution. The conventional AFC models have assumed that crystals are removed instantaneously from the magma body as they are produced. However, the petrographic observations of natural volcanic rocks suggest that the magmas generally contain a few percent to approximately 60% of suspended crystals. A coupled assimilation and imperfect fractional crystallization process (AIFC) is thus more realistic than the conventional AFC process employing perfect crystal-liquid separation. This study develops a mass balance model for trace element and isotope behavior during the AIFC process. Recent studies of isotopic micro-analysis have clarified that isotopic ratios recorded from core to rim of a mineral grain reflect the progressive changes in the liquid composition from which the mineral crystallized. The isotope ratio of liquid and that of the integrated (bulk) single crystals are therefore different in an open system case where the magma changes isotope composition with time. To incorporate the effect of the suspended crystals into the model, we assume isotopic and trace element zoning of crystals within a magma chamber. We solve simultaneously the mass balance differential equations for the liquid and the suspended crystals. The analytical solution of the AIFC equations gives quantitative trace element and isotope evolution paths of the bulk crystal, liquid and magma (crystals plus liquid). The chemical paths of the magma differ markedly from those that are expected for the conventional AFC model. The formula for the analysis of the AIFC can easily be expanded to other open system processes such as simultaneous recharge, crystal separation and eruption process.