Steady‐diffusion modelling of a reaction zone between a metamorphosed basic dyke and a marble from Hirao‐dai, Fukuoka, Japan

A reaction zone between a metamorphosed basic dyke and marble at Hirao‐dai, north Kyushu, Japan, consists of well‐organized sequential zones of diopside, garnet and wollastonite; textures are characteristic of diffusion‐controlled structures. The reaction zone formed during contact metamorphism associated with intrusion of a Cretaceous granodiorite at ∼300 MPa and 700 °C. The metamorphosed basic dyke consists of diopside, biotite and plagioclase ( X Ab  = 0.4–0.8), whereas the marble is almost pure calcite. The initial boundary between the dyke and the marble is probably located within the current diopside zone, as calcite occurs as remnants among diopside grains in areas close to the boundary with the garnet zone. This observation provides a criterion to judge the stability of the zonal sequence in our modelling. The formation of the reaction zone is attributed to a single‐stage steady‐state process with five overstepping reactions. CaO, MgO, FeO, SiO 2 and AlO 3/2 are the reaction‐controlling components that are necessary to describe the growth of the reaction zone. An isochemical steady‐diffusion model cannot reproduce the measured phase ratios of product minerals; this indicates open‐system behaviour of the reaction zone. The choice of closure components is an essential task in the treatment of open‐system modelling, together with determination of phase ratios (Ashworth & Birdi model) or estimation of boundary fluxes (Johnson & Carlson model). Of all the possible combinations of closure components, closure conditions for CaO and MgO provide the best results for both models. The stability of the zonal sequence is limited at relatively large values of L SiSi / L CaCa . Similar results from the two models confirm their consistency under the same closure conditions.