Igneous layering through oscillatory nucleation and crystal settling in well-mixed magmas

Oscillatory or competitive nucleation about a binary (or perhaps pseudo binary) eutectic and ensuing crystal growth and settling is a commonly suggested means of producing layering in magmatic systems. A quantitative model is presented of this, outwardly, relatively simple process of crystal nucleation, growth, and settling in an otherwise initially crystal-free magma. Avrami-style kinetics of crystallization in an always wellmixed body, buried in conductive wall rock, are coupled to a Stokes-like formulation of crystal settling in magma whose viscosity depends on temperature and crystallinity. Two dimensionless numbers (Se, the settling number and Av, the Avrami or kinetic number) govern all the results. Av and Se measure the relative importance of crystallization time and settling time, respectively, relative to the overall cooling time. For any value of Av, which increases strongly with the maximum nucleation and growth rates and cooling time, layering is possible only over a range or window of values of Se. Both above and below this window a single layer (crystalline below, vitric above) forms, and within this window the number of layers increases systematically with increasing Av and Se. Grain size within any single layer generally coarsens upward. Because the characteristic settling and cooling times both depend on body thickness, the lower limit of the settling window is also dependent on sheet thickness. Within the confines of this model and for nucleation and growth rates set by those observed in natural systems, layering is unlikely in sheet-like magmas thinner than about 100 m. When the body is not always well-mixed and crystallization is within inward-propagating solidification fronts, it is expected that this minimum body thickness will increase.