Chemical mass transfer in magmatic processes

Abstract

Numerical examples of the approach described in Part I of this series (Ghiorso, 1985) are presented in this paper. These examples include the calculation of the compositions and proportions of liquid and solid phases produced during (1) the equilibrium crystallization of a basaltic andesite at 1 bar, (2) the fractional crystallization of an olivine tholeiite at 1 bar and elevated pressures, (3) the fractional and equilibrium crystallization of an olivine boninite at 1 bar, and (4) the (a) isothermal and (b) isenthalpic assimilation of olivine (Fo₉₀) into a liquid/solid assemblage of quartz dioritic composition at ∼1,125° C and 3 kbars. The numerical results on the crystallization of the basaltic andesite are verified by comparison with experimental data while those calculations performed using olivine tholeiitic and olivine boninitic compositions are favorably compared against whole rock and mineral analytical data and petrographic and field observations.

In each of the examples presented, the heat effects associated with the modelled process are calculated (e.g. heat of crystallization, heat of assimilation), and free energies of crystallization are examined as a function of the degree of mineral supersaturation. The former quantities are on the order of 173 cal/grm for the cooling and fractional crystallization of an olivine tholeiite to a rhyolitic residuum (corresponding to a 400° C temperature interval). The latter represents an important petrological parameter, in that it quantifies the driving force for the rate of crystal growth and rate of nucleation in magmatic systems. Calculated free energies of crystallization are small (on the order of hundreds of calories per mole per 25° C of undercooling) which indicates that the kinetics of crystallization in magmatic systems are affinity controlled.

Melt oxygen fugacity and the degree of oxygen metasomatism play a major role in controlling the fractionation trends produced from crystallizing basaltic liquids. Calculations suggest that in order to generate a silica rich residuum and the characteristic iron enrichment trend during the fractional crystallization of a tholeiitic basalt, the magma must crystallize esentially along $f_{{\text{O}}_{\text{2}} }$ buffer. This buffered state can be maintained by exchange of oxygen (via hydrogen diffusion) between the magma and the surrounding country rocks or by magmatic oxidation-reduction equilibria. Additional calculations indicate the possibility that oxygen exchange may be unnecessary if the magma contains sufficient sulfur to maintain the system along an S₂/SO₂ oxygen buffer during the initial stages of crystallization.