A Volume Model for Monoclinic Amphiboles

Abstract:

The monoclinic amphibole group is a diverse family of igneous and metamorphic minerals with numerous end members. While amphibole is frequently observed as a primary igneous mineral, it is almost never predicted to crystallize in current implementations of the MELTS family of thermodynamic solution models. This is likely due to neglect of the stabilizing influence of the numerous minor components that partition into natural amphiboles and is a severe limitation on the use of MELTS for modeling the evolution of amphibole-bearing igneous suites.

Modeling how the volume of amphibole depends on composition and site ordering is an appropriate first step towards developing a better solution model compatible with MELTS. Knowledge of molar volumes is prerequisite to calibrating a thermodynamic model because they express the pressure derivative of molar Gibbs free energy at constant temperature. At the same time, molar volume is also essential for assessing the density and elasticity of amphibole group minerals and hence whether they will sink or float in magma chambers and how they will influence the seismic wave speeds of amphibole-bearing rocks.

We have developed and calibrated a model that incorporates all the named C2/m clino-amphiboles containing the components considered in MELTS. We defined compositional and order parameters that allow, per formula unit, Si⁴⁺ and Al³⁺ in the eight tetrahedral sites; Mg²⁺, Fe²⁺, Al³⁺, Fe³⁺, Cr³⁺, Ti⁴⁺ and Mn²⁺ in the five C sites; Ca²⁺, Mg²⁺, Fe²⁺, Na⁺ and Mn²⁺ in the two M₄ site; Na⁺, K⁺, Ca²⁺, and vacancies in the single A site; and OH^–, F^– and O^2– in the two O₃ sites. Available refinements of X-ray data acquired at STP were mapped onto points in a composition/ordering space to calibrate the volume model. The calibration of our current model, which was constructed with one constant parameter, 12 first-order compositional parameters, 5 first-order site-ordering parameters, and 11 second-order parameters, results in a reduced χ² of 0.89. That is, over a dynamic range from 872 to 935 ų, nearly every point is fit to better than ±1 ų. Next steps include (1) extension to high temperature using thermal expansion data, (2) extension to high pressure using a combination of compression data and density functional theory calculations, and (3) incorporation of a much larger set of X-ray refinements.