A statistical analysis of the distribution of cordierite and biotite in hornfels from the Bugaboo contact aureole: implications for the kinetics of porphyroblast crystallization

The three‐dimensional disposition of cordierite and biotite crystals in a hornfels from the contact aureole of the Bugaboo Batholith is quantified using high‐resolution X‐ray micro‐computed tomography and global as well as scale‐dependent pattern statistics. The results demonstrate a random distribution of cordierite and biotite crystal sizes for all scales across the entire rock volume studied indicative of interface‐controlled prograde metamorphic reaction kinetics. The reaction considered responsible for the mineral assemblage and the formation of cordierite and biotite in the hornfels is Ms + Chl + Qtz = Crd + And + Bt + . Rock‐specific phase equilibria point to metamorphic conditions of ~520 –550 °C and 3 kbar for this reaction. The common approach to approximate the shape of crystals as spherical underestimates the influence of the Strauss hard‐core process on rock texture and may be misinterpreted to reflect ordering of crystal sizes by inhibition of nucleation and growth commonly associated with diffusion‐controlled reaction kinetics. According to our findings, Strauss hard‐core ordering develops at length scales equal to and less than the average major axis of the crystal population. This is significantly larger than what is obtained if a spherical crystal geometry would be assumed, and increases with deviation from sphericity. For the cordierite and biotite populations investigated in this research, Strauss hard‐core ordering developed at length scales of up to ～2.2 and 1.25 mm, respectively, which is almost 1 mm longer than the scales that would be obtained if a spherical geometry would have been assumed. Our results highlight the importance of a critical assessment of the geometrical model assumptions commonly applied in the three‐dimensional analysis of crystal size distributions, and underline the need for a quantitative understanding of interface processes in order to appreciate their role in the kinetics of contact metamorphic reactions and rock texture formation.