Mineral growth in rocks: Kinetic-rheological models of replacement, vein formation, and syntectonic crystallization

Abstract We model three cases of coupling between mineral growth kinetics and mechanical response of the rock: (i) dispersed spherical crystals growing by replacement in a hydrostatically stressed elastic rock; (ii) growth of veins or vein networks accommodated by viscous relaxation of surrounding rock; and (iii) syntectonic crystallization in a rock undergoing bulk pure shear. Such models for the microscopic environment of mineral growth, together with additional assumptions or knowledge about rheological behavior and aggregate geometry, provide refined estimates of the behavior of a macroscopic volume element, which could be combined with geochemical reaction-transport models. Crucial in the models are the various consequences—pressure solution, creep, fracturing—of the local stress that is necessarily generated by mineral growth in rocks (other than in pores). In the first model, the dispersed spherical crystals of mineral A are assumed to grow within a spherical volume of rock consisting of mineral B, the “mineralized zone” (MZ), itself embedded in elastic rock. The macroscopic stress in the MZ and the far-field stress in the surrounding rock are uniform and hydrostatic. Mineral growth of the A crystals is driven by supersaturation with respect to mineral A, is accommodated by replacement of B grains, and leads to an expansion of the MZ described by an infinitesimal strain. The radial growth rate of a spherical crystal of mineral A, with replacement of mineral B, is da / dt = k A R Tln (Ω A )[ k B V 0 B /( k B V 0 B + k A V 0 A )] , where kA and kB are kinetic constants, R is the gas constant, T the temperature in kelvin, and V0A and V0B are specific volumes. Reference saturation states of mineral A, ΩA > 1, and host mineral B, ΩB = 1, are specified at the far-field hydrostatic stress, σ0. The microscopic environment of each crystal of A is modeled by a representative volume element (RVE) consisting of a sphere of mineral A embedded in a spherical shell of mineral B. In each RVE, stress is neither uniform nor hydrostatic. The model links the local microscopic stress with the macroscopic stress in the MZ and surrounding rock. The second model refers to veins that make room for themselves by growing, not to veins that form by cementation of previously opened, or opening, cracks. If the growth of mineral A as propagating veins or as an interconnected vein network takes place by deformation and expansion of the MZ—with the deformation itself driven by the stress arising from the supersaturation-driven growth—the surrounding rock undergoes deformation and is treated as viscous. The rate of growth in vein width, w, is dw / dt =2 k A [ RTln (Ω A )− SV 0 A ]/(1+ M ) , where M = 16ηkAV0Ac2/(3b3), η is the medium viscosity, c is the vein radius, and each vein is treated as centered in a spherical RVE of radius b. S is an effective tensile stress required for vein propagation. For a vein network, in which veins surround equant polyhedra of rock of radius b, we set c = b and drop the term in S for simplicity. Veins may also widen by replacement. The ratio of vein widening by expansion to that by replacement is ( dw / dt ) expansion /( dw / dt ) replacement ={(3 b /16η)/[(3 b /16η)+ k A V 0 A ]}/[ k B V 0 B /( K B V 0 B + k A V 0 A )] . Both mechanisms of accommodation contribute equally when η = 3b/(16kBV0B); at higher viscosity, replacement is dominant. The incipient growth of a cylindrical crystal with circular cross section in a medium deforming in pure shear simulates syntectonic crystallization. Both dissolution and deformation of the host accommodate growth. In the model, the crystal tends to grow faster in the direction of maximum rate of extension. In this direction, the host mineral may either dissolve to accommodate growth, or precipitate to form a pressure shadow. Accommodation by host dissolution is greatest in the direction of maximum rate of shortening.