Igneous microstructures from kinetic models of crystallization

Abstract

During crystallization, a variety of competing kinetic processes determine the evolution of the igneous microstructure, yet, the relative contribution of each process remains elusive. To this end, a stochastic algorithm is developed to yield a detailed spatial representation of the igneous microstructure during progressive crystallization. This algorithm is used to test a variety of kinetic models for nucleation and crystal growth that yield realistic igneous microstructures. The algorithm itself relies on a theoretical model of crystallization (the Avrami method) and can therefore be internally validated in addition to being verified against natural microstructures using crystal size distributions (CSDs). The most realistic simulated igneous microstructure, in which the CSDs remain approximately log-linear throughout the crystallization interval, is produced using a kinetic model involving exponential nucleation rate and constant growth rate. An extension of the algorithm is used to simulate multiply saturated mineral growth, emulating basalt crystallization through simultaneous nucleation and growth of plagioclase and clinopyroxene. A fundamentally important feature of this procedure is the numerical production of detailed 3D representations of the microstructure that can be interrogated to study many physical and chemical processes. For example, the critical crystallinity necessary for the onset of a finite yield strength and the interstitial melt flow within the igneous microstructure depend on the percolation of the solid and melt phases, respectively. Bounds on the percolation thresholds, the critical crystallinity at which the phase of interest is connected or contiguous such that it extends across the full microstructure from one face to the opposite face, are determined for the simulated igneous microstructure and are comparable with previously published results for the percolation threshold of both the melt phase and solid network. The simulated igneous microstructure can also be used as input into other physical models to ascertain the physical properties of partially molten magmas that are otherwise difficult to estimate by experiment. In a real sense, these computed microstructures are equivalent to 3D microtomographic images of partially molten basalt within a solidification front.

Introduction

The extreme variability of natural igneous microstructures in terms of crystal size, shape, number, and position is due to the interplay of competing kinetic processes operating during crystallization (e.g. nucleation, growth, aggregation, and grain boundary annealing). It has proven challenging to decipher the contribution of each kinetic process to the final microstructure, including the role of the intensive parameters (e.g. temperature, time) governing crystallization. Present knowledge of the crystallization kinetics of solidifying magmas is mainly limited to relatively short duration melting experiments that are most applicable to rapidly cooled magmas (i.e., lavas) and not coarse-grained, slowly cooled igneous rocks that record a fuller and more dynamic history of magmatic activity. To augment empirical results, some of which have been available from the late 1700s (e.g. Hall, 1798), a theory of crystallization kinetics was adapted from classical kinetic theory (e.g. Kirkpatrick, 1981), but this has proven too broad based to be of immediate practical use in predicting the styles of igneous microstructures. That is, this atomic scale theory is inherently incomplete for silicate melts and, in the light of sparse kinetic information from actual magmatic systems, is exceedingly awkward for direct application as a forward model of microstructural development.

An alternative approach is to view igneous microstructural development as a grain-scale process with fundamental rules describing the transient appearance and morphological evolution of crystals, which is consistent with but does not resolve atomic scale processes of diffusion and bonding during crystallization. This rule-based kinetic model of crystallization relies on long established general observations from crystallization experiments, from post-mortem studies of solidified magmas, and the results of both crystal size distribution (CSD) theory and CSD measurements on rocks. The thrust of the present work is to demonstrate that a stochastic numerical algorithm for forward modeling of igneous microstructural development can be used to delineate the relative contributions of individual kinetic processes in forming realistic igneous microstructures using various kinetic models of crystallization.

In brief, a 3D space of melt containing randomly orientated and randomly positioned crystals is represented by an ensemble of discrete volumetric elements; changes in time, and increasing crystallinity, are achieved by discrete temporal steps. In assuming that cooling and crystallization can be decoupled, as discussed below, the design of the algorithm is greatly simplified and crystallinity can be expressed solely as a function of time. Functions describing the change of crystallinity with time are derived using the Avrami method by employing any number of exponential variations (including constant) in functions describing the rates of nucleation and crystal growth (Marsh, 1998). An investigation of the sensitivity of the algorithm to variations in the input parameters precedes the evaluation of the microstructures generated by the various kinetic models. Three basic kinetic models are investigated: constant rates of nucleation and growth, exponential nucleation rate with constant growth rate, and exponential nucleation rate with crystal-dependent dispersive, but individually constant, growth rate. An extension of the algorithm is also demonstrated by modeling multiply saturated mineral growth, which simulates basalt crystallization involving simultaneous plagioclase and clinopyroxene nucleation and growth. Aside from understanding the kinetics of crystallization, the computed microstructures are invaluable as 3D samples of test materials necessary for input into models developed to obtain macro-scale physical properties under conditions unobtainable by experiment. Failure behavior, elastic moduli, permeability, and grain-scale melt flow patterns including flow channelization are critical for continuum scale models of magmatic processes and can, thus, be determined throughout the melting interval over a wide range of pressure.