Fragmentation phenomena in populations of magmatic crystals

Fragmentation of crystals is an important mechanism, and a component of particle dynamics in igneous and metamorphic rocks that has received surprisingly little attention. Recent advances in textural analysis, extraction techniques, digital imaging, and computer-assisted measurements enable rapid accumulation of 3D data on particle shapes and size distributions. This paper reviews fragment size distributions (FSD) that result from fragmentation: lognormal, fractal, loggamma, and Weibull; discusses their genesis mechanisms; and presents relevant examples of fragmentation from experimental physics. Next, the paper considers FSDs of feldspars on digitized images of thin sections and on published images, and quartz extracted from vesicular pumice by acid from eight well-known large-volume eruptive units. The acid solution of pumice enables examination of volume abundance, 3D shapes, proportions of fragmented crystals, and measurements of their CSDs and FSDs. FSDs were also measured in samples of welded tuff and a granite disaggregated by electric pulse. Products of syneruptive shock wave fragmentation, and fragmentation by an electric pulse are found to be fractal with large breakage probabilities, branching ratios, and fractal dimensions of 2 to 3. In contrast, most quartz fragments in pumice obey a lognormal distribution and fragmentation is driven by a melt inclusion decrepitation mechanism, which results in low breakage probability and small number (2−3) of fragments per breakage cycle. These results are consistent with one atmosphere heating experiments of quartz phenocrysts that led to melt inclusion decrepitation and caused quartz to break up into several smaller pieces collectively having lognormal FSD. Measured melt inclusion size distributions suggest decrepitation of outermost melt inclusions, and low survival rate for large inclusions, and inclusions with large radius/crystal size ratio. The modeling of periodic fragmentation of crystals with melt inclusions due to overheating and/or decompression, which may occur many times during the lifetime of a long-lived magma body, may explain concave-down, lognormal CSDs abundant in igneous rocks. The genesis of lognormality can be explained by the fragmentation algorithm of Kolmogorov (1941). Other algorithms may generate lognormal-like loggamma distributions. Fragmentation serves as an important size limiting factor, a nucleation aid, and it facilitates isotopic and trace elemental exchange. BINDEMAN: FRAGMENTATION PHENOMENA IN POPULATIONS OF MAGMATIC CRYSTALS 1802 nature and in crystallization experiments (e.g., Marsh 1998), but no fragment size distribution, or FSDs, have been discussed. This paper deals with particle size distribution and emphasizes the importance of breakage due to melt inclusion decrepitation in magma chambers. The study pursues several goals: (1) to describe relevant statistical distributions — lognormal, Weibull, loggamma, and fractal (power-law) — that most commonly result from geological fragmentation; (2) to review recent treatments of fragmentation processes in experimental physics that are relevant for petrology; (3) to consider FSDs measured in pumice and pyroclastic rocks; (4) to compare the natural FSD with experimental and numerical FSDs due to melt inclusion decrepitation; and (5) to argue that melt inclusion decrepitation is the leading cause of fragmentation in magma bodies that yields frequently observed lognormal FSDs and CSDs. Particle size distributions Fragmentation processes result in several types of size (mass)–frequency distributions, the most relevant are lognormal, fractal, loggamma, and Weibull distributions (see Appendix 1). These distributions are compared on Figure 1. Tests of statistical validity of Þ t (“goodness of Þ t”) are abundant in the literature, and the reader is referred to monographs by Crow and Shimizu (1988), Aitchison and Brown (1957), and spreadsheets of Eberl et al. (2001) and K.Wohletz (http://internet.cybermesa.com/ ~wohletz/KWare/KWare.htm). Distribution genesis laws Lognormal distributions, which were popular for the Þ rst half of the last century (Ahrens 1954) can be generated by the law of proportional effects (Kapteyn and van Uven 1903), which states that the variation of a parameter X (e.g., linear size or volume of a crystal) is proportional to its previous state: