Crystal growth mechanisms of quartz overgrowths in a Cambrian quartz arenite

Mechanisms of crystal growth during quartz cementation can be investigated by determining the relationship between growth increments and crystal radii . Crystal growth is theoretically described as (1) dr/dt = k for polynuclea r growth and spiral growth, where drl dt is the rate, r is the radius of th e crystal, and k is some constant, (2) dr/dt = kr(2) for mononuclear growth , and (3) dr/dt = k/r for diffusion-limited growth. Empirical results in th is study, where r = detrital grain radius and dr/dt = quartz overgrowth thi ckness, define another crystal growth mechanism, size-dependent growth desc ribed by the rate equation dr/dt = kr. Grain radii and quartz overgrowth thicknesses were measured in 16 thin sect ions of quartz arenite from the Galesville Sandstone (Cambrian, Wisconsin, U.S.A.) and plotted to determine correlation coefficients between radius an d rate. Correlation coefficients ranged from 0.145 to 0.855. Ten of 16 samp les show statistically significant correlations between detrital grain radi i and overgrowth thicknesses representing dr/dt = kr. Standard deviations ( sorting) of detrital grain size correlate with the correlation coefficient between radius and rate. Samples indicating no correlation may in fact grow by dr/dt = kr, but for smaller grain size ranges the overgrowth thicknesse s cannot be measured precisely enough to detect small variations. Size-dependent growth (dr/dt = kr) is a new type of mineral-water interacti on that has also been observed in ancient dolomites as well as metamorphic garnets and other various minerals grown in the laboratory and now in quart z-cemented sandstone. This indicates that crystal growth theory may not inc lude some significant growth mechanisms.