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 polynuclear growth and spiral growth, where dr/dt is the rate, r is the radius of the crystal, and k is some constant, (2) dr/dt = kr for mononuclear growth, and (3) dr/dt = k/r for diffusion-limited growth. Empirical results in this study, where r = detrital grain radius and dr/dt = quartz overgrowth thickness, define another crystal growth mechanism, size-dependent growth described by the rate equation dr/dt = kr.
Grain radii and quartz overgrowth thicknesses were measured in 16 thin sections of quartz arenite from the Galesville Sandstone (Cambrian, Wisconsin, U.S.A.) and plotted to determine correlation coefficients between radius and rate. Correlation coefficients ranged from 0.145 to 0.855. Ten of 16 samples show statistically significant correlations between detrital grain radii 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 thicknesses cannot be measured precisely enough to detect small variations.
Size-dependent growth (dr/dt = kr) is a new type of mineral-water interaction that has also been observed in ancient dolomites as well as metamorphic garnets and other various minerals grown in the laboratory and now in quartz-cemented sandstone. This indicates that crystal growth theory may not include some significant growth mechanisms.