Mean grain diameters from thin sections: matching the average to the problem

Abstract

It is common practice to estimate a mean diameter for spherical or sub-spherical particles or vesicles in a rock by multiplying the average diameter of the approximately circular cross-sections visible in thin section by a factor of 1.273. This number-weighted average may be dominatedby the hard-to-measure fine tail of the size distribution, and is unlikely to be representative of the average particle diameter of greatest interest for a wide range of geological problems or processes. Average particle size can be quantified in a variety of ways, based on the mass or surfacearea of the particles, and here we provide exact relations of these different average measures to straightforward measurements possible in thin section, including an analysis of how many particles to measure to achieve a desired level of uncertainty. The use of average particle diameter isillustrated firstly with a consideration of the accumulation of olivine phenocrysts on the floor of the 135 m thick picrodolerite/crinanite unit of the Shiant Isles Main Sill. We show that the 45 m thick crystal pile on the sill floor could have formed by crystal settling within about a year.The second geological example is provided by an analysis of the sizes of exsolved Fe-rich droplets during unmixing of a basaltic melt in a suite of experimental charges. We show that the size distribution cannot be explained by sudden nucleation, followed by either Ostwald ripening or Browniancoalescence. We deduce that a continuous process of droplet nucleation during cooling is likely to have occurred.

Crystal settling and convection in the Shiant Isles Main Sill

“…For polydisperse populations, there are different ways to quantify the average (3D) diameter, and the choice of which to use depends on the problem under consideration (Farr et al 2016). The volume-weighted mean diameter, D 4,3 (see "Appendix") represents the size around which most of the mass of the particles lies and is therefore a good measure of particle size for problems relating to composition.…”

“…For such a case, Farr et al (2016) showed that the rate of build-up of a settled layer, Ḣ , is approximated by:…”

“…For polydisperse populations, there are numerous types of moment-based (3 dimensional) average diameter, D p,q , (Farr et al 2016), where, for p ≠ q:…”

“…where n is the number of grain intersections measured (Farr et al 2016). A comparison of the volume-weighted and area-weighted mean diameters with the commonly used mean Heywood diameter is shown in Fig.…”

“…Following Farr et al (2016), the change in average diameter, δD i,j is given by: where ϕ sed is the initial volume fraction of the olivine and δϕ is the change in volume fraction due to overgrowth …”