Grain area as a statistical weight for polycrystal constituents

By using recently developed automatic instruments for fabric and texture measurements on ice, both the c-axis orientation and area of the individual crystals can be determined. Each grain can then be associated with its volume fraction, defined as a function of its measured cross-sectional area, to describe the microstructure of a polycrystal. The relevance of this approach is studied using a three-dimensional microstructure obtained from the Potts model. In particular, the area weighting is compared to the classical implicit equal weighting used by glaciologists, which assumes that all the grains have the same volume fraction (discrete uniform distribution). Then, using the measurements of c-axis orientation and crystal size performed on the North Greenland Icecore Project (NorthGRIP) ice core, we compare area-weighted and equal-weighted fabrics. All these comparisons are made with respect to the orientation tensor. According to the ability of the Potts model to reproduce the ice microstructure, it is shown that using the grain cross-sectional area to infer its volume fraction improves the description of the actual polycrystal fabric.