Thermal conductivity anisotropy of EBSD-resolved rock fabrics: multiscale homogenization of texture and microstructure

SUMMARY: Thermal conductivity anisotropy influences heat flow in the crust, yet predicting it from rock fabric remains difficult because the effective conductivity of a polycrystalline rock depends not only on mineral thermal properties and crystallographic preferred orientation, but also on grain shape, phase distribution and grain-scale interactions. Here we extend an asymptotic expansion homogenization–finite element framework for polycrystals to anisotropic heat conduction in rocks. Single-crystal conductivity tensors are rotated according to measured crystallographic orientations and assigned throughout the microstructure, and 2-D electron backscatter diffraction (EBSD) maps are analysed as representative sections extruded normal to the section. The method yields both the homogenized conductivity tensor and microscale heat-flux fields for prescribed macroscopic temperature gradients. To characterize section-based anisotropy, we define a coordinate-independent in-plane measure from the extrema of directional conductivity. We apply the method to a simple natural microstructure comprising a single mica grain in a quartz matrix and to three natural phyllosilicate-rich rocks representing planar foliation, transitional crenulation cleavage and fully developed crenulation cleavage. Progressive fabric reorganization reduces in-plane anisotropy (max/min thermal conductivity) from $A_{\rm 2D}=2.77$ for planar foliation to $A_{\rm 2D}=1.22$ for fully developed crenulation cleavage. The transitional fabric remains substantially anisotropic ($A_{\rm 2D}=2.26$) despite similar diagonal tensor components because a large off-diagonal term rotates the principal conductivity directions. Comparisons with Voigt, Reuss, Voigt–Reuss–Hill and geometric-mean estimates show that classical averages capture broad trends but can misrepresent both anisotropy magnitude and principal directions when microstructures are strongly textured or spatially organized. These results demonstrate that EBSD-resolved multiscale homogenization provides a physically grounded route from rock fabric to effective thermal conductivity tensors and microscale heat-flow patterns relevant to geophysical models of anisotropic crustal heat transport.