  While the microscopic structure of defected solid crystalline materials has
significant impact on their physical properties, efficient and accurate
determination of a given polycrystalline microstructure remains a challenge. In
this paper we present a highly generalizable and reliable variational method to
achieve this goal for two-dimensional crystalline and quasicrystalline
materials. The method is benchmarked and optimized successfully using a variety
of large-scale systems of defected solids, including periodic structures and
quasicrystalline symmetries to quantify their microstructural characteristics,
e.g., grain size and lattice misorientation distributions. We find that many
microstructural properties show universal features independent of the
underlying symmetries.
