Junction- and graph-based realisation of geometrical and topological features of the grains and its neighbours in polycrystalline microstructures.

Comprehensive analysis of polycrystalline microstructures, at times, demands information on the size and face-class of individual grains along with its neighbours. In experimental studies, this level of grain- and neighbourhood-resolved information is less routinely available when compared to average grain-size statistics owing to the intricate features of polycrystalline microstructures, which are characterised by closed grains, shared interfaces, and definite neighbour relations. In this work, a junction based algorithm is developed that estimates these critical geometrical and topological features of grains and their neighbours by converting the grain boundary network into a navigable graph. Within this framework, the polycrystalline microstructure is reconstructed as closed loops around individual grains, permitting quantitative estimation of grain size and face-class together with a direct realisation of these geometrical and topological properties of the neighbours. The performance of the algorithm is assessed against manual estimations of grain area obtained from careful boundary tracing, and a convincing agreement is observed, with deviations remaining small for the majority of grains. The topological output is additionally validated by comparing the algorithm-predicted number of sides with manually counted face class, and the full workflow is further demonstrated on an experimentally observed alumina microstructure. A central outcome is the complete digitisation of the available grain boundary network from experimental micrographs, in a form that closely parallels the detailed descriptions usually associated with computational investigations. This enables grain- and neighbourhood-resolved analysis of experimental polycrystalline microstructures, supporting a more comprehensive characterisation than largely size-based statistics.