Title: Particle pinning during grain growth -- A new analytical model for predicting the mean limiting grain size but also grain size heterogeneity in a 2D polycrystalline context

Abstract: This study proposes a new analytical model for grain boundary pinning by second phase particles in two-dimensional polycrystals. This approach not only considers how particles impede grain growth, but also elucidates their role in preventing grain disappearance, thereby leading to stabilised microstructures characterised by heterogeneous grain size distribution comprising a mixture of small and large grains. By quantifying the number of particles intercepted by grain boundaries during grain growth or shrinkage, we are able to calculate the respective sizes and fractions of large and small grains. Furthermore, we identify ranges of particle surface fractions and particle sizes that maximise the heterogeneity in grain size. Additionally, we demonstrate the significant influence of initial grain size on the limiting grain size in pinned microstructures. Our analytical model's results are compared with those obtained from full-field level-set simulations conducted in this study and from phase-field calculations reported in the literature, revealing very good agreement. Finally, the differences between the proposed model and existing ones in the literature are discussed.