  Segregation to grain boundaries affects their cohesion, corrosion and
embrittlement and plays a critical role in heterogeneous nucleation. In order
to quantitatively study segregation and phase separation at grain boundaries,
we derive a density-based phase-field model. In this model, we describe the
grain boundary free energy based on available bulk thermodynamic data while an
atomic grain boundary density is obtained using atomistic simulations. To
benchmark the performance of the model, we study Mn grain boundary segregation
in the Fe--Mn system. 3D simulation results are compared against atom probe
tomography measurements. We show that a continuous increase in the alloy
composition results in a discontinuous jump in the Mn grain boundary
segregation. This jump corresponds to an interfacial spinodal phase separation.
For alloy compositions above the interfacial spinodal, we found a transient
spinodal phase separation phenomenon which opens opportunities for
knowledge-based microstructure design through the chemical manipulation of
grain boundaries. The proposed density-based model provides a powerful tool to
study thermodynamics and kinetics of segregation and phase separation at grain
boundaries.
