  Density functional theory calculations have been performed to study the
structures and energetics of coherent and semicoherent TiC/Fe interfaces. A
systematic method for determining the interfacial energy for the semicoherent
interface with misfit dislocation network has been developed. The obtained
interfacial energies are used to calculate the aspect ratios for the disc-like
precipitates and a quantitative agreement with the experimental results is
reached. Based on the obtained interfacial energies and atomic structure
details, we propose models for describing the evolution of the interfacial
energy with respect to the size of TiC precipitate for heterogeneous nucleation
on an edge dislocation, shedding light on the thermodynamics of precipitate
nucleation and growth. The present method can be easily applied to any
heterophase interfaces between metals and oxides/carbides/nitrides.
