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Controlling the nucleation of graphite during solidification of spheroidal and lamellar graphite irons is achieved through minor additions of certain active elements such as Mg, Ca, Sr, Ba and Mn. In the present work, interfaces of graphite with alkaline earth oxides, sulfides and MnS are investigated by density functional simulations of model structures where interfacial strain has been optimized by controlling the twisting angle between the two materials. The bulk stabilities, surface energies and interfacial energies between the nucleant phases, graphite and iron are calculated. A new graphite nucleation model for estimating undercooling based on interfacial energies is proposed. It is found that CaS is the most potent nucleant particle in spheroidal graphite iron and MnS in lamellar graphite iron. The main driver of nucleation potency is found to be of chemical nature rather than related to lattice misfit. [Display omitted] [ABSTRACT FROM AUTHOR]