A correction to parallel tangent method for modelling segregation to grain boundaries and other interfaces for components of different atomic sizes

Hillert showed an elegant way to obtain the equilibrium composition of interfaces (including grain boundaries) and the equilibrium interfacial energy for binary solutions using his parallel tangent construction. However, this method is correct only for equal sizes of atoms of the components. A corrected equation is derived here from the two fundamental equations of Gibbs. Our resulting non-parallel tangent construction is less elegant, but more correct compared to the parallel tangent construction of Hillert. Our method is also extended to multi-component solid solutions. Our method is equivalent to the Butler equations, without a need to introduce partial interfacial energies. (C) 2019 Acta Materialia Inc Published by Elsevier Ltd. All rights reserved.