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Park et al. J Mater Inf 2023;3:5 https://dx.doi.org/10.20517/jmi.2022.37 Page 13 of 25

The Δg may be expanded in terms of pair fractions:
FeSn

where , and are the model parameters that can be functions of temperature.

The equilibrium pair distribution is determined by setting

which leads to the equilibrium constant for the pair formation in Reaction (1):

The composition of maximum SRO is defined by the ratio of the coordination numbers Z /Z , as given in
Sn
Fe
the following equations:

where and are the values of Z when all neighbors of Fe are Fes and when all nearest neighbors of
Fe
Fe are Sns, respectively, and where and are defined similarly. and represent the same
quantity and are interchangeable. The coordination numbers and were set to 6 , whereas the
[61]
ratio of Z /Z was set to 1 with = = 6 in the present study.
Sn
Fe
Solid solutions and stoichiometric compounds
Bcc and fcc solid solutions were modeled using the Compound Energy Formalism (CEF) with two
[23]
sublattices. Fe and Sn are located on the substitutional sites, while vacancy (Va) occupies the interstitial
sites. If all the sites in all but one of the sublattices are vacant, the CEF reduces to the BW random mixing
model . Note that the vacancy sublattice is only considered to incorporate the present descriptions into a
[23]
multicomponent steel database. The Gibbs energy for fcc and bcc is therefore defined by

where X and are the mole fraction and the molar Gibbs energy of component i. represent the
i
adjustable model parameters which can be a function of temperature. is the contribution due to
magnetic ordering. Its expression per mole of atoms was proposed by Hillert and Jarl :
[64]