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Since there are still research interests in the physical properties of quasi-binary thermoelectric $${\hbox {Mg}}_{2} {\hbox {X}}_{1-x}{\hbox {Y}}_{x}$$ Mg 2 X 1 - x Y x alloys, with X, Y = Si, Ge, Sn, we present an ab initio analysis that yields the relative formation energy and effective masses of the conduction bands, in the whole compositional range x. We base our calculations on the full-relativistic Korringa, Kohn and Rostocker (KKR) Green’s functions formalism within the coherent potential approximation (CPA). Formation energies, measured relative to the end $${\hbox {Mg}}_{2} \hbox {X}$$ Mg 2 X compounds, show no excess energy for the $${\hbox {Mg}}_{2} \hbox {Si} {-} {\hbox {Mg}}_{2} \hbox {Ge}$$ Mg 2 Si - Mg 2 Ge substitution thus indicating a complete solubility. In contrast, concave and asymmetric formation energies for intermediate compositions in the $${\hbox {Mg}}_{2} \hbox {X} {-} {\hbox {Mg}}_{2} \hbox {Sn}$$ Mg 2 X - Mg 2 Sn alloys manifest a miscibility gap. With this basis, we compute and discuss the crossing of the conduction bands observed in n-type $${\hbox {Mg}}_{2} {\hbox {X}}_{1-x} {\hbox {Sn}}_x$$ Mg 2 X 1 - x Sn x materials. We present direction- and band-dependent effective masses using a generalized single parabolic band effective mass approximation to discuss anisotropic effects, to interpret available experimental and theoretical data, and to predict intermediate and not yet published transport parameters on these alloys.

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