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Motivated by a decades-long controversy related to the crystal structure of Pb-supersaturated solid solutions of Pb in Sn, we have performed a quantum-mechanical study of these materials. Focusing on both bodycentred-tetragonal β-Sn and simple-hexagonal γ-Sn structures, we have computed properties of two alloys with the chemical composition Pb5Sn11, i.e. 31.25 at. % Pb, which is close to the composition of the experimentally found alloy (30 at. % Pb). The 16-atom computational supercells were designed as multiples of the elemental β- and γ-Sn unit cells, where the Pb atoms were distributed according to the special quasi-random structure (SQS) concept. Full structural relaxations of both β- and γ-phase-based alloys resulted in very significant rearrangements into structures which do not exhibit any apparent structural features typical for the original alloys, and are, therefore, difficult to classify. The formation energies of the β- and γ-phase-originating equilibrium phases are 50 meV/atom and 53 meV/atom, respectively. Therefore, they are not stable with respect to the decomposition into the elemental lead and tin. Moreover, our calculations of elastic constants of both phases revealed that they are close to mechanical instability. Our results indicate that the studied Pb-supersaturated Pb-Sn solid solutions may be prone to structural instability, transformations into different phases and decomposition. Our findings may contribute into the identification of the reason why the subsequent experimental studies did not reproduce the initial published data.

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