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Intermetallic compounds made of alkali metals and gold have intriguing electronic and structural properties that have not been extensively explored. We perform a systematic study of the phase diagram of one binary system belonging to this family, namely NaxAu1−x, using the ab initio minima hopping structural prediction method. We discover that the most stable composition is NaAu2, in agreement with available experimental data. We also confirm the crystal structures of NaAu2 and Na2Au, that were fully characterized in experiments, and identify a candidate ground-state structure for the experimental stoichiometry NaAu. Moreover, we obtain three other stoichiometries, namely Na3Au2, Na3Au and Na5Au, that could be thermodynamically stable. We do not find any evidence for the existence of the experimentally proposed composition NaAu5. Finally, we perform phonon calculations to check the dynamical stability of all reported phases and we simulate x-ray diffraction spectra for comparison with future experimental data.