Characterizing magnesium–silicon binaries in Al–Mg–Si supersaturated solid solution by first-principles calculations

AbstractMagnesium silicide Mg2Si is a well-studied binary of Mg and Si due to its potential technological applications like infrared photonic and thermoelectric. In many experimental scenarios, e.g., in supersaturated solid solution of Al–Mg–Si, some other Mg-Si binaries, e.g., Mg9Si5 and Mg5Si6, co-exist with Mg2Si. It was then computationally found that Mg9Si5 and Mg5Si6 are thermodynamically favorable under some non-zero pressures. Other than this, very little is known about these two new binaries. This paper aims to unveil some structural, electronic, and vibrational properties of Mg9Si5 and Mg5Si6, providing some information that may be useful for further possible investigations on the Al–Mg–Si solid solution

Cohen-Macaulay oriented graphs with large girth

We classify the Cohen-Macaulay weighted oriented graphs whose underlying graphs have girth at least $5$.Comment: We correct typos in Lemma 2.