Using ab initio calculations, we have studied the structural, elastic and electronic properties of XNCa3, with X = Ge, Sn and Pb. Geometrical optimization of the unit cell are in agreement with the available experimental data. The band structures show that all studied materials are electrical conductors. The analysis of the site and momentum projected densities, charge transfer and total valence charge density shows that the chemical bonding in XNCa3 compounds is of covalent-ionic nature with the presence of metallic character. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk, shear and Young's moduli for ideal polycrystalline XNCa3 aggregates. By analysing the ratio between the bulk and shear moduli, we conclude that: XNCa3 compounds are brittle in nature. We estimated the Debye temperature of XNCa3 from the average sound velocity.
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