Structural properties, phase stability and theoretical hardness of Cr23−xMxC6 (M = Mo, W; x = 0–3)

•Stability of Cr23−xMxC6 (M = Mo, W; x = 0–3) increases when M replacing 8c site Cr.•C–M bonds between the 4a (8c) sites atoms and C atom are not found in the M23C6.•Mo/W replacing 4a site Cr will decrease the hardness of M23C6.•Debye temperature of Cr23−xMxC6 (M = Mo, W; x = 0–3) decrease with the increase of Mo/W.

The stability of Cr23−xMxC6 (M = Mo, W; x = 0–3) increases when Mo/W replaces Cr at 8c site, and decreases when replacing at 4a site. The bonds of Cr23−xMxC6 (M = Mo, W; x = 0–3) are complex mixtures of metallic, covalent and ionic characters. The replacement of Mo and W at 4a site increases the metallicity of M23C6, while the ionicity of the chemical bond is less affected in the Cr23−xMxC6 (M = Mo, W; x = 1–3). The C–M bonds between the metal atoms (Cr/Mo/W) at 4a (8c) sites and C atoms are not found in the M23C6 type crystal. Mo/W replacing 4a site Cr will decrease the hardness of M23C6, while Mo/W replacing 8c site Cr enhances the hardness of M23C6. The Debye temperature (θD) of Cr23C6 is 666 K, and that of Cr23−xMxC6 (M = Mo, W; x = 0–3) decreases with the increase of the Mo/W content.

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