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supercell (left) and supercell (right). Dark large circles and light small circles represent Mo and Si atoms, respectively. Dark small circles indicate the lowest-energy positions for Al substitution. Lattice sites are marked by Arabic numerals 1–12.
vs with different : (a) 0 at. %, (b) 8.3 at. %, and (c) 16.7 at. %. The black circle and red (gray) square represent and , respectively. is the equilibrium volume of . of is set to zero.
DOS of (a) and (b) structure, respectively. From bottom to top, DOS of , 8.3 at. %, and 16.7 at. %, respectively. The peaks of reduced subbands are indicated by arrows for both structures. Insets are the enlargement of the DOS near the of both structures for . is set to zero, and represented by the vertical line.
The total energies with different occupation position of Al. The abbreviation “Num” means “the number of Al–Al pairs with distance shorter than ” and “Dis” means “the nearest distance of Al–Al pair,” respectively. In each case, the ground energy is set as zero.
The bulk modulus (Mbar) of and with different . The optical phonon frequencies of structure. Values in parenthesis are from Ref. 18.
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