First principles study on stability of base and precious metals pentlandite-like compounds

First principles method was used to investigate the phase stability of the platinum group elements (PGEs) precious metal sulphides, M 9 S 8 (M = Ru, Pd, Os, Ir, Rh, Pt), (Ru,Pd) 9 S 8 and (Os,Pt) 9 S 8 , in pentlandite-like structure from thermodynamic, electronic, mechanical and vibrational stability conditions. The heats of formation of binary systems predicted a decreasing stability: Os 9 S 8 > Ru 9 S 8 > Ir 9 S 8 > Rh 9 S 8 > Pt 9 S 8 > Pd 9 S 8 . For the ternary systems, the stability decreased in the order: Os 5 Pt 4 S 8 > Os 4 Pt 5 S 8 > Ru 5 Pd 4 S 8 > Ru 4 Pd 5 S 8 . The average number of electrons per atom ( e/a ) = 7.58, depicted stability for Rh 9 S 8 , Ir 9 S 8 , (Ru,Pd) 9 S 8 and (Os,Pt) 9 S 8 . The Rh 9 S 8 , Ir 9 S 8 , Pd 9 S 8 and Os 9 S 8 were mechanically and vibrational stable, whereas Pt 9 S 8 and Ru 9 S 8 were unstable. All ternary systems were mechanically stable except for Ru 4 Pd 5 S 8 due to C11