Investigation of out-of-plane ordered Ti₄MoSiB₂from first principles

The laminated ternary boride Mo₅SiB₂of T2 structure have two symmetrically inequivalent metallic sites, 16l and 4c, being occupied in a 4:1 ratio. The phase was recently shown to be stable for 80% substitution of Mo for Ti, at the majority site, forming an out-of-plane chemically ordered quaternary boride: Ti₄MoSiB₂. Considering that the hypothetical Ti₅SiB₂is theoretically predicted as not stable, a key difference in bonding characteristics is indicated for full substitution of Mo for Ti at the metallic sites. To explore the origin of formation of Ti₄MoSiB₂, we here investigate the electronic properties and bonding characteristics of Mo₅SiB₂, Ti₄MoSiB₂and Ti₅SiB₂through their density of states, projected crystal orbital Hamilton population (pCOHP), Bader charge partitioning and second order force constants. The bond between the two different metallic sites is found to be key to the stability of the compounds, evident from the pCOHP of this bond showing a peak of bonding states close to the Fermi level, which is completely filled in Mo₅SiB₂and Ti₄MoSiB₂, while only partially filled in Ti₅SiB₂. Furthermore, the lower electronegativity of Ti compared to Mo results in charge accumulation at the Si and B sites, which coincides with a reduced bond strength in Ti₅SiB₂compared to Mo₅SiB₂and Ti₄MoSiB₂. Bandstructure calculations show that all three structures are metallic. The calculated mechanical and elastic properties show reduced bulk (B) and elastic (E) moduli when introducing Ti in Mo₅SiB₂, from 279 and 365 GPa to 176 and 258 GPa, respectively. The Pugh criteria indicates also a slight reduction in ductility, with aG/Bratio increasing from 0.51 to 0.59.