Hardness in rare earth diboride systems: Ab initio full-potential study

We study in this paper the macroscopic hardness of TiB2 and TmB2 compounds and their corresponding ternary alloys Tm1−xTixB2 by calculating the mechanical properties and electronic structure of these systems. The mechanical results show that TiB2 compound is found ultra-hard compared with TmB2 and the covalent BB bonds have an enormous impact on the macroscopic hardness of these systems. These results are in excellent agreement with experiment. In addition, a large charge density was observed in the TiB2 compound comparing to that of TmB2 and of the considered alloys. For short interatomic distances BB, the hardness in Tm1−xTixB2 alloys is important.