Influence of boron vacancies on phase stability, bonding and structure of MB₂ (M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) with AlB₂ type structure.
TL;DR: Trends are identified showing that MB2 with M from group V and IV are stabilized when introducing B-vacancies, consistent with a decrease in the number of states at the Fermi level and by strengthening of the B-M interaction.
Abstract: Transition metal diborides in hexagonal AlB2 type structure typically form stable MB2 phases for group IV elements (M = Ti, Zr, Hf). For group V (M = V, Nb, Ta) and group VI (M = Cr, Mo, W) the sta ...
Summary (2 min read)
- Transition metal borides exhibit an interesting combination of properties such as high hardness, low wear rate and excellent electrical conductivity, making them suitable for various thin film applications.
- This structure can be described as close- packed layers of the metal separated by planar layers of boron.
- The stability of the AlB2 structure is dependent on the transition metal M. Typically, the group IV elements (Ti, Zr, Hf) form stable MB2 phases with a limited homogeneity range.
- Going to group V (V, Nb, Ta) and group VI (Cr, Mo, W), the stability of the hexagonal MB2 is reduced, and an alternative rhombohedral MB2 structure (R3̅m) with a puckered boron layer becomes more stable for transition metals in group VII and VIII.
- For the group V and VI elements, antibonding states are also filled, leading to a reduced stability of the structure.
2. Computational details
- B-vacancies in MB2 are modeled with the special quasi-random structure (SQS) method  to mimic an ideal random alloys of B-vacancies on the B-sites.
- These are defined in Table II along with enumerated B atoms in Fig. 1(b).
- Structures with disordered vacancies do break an initially assigned hexagonal crystal symmetry, though after complete relaxation there is no significant deviation from such complete symmetry.
- Using this method the calculated band-structure energy is reconstructed into orbital interactions.
3. Results and discussion
- 1. Stability of MB2 with boron vacancies For M = Ta, Cr, Mo, W, the rhombohedral MoB2 or hexagonal WB2 type structures are identified as a most competing phase.
- Common for energetically preferred ordered configurations for MB2-x with M from group IV are nearest neighbor vacancy pairs within the B-layer, see e.g. (1, 2) and (1,2,7,8) in Table II and Fig. 1(b), whereas group V and VI show tendencies of B-vacancy formation in separate B-layers, see e.g. (1, 9) in Table II and Fig. 1(b).
- For some configurations ∆𝐻cp order < ∆𝐺cp indicating tendency for ordered B-vacancies even at increase temperatures.
3.3. Electronic structure analysis
- The behavior within each group show similar trends with increasing B-vacancy concentration where MB2-x in group IV are destabilized, i.e., TiB2, ZrB2, and HfB2 are all line compounds, whereas MB2-x with M from group V and VI show tendency for becoming stabilized with vacancy formation.
- The site projected and total density of states (PDOS and DOS) of MB2 are shown in Fig. 7, where the vertical line indicates the Fermi level Ef.
- From the DOS curves in panel (a) and (b), it is clear that TiB2 and ZrB2 have close resemblance.
- Mind that the vacancies are distributed in a disordered manner.
- For NbB2 and MoB2 the overall shape of the DOS is close to unchanged upon introductions of B-vacancies and Ef is moved towards the minimum of the pseudo gap, with a decrease in N(Ef) with increasing x as seen in Fig. 8(e).
3.4. Bonding analysis
- In order to examine the nearest-neighbor interactions of B-B, M-B, and M-M bonds, with their respective distance being shown in Fig. 5, the projected crystal orbital Hamiltonian population curves were generated for MB2 and MB1.75 (x = 0.25).
- In order to facilitate interpretation and to preserve the analogy to crystal orbital overlap population (COOP) analysis, results are here presented as –COHP, rather than COHP.
- When B-vacancies are introduced in ZrB2, antibonding orbitals becomes filled just below the Ef for the B-B interaction, resulting in a weakened bond with an average ICOHP = -3.94 eV/bond.
- For MoB1.75 the B-B and Mo-Mo interactions are weakened, ICOHP = -3.70 and -0.92 eV/atom, with introduction of antibonding orbitals close to Ef for the latter and corresponding increase of their bond lengths as seen Fig. 5(d).
- In conclusion, the phase stability, structural parameters, electronic structure, and bonding characteristics of MB2 (M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) upon B-vacancy formation have been investigated.
- NbB2, TaB2, CrB2, MoB2, and WB2 are found to be stabilized when forming B-vacancies, which can be correlated to a decrease in the number of states at the Fermi level and by strengthening of the B-M interaction.
- This might explain why the bulk modulus for group VI is constant or increases with increasing B-vacancy concentration.
- For TiB2, ZrB2, and HfB2 the introduction of B-vacancies have a destabilizing effect at least in part explained by the introduction of filled antibonding orbitals for the B-B interactions close to the Fermi level and an increase in states at the Fermi level.
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Q1. What are the contributions mentioned in the paper "Influence of boron vacancies on phase stability, bonding and structure of mb2 (m = ti, zr, hf, v, nb, ta, cr, mo, w) with alb2 type structure" ?
In this paper, the authors investigated the effect of vacancies on the structure of borides for the early transition metals and found that the stability of the boride structure is dependent on the transition metal M.