Boron vacancy-driven thermodynamic stabilization and improved mechanical properties of AlB₂-type tantalum diborides as revealed by first-principles calculations

Abstract

Thermodynamic stability as well as structural, electronic, and elastic properties of boron-deficient AlB$_{2}$-type tantalum diborides, which is designated as $\alpha$$-$TaB$_{2-x}$, due to the presence of vacancies at its boron sublattice are studied $via$ first-principles calculations. The results reveal that $\alpha$$-$TaB$_{2-x}$, where 0.167 $\lesssim$ $x$ $\lesssim$ 0.25, is thermodynamically stable even at absolute zero. On the other hand, the shear and Young's moduli as well as the hardness of stable $\alpha$$-$TaB$_{2-x}$ are predicted to be superior as compared to those of $\alpha$$-$TaB$_{2}$. The changes in the relative stability and also the elastic properties of $\alpha$$-$TaB$_{2-x}$ with respect to those of $\alpha$$-$TaB$_{2}$ can be explained by the competitive effect between the decrease in the number of electrons filling in the antibonding states of $\alpha$$-$TaB$_{2}$ and the increase in the number of broken bonds around the vacancies, both induced by the increase in the concentration of boron vacancies. A good agreement between our calculated lattice parameters, elastic moduli and hardness of $\alpha$$-$TaB$_{2-x}$ and the experimentally measured data of as-synthesized AlB$_{2}$-type tantalum diborides with the claimed composition of TaB$_{\thicksim2}$, available in the literature, suggests that, instead of being a line compound with a stoichiometric composition of TaB$_{2}$, AlB$_{2}$-type tantalum diboride is readily boron-deficient, and its stable composition in equilibrium may be ranging at least from TaB$_{\thicksim1.833}$ to TaB$_{\thicksim1.75}$. Furthermore, the substitution of vacancies for boron atoms in $\alpha$$-$TaB$_{2}$ is responsible for destabilization of WB$_{2}$-type tantalum diboride and orthorhombic Ta$_{2}$B$_{3}$, predicted in the previous theoretical studies to be thermodynamically stable in the Ta$-$B system, and it thus enables the interpretation of why the two compounds have never been realized in actual experiments.

First-principles demonstration of band filling-induced significant improvement in thermodynamic stability and mechanical properties of Sc$$_{1-x}$$Ta$$_{x}$$B$$_{2}$$ solid solutions

“…As demonstrated and discussed in the theoretical works on metal diborides, previously published in the literature 12 , 14 – 16 , 18 , 19 , 38 , the negative values of for both ordered and disordered Sc Ta B solid solutions, indicating their thermodynamic stability relative to ScB and TaB , can be directly explained by the changes in the number of electrons filling bonding and antibonding states of Sc Ta B . Due to the interactions between metal atoms arranging themselves in the simple hexagonal geometry 2 , as in the case of metal diborides, the electronic density of states of the diborides displays a valley-like feature, frequently separating the bonding states from the antibonding states, around the Fermi level 14 , 15 , 18 , 38 – 40 .…”

“…S1 , the −COHP bonding analysis for ScB clearly show non-zero bonding states at the Fermi level. On the other hand, the electronic density of states of TaB apparently reveal that the valley lies below the Fermi level 15 , 18 , 19 , 39 , 42 . This indicates that, for TaB , not only the bonding states of the material are fully occupied, but some of its antibonding states resulting particularly from the interactions between the 5 d orbitals of Ta atoms and the 2 p orbitals of B atoms are also filled by electrons 39 , 43 , see also Fig.…”

“…The two effects arising from the formation of vacancies on the boron sublattice of TaB counterbalance and eventually result in stabilization of B-deficient TaB over a small range of x (0.167 x 0.25) in thermodynamic equilibrium. Besides, the shear strength, stiffness, hardness of thermodynamically stable TaB are superior to those of TaB 18 , 19 . Hypothetically, replacing some Ta atoms of TaB by any group-III or group-IV metallic element (Sc, Y, Ti, Zr, or Hf) to form solid solutions of Ta-containing double-metal diboride should as well yield a decrease in the number of electron occupying the antibonding states of the material without a need for forming the vacancies, and thus give rise to the aforementioned band filling-induced enhancement of thermodynamic stability and mechanical properties of the solid solutions with respect to their constituent compounds, as theoretically predicted for Sc V B solid solutions.…”

“…Apart from the double-metal diborides, such a band-filling scenario has theoretically been found to play a crucial role in determining the thermodynamic stability and mechanical properties of some single-metal diborides − for example, AlB 17 and TaB 18 , 19 . In the case of TaB , the effect of band filling can be triggered by partial substitution of vacancies for B atoms in the diboride.…”

Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling

“…Nevertheless, both the and the mode of exhibit relatively high values. In many cases, the formation energy of synthesized compounds is reported to be above the convex hull less than 36 meV/atom 41 – 43 . To obviate the need for time-consuming DFT relaxation, it is essential for the generated structures to be even closer to the ground state.…”