Be-B/B-Ta based compounds are very attractive to researchers because of their high density and ultra-hardness. But ternary Be-B-Ta compounds are neither synthesized nor predicted. In this paper, variable composition evolutionary crystal structure prediction calculations based on firstprinciples method have been performed to find the stable crystal structure containing Be-B-Ta at ambient condition. The predicted five compounds BeB2Ta, BeB3Ta2 (high-pressure phase), BeBTa, BeBTa2, and Be2B2Ta have been found to be highly dense and very hard materials. All these compounds are metallic and spin-orbit coupling (SOC) effect is significant in them. Only two of them (BeB2Ta and Be2B2Ta) have been found to be superconductors within Migdal-Eliashberg theory. The calculated critical temperature including SOC effect is 8 and 9 K for BeB2Ta and Be2B2Ta, respectively. Because of their energetic and dynamic stability, these compounds might be favorable to synthesize in the laboratory.
IntroductionBeryllium (Be) and boron (B) are light elements with different electronic structures, first one is the metal and the second one is the semiconductor, while tantalum is the electron-rich transition metal. Beryllium has applications in X-ray equipment 1 , as effective moderators and reflectors for neutrons 2 , aircraft, rockets, etc. 3,4 . The use of a glove box is very effective way to synthesize industrially beryllium-containing compounds 5 . Different phases are possible by the combination of Be and B, such as Be2B 6 , Be4B 7 , and boron-rich compounds BeB2 8-12 and BeB4 (high-pressure phase) 10 . Usually, covalent-bond forming element based compounds show high hardness, for example, BeB2 (Cmcm) 9 , diamond 13 , c-BN 14 , and BC2N 15 . The diamond, c-BN, and BC2N would be synthesized at high pressure and high-temperature condition 16 . On the other way, light element combined with electron-rich transition metal-based materials show also high hardness 17-21 , such as ReB2 22 , IrN2 23 , RuO2 24 , WB4 25 , MnB4 and CrB4 26 . This method is very effective to design superhard materials. The different phases of tantalum borides (TaB, TaB2, Ta3B4) have been synthesized at ambient pressure 27 . It has been found that TaB and TaB2 have high hardness (~30 GPa) 27-29 . The theoretically calculated Vickers hardness of TaB is 28.6 GPa 30 . Thus, transition metal rich borides show good mechanical behavior for practical applications.Boron-rich BeB2 and MgB2 shows superconductivity, although the first one has very low transition temperature (0.72 K) 8 , the second one has the highest transition temperature (39 K) among simple binary structure 31 . In MgB2, σ-band electrons strongly bonded with in-plane phonons to induce a high superconducting transition temperature. Boron-rich transition metal boride TaB2 might show superconductivity with a critical temperature of 9.5 K 32,33 , although others reported the absence of superconductivity 34,35 . The strong hybridization between Ta 5d and B 2p orbitals outside the hexagonal basis plane might be responsi...