Stability and superconductivity properties of metal substituted aluminum diborides (M0.5Al0.5B2)
Graphical abstract
Introduction
Due to the exclusive property of superconductivity character [1], [2], [3], [4], [5], [6], [7], [8], the structures with stacking layers are recently becoming interest [9], [10], [11], [12], [13], [14], [15], [16], [17]. One of well-known extraordinary layered structure is MgB2 [1], and its unexpectedly high superconductivity Tc (∼39 K) stimulated the extensive searches on understanding how these kinds of materials behave structurally and electronically [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. Recent observations and calculations showed that boron-based ternary alkali, alkaline-earth and transition metal borides in the form of honeycomb network systems confident the researchers for increasing critical temperature (Tc) [1], [9], [10], [28], [29], [30], [31]. However, to develop the superconductivity of binary, ternary, quaternary borides and borocarbides, the impressive results have been recently reported by experiment and theory [28], [29], [32], [33], [34], [35]. For instance, it was shown that hole doping to LiBC, which is a layered semiconductor structure, leads to superconductivity character [16], [29], [33], [35], [36], [37]. Moreover, numerous elemental boron allotropes [26], [38], [39] may gain superconductivity character by compressing [34], [40]. And also, a number of honeycomb network systems of metal borides are improving the superconducting characters with doping of 1A group elements such as lithium, sodium, potassium, etc. [8], [27], [41], [42], [43], [44], [45], [46].
However, using the knowledge of being the boron p-electrons were dominant at near the Fermi energy in the electronic structure of MgB2, Slusky et al. [47] shown that the addition of electrons to the MgB2 with partial substation of Al for Mg loss the superconductivity. Also, recent experiments and calculated Eliashberg functions showed that it depends very sensitively on concentrations of Al and C [12], [48], [49], [50]. It has been primarily observed that the superconductivity in Mg1−xAlxB2 decrease with Al doping [51], [52], [53], [54], [55], [56], [57], [58], and Tc(x) fall with increasing Al concentration x and diminish for x > 0.5 [59], [60], [61]. On the other hand, it was shown that electron-phonon coupling in MgB2 and the strong covalent nature of the σ bands lead the interaction of the bond-stretching modes [23], [62], [63], [64], [65], [66], and phonon anomalies can be used to predict superconducting Tc for AlB2-type structures [67], [68], [69]. In this concept, the structural, electronic band structure, and full phonon dispersion properties were analyzed for the phases of Mg1−xAlxB2 (in the range of 0 < x < 1) within the framework of density-functional theory using the self-consistent virtual-crystal approximation [48], [49], [70], [71]. Moreover, with the Raman [72] and EPR [73] study, it was shown that the optimal composition of the superstructure phase is M0.5Al0.5B2, a superconductor with Tc ∼ 12 K. Bianconi et al. [74] studied the superconducting properties of Mg1−xAlxB2 and it was pointed out that by changing the Al/Mg, the boron σ bands cross Fermi surface and they have also indicated the origin of Tc amplification in Al1−xMgxB2 from 5 K in AlMgB4 to 39 K in MgB2. Superconducting and structural properties of a Al1−xMgxB2 series were studied systematically and superconducting gaps variation as a function of Al substance investigated experimentally [69], [75], [76], [77], [78], [79], [80], [81], and superconducting phenomena described within a multiband version into intraband and interband contributions [82], [83], [84], [85].
In this study, the structural, mechanical and superconducting properties of MgB2-type ternary M0.5Al0.5B2 (M = Li, Be, Na, Mg, K, Ca, Sc, Ti, V, Y, Zr, Nb, Mo, Tc, Ru, Hf, Ta, W, Re, and Os) compounds are systematically studied by using first-principles of density functional theory with and without spin-orbit coupling. Detailed stability analysis which includes thermodynamic, mechanic and dynamic properties is presented. Possible correlations are inquired between the calculated results and the available literature such as atomic size, data of MgB2 and Mg0.5Al0.5B2.
Section snippets
Computational details
The first-principles plane-wave pseudopotential calculations are performed by using CASTEP (CAmbridge Serial Total Energy Package) [86]. In the calculations, atomic coordinates and unit cell parameters are fully relaxed with BFGS (Broyden, Fletcher, Goldfarb, Shanno) scheme [87]. The Vanderbilt ultrasoft (USPP) [88] and norm-conserving (NCPP) pseudopotentials [89] are used to model the ion-electron interactions, and exchange-correlation effects are treated within the generalized gradient
Crystal structure
In this study, the X-ray powder diffraction data [54] for Mg0.5Al0.5B2 is used to begin the simulations and to design the crystal structure of M0.5Al0.5B2 compounds. The crystal structure resembles AlB2-type (or MgB2) hexagonal structure of P6/mmm space group (see Fig. 1(a)). The unit cell contains one formula unit of M0.5Al0.5B2, and the structure includes parallel boron layers which form of interconnected six-member regular honey-comb boron hexagons intercalated with aluminum and other metal
Conclusion
In conclusion, the stability characteristics and superconductivity properties of M0.5Al0.5B2 (M = Li, Be, Na, Mg, K, Ca, Sc, Ti, V, Y, Zr, Nb, Mo, Tc, Ru, Hf, Ta, W, Re, and Os) compounds have been studied by first-principles density functional calculations. With the thermodynamic, mechanic and dynamic stability analysis, it is concluded that M = Li, Mg, Ca, Sc, Ti, V, Zr, Nb, Mo, Tc, Hf, and Ta-substituted compounds are stable. In all structures, the actual binding properties consist of the
Author contribution
All authors contribute equally in all processes of the work.
Acknowledgment
All first-principles calculations were performed by high-performance computing center (HPCC) at Gazi University. Also, the some numerical calculations including superconducting properties with spin-orbit coupling (SOC) reported in this paper were partially performed at TUBITAK ULAKBIM, High Performance and Grid Computing Center (TRUBA resources).
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