Stability and superconductivity properties of metal substituted aluminum diborides (M0.5Al0.5B2)

doi:10.1016/j.commatsci.2018.08.005

Computational Materials Science

Volume 154, November 2018, Pages 234-242

https://doi.org/10.1016/j.commatsci.2018.08.005 Get rights and content

Abstract

The stability table and superconducting properties such as screened Coulomb potential, electron-phonon coupling and critical temperature of planar boron sheet included ternary crystalline compounds of MgB₂-type M_0.5Al_0.5B₂ (M = Li, Be, Na, Mg, K, Ca, Sc, Ti, V, Y, Zr, Nb, Mo, Tc, Ru, Hf, Ta, W, Re, and Os) have been investigated by first-principles density functional theory calculations with spin-orbit coupling. It is shown that the M = Li, Mg, Ca, Sc, Ti, V, Y, Zr, Nb, Mo, Tc, Hf, Ta, and W-substituted compounds are thermodynamically stable at the ambient conditions. Among them, Nb_0.5Al_0.5B₂ has the lowest cohesive energy while Ti_0.5Al_0.5B₂ has the lowest formation enthalpy. Except for Be_0.5Al_0.5B₂, all compounds are mechanically stable, and fourteen of them are dynamically stable also. So, a dozen of M_0.5Al_0.5B₂ (M = Li, Mg, Ca, Sc, Ti, V, Zr, Nb, Mo, Tc, Hf, and Ta) compounds are satisfying all three stability conditions. The calculated electronic properties show that all structures have metallic character and interestingly the radii of the substituted atoms correlate with surface area of regular B6 hexagons and volumes of metal-boron pyramids. All of them are hard materials, and V_0.5Al_0.5B₂ has the highest semi-empirical microhardness (27 GPa). According to the precise phonon dispersion and electron-phonon coupling calculations, T_c’s of the stable compounds are lower than that of MgB₂ (39 K), and Tc_0.5Al_0.5B₂ has higher T_c (∼7 K) than the others.

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 T_c (∼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 (T_c) [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 Mg_1−xAl_xB₂ decrease with Al doping [51], [52], [53], [54], [55], [56], [57], [58], and T_c(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 T_c 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 Mg_1−xAl_xB₂ (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 M_0.5Al_0.5B₂, a superconductor with T_c ∼ 12 K. Bianconi et al. [74] studied the superconducting properties of Mg_1−xAl_xB₂ 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 T_c amplification in Al₁₋_xMg_xB₂ from 5 K in AlMgB₄ to 39 K in MgB₂. Superconducting and structural properties of a Al₁₋_xMg_xB₂ 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 M_0.5Al_0.5B₂ (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 Mg_0.5Al_0.5B₂.

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 Mg_0.5Al_0.5B₂ is used to begin the simulations and to design the crystal structure of M_0.5Al_0.5B₂ 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 M_0.5Al_0.5B₂, 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 M_0.5Al_0.5B₂ (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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Stability and superconductivity properties of metal substituted aluminum diborides (M0.5Al0.5B2)

Abstract

Graphical abstract

Introduction

Section snippets

Computational details

Crystal structure

Conclusion

Author contribution

Acknowledgment

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Physica C

Solid State Commun.

Physica C

Physica C

J. Solid State Chem.

Physica C

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Solid State Commun.

J. Comput. Phys.

Comput. Phys. Commun.

Nature

Phys. Rev. Lett.

J. Phys. Soc. Jpn.

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B

J. Phys.: Condens. Matter

Phys. Rev. Lett.

Angew. Chem. Int. Ed.

Phys. Rev. B

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Supercond. Sci. Tech.

Supercond. Sci. Tech.

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

J. Phys. Soc. Jpn.

Phys. Rev. Lett.

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

Phys. Rev. B

Supercond. Sci. Tech.

PCCP

Phys. Rev. B

PCCP

PCCP

Phys. Rev. B

Superconductivity in Ternary Compounds II

Supercond. Sci. Tech.

Phys. Rev. Lett.

Phys. Rev. B

Science

Phys. Rev. B

Phys. Rev. B

J. Phys. Soc. Jpn.

Stability and superconductivity properties of metal substituted aluminum diborides (M_0.5Al_0.5B₂)