Thermodynamic stabilities of ternary metal borides: An ab initio guide for synthesizing layered superconductors

Density-functional theory calculations have been used to identify stable layered Li-M-B crystal structure phases derived from a recently proposed binary metal-sandwich (MS) lithium monoboride superconductor. We show that the MS lithium monoboride gains in stability when alloyed with electron-rich metal diborides; the resulting ordered Li_{2 (1-x)} M_x B ₂ ternary phases may form under normal synthesis conditions in a wide concentration range of x for a number of group-III-V metals M. In an effort to preselect compounds with the strongest electron-phonon coupling we examine the softening of the in-plane boron phonon mode at Γ in a large class of metal borides. Our results reveal interesting general trends for the frequency of the in-plane boron phonon modes as a function of the boron-boron bond length and the valence of the metal. One of the candidates with a promise to be an MgB ₂-type superconductor, Li₂ AlB₄, has been examined in more detail: According to our ab initio calculations of the phonon dispersion and the electron-phonon coupling λ, the compound should have a critical temperature of ∼4 K.