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Density functional theory calculations have been used to identify stablelayered Li-$M$-B crystal structure phases derived from a recently proposedbinary metal-sandwich (MS) lithium monoboride superconductor. We show that theMS lithium monoboride gains in stability when alloyed with electron-rich metaldiborides; the resulting ordered Li$_{2(1-x)}M_x$B$_2$ ternary phases may formunder normal synthesis conditions in a wide concentration range of $x$ for anumber of group-III-V metals $M$. In an effort to pre-select compounds with thestrongest electron-phonon coupling we examine the softening of the in-planeboron phonon mode at $\Gamma$ in a large class of metal borides. Our resultsreveal interesting general trends for the frequency of the in-plane boronphonon modes as a function of the boron-boron bond length and the valence ofthe metal. One of the candidates with a promise to be an MgB$_2$-typesuperconductor, Li$_2$AlB$_4$, has been examined in more detail: according toour {\it ab initio} calculations of the phonon dispersion and theelectron-phonon coupling $\lambda$, the compound should have a criticaltemperature of $\sim4$ K.

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