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It is generally difficult to quantify the amounts of light elements inmaterials because of their low X-ray-scattering power, as this means that theycannot be easily estimated via X-ray analyses. Meanwhile, the recently reportedlayered superconductor, Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$, requires a smallamount of boron, which is a light element, for its structural stability. Inthis context, here, we quantitatively evaluate the optimal $x$ value using boththe experimental and computational approaches. Using the high-pressuresynthesis approach that can maintain the starting composition even aftersintering, we obtain the Sc$_{20}$(C,B)$_{8}$C$_{20}$ phase by the reaction ofthe previously reported Sc$_{15}$C$_{19}$ and B (Sc$_{15}$B$_y$C$_{19}$). Ourexperiments demonstrate that an increase in $y$ values promotes the phaseformation of the Sc$_{20}$(C,B)$_{8}$C$_{20}$ structure; however, there appearsto be an upper limit to the nominal $y$ value to form this phase. The maximum$T_\mathrm{c}$ $(=7.6\text{ K})$ is found to correspond with the actual $x$value of $x \sim 5$ under the assumption that the sample with the same$T_\mathrm{c}$ as the reported value $(=7.7\text{ K})$ possesses the optimal$x$ amount. Moreover, we construct the energy convex hull diagram bycalculating the formation enthalpy based on first principles. Our computationalresults indicate that the composition of Sc$_{20}$C$_4$B$_4$C$_{20}$ $(x=4)$ isthe most thermodynamically stable, which is reasonably consistent with theexperimentally obtained value.

Experimental and Computational Determination of Optimal Boron Content in Layered Superconductor Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$