Figure 1

Competing high-pressure structures of ${\mathrm{CaB}}_6$, the B and Ca atoms are shown as small black and large silver spheres, respectively. The known cubic structure ($cP7$ in Pearson notation, space group $Pm\overline{3}m$) is made out of boron octahedra. $oP28$ ($Pnma$) is one of the possible distortions of $cP7$. $oS28$ ($Cmmm$) is a metastable structure made out of twinned pentagonal bipyramids. $oS56$ ($Cmcm$) is our lowest enthalpy structure for 13–32 GPa pressures in which half of the boron octahedra opened up to form zig-zag strips. $tI56$ ($I4/mmm$), comprised of large 24-atom boron units, is a new ground state candidate above 32 GPa supported by x-ray data in the present study. The cell parameters are given in the Supplemental Material [31].Reuse & Permissions

Figure 2

Calculated properties of known ($cP7$) and predicted ($oP28$, $oS28$, $oS56$, and $tI56$) structures of ${\mathrm{CaB}}_6$ as a function of pressure at $T=0\mathrm{K}$ [25, 31]: (a) $M$-point phonon frequency in $cP7$ becoming imaginary above 25 GPa for ${\mathrm{CaB}}_6$ in the divalent series (b) formation enthalpy at $T=0\mathrm{K}$ referenced to $cP7$ showing $cP7\to oS56\to tI56$ transformation at 13 and 32 GPa, respectively; (c) atomic volume.Reuse & Permissions

Figure 3

Observed (thin lines) and simulated patterns (shaded areas) collected at room $T$ and high pressures for ${\mathrm{CaB}}_6$ after room-$T$ compression (a) and laser-heating (b–d). The blue, red, and grey curves correspond to $cP7\mathrm{\text{−}}{\mathrm{CaB}}_6$, $tI56\mathrm{\text{−}}{\mathrm{CaB}}_6$, and fcc-Ar respectively. The green dotted line in (d) showing near 8.6 and 12.8 degrees corresponds to masked signal as described in the text. All the patterns were simulated with the lazy algorithm as implemented in the Inorganic Crystal Structure Database [37]; the used lattice parameters were refined via Le Bail fitting but remained close to the predicted ones (see Fig. S5 in Ref. [31]). All datasets are shown for $\lambda =0.4084\AA$, see Fig. S6 in Ref. [31] for more details.Reuse & Permissions

Figure 4

Output of the ground state search for ${\mathrm{Ca}}_4{\mathrm{B}}_{24}$ unit cells carried out with MAISE [35] linked to VASP [25, 27, 28, 29] using different optimization strategies [31]. The populations were created either randomly (green hollow diamonds and magenta circles) or via distortion of $cP7$ supercells (cyan crosses and grey circles) as detailed in Ref. [31]. At both pressures, we carried out the evolutionary algorithm (EA)-driven searches with both crossover and mutation operations. At 30 GPa, an additional EA search was carried out with just the mutation operation. At 50 GPa, a nonevolutionary approach based on the local conjugate-gradient (CG) relaxation of distorted $cP7$ supercells was also able to produce the complex $tI56$ solution (the numbers in grey show how many times a particular structure was found in ${10}^4$ tries). Note that $cP7$ is dynamically unstable above 23 GPa and close solutions are grouped as $cP{7}^{\prime }$.Reuse & Permissions