Ca-VII: A Chain Ordered Host-Guest Structure of Calcium above 210 GPa

The recently discovered high pressure phase VII of calcium [M. Sakata et al., Phys. Rev. B 83, 220512(R) (2011)] has the highest superconducting transition temperature ($T_c$) of 29 K among all the elements. Understanding the cause for such a high $T_c$ state is necessary to clarify its crystal structure. The structure of this phase was determined by an x-ray powder diffraction experiment and a density functional theory calculation and was not found to be the usual host-guest type but consisted of a $2\times 2$ supercell in the tetragonal $ab$ plane with a commensurate host-guest ratio of $4/3$ along the $c$ axis containing 128 atoms.

Figure 1

(a) Diffraction pattern and Rietveld analysis with the $I4/mcm$-32 model for Ca-VII at 241 GPa. The closed circles show the experimental values. The dark green solid lines show the calculated diffraction pattern. The labels “Re” denote the diffraction peaks from the rhenium gasket. The reliability factors are $R_{\mathrm{wp}}=1.63\%$, $R_p=1.03\%$, and $R_{\mathrm{wp}}$ $(\mathrm{\text{without background}})=24.32\%$. Its structure for $2\times 2\times 1$ cells are drawn in (b) $ab$ and (c) $ac$ planes. The Ca atoms forming the host and guest structure are shown in green and brown, respectively. The crystallographic information file (CIF) for this model and the Rietveld analysis result as a four-dimensional composite crystal are provided in the Supplemental Material [39].

Figure 2

(a) Rietveld fit with the proposed $P{4}_2/ncm$-128 model for Ca-VII. The preferred orientation direction and the $R_0$ value for the March-Dollase function were converged to (0.732, 0.682, 0.005) and 0.834, respectively. The final fit resulted in reliability factors of $R_{\mathrm{wp}}=0.95\%$, $R_p=0.68\%$, and $R_{\mathrm{wp}}$ $(\mathrm{\text{without background}})=13.93\%$. Its structure is drawn in the (b) $ab$ and (c) $ac$ planes. The labels $A$ and $B$ show the two different types of heights of the guest atom. The CIF for this model and the Rietveld analysis result as a four-dimensional composite crystal are provided in the Supplemental Material [39].

Figure 3

Pressure dependence of the atomic volume for calcium. Data points for Ca-VII were obtained by the Rietveld analysis with the $P{4}_2/ncm$-128 model. Numerical values for Ca-VII are given in Table S2 in the Supplemental Material [39].

Figure 4

Pressure change of the interatomic distances for calcium. Ca-VII data include numerous distances; therefore, its data points are marked with thin lines.