Sodium-potassium system at high pressure

Mixtures of sodium and potassium differ substantially from the pure elements, while retaining the high compressibility, which is important to the complex behavior of dense alkali metals. We present powder x-ray diffraction of mixtures of Na and K compressed in diamond anvil cells to 48 GPa at 295 K. This reveals two stoichiometric intermetallics: an ${\mathrm{Na}}_2\mathrm{K}$ phase known at ambient pressure and low temperature, and a novel NaK phase formed of interpenetrating sodium and potassium diamond lattices. Density functional theory calculations find the new phase to be dynamically stable and, in contrast to pure alkali metals, reveal decreasing electron localization with applied pressure. Depending on the mixture composition these intermetallics are accompanied by sodium or potassium rich phases suggesting that there are no other intermetallics under the range of P-T conditions studied. Alkali-metal mixtures have seen little study at high pressure and represent an unusual class of materials with very high compressibility and multiple constituents. Such materials exhibit significant compression at experimentally accessible pressures and open a way to measure multispecies structures at high compression. These results challenge structural finding algorithms for mixtures in high-pressure conditions.

Figure 1

Top: integrated powder pattern of a 2Na:K molar ratio mixture at 2.8 GPa. Background subtracted data (black) with LeBail fit (blue) and residual (below). Tics indicate possible peak locations of $P{6}_3/mmc {\mathrm{Na}}_2\mathrm{K}$, a sodium-rich bcc phase, and tungsten as marked. The unintegrated pattern is inset. The ${\mathrm{Na}}_2\mathrm{K}$ phase has lattice parameters $a=6.768\left(1\right)$ Å and $c=11.051\left(2\right)$ Å. Middle: a similar plot for an equimolar Na:K mixture at 9.4 GPa showing the novel $Fd\overline{3}m$ NaK phase, a sodium-rich bcc phase and tungsten. Bottom: a similar plot for a Na:2K mixture at 22.7 GPa showing $tI19$ potassium, $Fd\overline{3}m$ NaK and tungsten. The $tI19$ tics are for the host lattice only. Asymmetric broadening in the $Fd\overline{3}m$ NaK phase is fitted using Stephen's method [41] in both cases and is attributed to strain. Additional diffraction data is presented in the Supplemental Material [42].

Figure 2

Pressure-volume curves for the bcc phases. Vertical axis is volume per two atoms corresponding to one unit cell of bcc. The coexisting intermetallic transitions from ${\mathrm{Na}}_2\mathrm{K}$ to NaK at 5.9 GPa as indicated, this change in stoichiometry coincides with a discontinuity in the lattice parameter of the excess bcc phase in the Na:K mixture as it goes from K-rich to Na-rich. Pressure-volume curves for bcc sodium [44] and bcc potassium [43] use the Holzapfel $H02$ equation of state [45]. Error bars are smaller than plotting points.

Figure 3

Experimental and simulated pressure-volume relations for $Fd\overline{3}m$ NaK show close agreement. Vertical axis is volume per two atoms corresponding to one formula unit of $Fd\overline{3}m$ NaK or one bcc unit cell of the pure elements. Pressure-volume curves for bcc sodium [44] and bcc potassium [43] use the Holzapfel $H02$ equation of state [45]. Error bars are smaller than plotting points.

Figure 4

Unit cell of the high-pressure $Fd\overline{3}m$ NaK phase. Sodium atoms are in yellow, potassium in purple.

Figure 5

Binary phase diagram of the Na – K system at 295 K. The green shaded region corresponds to the solid solution, which may be metastable over at least some of the area is covers.

Figure 6

The phonon density of states for $Fd\overline{3}m$ NaK at low and high pressure show the proposed structure to be dynamically stable.

Figure 7

The 0.6 isosurface of the electron localisation function around a sodium atom in $Fd\overline{3}m$ NaK. The isosurface from adjacent sodium-sodium interstitials and near the potassium atoms is ommitted for clarity. (a) with lattice parameter of 8.25 Å, corresponding to a calculated pressure of 4.3 GPa. (b) with lattice parameter of 6.25 Å, corresponding to a calculated pressure of 50.6 GPa. The hexagonal disks of electron localization between nearest neighbor sodium atoms disappear at higher pressure where there is no significantly localised interstitial electron density. Inset arrows show crystallographic axes; sodium atoms are yellow, potassium purple and the isosurface is teal.