One-dimensional chain melting in incommensurate potassium

Between 19 and 54 GPa, potassium has a complex composite incommensurate host-guest structure which undergoes two intraphase transitions over this pressure range. The temperature dependence of these host-guest phases is further complicated by the onset of an order-disorder transition in their guest chains. Here, we report single-crystal, quasi-single-crystal, and powder synchrotron x-ray diffraction measurements of this order-disorder phenomenon in incommensurate potassium to 47 GPa and 750 K. The so-called chain melting transition is clearly visible over a 22 GPa pressure range, and there are significant changes in the slope of the phase boundary which divides the ordered and disordered phases, one of which results from the intraphase transitions in the guest structure.

Figure 1

The composite incommensurate structure of K-IIIa, as viewed down the $c$ axis. The tetragonal 16-atom host component is shown in light gray, and the guest atom chains in dark gray. A unit cell is shown by the solid lines, and the crystallographic axes are labeled.

Figure 2

Composite two-dimensional (2D) diffraction image from the high-quality single crystal of K-IIIa at 20.3 GPa and 295 K. This composite image is formed from the summation of several $1^{\circ }$ contiguous images obtained during the collection of a single-crystal data set. The layer lines of host and guest reflections are labeled, and reflections from the diamond anvils are labeled with “D.” The lower inset shows an enlarged view of the $\left(hk20\right)$ host and $\left(hk01\right)$ guest reflections, highlighting the distinct differences in their shape. The host reflections are sharp Bragg spots, as expected from a three-dimensional crystal, while the guest reflections are disk-shaped, elongated perpendicular to the crystallographic $c$ axis. The $\left(hk01\right)$ guest reflections are located on a sheet of diffuse scattering (seen as a line in this projection) that arises from the 1D nature of the guest chains.

Figure 3

Enlargements of 2D diffraction images collected from the single crystal of K-IIIa at 20.3 GPa, highlighting the $\left(0\overline{2}20\right)$ and $\left(\overline{1}320\right)$ host reflections, and the $\left(0\overline{2}01\right)$ and $\left(\overline{1}301\right)$ guest reflections. The images were obtained using a $1^{\circ }$ oscillation of the crystal. Panels (a)–(f) show the changes in the diffraction peaks as the sample temperature was increased from 295 to 345 K in 10 K steps. The host reflections remain unchanged with increasing temperature, whereas the guest reflections first weaken and broaden (305 and 315 K), then the Bragg scattering disappears and only disks of diffuse scattering remain (325 and 335 K), before all structure in the scattering disappears, and only a uniform sheet of diffuse scattering remains (345 K).

Figure 4

Panel (a) shows the additional peak width of the $\left(0\overline{2}01\right)$ and $\left(\overline{1}301\right)$ guest reflections (plotted with unfilled and filled symbols, respectively) over that of the host reflections, perpendicular to the (001) direction at 20.3 GPa as a function of temperature. The additional peak width was determined by subtracting the peak width of the host peaks, which were found to have negligible variation in width with temperature. Panel (b) shows the effect of temperature on the interchain correlation length of the guest chains. The resolution of this measurement was determined from the peak width of the host reflection, and found to be 300 Å. There is an exponential reduction in correlation length above 315 K. In panels (a) and (b), error bars which are smaller than the symbol size and have been omitted for clarity. Inset (c) shows 1D diffraction profiles of the $\left(0\overline{2}01\right)$ and $\left(\overline{1}301\right)$ guest reflections integrated along a line perpendicular to (001). One may see that as temperature increases the guest reflections reduce in intensity before disappearing entirely above 335 K.

Figure 5

The phase diagram of potassium to 50 GPa and 800 K. The melting curve is shown by the solid line and is a combination of the study by Narygina et al. [16] and the additional data obtained in this study. The $P-T$ conditions at which the fcc and liquid phases were observed in the current study are shown by the filled (red) diamonds and the filled (blue) circles, respectively. The $P-T$ conditions at which the incommensurate host-guest phases were observed are shown by the open and closed (black) triangles. Closed (black) triangles show where ordered guest chains were observed, and open triangles show where disordered guest chains were observed. The dot-dashed line through these points is the best-fitting order-disorder transition line, and is drawn as a guide to the eye. The observation of the K-IIIa $\to$ K-IIIb transition at 29.6 GPa and 340 K, results in a negative gradient of the transition line of $\sim 70$ K/GPa, whereas the reentrant transition back to K-IIIa at 38 GPa and 530 K allows the almost vertical transition line to be determined—transition lines are shown with dashed lines. No disordering of the chains was observed above 42 GPa and 596 K.

Figure 6

(a) 1D integrated diffraction profiles from potassium as a function of pressure and temperature, showing the disappearance of the guest reflections in tetragonal K-IIIa [marked with their indices (1101) and (2001) in profile (i)], on temperature increase at 25.3 GPa, profiles (i)–(iii). The arrow below profile (i) shows the calculated position of the (0001) guest reflection, which is absent due to the large degree of preferred orientation in the sample. The asterisk marks a weak contaminant peak. On further increases in $P$ and $T$, the (1010) host reflection appears, which signals the loss of $c$-glide symmetry, profile (iv), and the guest reflections reappear [marked with their indices (0101), (1101), and (0301)] as the structure orders into orthorhombic K-IIIb, profiles (v) and (vi). The arrows beneath profile (vi) mark the calculated positions of the guest reflections if the guest structure was tetragonal. (b) The pressure dependence of the $c_H/c_G$ ratio at high temperature, along the order-disorder line. Closed triangles indicate where the guest structure is tetragonal in K-IIIa, and open triangles indicate where the guest structure is orthorhombic in K-IIIb. Dotted lines indicate commensurate values of $c_H/c_G$. The solid curve is a fit to the room temperature data of the pressure dependence of the $c_H/c_G$ ratio by Lundegaard et al. [23], and the closed circle indicates a high-pressure data point from the current study, close to room temperature, in good agreement with the data from Lundegaard et al. The dashed vertical lines are the room temperature intraphase transition pressures [23].

Figure 7

The pressure dependence of the (a) $a_H$, (b) $c_H$, and (c) volume of the host unit cell along the order-disorder phase line. $a_H$ and $c_H$ can be determined in both the ordered and disordered phases, while $c_G$ can be determined only in the ordered phase. At $\sim 29$ GPa, there is a volume discontinuity of $\sim 2\%$ in the host structure, due largely to a discontinuity in the $a_H$ lattice parameter. Above 29 GPa the $a_H$ lattice parameter decreases steadily with increasing pressure, whereas there is a distinct change in the compressibility of the $c_H$ lattice parameter near $\sim 32$ GPa. This is not accompanied by a change in structure, yet does coincide with a change in gradient of the order-disorder transition line.