Structure of sodium above 100 GPa by single-crystal x-ray diffraction

Abstract

At pressures above a megabar (100 GPa), sodium crystallizes in a number of complex crystal structures with unusually low melting temperatures, reaching as low as 300 K at 118 GPa. We have utilized this unique behavior at extreme pressures to grow a single crystal of sodium at 108 GPa, and have investigated the complex crystal structure at this pressure using high-intensity x-rays from the new Diamond synchrotron source, in combination with a pressure cell with wide angular apertures. We confirm that, at 108 GPa, sodium is isostructural with the cI16 phase of lithium, and we have refined the full crystal structure of this phase. The results demonstrate the extension of single-crystal structure refinement beyond 100 GPa and raise the prospect of successfully determining the structures of yet more complex phases reported in sodium and other elements at extreme pressures.

At ambient pressure the alkali metals are simple metals; i.e., they can be described as nearly-free-electron metals that are characterized by a weak interaction between their single valence electron and the atomic core (1, 2). At ambient conditions the alkali metals all crystallize in the close-packed body-centered cubic (bcc) structure. However, under sufficient compression, they undergo a series of structural phase transitions. At pressures ranging from 2.2 GPa in cesium to 65 GPa in sodium, they transform from the bcc to the face-centered-cubic (fcc) structure (3–5). Further compression leads to the formation of a wide variety of lower-symmetry and often very complex crystal structures (6, 7), which range from distorted variants of the bcc structure in lithium and sodium (5, 8, 9) to an incommensurate composite or “host–guest” crystal structure in rubidium (10, 11). The discovery of a whole series of these symmetry-lowering transitions over the last decade—not only in the alkali metals, but also in various other elements (6, 7, 9)—had been unexpected because it often involves a reduction in coordination number, which is opposite to the usual trend for pressure-induced phase transitions. The experimental discoveries have been complemented by computational studies, but the physical mechanisms that lead to the formation of the complex phases are not yet fully understood, and their physical properties not yet known in detail.

Because of the low x-ray scattering power and relatively high transition pressures of sodium, it is only recently that it has become possible to investigate its high-pressure behavior. A number of high-pressure phases have been identified above 100 GPa (ref. 12 and M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, unpublished data—see ref. 5), and the melting line was discovered to be very unusual: it first rises close to 1,000 K at ≈30 GPa and then falls to room temperature (≈300 K) at 118 GPa (12) (see Fig. 1). Previous x-ray diffraction studies have shown that, with increasing pressure at room temperature, sodium transforms first from the bcc phase to fcc at 65 GPa, as said, and then to a more complex body-centered cubic structure with 16 atoms in the unit cell (cI16) at 103 GPa (5, 9). Further studies up to higher pressures have revealed at least two more transitions (ref. 12 and M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, unpublished data—see ref. 5), and theoretical calculations (9, 13) have suggested these phases may have the tetragonal β-Sn-type structure of cesium phase IV (7) (tI4 in Pearson's notation; ref. 14) and the orthorhombic C-face-centered (oC8) structure of α-gallium (7). Theoretical studies have explored the possibility of the onset of superconductivity in the solid phases (15, 16), and suggest the possible onset of a dimerized phase at pressures >200 GPa (13, 17). Here we are concerned with the crystal structure of the cI16 phase. It is the first of the complex phases in sodium; however, although its symmetry and density are known (9) and some calculations have been performed (13, 15), the experimental determination of its structure has remained incomplete.

Fig. 1.

The phase diagram of Na to 140 GPa (adapted from ref. 12), showing the stability fields of the bcc, fcc, and cI16 phases, and the remarkable decrease in the melting temperature observed above 30 GPa.

The cI16 structure has already been determined in lithium, which exists in this phase above 40 GPa at 180 K (8). The structure is shown in Fig. 2 and has space group I4̄3d with 16 atoms on a 16c site, (x, x, x). Refinements of powder diffraction data for Li give a value of 0.055(1) for the variable atomic coordinate x at 46 GPa and 180 K (8). The value of x was found to vary between 0.054 at 45 GPa and 0.060 at 50 GPa (both at 180 K), and a value of 0.046 was obtained on pressure decrease in an experiment at 100 K where the phase was observed down to 37.5 GPa—well below the pressure at which the phase first appears on pressure increase at 180 K, probably due to hysteresis effects. The structure would be bcc for x = 0, and it is a simple distortion of bcc in which atoms are displaced along the body-diagonal directions of the cubic unit cell (8).

Fig. 2.

The cI16 crystal structure. It can be regarded as a distorted 2 × 2 × 2 superstructure of the bcc structure. One of the eight distorted-bcc subunits is highlighted, and the local coordination is indicated for two further subunits. The atoms occupy the 16c Wyckoff site, (x, x, x), of space group I4̄3d and positions are shown for x = 0.044.

Here we report a determination of the structure of cI16 sodium at 108(1) GPa using single-crystal x-ray diffraction techniques. Details of experimental techniques are given in Materials and Methods. At pressures <90 GPa, the diffraction patterns from the sample were powder-like and contained a number of Debye–Scherrer rings. However, above that pressure, the sample became more textured and single-crystal like because of the proximity of the experimental conditions to the melting curve (Fig. 1), and the diffraction patterns contained a number of strong Bragg reflections. The single-crystal nature of the sample became still more evident once the pressure was increased into the cI16 phase at 108 GPa, and the sample quality was improved by careful annealing just below the melting curve at 40°C.

Fig. 3 shows some of the diffraction data, which were collected on an image-plate detector in a sequence of contiguous ±0.25° oscillations over a total scan range of 14° around the vertical axis. The short x-ray wavelength (0.3444 Å) and the 50° aperture in the pressure cell, which is significantly larger than in typical megabar cells currently in use, were chosen to allow us to extend the accessible part of reciprocal space and thereby increase considerably the number of observable reflections. Inspection of the data revealed reflections from a much smaller second crystal with a slightly different orientation from the main one, and an intensity ratio between the two of ≈10:1. Evidence of the weaker (≈10%) component can be seen just to the left of the box around the main (103) reflection in Fig. 3. The difference in orientation made it straightforward to fit an orientation matrix and obtain accurate integrations of the data from the main crystal alone.

Fig. 3.

One quadrant of a composite image of five superimposed Mar345 images selected from the overall 14° scan range to show representative data. Eight observed reflections are marked. As discussed in the text, the (204) and (222) reflections are absent. Weak intensity just to the left of the (103) reflection arises from a second crystal; reflections from this are ≈10 times weaker than from the main crystal. The powder diffraction rings are from the rhenium gasket and from some tantalum included with the sample as a pressure marker. One part of the image has been enhanced to reveal the (112) reflection on one of the rhenium diffraction rings. Other small diffraction spots in the image are of a different appearance from the sample reflections, and are not from the sample.

The lattice parameter of the sodium at 108(1) GPa was refined from the measured reflection d-spacings as 5.461(1) Å. This corresponds to an atomic volume of 10.18 ų (a V/V₀ of 0.258 and a density of 3.76 gcm⁻³), in good agreement with the value shown in ref. 9 for the same pressure of 108 GPa.

The orientation matrix showed that 31 different allowed reflections, consistent with a body-centered cubic lattice, had passed completely through the reflection condition in the range of the scans. These were averaged over symmetry equivalents to give 15 unique reflections, six of which were observed as having no detectable intensity at a level below 0.02% of the strongest reflections. Five of these six have (hkl) indices that break some general conditions for allowed reflections in space group I4̄3d: 2h + l = 4n for (hhl) or h = 4n for (h00). An example is the absent (222) reflection in Fig. 3. The remaining absent reflection is the (204) reflection seen in Fig. 3, which has indices that break the special conditions for atoms in the 16c sites: h + k + l = 4n or h = 2n + 1. Two of the allowed reflections were omitted from the least-squares refinement because they were saturated on the detector. The final refinement converged to an R factor of 3.3% and a goodness of fit (χ²) of 1.37.

The isotropic atomic displacement parameter refined to 0.03(1) Ų and the value of the variable atomic coordinate x refined to 0.044(1), giving a displacement of the atoms from the bcc structure of 0.42(1) Å. The fractional distortion from the bcc structure is smaller than the 0.054 observed at the onset of the cI16 phase in lithium at 180 K, and even slightly less than the value of 0.046 found at the limit of existence of the phase on pressure decrease at 100 K (8). At the V/V₀ of 0.258 for sodium at 108 GPa, Christensen and Novikov (13) calculated x to be 0.028 (figure 7 of ref. 13). Our value is significantly larger, but is in quite close agreement with the calculations of Neaton and Ashcroft at the same V/V₀, as estimated from the values for the ionic radius, r_s, given in ref. 15.^¶

At temperatures below 35 K at atmospheric pressure, bcc-Na transforms to one or more rhombohedral structures, the exact nature of which is unclear (18, 19). Because cI16 is a bcc-like structure, there is the interesting possibility of a corresponding transition to a lower-symmetry structure at low temperatures. Nothing is currently known about the structural behavior of sodium at 100 GPa and low temperatures, and further studies would be worthwhile.

Single-crystal techniques at high pressure have been significantly developed over the past decade, and have been successfully applied to solving many highly complex structures that had defied solution with powder diffraction methods (7). The data are best collected with monochromatic techniques, but then a wide-angle aperture is needed in the pressure cell to collect complete data. Suitable pressure cells for work in the range up to ≈50 GPa have been available for some time; however, for work over a megabar (100 GPa), cells have typically had apertures with (full) angles no larger than ≈35°. That size of aperture, even with the short x-ray wavelength used here, would have occluded most of the reflections seen in Fig. 3: only the (222), (112), and (103) reflections would have been completely measurable. It is not just that the aperture is restricted but that reflection d spacings are reduced by the very high pressure, thus moving reflections to higher scattering angles, 2θ. For example, sodium at 108 GPa is approximately four times denser than at ambient pressure (V/V₀ ≈ 0.25), and so average d spacings are reduced by ≈37%. The cI16 structure is not particularly complex, but it could not have been satisfactorily determined by single-crystal methods with previously existing limits on the scattering angle. In principle, a reduced aperture can be overcome partially by using even shorter x-ray wavelengths, but then integrated intensities fall as λ³ and other limitations may arise, including weak scattering from low-Z samples or lack of resolution in the diffraction pattern. Large apertures will always allow for more options in solving the most challenging structural problems.

Extension of single-crystal structure refinement beyond a megabar opens up the prospect of successful structural studies of intriguing complex phases already believed to exist in elements in this range, including in sodium (refs. 9, 12, and 13, and M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, unpublished data—see ref. 5).

Materials and Methods

Sodium with a stated purity of 99.95% was loaded into the diamond anvil cell in a dry argon atmosphere to prevent oxidation of the sample. The pressure cell was equipped with beveled Boehler–Almax-type diamond anvils and seats (20), which provided a conical aperture (full angle) of 50°. The diamond anvils were 1.70 mm thick, and had a girdle diameter of 3.10 mm, with 100-μm-diameter culets beveled to 300 μm at an angle of 8°. The initial sample chamber in the rhenium gasket was 30 μm in diameter and preindented to ≈15 μm in thickness. Three or four grains of polycrystalline tantalum (grain size 2–3 μm) were enclosed with the sodium for pressure measurement via the Ta equation of state (21). Because sodium itself has been identified as an excellent quasihydrostatic pressure medium (21), no other pressure-transmitting medium was added. Diffraction patterns of the low-pressure bcc and fcc sodium phases showed no discernible contaminant peaks, confirming that the sample was pure. The sharpness of the diffraction peaks observed from both the sodium and Ta at pressures above 100 GPa confirms that sodium is indeed quite hydrostatic in this pressure range where the melting curve is close to room temperature (12).

The pressure cell was placed in an oven and gently heated at 40°C, very close to the melting curve at 108 GPa (12), for ≈30 min. This resulted in the production of a good quality single crystal ≈25 μm in diameter and ≈2.5 μm thick. Diffraction data were collected on the Extreme Conditions Beamline (I15) at the Diamond Light Source (www.diamond.ac.uk/Beamlines/Beamlineplan/I15/TechSpecs.htm) using an x-ray wavelength of 0.3444 Å (36 keV) from a double-bounce Si monochromator. The incident beam was collimated to a beam size of 50 μm. The distance from the sample to the Mar345 image-plate detector and the detector tilt angles were determined with a Si standard. The sample pressure was determined from the tantalum diffraction pattern and its known equation of state (21) as 108(1) GPa, and the single-crystal diffraction data were collected at 300 K. The intensities of the reflections were integrated by using the SAINT+ program (22), and the structure was refined on squared structure factors (F²) using SHELXL97 (23). (No absorption corrections were applied because these will be negligible for such a small sodium sample with 36 keV x-rays.) The three variable parameters refined were an overall scale factor and the isotropic atomic displacement factor and fractional coordinate of the sodium atom.