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Structure, Bonding, and Geochemistry of Xenon at High Pressures

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Science  15 Aug 1997:
Vol. 277, Issue 5328, pp. 930-933
DOI: 10.1126/science.277.5328.930

Abstract

Although xenon becomes metallic at pressures above about 100 gigapascals, a combination of quantum mechanical calculations and high pressure–temperature experiments reveals no tendency on the part of xenon to form a metal alloy with iron or platinum to at least 100 to 150 gigapascals. The transformation of xenon from face-centered cubic (fcc) to hexagonal close-packed (hcp) structures is kinetically hindered, the differences in volume and bulk modulus between the two phases being smaller than we can resolve (less than 0.3 percent and 0.6 gigapascals, respectively). The equilibrium fcc-hcp phase boundary is at 21 (±3) gigapascals, which is a lower pressure than was previously thought, and it is unlikely that Earth's core serves as a reservoir for primordial xenon.

Like the other noble elements, Xe is characterized by a reluctance to form chemical bonds. Indeed, chemical inertness makes the noble gases useful as tracers that help reveal the evolution of planetary atmospheres and interiors (1-6). That Xe can bond to form compounds (7-9) and even, at high pressures, a hexagonal close-packed (hcp) metal (10-12), opens up the possibility that geochemical trends of the planets' noble gas abundances can be influenced by chemical reactions taking place at the elevated pressures and temperatures of planetary interiors. Specifically, the relative depletion of Earth's atmospheric Xe compared with meteoritic and solar abundances—the geochemical “missing Xe” problem (2, 13, 14)—suggests that significant amounts of Earth's primordial Xe could be sequestered at depth, inside the core (15, 16).

Here we investigate whether chemical interactions taking place at high pressures may influence the distribution of Xe within the planet. This is an extension of lower pressure studies that indicate no special tendency of Xe to bind with and partition into core-forming Fe up to pressures of 10 gigapascals(GPa) (17). However, the properties and even the equilibrium phase transitions of Xe at high pressures remain unclear. For example, Jephcoat et al.(18) found from x-ray diffraction studies at room temperature that Xe is stable in the face-centered cubic (fcc) phase up to 14 GPa and in the hcp phase above 75 GPa up to at least 137 GPa, but the diffraction pattern and crystal structure were not well resolved at intermediate pressures.

Using a laser-heated diamond-anvil cell we carried out experiments on samples of Xe and Fe up to pressures of 70 GPa (19). For a sample held at a pressure of about 50 GPa, the x-ray diffraction pattern changed as the sample was heated to peak temperatures of 3000 K (Fig. 1) (20). We believe that the change in diffraction pattern is due to the Xe transforming from fcc to hcp structures, without any indication of chemical reaction between the Fe and Xe, for two reasons. First, the diffraction pattern after heating at 50 GPa corresponds to that expected for a mixture of fcc and hcp Xe, along with unreacted hcp Fe. After accounting for the pressure dependence of lattice parameters and the presence of Fe, our 50-GPa diffraction pattern is identical to the diffraction patterns obtained by us and by Jephcoat et al. (18) for Xe taken to 70 to 75 GPa without heating. Chemical reactions are unlikely to occur in the unheated samples. Therefore, our interpretation for the 50-GPa samples after heating is that these are just like the unheated samples at 70 to 75 GPa: In both cases, Xe is simply in the process of undergoing a structural transformation that is kinetically sluggish but is aided by laser heating in the 50-GPa experiment. Second, we carried out independent experiments on samples of Pt and Xe laser-heated at 50 GPa. Platinum is expected to be less reactive than Fe, and we obtained identical results as before: The x-ray diffraction patterns can be entirely explained in terms of a combination of fcc and hcp phases of Xe, along with unreacted fcc Pt. The results for Pt + Xe samples confirm that the fcc → hcp transformation of Xe is kinetically sluggish and therefore goes toward completion at much lower pressures on laser heating than when the sample is merely compressed at room temperature. The crystallographic unit-cell parameters for the fcc and hcp structures are coherent over the broad pressure range in which the two phases are observed to coexist (Fig. 2). The fact that we can continuously and reversibly track the evolution of diffraction patterns, from fcc at low pressures to nearly pure hcp at higher pressures, gives us confidence that we are documenting a crystal structural transformation rather than a chemical reaction.

Figure 1

Structural transformation of crystalline Xe shown by changes in x-ray diffraction patterns taken at high pressure but room temperature, before and after partial and then complete heating to peak temperatures of 3000 (±300) K at 53 (±2) to 47 (±2) GPa (pressure relaxes slightly upon heating) (f, fcc; h, hcp). Arrows indicate shifts in peak intensities due to growth of the hcp relative to the fcc phase of Xe with increased heating, and asterisks indicate peaks due to Fe in the sample. Two peaks in the unheated sample are identified as the (101) and (100) diffraction lines from hcp Xe. After the sample is heated, first partially then fully, the hcp (101) and (100) peaks grow in intensity while the fcc (200) peak diminishes in intensity. The diffraction pattern of the fully heated sample also shows evidence of new peaks that can be indexed as hcp (201) and (103) peaks.

Figure 2

Unit cell parameters for the fcc (a) and hcp (a,c) phases of Xe plotted against pressure. Lines are from our theoretical calculations for the static lattices, whereas symbols indicate experimental results from the present study (upward-pointing triangles, samples containing Xe and Fe; downward-pointing triangles, samples containing Xe and Pt; solid and open symbols indicate measurements taken upon compression and decompression, respectively); from the work of Jephcoat et al. (18) (squares); and from previous determinations of the fcc lattice parameter at zero pressure and 88 K (30) (asterisk at upper left). In our study, the lattice parameters were determined from (111), (220), and (311) and from (100), (002), (101), and (110) diffraction peaks for the fcc and hcp structures, respectively, and the uncertainties are smaller than the symbols.

In order to further check this conclusion, we carried out ab initio total-energy calculations within the framework of density functional theory in the local density approximation (LDA) (21). Enthalpy calculations were performed to determine the stability of a set of Xe and Fe compounds—XeFe, Xe2Fe, and XeFe2—in hcp packing relative to that of separated Xe and Fe in their high-pressure hcp phases (Table1). For high pressures (>100 GPa), we also considered the hexagonal Laves phase of XeFe2, a structure that corresponds to an optimal packing of Fe and Xe atoms having different atomic radii (22). One way of checking the validity of the theoretical calculations is to compare them with the high-pressure x-ray diffraction measurements on the fcc and hcp phases of Xe. We find agreement between the calculated and observed lattice parameters of the two phases of Xe; the theoretical lattice parameters are slightly lower than the observed values, as is expected, because the former is for the static lattice (Figs. 2 and3).

Figure 3

Comparison of experimentally and theoretically determined ratios of Xe hcp unit cell parameters, c/a, plotted against pressure. Solid and open circles indicate measurements taken on compression and decompression, respectively, whereas the line indicates results from theory squares are from the work of Jephcoat et al. (18). Compatible with experimental results, the theoretical values are generally close to the ideal ratio for hcp packing of identical spheres, Embedded Image = 1.633, and rise slowly with increasing pressure.

Table 1

Formation enthalpies of XeFe compounds from theory* (electron volts per formula unit).

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Over the pressure range 0 to 500 GPa, the Xe-Fe compounds are all energetically unfavorable (Table 1). Even at 500 GPa, the enthalpy of the most favorable compound that we considered, the Laves phase, exceeds that of separate Xe and Fe by a respectable 0.9 eV per formula unit. Indeed, theoretical diffraction patterns calculated for each of the four Xe-Fe phases listed in Table 1 yield no match with any of the experimental results.

More than just confirming the experimental findings, the theoretical calculations are important for understanding why the compounds are so energetically unstable. We find that although the Fe atoms form bonds among each other, the spherical charge distribution around the Xe sites remains relatively undistorted, showing the lack of any significant bonding with the Xe at high pressures. Thus, any incipient Xe-Fe bonding is so weak that it does not compensate for the energetic cost of breaking the strong Fe-Fe bond in iron, even at 150 to 500 GPa; the energetics are so unfavorable that this is likely to be true for other structures and Fe/Xe stoichiometries than those we have considered. In short, the theoretical calculations support our conclusion that the experiments solely document the transformation of Xe from fcc to hcp structures.

Systematic experiments with increasing and decreasing pressure provide an estimate of 18 to 24 GPa for the equilibrium fcc ↔ hcp transition pressure of Xe at room temperature and to ∼2000 to 3000 K, but with a pressure range of 9 to 70 GPa, over which we observe the coexistence of both phases because of the sluggish kinetics (Figs. 2 and 3). Theoretically, we calculate that the phase transition is expected to occur at about 5 GPa for the static lattice, which is in general agreement with the experimental results. Our static-lattice calculations ignore vibrational (zero-point and thermal) effects and may suffer from the shortcomings of the LDA. Therefore, the agreement between theory and experiment may be somewhat fortuitous, yet the small energy difference calculated for the two phases is in accord with the experimentally observed sluggishness of the phase transition. The thermodynamic driving force for the fcc → hcp transition is small (23). McMahan (24) discusses the origin of this driving force for argon.

The similarity in energies between the fcc and hcp phases is highlighted by our finding that the two phases have experimentally indistinguishable pressure-volume equations of state (25-27). The close similarity between the fcc and hcp structures, which have identical first- and second-neighbor coordination shells, explains why the volumes of the two phases are difficult to distinguish (23, 28). Along with the sluggishness of the transformation, the close orientation relation between the two structures (26) can explain why Jephcoatet al. (18) observed complex x-ray diffraction patterns from Xe compressed at room temperature (without heating) between 14 and 75 GPa.

Although the bonding in Xe, like the other noble gases, has often been modeled through the use of pair potentials, the relatively low fcc-hcp transition pressure illustrates a deviation from such a simple model for the interatomic forces at high pressures; the transition pressure is predicted to be about 64 GPa, even when three-body interaction terms are included (29). For comparison, the ab initio quantum mechanical approach presented here is in agreement with the experimental determinations of the transition pressure and equations of state of the two known crystalline phases of Xe.

In summary, theory and experiment argue against the likelihood of Xe bonding with Fe over the pressure range examined here, and hence of Xe having partitioned into core-forming metal to any significant degree inside Earth. It appears that the “missing Xe” problem of planetary geochemistry must be resolved by other mechanisms (2, 3, 14,17). In particular, the observed pattern of noble gas abundances appears to have been set before Earth and the terrestrial planets were fully accreted, rather than having been subsequently modified due to inclusion into the core.

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