A High-Pressure Structure in Curium Linked to Magnetism

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Science  01 Jul 2005:
Vol. 309, Issue 5731, pp. 110-113
DOI: 10.1126/science.1112453


Curium lies at the center of the actinide series and has a half-filled shell with seven 5f electrons spatially residing inside its radon core. As a function of pressure, curium exhibits five different crystallographic phases up to 100 gigapascals, of which all but one are also found in the preceding element, americium. We describe here a structure in curium, Cm III, with monoclinic symmetry, space group C2/c, found at intermediate pressures (between 37 and 56 gigapascals). Ab initio electronic structure calculations agree with the observed sequence of structures and establish that it is the spin polarization of curium's 5f electrons that stabilizes Cm III. The results reveal that curium is one of a few elements that has a lattice structure stabilized by magnetism.

The contribution of various factors in the electronic structure of a material to the bonding in its solid phase is at the heart of materials science and is a subject of extensive experimental and theoretical interest. It is well known that, when approaching the center of the actinide (5f) series of elements, a marked change occurs in the elemental volumes. The atomic volume of americium (Am) is almost 50% larger than that for the preceding element plutonium (Pu) (Fig. 1). The lighter actinides (Pa to Pu) have smaller atomic volumes and itinerant 5f states that participate in the (metallic) bonding and thus contribute to the cohesive properties of the solid. However, the 5f states are also capable of spin-polarization and hence magnetism. When the 5f bands are broad, as in the itinerant metals (Pa to Pu), there is an absence of magnetic correlations (1, 2). However, for heavier actinide elements (Am and beyond), there is no 5f bonding, and magnetic correlations give rise to local moments, as found in the analogous 4f elements. Of particular interest with these heavier actinides is whether applied pressure can bring about the delocalization (a change of character from localized to itinerant) of their 5f electrons, and, if so, what are the consequent crystallographic, electronic, and magnetic structures?

Fig. 1.

Relative volume (V/V0) as a function of pressure for α-uranium (7), Am (8, 9) and Cm (this work). Vertical lines separate the pressure ranges for each Am and Cm (crystallographic) phase. Percentage values indicate the collapses in atomic volume. (Inset) Ambient pressure atomic volumes (solid circles, left-hand side) and bulk moduli (open squares, right-hand side) across the actinide series.

In the periodic table, iron and cobalt are unique in the sense that the magnetic interactions between d electron states determine their crystal structures (35). Given that the magnetic correlations are between f electron states in the actinides, we may ask whether such magnetic interactions can influence the sequence of crystal structures.

There are fundamental differences in the pressure-volume relationships of the light (6, 7) and heavy actinide metals (Fig. 1). Under compression, the relative volume changes with pressure for α-uranium (the room-temperature–stable form of uranium metal) (7) are clearly different from those for either Am or curium (Cm). We have investigated in detail the case of Am (8, 9), where four crystal structures are found to exist between ambient pressure and 100 GPa. The delocalization of the 5f electrons of Am by pressure occurs in two stages, with the progressive formation of two lower symmetry structures, a face-centered orthorhombic Am III and a primitive orthorhombic structure, Am IV; the transition to each is accompanied by an abrupt decrease in the relative atomic volume. The formation of the Am IV structure (space group, Pnma), which was subsequently confirmed by theory (10), is now recognized as an important high-pressure structure for f electron metals.

In Cm, the 5f 7 half-filled orbital provides a stabilizing effect. Consequently, forcing its 5f electrons to participate in its bonding requires higher pressures than in the case of Am. At ambient pressure, only the 6d 7s states of these elements are involved in their metallic bonding (2). With the application of pressure, the double hexagonal close packed (dhcp) form of Cm (P63/mmc, Cm I) converts to a face-centered cubic (fcc) structure (Fm3m, Cm II) at 17(2) GPa. This transformation requires little energy and reflects an increase in the d character of the bonding. There is a smooth transition between the Cm I and Cm II phases (Fig. 1), indicating that each phase has a comparable bulk modulus. This same transition occurs in Am, but at a lower pressure (6 GPa) (8, 9).

Previous work (11, 12) has identified the initial dhcp-fcc transition and also reported a phase transition above 40 GPa, but was unable to determine the correct structure. Given the pressure behavior of Am, one could have anticipated finding a structure similar to the Am III structure (Fddd) after the Cm II phase. However, our synchrotron radiation data show unambiguously that the Cm III phase is not Fddd as found for Am III. Before looking in detail at this Cm III phase, we will discuss the higher pressure phases of Cm.

Increasing the pressure above 56(4) GPa results in a third phase transition (Cm III to Cm IV), and this phase can indeed be identified with the Fddd structure as found for Am III. A smooth transition is observed between the Cm III and Cm IV phases. Above 95(5) GPa, the fourth phase transition (Cm IV to Cm V) is observed and yields a Pnma phase, which was previously identified for the Am IV structure. The Fddd to Pnma (Cm IV to Cm V) transition is accompanied by an ∼11.7% volume collapse, whereas at the Cm II to Cm III transition, the collapse is ∼4.5%. These abrupt volume changes signify the stepwise delocalization of the 5f electrons and their subsequent participation in the metallic bonding. In Am, the total collapse of ∼9% for two transitions is smaller than that for Cm, but in both elements the collapses occur in two stages. The appearance of the Fddd and Pnma forms for Am (8, 9) and Cm at higher pressures is a clear indication that the 5f delocalization process favors these structures.

The puzzle, however, remains the formation of the Cm III phase. This phase, starting at ∼37 GPa and extending to 56 GPa, has a monoclinic structure with the space group C2/c. A Rietveld fit of the Cm III data for this phase is shown in Fig. 2 at 45 GPa. This structure has not previously been reported for any element with f electrons.

Fig. 2.

Rietveld refinement of Cm III at 45 GPa, showing the observed (crosses) and calculated (line) diffraction patterns, reflection tick marks (vertical lines), principal Miller indices, and difference profile (lower line). The inset shows a detailed view of the strongest diffraction lines of the pattern, labeled by their Miller indices. Monoclinic space group C2/c, Cm on 4e sites (x = 0, y = 0.1753, Embedded Image) has characteristics a = 5.346(1) Å, b = 2.886(1) Å, c = 5.328(1) Å, β = 116.2(2)°, and Bragg-R Factor = 5.6%.

An illustration of the different structures observed in Cm is given in Fig. 3. In comparison to the Am III or Cm IV (Fddd) structures, the Cm III (C2/c) structure is composed of slightly distorted (rectangularly distorted) close-packed hexagonal planes, but in contrast to the (Fddd) structure, it has a stacking arrangement that reduces the symmetry to monoclinic.

Fig. 3.

Structural models of the Cm I to Cm V phases permit the visualization of transformation processes under pressure. The structures can be viewed as being composed of close-packed hexagonal planes (Cm I and Cm II) or distorted close-packed hexagonal planes (Cm III, Cm IV, and Cm V), with a stacking sequence that changes in going from one structure to the next. Thus, for the dhcp Cm I structure, the sequence is (A-B-A-C-A), which changes to (A-B-C-A) for the fcc Cm II phase by shifting planes. The fcc converts to an (A-B-A) in the Cm III phase by a shift and distortion of the planes. As in the orthorhombic Cm IV structure (space group Fddd, Cm on 8a sites), Cm III is composed of slightly distorted close-packed hexagonal planes (rectangular distortion), but in contrast to Cm IV, has a stacking that reduces the symmetry to monoclinic (the monoclinic angle is between a and c). Finally, a shift, distortion, and zigzag bending of the quasihexagonal planes yields, as in the case of Am, an (A-B-A) stacking for the Cm V phase (space group Pnma, Cm on 4c sites). The lattice parameters for Cm IV at 81(2) GPa are a = 8.925(1), b = 5.315(1), and c = 2.737(1) Å (all atomic positions fixed by symmetry) and for Cm V at 100(5) GPa are a = 4.634(1), b = 4.394(1), and c = 2.682(1) Å with atomic positions x = 0.397, y = 1/4, and z = 0.134.

The isothermal bulk modulus (B0) and its pressure derivative (B0) for Cm were determined from experimental data for the Cm I and Cm II low-pressure phases (localized f electrons) by fitting the experimental data to the Birch-Murnaghan (13) and Vinet (14) equations of state. Values of 36.5(3) GPa for B0 and 4.6(2) for B0 were obtained with both equations. The inset of Fig. 1 shows the atomic volumes of the actinide metals at ambient pressure plotted together with their bulk moduli (69, 1517).

In an attempt to understand the stability of the unusual Cm III structure with its lower C2/c symmetry, we performed calculations using the full potential linear muffin-tin orbital (FPLMTO) method (1820), in which basis functions, electron densities, and potentials are calculated without geometrical approximations. These quantities were expanded in spherical waves (with a cut-off maximum orbital angular momentum of 6) inside non-overlapping spheres surrounding the atomic sites (muffin-tin spheres) and in a Fourier series in the interstitial region between the spheres. Total energy calculations were performed with two magnetic configurations, ferromagnetic (FM) and antiferromagnetic (AFM), as a function of volume. The calculations show that the AFM configuration is always lower in energy compared to the FM configuration for all structures. For example, for the Cm III structure, the difference in energy between the AFM and FM configurations at a volume of 16 Å3 per atom (where Cm III is the stable phase) is around 30 millirydberg (mRy) per atom in favor of the AFM configuration. Total energy differences for different magnetic configurations over a wide volume range are shown in fig. S2. Furthermore, the calculations also show that the correct structural sequence can only be obtained if we treat all the structures in the AFM configuration.

Calculated total energy differences between the various structures using Cm II as the reference structure are shown in Fig. 4. The Cm III phase is theoretically stable between 17 and 15 Å3, whereas experimentally it is found between 19.6 and 17.2 Å3. In all cases, the theoretically derived critical volumes are smaller than those observed experimentally, but this is a general problem probably associated with the simulation of the core states. However, the relative sequence of phase transitions is reproduced. More importantly, the Cm III structure without magnetic correlations is not the favored crystal structure. By comparing enthalpies, we calculated the transition pressures for Cm III and found good agreement with those determined experimentally (table S1).

Fig. 4.

Calculated ab initio total energy difference between Cm II, Cm III, Cm IV, and Cm V structures as a function of volume. The energy of the Cm II phase is taken as a reference level and is shown as a horizontal line at zero. The vertical dashed lines indicate the crossover points for each phase.

The calculated magnetic moment for the Cm I phase in the AFM state starts at almost 7 Bohr magnetons (μB), as expected for the half-filled shell and full spin polarization, and in agreement with experiments at ambient pressure (21). Theoretically, as the volume is decreased, the moment decreases gradually and disappears at the Cm IV to Cm V phase transition, when the 5f electrons are completely delocalized. In the Cm III phase, the calculated AFM moment decreases from 5 to 4 μB as the pressure is increased. Experiments giving the magnetic moment of Cm as a function of pressure have not been reported.

The experiments presented here on Cm, a pivotal element at the center of the 5f actinide series, have shown that it exhibits a complex sequence of phase transitions up to 100 GPa (1 Mbar). As expected, given the immediate proximity between Am and Cm in the periodic table and that, under high pressures, both will reach states with fully delocalized (itinerant) 5f behavior, the sequences of phase transitions as a function of pressure in Am (8, 9) and Cm are similar. However, Cm exhibits an additional intermediate phase, Cm III, a monoclinic C2/c structure, that occurs before the 5f states become fully delocalized. Theoretical calculations have reproduced the experimentally observed sequence of phase transitions, but only when an AFM state is assumed for Cm with 5f electrons throughout the first few phases. The magnetic correlations in Cm are very strong in contrast to Am in which the spin (S) and orbital (L) angular momenta of the six 5f electrons cancel (S = –L = 3, thus J = L + S = 0 in Russell-Saunders coupling) and there is no magnetic moment. We thus find that the magnetic correlation energy in AFM Cm plays a crucial role in establishing its structural characteristics and, in particular, in leading to the stabilization of the Cm III structure.

In only two known cases, iron and cobalt, does the energy associated with magnetic interactions influence the crystal structure of an element as a function of volume (35). The reason is that magnetic interactions are on the scale of meV, whereas structural stabilities are on the scale of eV, although at phase transitions these differences are in the meV range. Now we have found a third element, curium, which has a half-filled shell of 5f electrons, where this magnetic phenomenon is again observed and where the magnetic correlations of f electrons determine the crystal structure. The nature of the interactions and the associated crystal structure of Cm III suggest that such effects may become prevalent in other f elements at small atomic volumes.

Supporting Online Material

Materials and Methods

Figs. S1 and S2

Table S1

References and Notes

References and Notes

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