Role of the Lattice in theγ→αPhase Transition of Ce: A High-Pressure Neutron and X-Ray Diffraction Study

Abstract

The temperature and pressure dependence of the thermal displacements and lattice parameters were obtained across the γ → α phase transition of Ce using high-pressure, high-resolution neutron and synchrotron x-ray powder diffraction. The estimated vibrational entropy change per atom in the γ → α phase transition, ∆S γ−α vib ≈ (0.75±0.15)kB, is about half of the total entropy change. The bulk modulus follows a power-law pressure dependence which is well described using the framework of electron-phonon coupling. These results clearly demonstrate the importance of lattice vibrations, in addition to the spin and charge degrees of freedom, for a complete description of the γ → α phase transition in elemental Ce.PACS numbers: 64.70. Kb, 71.27.+a, 61.12.Ld Materials with electrons near the boundary between itinerant and localized behavior continue to present a major theoretical challenge to a complete description of their properties, including multiple phases and anomalous thermodynamics. This is particularly true in the 4f and 5f systems, where this boundary appears to occur in or near the elements Ce and Pu, respectively [1]. In Pu, which possesses five allotropic phases at ambient pressure, a partial localization of some of the five 5f electrons appears necessary to understand the higher temperature phases [2]. Partial localization may also be present in U compounds [3]. Ce metal is in principle simpler, possessing only a single 4f electron, but still displays four different phases at ambient pressure. One of the most interesting and still not completely understood phenomena in Ce is the isostructural (fcc) γ → α phase transition, which involves about 17% volume collapse at room temperature and pressure of roughly 0.8 GPa [4].In the majority of theoretical models [4,5,6,7,8,9, 10] the γ → α transition has been attributed to an instability of the single 4f 1 electron. The earliest models focused on charge instability, while later models dealt with spin instability. The promotional model postulates a transition from 4f 1 5d 1 6s 2 (γ-phase) to 4f 0 5d 2 6s 2 (α-phase), but is inconsistent with the 4f binding energy and the cohesive energies of other 5d 2 6s 2 materials [5]. In the Mott transition (MT) model [5,6] the 4f electron in the γ phase is localized and non-binding, but is itinerant and binding in the lower volume α phase. The energy for the phase transition is provided by the kinetic energy of the itinerant f electron. In the Kondo-volumecollapse (KVC) model [9, 10] the 4f electron is assumed to be localized in both the γ and α phases, and the phase transition is driven by the Kondo spin fluctuation energy and entropy within the context of the single-impurity Anderson model. These early models ignored altogether an explicit treatment of the lattice degrees of freedom; even the lattice entropy is not considered. More recent treatments [8,11,12] include both the lattice and spin entropies, but still do not deal explicitly with the consequences of electron-lattice coupling despite the large volume collapse at t...

Screening of4fmoments and delocalization in the compressed light rare earths

“…Since LDA+DMFT calculations do hint at a Van der Waals loop in the Ce free energy at about the right place, 42,43,44,46 the full story for Pr and Nd may await inclusion of the Hund's rules exchange for these multi-f electron cases, assumption of the correct structures for all phases (e.g., α-U), and possibly also adding lattice vibrational contributions. 56,57 Even so, this work suggests that the collapse transitions may not be the predominant story in the compressed trivalent rare earths, but rather consequences of an underlying and more robust evolution associated with 4f -electron delocalization. the latter are essentially on top of one another except for the charge case at the smallest volumes.…”

“…14 These temperature senstivities are also a reminder of the need to include lattice vibrational contributions, which may themselves further modify the nature of the collapse transitions. 56,57 …”

Phonons of the anomalous element cerium

“…The phonon density of states (PDOS) of a Ce 0.9 Th 0.1 alloy at 150 K (γ-phase) and 140 K (α-phase) determined by inelastic neutron scattering (INS) (11) display very small differences across the transition, so that changes in the vibrational entropy, ΔS γ−α vib , have been suggested to be negligible. In contrast, high-pressure X-ray and neutron diffraction studies on polycrystalline Ce concluded that ΔS γ−α vib accounts for roughly half of the total entropy change (12). Further evidence for a large role of the vibrational energetics is provided by recent ultrasonic investigations (13,14) and a combined highpressure and high-temperature X-ray diffraction study (15).…”

Thermodynamics of volume-collapse transitions in cerium and related compounds

“…The divergence of the compressibility discussed above implies that the bulk modulus vanishes as |p − p ↑ | 1/2 and jumps discontinuously to a finite value for p > p ↑ . Remarkably, after this work was completed and a preliminary version of it was posted [29] this prediction was experimentally verified in Ce [30].…”