Thermal signatures of the Kondo volume collapse in cerium

Dynamic compression of Ce and Pr with millisecond time-resolved X-ray diffraction

Both cerium (Ce) and praseodymium (Pr) undergo a volume collapse transition under compression that originate from similar electronic mechanisms. Yet the outcome could not be more different. In the case of Ce with one affected 4f electron the volume collapse leaves the crystal symmetry intact, whereas for Pr with two 4f electrons the crystal symmetry changes from a distorted face centered cubic structure to a lower symmetry orthorhombic structure. In this paper, we present a study of the effect of strain/compression rate spanning nearly 4 orders of magnitude on the volume collapse phase transitions in Ce and Pr. These dynamic compression experiments in a diamond anvil cell also reveal kinetic differences between the phase transformations observed in these two materials. The transition cannot be overdriven in pressure in Ce, which indicates a fast kinetic process, whereas fast compression rates in Pr lead to a shift of the phase boundary to higher pressures, pointing to slower kinetics possibly due to the realization of a new crystal structure.

γ-αphase transition of elemental cerium metal

The isostructuralγ-αphase transition in elemental cerium has been the subject of many experimental and theoretical studies over almost the past century without a universally agreed upon mechanism. Here, we report the results of an extensive study of electronic and magnetic structures,f-electron number, entanglement entropy, and elastic properties of cerium in the GGA +Uframework. We have found that almost all changes in the studied quantities mimic their behavior in the phase transition and could be related to the symmetry of the 4foccupation and the small change in HubbardUnear a critical value.

Pressure-Driven Sequential Lattice Collapse and Magnetic Collapse in Transition-Metal-Intercalated Compounds FexNbS2

Volume collapse under high pressure is an intriguing phenomenon involving subtle interplay between lattice, spin, and charge. The two most important causes of volume collapse are lattice collapse (low-density to high-density) and magnetic collapse (high-spin to low-spin). Herein we report the pressure-driven sequential volume collapses in partially intercalated Fe_xNbS₂ (x = 1/4, 1/3, 1/2, 2/3). Because of the distinct interlayer atomic occupancy, the low-iron-content samples exhibit both lattice and magnetic collapses under compression, whereas the high-iron-content samples exhibit only one magnetic collapse. Theoretical calculations indicate that the low-pressure volume collapses for x = 1/4 and x = 1/3 are lattice collapses, and the high-pressure volume collapses for all four samples are magnetic collapses. The magnetic collapse involving the high-spin to low-spin crossover of Fe²⁺ has also been verified by in situ X-ray emission measurements. Integrating two distinct volume collapses into one material provides a rare playground of lattice, spin, and charge.

Colossal Pressure-Induced Softening in Scandium Fluoride

The counterintuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behavior that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealized model and neutron diffraction at variable temperature and pressure, we show the existence of extraordinary and unprecedented pressure-induced softening in the negative thermal expansion material scandium fluoride ScF_{3}. The pressure derivative of the bulk modulus B, B^{'}=(∂B/∂P)_{P=0}, reaches values as low as -220±30 at 50 K, and is constant at -50 between 150 and 250 K.

The high-pressure, high-temperature phase diagram of cerium

We present an experimental study of the high-pressure, high-temperature behaviour of cerium up to ∼22 GPa and 820 K using angle-dispersive x-ray diffraction and external resistive heating. Studies above 820 K were prevented by chemical reactions between the samples and the diamond anvils of the pressure cells. We unambiguously measure the stability region of the orthorhombicoC4 phase and find it reaches its apex at 7.1 GPa and 650 K. We locate the α-cF4-oC4-tI2 triple point at 6.1 GPa and 640 K, 1 GPa below the location of the apex of theoC4 phase, and 1-2 GPa lower than previously reported. We find the α-cF4 →tI2 phase boundary to have a positive gradient of 280 K (GPa)-1, less steep than the 670 K (GPa)-1reported previously, and find theoC4 →tI2 phase boundary to lie at higher temperatures than previously found. We also find variations as large as 2-3 GPa in the transition pressures at which theoC4 →tI2 transition takes place at a given temperature, the reasons for which remain unclear. Finally, we find no evidence that the α-cF4 →tI2 is not second order at all temperatures up to 820 K.

Kondo-Induced Giant Isotropic Negative Thermal Expansion

Negative thermal expansion is an unusual phenomenon appearing in only a handful of materials, but pursuit and mastery of the phenomenon holds great promise for applications across disciplines and industries. Here we report use of x-ray spectroscopy and diffraction to investigate the 4f-electronic properties in Y-doped SmS and employ the Kondo volume collapse model to interpret the results. Our measurements reveal an unparalleled decrease of the bulk Sm valence by over 20% at low temperatures in the mixed-valent golden phase, which we show is caused by a strong coupling between an emergent Kondo lattice state and a large isotropic volume change. The amplitude and temperature range of the negative thermal expansion appear strongly dependent on the Y concentration and the associated chemical disorder, providing control over the observed effect. This finding opens avenues for the design of Kondo lattice materials with tunable, giant, and isotropic negative thermal expansion.

Probing Cerium 4f States across the Volume Collapse Transition by X-ray Raman Scattering

Understanding the volume collapse phenomena in rare-earth materials remains an important challenge due to a lack of information on 4f electronic structures at different pressures. Here, we report the first high-pressure inelastic X-ray scattering measurement on elemental cerium (Ce) metal. By overcoming the ultralow signal issue in the X-ray measurement at the Ce N_4,5-edge, we observe the changes of unoccupied 4f states across the volume collapse transition around 0.8 GPa. To help resolve the longstanding debate on the Anderson-Kondo and Mott-Hubbard models, we further compare the experiments with extended multiplet calculations that treat both screening channels on equal footing. The results indicate that a modest change in the 4f-5d Kondo coupling can well describe the spectral redistribution across the volume collapse, whereas the hybridization between neighboring atoms in the Hubbard model appears to play a minor role. Our study helps to constrain the theoretical models and opens a promising new route for systematic investigation of volume collapse phenomena in rare-earth materials.

Pressure Effects on the 4f Electronic Structure of Light Lanthanides

Using the satellite structure of the Lγ_{1} line in nonresonant x-ray emission spectra, we probe the high-pressure evolution of the bare 4f signature of the early light lanthanides at ambient temperature. For Ce and Pr the satellite peak experiences a sudden reduction concurrent with their respective volume collapse (VC) transitions. These new experimental results are supported by calculations using state-of-the-art extended atomic structure codes for Ce and Pr, and also for Nd, which does not exhibit a VC. Our work suggests that changes to the 4f occupation are more consistently associated with evolution of the satellite than is the reduction of the 4f moment. Indeed, we show that in the case of Ce, mixing of a higher atomic angular momentum state, driven by the increased hybridization, acts to obscure the expected satellite reduction. These measurements emphasize the importance of a unified study of a full set of microscopic observables to obtain the most discerning test of the underlying, fundamental f-electron phenomena at high pressures.

Electronic correlations in cerium's high-pressure phases

Under high pressure, cerium exhibits three distinct phases, namely [Formula: see text], [Formula: see text], and ϵ-cerium. It is unclear whether the 4f electronic correlations will play a vital role in these phases or not. By utilizing the combination of traditional density functional theory and single-site dynamical mean-field theory, we tried to calculate the electronic structures of cerium's high-pressure phases. Their momentum-resolved spectral functions, total and 4f partial density of states, local self-energy functions, and 4f electronic configurations were exhaustively studied. The calculated results show that the correlated 4f bands strongly hybridize with the conducting spd bands around the Fermi level. The Matsubara self-energy functions exhibit Fermi-liquid like characteristic in the low-frequency regime. In addition, the fluctuations among the 4f atomic eigenstates are somewhat prominent (especially for the ϵ phase), which lead to slight modification of the 4f occupancy. It is suggested that the 4f electrons in these phases tend to be itinerant.

Molecular Dynamics Investigation of Residual Stress and Surface Roughness of Cerium under Diamond Cutting

Machined surface quality in terms of residual stress and surface roughness has an important influence on the performance of devices and components. In the present work, we elucidate the formation mechanisms of residual stress and surface roughness of single crystalline cerium under ultraprecision diamond cutting by means of molecular dynamics simulations. Influences of machining parameters, such as the rake angle of a cutting tool, depth of cut, and crystal orientation of the workpiece on the machined surface quality were also investigated. Simulation results revealed that dislocation activity and lattice distortion are the two parallel factors that govern the formation of both residual stress and surface roughness. It was found that both distributions of residual stress and surface roughness of machined surface are significantly affected by machining parameters. The optimum machining parameters for achieving high machined surface quality of cerium by diamond cutting are revealed.

Molecular Dynamics Modeling and Simulation of Diamond Cutting of Cerium

The coupling between structural phase transformations and dislocations induces challenges in understanding the deformation behavior of metallic cerium at the nanoscale. In the present work, we elucidate the underlying mechanism of cerium under ultra-precision diamond cutting by means of molecular dynamics modeling and simulations. The molecular dynamics model of diamond cutting of cerium is established by assigning empirical potentials to describe atomic interactions and evaluating properties of two face-centered cubic cerium phases. Subsequent molecular dynamics simulations reveal that dislocation slip dominates the plastic deformation of cerium under the cutting process. In addition, the analysis based on atomic radial distribution functions demonstrates that there are trivial phase transformations from the γ-Ce to the δ-Ce occurred in both machined surface and formed chip. Following investigations on machining parameter dependence reveal the optimal machining conditions for achieving high quality of machined surface of cerium.

Anomalous elastic properties across the γ to α volume collapse in cerium

The behavior of the f-electrons in the lanthanides and actinides governs important macroscopic properties but their pressure and temperature dependence is not fully explored. Cerium with nominally just one 4f electron offers a case study with its iso-structural volume collapse from the γ-phase to the α-phase ending in a critical point (p_C, V_C, T_C), unique among the elements, whose mechanism remains controversial. Here, we present longitudinal (c_L) and transverse sound speeds (c_T) versus pressure from higher than room temperature to T_C for the first time. While c_L experiences a non-linear dip at the volume collapse, c_T shows a step-like change. This produces very peculiar macroscopic properties: the minimum in the bulk modulus becomes more pronounced, the step-like increase of the shear modulus diminishes and the Poisson’s ratio becomes negative—meaning that cerium becomes auxetic. At the critical point itself cerium lacks any compressive strength but offers resistance to shear.

The origin of the volume collapse of cerium, the only elemental metal with a critical point in the solid phase, remains elusive. Here the authors show that, near the critical point, the f-electrons make cerium lose its compressive strength while maintaining a finite shear strength—which makes cerium unexpectedly auxetic.

High-pressure studies with x-rays using diamond anvil cells

Pressure profoundly alters all states of matter. The symbiotic development of ultrahigh-pressure diamond anvil cells, to compress samples to sustainable multi-megabar pressures; and synchrotron x-ray techniques, to probe materials' properties in situ, has enabled the exploration of rich high-pressure (HP) science. In this article, we first introduce the essential concept of diamond anvil cell technology, together with recent developments and its integration with other extreme environments. We then provide an overview of the latest developments in HP synchrotron techniques, their applications, and current problems, followed by a discussion of HP scientific studies using x-rays in the key multidisciplinary fields. These HP studies include: HP x-ray emission spectroscopy, which provides information on the filled electronic states of HP samples; HP x-ray Raman spectroscopy, which probes the HP chemical bonding changes of light elements; HP electronic inelastic x-ray scattering spectroscopy, which accesses high energy electronic phenomena, including electronic band structure, Fermi surface, excitons, plasmons, and their dispersions; HP resonant inelastic x-ray scattering spectroscopy, which probes shallow core excitations, multiplet structures, and spin-resolved electronic structure; HP nuclear resonant x-ray spectroscopy, which provides phonon densities of state and time-resolved Mössbauer information; HP x-ray imaging, which provides information on hierarchical structures, dynamic processes, and internal strains; HP x-ray diffraction, which determines the fundamental structures and densities of single-crystal, polycrystalline, nanocrystalline, and non-crystalline materials; and HP radial x-ray diffraction, which yields deviatoric, elastic and rheological information. Integrating these tools with hydrostatic or uniaxial pressure media, laser and resistive heating, and cryogenic cooling, has enabled investigations of the structural, vibrational, electronic, and magnetic properties of materials over a wide range of pressure-temperature conditions.

Free Energy from Stationary Implementation of the DFT+DMFT Functional

The stationary functional of the density functional plus embedded dynamical mean field theory formalism to perform free energy calculations and structural relaxations is implemented for the first time. Here, the first order error in the density leads to a much smaller, second order error in the free energy. The method is applied to several well-known correlated materials: metallic SrVO_{3}, Mott insulating FeO, and elemental cerium, to show that it predicts the lattice constants with good accuracy. In cerium, we show that our method predicts the isostructural transition between the α and γ phases, and resolve the long-standing controversy in the driving mechanism of this transition.

New developments in micro-X-ray diffraction and X-ray absorption spectroscopy for high-pressure research at 16-BM-D at the Advanced Photon Source

The monochromator and focusing mirrors of the 16-BM-D beamline, which is dedicated to high-pressure research with micro-X-ray diffraction (micro-XRD) and X-ray absorption near edge structure (XANES) (6-45 keV) spectroscopy, have been recently upgraded. Monochromatic X-rays are selected by a Si (111) double-crystal monochromator operated in an artificial channel-cut mode and focused to 5 μm × 5 μm (FWHM) by table-top Kirkpatrick-Baez type mirrors located near the sample stage. The typical X-ray flux is ∼5 × 10(8) photons/s at 30 keV. The instrumental resolution, Δq/qmax, reaches to 2 × 10(-3) and is tunable through adjustments of the detector distance and X-ray energy. The setup is stable and reproducible, which allows versatile application to various types of experiments including resistive heating and cryogenic cooling as well as ambient temperature compression. Transmission XANES is readily combined with micro-XRD utilizing the fixed-exit feature of the monochromator, which allows combined XRD-XANES measurements at a given sample condition.

Cerium; crystal structure and position in the periodic table

The properties of the cerium metal have intrigued physicists and chemists for many decades. In particular a lot of attention has been directed towards its high pressure behavior, where an isostructural volume collapse (γ phase → α phase) has been observed. Two main models of the electronic aspect of this transformation have been proposed; one where the 4f electron undergoes a change from being localized into an itinerant metallic state, and one where the focus is on the interaction between the 4f electron and the conduction electrons, often referred to as the Kondo volume collapse model. However, over the years it has been repeatedly questioned whether the cerium collapse really is isostructural. Most recently, detailed experiments have been able to remove this worrisome uncertainty. Therefore the isostructural aspect of the α-γ transition has now to be seriously addressed in the theoretical modeling, something which has been very much neglected. A study of this fundamental characteristic of the cerium volume collapse is made in present paper and we show that the localized ⇌ delocalized 4f electron picture provides an adequate description of this unique behavior. This agreement makes it possible to suggest that an appropriate crossroad position for cerium in The Periodic Table.

Strength and Debye temperature measurements of cerium across the γ → α volume collapse: the lattice contribution

The longitudinal and transverse sound speeds, cL and cT, of polycrystalline cerium were measured under pressure across the iso-structural γ-α phase transition at 0.75 GPa to beyond 3 GPa. In contrast to previous methods all quantities were directly obtained and no assumptions were made about the size of the volume collapse. Up to the transition our values for cL are in excellent agreement with previous ones, while our values for cT are significantly lower. We deduce values for the adiabatic bulk modulus BS, the shear modulus [Formula: see text], and the pressure dependent Debye temperature, ΘD(p). ΘD(p) is in good agreement with recent results derived from phonon dispersion measurements on single crystals. The ratio of the Debye temperature values bracketing the transition indicates a lattice contribution to the entropy change across the volume collapse, ΔSvib(γ → α) ≈ (0.68 ± 0.06)kB, consistent with previous results obtained by neutron scattering, but significantly larger than other previously determined values.

First-order liquid-liquid phase transition in cerium

We report the first experimental observation of a liquid-liquid phase transition in the monatomic liquid metal cerium, by means of in situ high-pressure high-temperature x-ray diffraction experiments. At 13 GPa, upon increasing temperature from 1550 to 1900 K high-density liquid transforms to a low-density liquid, with a density difference of 14%. Theoretic models based on ab initio calculations are built to investigate the observed phase behavior of the liquids at various pressures. The results suggest that the transition primarily originates from the delocalization of f electrons and is deemed to be of the first order that terminates at a critical point.

X-ray emission spectroscopy of cerium across the γ-α volume collapse transition

High-pressure x-ray emission measurements are used to provide crucial evidence in the longstanding debate over the nature of the isostructural (α, γ) volume collapse in elemental cerium. Extended local atomic model calculations show that the satellite of the Lγ emission line offers direct access to the total angular momentum observable (J(2)). This satellite experiences a 30% steplike decrease across the volume collapse, validating the Kondo model in conjunction with previous measurements. Direct comparisons are made with previous predictions by dynamical mean field theory. A general experimental methodology is demonstrated for analogous work on a wide range of strongly correlated f-electron systems.

Density-functional theory for f-electron systems: the α-γ phase transition in cerium

The isostructural α-γ phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact-exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional gives rise to two distinct solutions at zero temperature that can be associated with the α and γ phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the γ phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare-earth systems.

A miniature X-ray emission spectrometer (miniXES) for high-pressure studies in a diamond anvil cell

Core-shell X-ray emission spectroscopy (XES) is a valuable complement to X-ray absorption spectroscopy (XAS) techniques. However, XES in the hard X-ray regime is much less frequently employed than XAS, often as a consequence of the relative scarcity of XES instrumentation having energy resolutions comparable with the relevant core-hole lifetimes. To address this, a family of inexpensive and easily operated short-working-distance X-ray emission spectrometers has been developed. The use of computer-aided design and rapid prototype machining of plastics allows customization for various emission lines having energies from ∼3 keV to ∼10 keV. The specific instrument described here, based on a coarsely diced approximant of the Johansson optic, is intended to study volume collapse in Pr metal and compounds by observing the pressure dependence of the Pr Lα emission spectrum. The collection solid angle is ∼50 msr, roughly equivalent to that of six traditional spherically bent crystal analyzers. The miniature X-ray emission spectrometer (miniXES) methodology will help encourage the adoption and broad application of high-resolution XES capabilities at hard X-ray synchrotron facilities.

Phonons of the anomalous element cerium

Many physical and chemical properties of the light rare-earths and actinides are governed by the active role of f electrons, and despite intensive efforts the details of the mechanisms of phase stability and transformation are not fully understood. A prominent example which has attracted a lot of interest, both experimentally and theoretically over the years is the isostructural γ - α transition in cerium. We have determined by inelastic X-ray scattering, the complete phonon dispersion scheme of elemental cerium across the γ → α transition, and compared it with theoretical results using ab initio lattice dynamics. Several phonon branches show strong changes in the dispersion shape, indicating large modifications in the interactions between phonons and conduction electrons. This is reflected as well by the lattice Grüneisen parameters, particularly around the X point. We derive a vibrational entropy change ΔS(γ-α)(vib) ≈ (0.33+/-0.03)k(B), illustrating the importance of the lattice contribution to the transition. Additionally, we compare first principles calculations with the experiments to shed light on the mechanism underlying the isostructural volume collapse in cerium under pressure.

Diffusionless γ⇄α phase transition in polycrystalline and single-crystal cerium

The cerium γ⇄α transition was investigated using high-pressure, high-temperature angle-dispersive x-ray diffraction measurements on both poly- and single-crystalline samples, explicitly addressing symmetry change and transformation paths. The isomorphic hypothesis of the transition is confirmed, with a transition line ending at a solid-solid critical point. The critical exponent is determined, showing a universal behavior that can be pictured as a liquid-gas transition. We further report an isomorphic transition between two single crystals (with more than 14% of volume difference), an unparalleled observation in solid-state matter interpreted in terms of dislocation-induced diffusionless first-order phase transformation.

Reentrant and isostructural transitions in a cluster-crystal former

We study the low-temperature behavior of a simple cluster-crystal forming system through simulation. We find the phase diagram to be hybrid between the Gaussian core model and the penetrable sphere model. The system additionally exhibits S-shaped doubly reentrant phase sequences as well as critical isostructural transitions between crystals of different average lattice site occupancy. Because of the possible annihilation of lattice sites and accompanying clustering, the system moreover shows an unusual softening upon compression.

Low-density to high-density transition in Ce75Al23Si2 metallic glass

Using in situ high-pressure x-ray diffraction (XRD), we observed a pressure-induced polyamorphic transition from the low-density amorphous (LDA) state to the high-density amorphous (HDA) state in Ce(75)Al(23)Si(2) metallic glass at about 2 GPa and 300 K. The thermal stabilities of both LDA and HDA metallic glasses were further investigated using in situ high-temperature and high-pressure XRD, which revealed different pressure dependences of the onset crystallization temperature (T(x)) between them with a turning point at about 2 GPa. Compared with Ce(75)Al(25) metallic glass, minor Si doping shifts the onset polyamorphic transition pressure from 1.5 to 2 GPa and obviously stabilizes both LDA and HDA metallic glasses with higher T(x) and changes their slopes dT(x)/dP. The results obtained in this work reveal another polyamorphous metallic glass system by minor alloying (e.g. Si), which could modify the transition pressure and also properties of LDA and HDA metallic glasses. The minor alloying effect reported here is valuable for the development of more polyamorphous metallic glasses, even multicomponent bulk metallic glasses with modified properties, which will trigger more investigations in this field and improve our understanding of polyamorphism and metallic glasses.

Large volume collapse observed in the phase transition in cubic PbCrO3 perovskite

When cubic PbCrO(3) perovskite (Phase I) is squeezed up to approximately 1.6 GPa at room temperature, a previously undetected phase (Phase II) has been observed with a 9.8% volume collapse. Because the structure of Phase II can also be indexed into a cubic perovskite as Phase I, the transition between Phases I and II is a cubic to cubic isostructural transition. Such a transition appears independent of the raw materials and synthesizing methods used for the cubic PbCrO(3) perovskite sample. In contrast to the high-pressure isostructural electronic transition that appears in Ce and SmS, this transition seems not related with any change of electronic state, but it could be possibly related on the abnormally large volume and compressibility of the PbCrO(3) Phase I. The physical mechanism behind this transition and the structural and electronic/magnetic properties of the condensed phases are the interesting issues for future studies.

Origin of pressure-induced polyamorphism in Ce75Al25 metallic glass

Using high-pressure synchrotron x-ray absorption spectroscopy, we observed the Ce 4f electron in Ce(75)Al(25) metallic glass transform from its ambient localized state to an itinerant state above 5 GPa. A parallel x-ray diffraction study revealed a volume collapse of about 8.6%, coinciding with 4f delocalization. The transition started from a low-density state below 1.5 GPa, went through continuous densification ending with a high-density state above 5 GPa. This new type of electronic polyamorphism in densely packed metallic glass is dictated by the Ce constituent, and is fundamentally distinct from the well-established structural polyamorphism in which densification is caused by coordination change and atomic rearrangement.

Substitutional alloy of Ce and Al

The formation of substitutional alloys has been restricted to elements with similar atomic radii and electronegativity. Using high-pressure at 298 K, we synthesized a face-centered cubic disordered alloy of highly dissimilar elements (large Ce and small Al atoms) by compressing the Ce(3)Al intermetallic compound >15 GPa or the Ce(3)Al metallic glass >25 GPa. Synchrotron X-ray diffraction, Ce L(3)-edge absorption spectroscopy, and ab initio calculations revealed that the pressure-induced Kondo volume collapse and 4f electron delocalization of Ce reduced the differences between Ce and Al and brought them within the Hume-Rothery (HR) limit for substitutional alloying. The alloy remained after complete release of pressure, which was also accompanied by the transformation of Ce back to its ambient 4f electron localized state and reversal of the Kondo volume collapse, resulting in a non-HR alloy at ambient conditions.