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

Pressure-induced structural phase transitions of zirconium: anab initiostudy based on statistical ensemble theory

Recently, we put forward a direct integral approach to solve the partition function with ultrahigh efficiency and precision, which enables the rigorous ensemble theory to investigate phase behaviors of realistic condensed matters and has been successfully applied to the phase transition of vanadium metal (Ninget al2022J. Phys.: Condens. Matter34425404). In this work, the approach is applied to the structural phase transitions of zirconium metal under compressions up to 160 GPa and ultrahigh calculation precision is achieved. For the obtained equation of state with pressure over 40 GPa, the deviations from latest experiments are within0.7%and the computed transition pressure ofα→ωis 6.93 GPa, which is about five times larger than previous theoretical predictions and in excellent agreement with the measured range of 5-15 GPa. Our results support the argument that there is no existence of the isostructural phase transition of Zr metal that was asserted by recent experimental observations.

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.

Density Functional Theory Plus Dynamical Mean Field Theory within the Framework of Linear Combination of Numerical Atomic Orbitals: Formulation and Benchmarks

The combination of density functional theory with dynamical mean-field theory (DFT+DMFT) has become a powerful first-principles approach to tackle strongly correlated materials in condensed matter physics. The wide use of this approach relies on robust and easy-to-use implementations, and its implementation in various numerical frameworks will increase its applicability on the one hand and help crosscheck the validity of the obtained results on the other. In this work, we develop a formalism within the linear combination of numerical atomic orbital (NAO) basis set framework, which allows for merging of NAO-based DFT codes with DMFT quantum impurity solvers. The formalism is implemented by interfacing two NAO-based DFT codes with three DMFT impurity solvers, and its validity is testified by benchmark calculations for a wide range of strongly correlated materials, including 3d transition metal compounds, lanthanides, and actinides. Our work not only enables DFT+DMFT calculations using popular and rapidly developing NAO-based DFT code packages but also facilitates the combination of more advanced beyond-DFT methodologies available in these codes with the DMFT machinery.

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.

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.

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.

A compact dispersive refocusing Rowland circle X-ray emission spectrometer for laboratory, synchrotron, and XFEL applications

X-ray emission spectroscopy is emerging as an important complement to x-ray absorption fine structure spectroscopy, providing a characterization of the occupied electronic density of states local to the species of interest. Here, we present details of the design and performance of a compact x-ray emission spectrometer that uses a dispersive refocusing Rowland (DRR) circle geometry to achieve excellent performance for the 2-2.5 keV range, i.e., especially for the K-edge emission from sulfur and phosphorous. The DRR approach allows high energy resolution even for unfocused x-ray sources. This property enables high count rates in laboratory studies, approaching those of insertion-device beamlines at third-generation synchrotrons, despite use of only a low-powered, conventional x-ray tube. The spectrometer, whose overall scale is set by use of a 10-cm diameter Rowland circle and a new small-pixel complementary metal-oxide-semiconductor x-ray camera, is easily portable to synchrotron or x-ray free electron laser beamlines. Photometrics from measurements at the Advanced Light Source show excellent overall instrumental efficiency. In addition, the compact size of this instrument lends itself to future multiplexing to gain large factors in net collection efficiency or its implementation in controlled gas gloveboxes either in the lab or in an endstation.

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.

New developments in high pressure x-ray spectroscopy beamline at High Pressure Collaborative Access Team

The 16 ID-D (Insertion Device - D station) beamline of the High Pressure Collaborative Access Team at the Advanced Photon Source is dedicated to high pressure research using X-ray spectroscopy techniques typically integrated with diamond anvil cells. The beamline provides X-rays of 4.5-37 keV, and current available techniques include X-ray emission spectroscopy, inelastic X-ray scattering, and nuclear resonant scattering. The recent developments include a canted undulator upgrade, 17-element analyzer array for inelastic X-ray scattering, and an emission spectrometer using a polycapillary half-lens. Recent development projects and future prospects are also discussed.

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.

γ-α isostructural transition in cerium

We present zero-temperature first-principles calculations of elemental cerium and we compute its pressure-volume phase diagram within a theoretical framework able to describe simultaneously both the α and the γ phases. A surprising result revealed by our study is the presence of a clear signature of the transition at zero temperature and that this signature can be observed if and only if the spin-orbit coupling is taken into account. Our calculations indicate that the transition line in the pressure-temperature phase diagram of this material has a low-T critical point at negative pressures, placed very close to zero temperature. This suggests that cerium is very close to being "quantum critical," in agreement with recent experiments.

A versatile medium-resolution x-ray emission spectrometer for diamond anvil cell applications

We present design and performance details for a polycapillary-coupled x-ray spectrometer that provides very high collection efficiency at a moderate energy resolution suitable for many studies of nonresonant x-ray emission spectroscopy, especially for samples of heavy elements under high pressures. Using a single Bragg analyzer operating close to backscattering geometry so as to minimize the effect of the weak divergence of the quasicollimated exit beam from the polycapillary optic, this instrument can maintain a typical energy resolution of 5 eV over photon energies from 5 keV to 10 keV. We find dramatically improved count rates as compared to a traditional higher-resolution instrument based on a single spherically bent crystal analyzer.

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.