Mannardite, Ba[(Ti 4+ ) 6 (V 3+ ) 2 ]O 16 , a mineral of the hollandite supergroup, is characterized by a tunnel structure built up from double chains of edge-sharing octahedra. It shows complex order/disorder phenomena that are often related to the occurrence of diffuse scattering, satellite reflections or both. So far, diffuse scattering features have been linked to ordering of large cations in the tunnel, but recent studies on hollandite sensu stricto suggested that other contributions could play an important role in determining diffuse scattering features. New single-crystal X-ray diffuse scattering data, modelling with Monte Carlo simulations and the three-dimensional difference pair-distribution function (3D-ΔPDF) approach unveil a complex scenario, involving interactions not only between the Ba 2+ cations in the tunnel, trying to avoid each other, but also among neighbouring tunnels. Short-range order observed within and between the tunnels is coupled with framework relaxation. The possible occurrence of additional cation sites in the channel, as reported in some synthetic hollandites and electrode materials, is discussed on the basis of the diffuse scattering features and modelling. This study highlights the importance of a thorough characterization of short-range order to understand, and thus tune, the physical properties of hollandite-like materials.

The crux of understanding the superconducting mechanism in pressurized Ruddlesden-Popper nickelates hinges on elucidating their structural phases. Under ambient conditions, the trilayer nickelate La4Ni3O10 stabilizes in a twinned monoclinic structure with space group P21/c. Upon heating, it undergoes a structural transition to the tetragonal I4/mmm phase at Ts ≈ 1030 K, while a second transition associated with the onset of density-wave (DW) ordering emerges upon cooling below TDW ≈ 135 K. Here, from pressure-temperature x-ray diffraction (XRD) on high quality flux-grown single crystals we demonstrate a direct tetragonal-to-monoclinic transition without an intermediate orthorhombic Bmab phase. Ab initio density-functional theory calculations as a function of pressure corroborate the experimental observations. The tetragonal-to-monoclinic transition unfolds as the formation of a two-fold superstructure, as evidenced by the emergence of commensurate superlattice reflections and can be progressively suppressed from 1030 K down to 20 K under 14 GPa. Notably, from XRD we establish the observation of weak incommensurate satellite reflections associated with the DW ordering in flux-grown samples, as previous findings were confined only to crystals grown by the floating-zone technique. This is further reinforced by Raman spectroscopy that reveal the emergence of additional phonon modes below 130 K, concomitant with the onset of the incommensurate DW state. Understanding the superconducting mechanism in pressurized Ruddlesden-Popper nickelates requires insight into their structural phases. Here, the authors use pressure-temperature XRD and ab initio calculations to reveal a direct tetragonal-to-monoclinic transition in La4Ni3O10, highlighting the suppression of this transition under pressure and the presence of intrinsic incommensurate density-wave ordering.

Nanometer-scale modulations can spontaneously emerge in complex materials when multiple degrees of freedom interact. Here we demonstrate that ferroelectric Sr_{1-x}Ca_{x}TiO_{3} lies in close proximity to a finite-q lattice instability associated with a tendency toward structural modulation. Using inelastic neutron and x-ray scattering, we show that upon cooling, dipolar fluctuations strongly couple to and soften the c_{44} transverse acoustic mode. We identify the wave vector at which this softening is maximal, thereby defining the characteristic length scale of the instability. Calcium substitution enhances both the amplitude and the wavevector of the softening by strengthening the ferroelectric and antiferrodistortive instabilities. Our results demonstrate that the flexoelectric phonon coupling promotes a tendency toward a dynamically modulated state that cooperates with, rather than competes against, the other lattice instabilities in SrTiO_{3}.

Mannardite, Ba[(Ti4+)6(V3+)2]O16, a mineral of the hollandite supergroup, is characterized by a tunnel structure built up from double chains of edge-sharing octahedra. It shows complex order/disorder phenomena that are often related to the occurrence of diffuse scattering, satellite reflections or both. So far, diffuse scattering features have been linked to ordering of large cations in the tunnel, but recent studies on hollandite sensu stricto suggested that other contributions could play an important role in determining diffuse scattering features. New single-crystal X-ray diffuse scattering data, modelling with Monte Carlo simulations and the three-dimensional difference pair-distribution function (3D-ΔPDF) approach unveil a complex scenario, involving interactions not only between the Ba2+ cations in the tunnel, trying to avoid each other, but also among neighbouring tunnels. Short-range order observed within and between the tunnels is coupled with framework relaxation. The possible occurrence of additional cation sites in the channel, as reported in some synthetic hollandites and electrode materials, is discussed on the basis of the diffuse scattering features and modelling. This study highlights the importance of a thorough characterization of short-range order to understand, and thus tune, the physical properties of hollandite-like materials.

Nanometer-scale modulations can spontaneously emerge in complex materials when multiple degrees of freedom interact. Here we demonstrate that ferroelectric Sr_1-xCa_xTiO_3 lies in close proximity to an incipient structurally modulated phase. Using inelastic neutron and X-ray scattering, we show that upon cooling, dipolar fluctuations strongly couple to and soften the c_44 transverse acoustic mode. We identify the wavevector at which this softening is maximal, thereby defining the characteristic length scale of the modulation. Calcium substitution enhances both the amplitude and the wavevector of the softening by strengthening the ferroelectric and antiferrodistortive instabilities. Our results demonstrate that nonlinear flexoelectric phonon coupling tends to stabilize a modulated state that cooperates with, rather than competes against, the other lattice instabilities in SrTiO_3.

This contribution presents a measurement protocol and a data-reduction workflow for obtaining single-crystal X-ray total-scattering datasets that capture both Bragg-peak and diffuse-scattering intensities on an absolute (electrons 2 per atom) scale. It demonstrates that the intensity scale factor derived from crystallographic refinements using Bragg peaks is in reasonable agreement with the scale obtained by matching the scattering function, computed via spherical integration of the 3D total-scattering signal, to the theoretical coherent baseline. This baseline is calculated from the Debye–Waller factor. The latter scaling approach can be applied to diffuse scattering without including Bragg peaks. These results lay the groundwork for structural refinements using large atomic configurations while simultaneously fitting Bragg intensities and diffuse scattering from a single crystal. Moreover, with the convergence between the two scaling methods, the Bragg and diffuse components can be obtained from the same total-scattering dataset, as achieved in this work, or measured independently.

The m = 2 member of the monophosphate tungsten bronze family had been thought to be the only one without an electronic instability at low temperature. In this paper, we report the discovery of a charge density wave phase in this compound, with a transition temperature of 290 K and an incommensurate modulation vector q = 0.245b* + ξc*, which reaches a lock-in with a commensurate vector at 130 K. The presence of this new phase is confirmed by diffraction and resistivity measurements. Pre-transitional dynamics are investigated using diffuse and inelastic X-ray scattering, revealing a clear Kohn anomaly. We analyze both structural and electronic contributions to the phase transition, providing a comprehensive picture of the mechanism driving this newly identified instability.

Charge-density-wave (CDW) order and superconductivity coexist in the kagome metals AV_3Sb_5 (A=K, Cs, Rb), raising fundamental questions about the mechanisms driving their intertwined phases. Here we combine high-resolution inelastic X-ray scattering with first-principles calculations to uncover the origin of CDW formation in CsV_3Sb_5. Guided by structure factor analysis, we identify a soft phonon mode along the reciprocal M-L direction, with the strongest effect at the L point, where the elastic scattering intensity also grows most rapidly upon cooling. First-principles calculations incorporating lattice anharmonicity and electron-phonon coupling reproduce these observations and establish a soft-mode instability at the L point as the driving mechanism of CDW formation. Despite the weakly first-order character of the transition, our results unambiguously demonstrate that the CDW in CsV_3Sb_5 originates from a softened phonon, clarifying its microscopic origin and highlighting the central role of lattice dynamics in kagome metals.

VO2 features concomitant structural and metal-insulator transitions. This poses a challenge for understanding the underlying mechanism: Is the transition triggered by a structural or by an electronic instability? The two scenarios are expected to produce very different pretransitional fluctuations above TC. By combining magnetic susceptibility, IR reflectivity, and x-ray diffuse scattering measurements, we observe that metallic VO2 features strong electronic and structural fluctuations toward the insulating monoclinic phase. By measuring resonant diffuse x-ray scattering across the vanadium K edge, we search for a potential decoupling between electronic and structural ordering in these fluctuations, finding no evidence of it. While our results do not completely rule out pure electronic fluctuations, they constrain them, favoring the interpretation that the VO2 metal-insulator transition is triggered by a structural instability. Our work offers a unique approach to solve similar problems in other strongly correlated systems.

Relaxor ferroelectrics underpin high-performance actuators and sensors, yet the nature of polar heterogeneities driving their broadband dielectric response remains debated. Using a unified, multimodal structural refinement framework- simultaneously fitting complementary X-ray and neutron total scattering, X-ray absorption spectra, and diffuse scattering-we reconstruct 3D mesoscale polarization maps in the classic relaxor system PbMg1/3Nb2/3O3-PbTiO3. We uncover self-organized swirling polarization textures with half-skyrmion (meron) vortices, challenging models of independent polar nanoregions. These textures, characterized by smooth changes in the polarization direction, originate from overlapping volumes in which the projections of locally correlated polarization vectors onto each volume's long axis share the same sign. Vortex cores correlate strongly with local charge and strain gradients imposed by compositional heterogeneities. In this work, our results suggest that chemical disorder, acting via depolarizing and strain fields, stabilizes topological vortex textures of the polarization field, offering a route for engineering new dielectric and ferroelectric functionalities.

Suppressing of an ordered state that competes with superconductivity is one route to enhance superconducting transition temperatures. Whereas the effect of suppressing magnetic states is still not fully understood, materials featuring charge-density waves and superconductivity offer a clearer scenario as both states can be associated with electron-phonon coupling. Metallic transition-metal dichalcogenides are prime examples for such intertwined electron-phonon-driven phases, yet, various compounds do not show the expected interrelation or feature additional mechanisms which makes an unambiguous interpretation difficult. Here, we report high-pressure X-ray diffraction and inelastic X-ray scattering measurements of the prototypical transition-metal dichalcogenide 2$H$-TaSe$_2$ and determine the evolution of the charge-density-wave state and its lattice dynamics up to and beyond its suppression at the critical pressure $p_c = 19.9(1)\,\rm{GPa}$ and at low temperatures. The high quality of our data allows the full refinement of the commensurate charge-density-wave superstructure at low pressure and we find the quantum critical point of the charge-density-wave to be in close vicinity to the reported maximum superconducting transition temperature $T_{sc} = 8.2\,\rm{K}$. $Ab-initio$ calculations corroborate that 2$H$-TaSe$_2$ is a reference example of order-suppressed enhanced superconductivity and can serve as a textbook case to investigate superconductivity near a charge-density-wave quantum critical point.

Crystals of l-pyroglutamic acid exhibit a thermosalient phenomenon. During nondestructive, reversible phase transitions, the crystals can jump vertically by several centimeters. Such phase transitions have been described as martensitic; displacive, diffusionless transitions. The molecular reorganizations that impart the thermosalient effect have previously been characterized in detail; however, less attention has been given to the dynamics that precede the phase transition. In this study, we analyze the thermal motion and structural organization of the crystals at temperatures close to the phase transition using X-ray diffraction and low-frequency Raman spectroscopy. These analyses are supported by periodic density functional theory (DFT) calculations. The free energies derived from the lattice dynamics models refined against X-ray data provide a qualitative picture of the relative free energies of the involved crystal phases. The low-frequency phonons are analyzed to find possible molecular motion that can drive the phase transitions. The Raman measurements interpreted in light of spectra derived the periodic DFT calculations, as well as the observed diffuse scattering and correlated disorder, imply that a simplistic picture of a clean phase transition from one periodic crystal lattice to another must be abandoned.

The presence of a quantum-critical point (QCP) at which a nearby ordered phase is suppressed to zero temperature is often invoked to explain emergent quantum phases, e.g. superconductivity. Yet, identifying a QCP and establishing its correlation with superconductivity remains challenging. Materials featuring charge-density-wave (CDW) order and superconductivity offer a clear scenario as both states can be associated with electron-phonon coupling. Here, we uncover a CDW-QCP and demonstrate its interrelation with superconductivity in the prototypical transition-metal dichalcogenide 2H-TaSe2. We determine the evolution of the CDW state up to and beyond its suppression at the critical pressure pc = 19.9(1) GPa by means of X-ray diffraction and inelastic X-ray scattering measurements providing a full crystallographic refinement of the commensurate CDW superstructure. The pressure-induced CDW-QCP in close vicinity to the maximum superconducting transition temperature. Ab-initio lattice dynamical calculations corroborate that 2H-TaSe2 features order-parameter fluctuation enhanced superconductivity and can serve as a paradigm to investigate superconductivity near a CDW-QCP. A quantum critical point (QCP) describes a phase change independent of thermal fluctuations and instead can be driven by chemical or hydrostatic pressure. Here, the authors investigate by X-ray diffraction the evolution of the charge density wave in 2H-TaSe2 as a function of pressure and demonstrate how it is intertwined with a QCP and the superconducting phase of the system.

The emergence of correlated phenomena arising from the combination of 1$\mathrm{T}$ and 1$\mathrm{H}$ van der Waals layers is the focus of intense research. Here, we synthesize a novel self-stacked 6$\mathrm{R}$ phase in NbSeTe, showing a perfect alternating 1T and 1H layers that grow coherently along the c-direction, as revealed by scanning transmission electron microscopy. Angle resolved photoemission spectroscopy shows a mixed contribution of the trigonal and octahedral Nb bands to the Fermi level. Diffuse scattering reveals temperature-independent short-range charge fluctuations with propagation vector $\mathrm{q_{CO}}$=(0.25,0), derived from the condensation of a longitudinal mode in the 1T layer. We observe that ligand disorder quenches the formation of a charge density wave. Magnetization measurements suggest the presence of an inhomogeneous, short-range magnetic order, further supported by the absence of a clear phase transition in the specific heat. These experimental analyses in combination with \textit{ab initio} calculations indicate that the ground state of 6$\mathrm{R}$-NbSeTe is described by a statistical distribution of short-range charge-modulated and spin-correlated regions driven by ligand disorder. Our results devise a route to synthesize 1$\mathrm{T}$-1$\mathrm{H}$ self-stacked bulk heterostructures to study emergent phases of matter.

The ID28 beamline (ESRF) hosts the only inelastic x-ray scattering spectrometer in Europe and is devoted to the study of phonons. As part of a rich portfolio of user activities high-pressure research represents a vital segment of the beamline's research portfolio, constituting approximately 30% of allocated beamtime, with users benefiting from both the extreme brightness and tight focusing capabilities of the European synchrotron. Here we present the current status of lattice dynamics studies under (quasi)hydrostatic pressure which have become close-to-routine measurements, detail a selection of example studies and briefly discuss potential future advances.

The observation of unexpected polarisation textures such as vortices, skyrmions and merons in various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain walls as being Ising-like. Bloch components in the 180 domain walls of PbTiO3 have recently been reported in PbTiO3/SrTiO3 superlattices and linked to domain wall chirality. While this opens exciting perspectives, the ubiquitous nature of this Bloch component remains to be further explored. In this work, we present a comprehensive investigation of domain walls in PbTiO3/SrTiO3 superlattices, involving a combination of first- and second-principles calculations, phase-field simulations, diffuse scattering calculations, and synchrotron based diffuse x-ray scattering. Our theoretical calculations highlight that the previously predicted Bloch polarisation in the 180 domain walls in PbTiO3/SrTiO3 superlattices might be more sensitive to the boundary conditions than initially thought and is not always expected to appear. Employing diffuse scattering calculations for larger systems we develop a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the centres of the 180 domain walls of PbTiO3/SrTiO3 superlattices, suggesting that the precise nature of domain walls in the ultrathin PbTiO3 layers is more intricate than previously thought and deserves further attention.

The observation of unexpected polarization textures such as vortices, skyrmions, and merons in The observation of unexpected polarization textures such as vortices, skyrmions, and merons in various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain walls as being Ising-like. Bloch components in the 180 degrees domain walls of PbTiO3 have recently been walls as being Ising-like. Bloch components in the 180 degrees domain walls of PbTiO3 have recently been reported in PbTiO3/SrTiO3 superlattices and linked to domain wall chirality. While this opens reported in PbTiO3/SrTiO3 superlattices and linked to domain wall chirality. While this opens exciting perspectives, the ubiquity of this Bloch component remains to be further explored. In this exciting perspectives, the ubiquity of this Bloch component remains to be further explored. In this work, we present a comprehensive investigation of domain walls in PbTiO3/SrTiO3 superlattices, work, we present a comprehensive investigation of domain walls in PbTiO3/SrTiO3 superlattices, involving a combination of first- and second-principles calculations, phase-field simulations, diffuse involving a combination of first- and second-principles calculations, phase-field simulations, diffuse scattering calculations, and synchrotron-based diffuse x-ray scattering. Our theoretical calculations scattering calculations, and synchrotron-based diffuse x-ray scattering. Our theoretical calculations highlight that the previously predicted Bloch polarization in the 180 degrees domain walls in PbTiO3/SrTiO3 highlight that the previously predicted Bloch polarization in the 180 degrees domain walls in PbTiO3/SrTiO3 superlattices might be more sensitive to the boundary conditions than initially thought and is not superlattices might be more sensitive to the boundary conditions than initially thought and is not always expected to appear. Employing diffuse scattering calculations for larger systems, we develop always expected to appear. Employing diffuse scattering calculations for larger systems, we develop a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the centers of the 180 degrees domain walls of PbTiO3/SrTiO3 superlattices, suggesting that the precise nature centers of the 180 degrees domain walls of PbTiO3/SrTiO3 superlattices, suggesting that the precise nature of domain walls in the ultrathin PbTiO3 layers is more intricate than previously thought and deserves of domain walls in the ultrathin PbTiO3 layers is more intricate than previously thought and deserves further attention. further attention.

The emergence of correlated phenomena arising from the combination of 1T and 1H van der Waals layers is the focus of intense research. Here, we synthesize a self-stacked 6R phase in NbSeTe, showing perfect alternating 1T and 1H layers that grow coherently along the c-direction, as revealed by scanning transmission electron microscopy. Angle-resolved photoemission spectroscopy shows a mixed contribution of the trigonal and octahedral Nb bands to the Fermi level. Diffuse scattering reveals temperature-independent short-range charge fluctuations with propagation vector qCO = (0.25 0), derived from the condensation of a longitudinal mode in the 1T layer, while the long-range charge density wave is quenched by ligand disorder. Magnetization measurements suggest the presence of an inhomogeneous, short-range magnetic order, further supported by the absence of a clear phase transition in the specific heat. These experimental analyses in combination with ab initio calculations indicate that the ground state of 6R-NbSeTe is described by a statistical distribution of short-range charge-modulated and spin-correlated regions driven by ligand disorder. Our results demonstrate how natural 1T-1H self-stacked bulk heterostructures can be used to engineer emergent phases of matter.

We investigate phonon lifetimes in VO2 single crystals. We do so in the metallic state above the metal-insulator transition (MIT), where strong structural fluctuations are known to take place. By combining inelastic X-ray scattering and Raman spectroscopy, we track the temperature dependence of several acoustic and optical phonon modes up to 1000 K. Contrary to what is commonly observed, we find that phonon lifetimes decrease with decreasing temperature. Our results show that pre-transitional fluctuations in the metallic state give rise to strong electron-phonon scattering that onsets hundreds of degrees above the transition and increases as the MIT is approached. Notably, this effect is not limited to specific points of reciprocal space that could be associated with the structural transition.

(1−x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) perovskite-like solid solutions are recognized for their outstanding electromechanical properties, which are of technological importance. However, some significant aspects of the crystal structures and domain assemblages in this system and the role of these characteristics in defining the functional performance of PMN-PT remain uncertain. Here, we used synchrotron x-ray diffraction to investigate the phase transition linking the paraelectric (cubic) and ferroelectric (tetragonal) phases in a single crystal of 0.65PMN-0.35PT. We analyzed the evolution of reciprocal-space maps across this transition. These maps were collected using small temperature step (1 K) and a high reciprocal-space resolution to reveal changes in the splitting of Bragg peaks caused by the formation of ferroelastic domains in the low-symmetry phase. Our results uncovered a two-phase state, cubic plus tetragonal phases, which exists over a narrow temperature range of only ≈4 K and exhibits a thermal hysteresis of ≈1.8 K. Remarkably, within this state, the lattice parameter of the cubic phase, aC, matches the orientational average of the lattice parameters for the tetragonal polymorph, 23aT+13cT. We discuss the implications of this matching, highlighting the possibility of it being realized by the formation of an assemblage of tetragonal twin domains separated from the cubic phase by a strain-free {110} boundary, as in the “adaptive phase” but without domain miniaturization.