Synthesis of Single Crystals of ε-Iron and Direct Measurements of Its Elastic Constants.

Seismology finds that Earth's solid inner core behaves anisotropically. Interpretation of this requires a knowledge of crystalline elastic anisotropy of its constituents-the major phase being most likely ε-Fe, stable only under high pressure. Here, single crystals of this phase are synthesized, and its full elasticity tensor is measured between 15 and 33 GPa at 300 K. It is calculated under the same conditions, using the combination of density functional theory and dynamical mean field theory, which describes explicitly electronic correlation effects. The predictive power of this scheme is checked by comparison with measurements; it is then used to evaluate the crystalline anisotropy in ε-Fe under higher density. This anisotropy remains of the same amplitude up to densities typical of Earth's inner core.

Effect of Nanodiamond Sizes on the Efficiency of the Quasi-Specular Reflection of Cold Neutrons.

Nanomaterials can intensively scatter and/or reflect radiation. Such processes and materials are of theoretical and practical interest. Here, we study the quasi-specular reflections (QSRs) of cold neutrons (CNs) and the reflections of very cold neutrons (VCNs) from nanodiamond (ND) powders. The fluorination of ND increased its efficiency by removing/replacing hydrogen, which is otherwise the dominant cause of neutron loss due to incoherent scattering. The probability of the diffuse reflection of VCNs increased for certain neutron wavelengths by using appropriate ND sizes. Based on model concepts of the interaction of CNs with ND, and in reference to our previous work, we assume that the angular distribution of quasi-specularly reflected CNs is narrower, and that the probability of QSRs of longer wavelength neutrons increases if we increase the characteristic sizes of NDs compared to standard detonation nanodiamonds (DNDs). However, the probability of QSRs of CNs with wavelengths below the cutoff of ~4.12 Å decreases due to diffraction scattering on the ND crystal lattice. We experimentally compared the QSRs of CNs from ~4.3 nm and ~15.0 nm ND. Our qualitative conclusions and numerical estimates can help optimize the parameters of ND for specific practical applications based on the QSRs of CNs.

Multiscale Reciprocal Space Mapping of Magnetite Mesocrystals.

Mesocrystals are a class of nanostructured material, where a multiple-length-scale structure is a prerequisite of many interesting phenomena. Resolving the mesocrystal structure is quite challenging due to their structuration on different length scales. The combination of small- and wide-angle X-ray scattering (SAXS and WAXS) techniques offers the possibility of non-destructively probing mesocrystalline structures simultaneously, over multiple length scales to reveal their microscopic structure. This work describes how high dynamical range of modern detectors sheds light on the weak features of scattering, significantly increasing the information content. The detailed analysis of X-ray diffraction (XRD) from the magnetite mesocrystals with different particle sizes and shapes is described, in tandem with electron microscopy. The revealed features provide valuable input to the models of mesocrystal growth and the choice of structural motif; the impact on magnetic properties is discussed.

Phonon behavior in a random solid solution: a lattice dynamics study on the high-entropy alloy FeCoCrMnNi.

High-Entropy Alloys (HEAs) are a new family of crystalline random alloys with four or more elements in a simple unit cell, at the forefront of materials research for their exceptional mechanical properties. Their strong chemical disorder leads to mass and force-constant fluctuations which are expected to strongly reduce phonon lifetime, responsible for thermal transport, similarly to glasses. Still, the long range order would associate HEAs to crystals with a complex disordered unit cell. These two families of materials, however, exhibit very different phonon dynamics, still leading to similar thermal properties. The question arises on the positioning of HEAs in this context. Here we present an exhaustive experimental investigation of the lattice dynamics in a HEA, Fe20Co20Cr20Mn20Ni20, using inelastic neutron and X-ray scattering. We demonstrate that HEAs present unique phonon dynamics at the frontier between fully disordered and ordered materials, characterized by long-propagating acoustic phonons in the whole Brillouin zone.

Mesocrystalline structure and mechanical properties of biogenic calcite from sea urchin spine.

Using X-ray scattering, we measured detailed maps of the diffuse scattering intensity distribution and a number of phonon dispersion branches for a single crystal of inorganically formed natural calcite and for high-quality mesocrystals of biogenic calcite from a Mediterranean sea urchin spine. A comparison shows that the known differences in the mechanical properties between the `strong' biogenic and `brittle' abiotic material should be attributed to the mesoscopic architecture of the crystal rather than to a modification of the calcite crystal structure. The data are rationalized by comparing them to the results of ab initio model calculations of lattice dynamics. For the mesocrystal, they are augmented by the evaluation of the faceting of the constituent nanocrystals.

Effect of Particle Sizes on the Efficiency of Fluorinated Nanodiamond Neutron Reflectors.

Over a decade ago, it was confirmed that detonation nanodiamond (DND) powders reflect very cold neutrons (VCNs) diffusively at any incidence angle and that they reflect cold neutrons quasi-specularly at small incidence angles. In the present publication, we report the results of a study on the effect of particle sizes on the overall efficiency of neutron reflectors made of DNDs. To perform this study, we separated, by centrifugation, the fraction of finer DND nanoparticles (which are referred to as S-DNDs here) from a broad initial size distribution and experimentally and theoretically compared the performance of such a neutron reflector with that from deagglomerated fluorinated DNDs (DF-DNDs). Typical commercially available DNDs with the size of ~4.3 nm are close to the optimum for VCNs with a typical velocity of ~50 m/s, while smaller and larger DNDs are more efficient for faster and slower VCN velocities, respectively. Simulations show that, for a realistic reflector geometry, the replacement of DF-DNDs (a reflector with the best achieved performance) by S-DNDs (with smaller size DNDs) increases the neutron albedo in the velocity range above ~60 m/s. This increase in the albedo results in an increase in the density of faster VCNs in such a reflector cavity of up to ~25% as well as an increase in the upper boundary of the velocities of efficient VCN reflection.

Clustering of Diamond Nanoparticles, Fluorination and Efficiency of Slow Neutron Reflectors.

Neutrons can be an instrument or an object in many fields of research. Major efforts all over the world are devoted to improving the intensity of neutron sources and the efficiency of neutron delivery for experimental installations. In this context, neutron reflectors play a key role because they allow significant improvement of both economy and efficiency. For slow neutrons, Detonation NanoDiamond (DND) powders provide exceptionally good reflecting performance due to the combination of enhanced coherent scattering and low neutron absorption. The enhancement is at maximum when the nanoparticle diameter is close to the neutron wavelength. Therefore, the mean nanoparticle diameter and the diameter distribution are important. In addition, DNDs show clustering, which increases their effective diameters. Here, we report on how breaking agglomerates affects clustering of DNDs and the overall reflector performance. We characterize DNDs using small-angle neutron scattering, X-ray diffraction, scanning and transmission electron microscopy, neutron activation analysis, dynamical light scattering, infra-red light spectroscopy, and others. Based on the results of these tests, we discuss the calculated size distribution of DNDs, the absolute cross-section of neutron scattering, the neutron albedo, and the neutron intensity gain for neutron traps with DND walls.

Elastic stiffness coefficients of thiourea from thermal diffuse scattering.

The complete elastic stiffness tensor of thiourea has been determined from thermal diffuse scattering (TDS) using high-energy photons (100 keV). Comparison with earlier data confirms a very good agreement of the tensor coefficients. In contrast with established methods to obtain elastic stiffness coefficients (e.g. Brillouin spectroscopy, inelastic X-ray or neutron scattering, ultrasound spectroscopy), their determination from TDS is faster, does not require large samples or intricate sample preparation, and is applicable to opaque crystals. Using high-energy photons extends the applicability of the TDS-based approach to organic compounds which would suffer from radiation damage at lower photon energies.

Mode Coupling at around M-Point in PZT.

The question of the microscopic origin of the M-superstructure and additional satellite peaks in the Zr-rich lead zirconate-titanate is discussed for nearly 50 years. Clear contradiction between the selection rules of the critical scattering and the superstructure was found preventing unambiguous attributing of the observed superstructure either to the rotation of the oxygen octahedra or to the antiparallel displacements of the lead cations. Detailed analysis of the satellite pattern explained it as the result of the incommensurate phase transition rather than antiphase domains. Critical dynamics is the key point for the formulated problems. Recently, the oxygen tilt soft mode in the PbZr0.976Ti0.024O3 (PZT2.4) was found. But this does not resolve the extinction rules contradiction. The results of the inelastic X-ray scattering study of the phonon spectra of PZT2.4 around M-point are reported. Strong coupling between the lead and oxygen modes resulting in mode anticrossing and creation of the wide flat part in the lowest phonon dispersion curves is identified. This flat part corresponds to the mixture of the displacements of the lead and oxygen ions and can be an explanation of the extinction rules contradiction. Moreover, a flat dispersion surface is a typical prerequisite for the incommensurate phase transition.

Incommensurate crystal structure of PbHfO3.

Controversy in the description/identification of so-called intermediate phase(s) in PbHfO3, stable in the range ∼420-480 K, has existed for a few decades. A synchrotron diffraction experiment on a partially detwinned crystal allowed the structure to be solved in the superspace group Imma(00γ)s00 (No. 74.2). In contrast to some previously published reports, in the pure compound only one distinct phase was observed between Pbam PbZrO3-like antiferroelectric and Pm3m paraelectric phases. The modulation vector depends only slightly on temperature. The major structure modulation is associated with the displacement of lead ions, which is accompanied by a smaller amplitude modulation for the surrounding O atoms and tilting of HfO6 octahedra. Tilting of the octahedra results in a doubling of the unit cell compared with the parent structure.

Fluorination of Diamond Nanoparticles in Slow Neutron Reflectors Does Not Destroy Their Crystalline Cores and Clustering While Decreasing Neutron Losses.

If the wavelength of radiation and the size of inhomogeneities in the medium are approximately equal, the radiation might be intensively scattered in the medium and reflected from its surface. Such efficient nanomaterial reflectors are of great scientific and technological interest. In previous works, we demonstrated a significant improvement in the efficiency of reflection of slow neutrons from a powder of diamond nanoparticles by replacing hydrogen located on the surface of nanoparticles with fluorine and removing the residual sp2 amorphous shells of nanoparticles via the fluorination process. In this paper, we study the mechanism of this improvement using a set of complementary experimental techniques. To analyze the data on a small-angle scattering of neutrons and X-rays in powders of diamond nanoparticles, we have developed a model of discrete-size diamond nanospheres. Our results show that fluorination does not destroy either the crystalline cores of nanoparticles or their clustering in the scale range of 0.6-200 nm. This observation implies that it does not significantly affect the neutron scattering properties of the powder. We conclude that the overall increase in reflectivity from the fluorinated nanodiamond powder is primarily due to the large reduction of neutron losses in the powder caused by the removal of hydrogen contaminations.

Archetypal Soft-Mode-Driven Antipolar Transition in Francisite Cu_{3}Bi(SeO_{3})_{2}O_{2}Cl.

Model materials are precious test cases for elementary theories and provide building blocks for the understanding of more complex cases. Here, we describe the lattice dynamics of the structural phase transition in francisite Cu_{3}Bi(SeO_{3})_{2}O_{2}Cl at 115 K and show that it provides a rare archetype of a transition driven by a soft antipolar phonon mode. In the high-symmetry phase at high temperatures, the soft mode is found at (0,0,0.5) at the Brillouin zone boundary and is measured by inelastic x-ray scattering and thermal diffuse scattering. In the low-symmetry phase, this soft-mode is folded back onto the center of the Brillouin zone as a result of the doubling of the unit cell, and appears as a fully symmetric mode that can be tracked by Raman spectroscopy. On both sides of the transition, the mode energy squared follows a linear behavior over a large temperature range. First-principles calculations reveal that, surprisingly, the flat phonon band calculated for the high-symmetry phase seems incompatible with the displacive character found experimentally. We discuss this unusual behavior in the context of an ideal Kittel model of an antiferroelectric transition.

Structural, elastic and vibrational properties of celestite, SrSO4, from synchrotron x-ray diffraction, thermal diffuse scattering and Raman scattering.

In order to resolve inconsistencies encountered in published data for SrSO[Formula: see text], the elasticity and the phase stability of celestite has been studied using thermal diffuse scattering, high pressure powder synchrotron x-ray diffraction, Raman scattering and DFT calculations. The structure of SrSO[Formula: see text] is found to be stable up to 62 GPa at ambient temperature. The preferred values for the components of the elastic stiffness tensor have been determined using x-ray thermal diffuse scattering and are (in GPa): [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. The preferred value for the bulk modulus is [Formula: see text] GPa. This work shows that thermal diffuse scattering collected at two temperatures allows the determination of the full elastic tensor of crystals with low space group symmetry.

Full Elasticity Tensor from Thermal Diffuse Scattering.

We present a method for the precise determination of the full elasticity tensor from a single crystal diffraction experiment using monochromatic x rays. For the two benchmark systems calcite and magnesium oxide, we show that the measurement of thermal diffuse scattering in the proximity of Bragg reflections provides accurate values of the complete set of elastic constants. This approach allows for a reliable and model-free determination of the elastic properties and can be performed together with crystal structure investigation in the same experiment.

Phonon triggered rhombohedral lattice distortion in vanadium at high pressure.

In spite of the simple body-centered-cubic crystal structure, the elements of group V, vanadium, niobium and tantalum, show strong interactions between the electronic properties and lattice dynamics. Further, these interactions can be tuned by external parameters, such as pressure and temperature. We used inelastic x-ray scattering to probe the phonon dispersion of single-crystalline vanadium as a function of pressure to 45 GPa. Our measurements show an anomalous high-pressure behavior of the transverse acoustic mode along the (100) direction and a softening of the elastic modulus C44 that triggers a rhombohedral lattice distortion occurring between 34 and 39 GPa. Our results provide the missing experimental confirmation of the theoretically predicted shear instability arising from the progressive intra-band nesting of the Fermi surface with increasing pressure, a scenario common to all transition metals of group V.

Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal.

The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = -0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye-Waller factor, which explains the vanishing of 'high-Q perp' reflections.

Sensitivity to actinide doping of uranium compounds by resonant inelastic X-ray scattering at uranium L3 edge.

Valence-to-core resonant inelastic X-ray scattering (RIXS) and high energy resolution fluorescence detection (HERFD) X-ray absorption measurements were performed at the U L3 edges of UO2 and UO2(NO3)2(H2O)6. The results are compared with model calculations based on the local-density-approximation formalism, taking into account Coulomb interaction U (LDA + U). We show that despite strong 5f-5f electronic correlations in the studied systems and the use of core-level excitations in the intermediate stage of the spectroscopic process, the RIXS technique probes a convolution of the single-particle densities of states in the valence and conduction bands. For UO2, the detected crystal-field splitting between the U 6d eg and t2g orbitals from the RIXS spectra (∼3.5 eV) is larger than that previously derived from optical spectroscopy. Furthermore, by using an example of the U0.75Pu0.25O2 mixed oxide, we show that the RIXS technique at the U L3 edges is sensitive to the substitution of U with other actinide, in contrast to conventional X-ray absorption methods. That is, due to changes in the occupied part rather than in the unoccupied part of the U 6d states caused by the substitution.

Lattice dynamics of α-cristobalite and the Boson peak in silica glass.

The lattice dynamics of the silica polymorph [Formula: see text]-cristobalite has been investigated by a combination of diffuse and inelastic x-ray scattering and ab initio lattice dynamics calculations. Phonon dispersion relations and vibrational density of states are reported and the phonon eigenvectors analyzed by a detailed comparison of scattering intensities. The experimentally validated calculation is used to identify the vibration contributing most to the first peak in the density of vibrational states. The comparison of its displacement pattern to the silica polymorphs [Formula: see text]-quartz and coesite and to vitreous silica reveals a distinct similarity and allows for decisive conclusions on the vibrations causing the so-called Boson peak in silica glass.

The creation of modulated monoclinic aperiodic composites in n-alkane/urea compounds.

n-Dodecane/urea is a member of the prototype series of n-alkane/urea inclusion compounds. At room temperature, it presents a quasi-one dimensional liquid-like state for the confined guest molecules within the rigid, hexagonal framework of the urea host. At lower temperatures, we report the existence of two other phases. Below Tc=248 K there appears a phase with rank four superspace group P6122(00γ), the one typically observed at room temperature in n-alkane/urea compounds with longer guest molecules. A misfit parameter, defined by the ratio γ=ch /cg (chost/cguest), is found to be 0.632±0.005. Below Tc1=123 K, a monoclinic modulated phase is created with a constant shift along c of the guest molecules in adjacent channels. The maximal monoclinic space group for this structure is P1211(α0γ). Analogies and differences with n-heptane/urea, which also presents a monoclinic, modulated low-temperature phase, are discussed.

Diffuse scattering in Ih ice.

Single crystals of ice Ih, extracted from the subglacial Lake Vostok accretion ice layer (3621 m depth) were investigated by means of diffuse x-ray scattering and inelastic x-ray scattering. The diffuse scattering was identified as mainly inelastic and rationalized in the frame of ab initio calculations for the ordered ice XI approximant. Together with Monte-Carlo modelling, our data allowed reconsidering previously available neutron diffuse scattering data of heavy ice as the sum of thermal diffuse scattering and static disorder contribution.