Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctness.

The Debye scattering equation (DSE) [Debye (1915). Ann. Phys. 351, 809-823] is widely used for analyzing total scattering data of nanocrystalline materials in reciprocal space. In its modified form (MDSE) [Cervellino et al. (2010). J. Appl. Cryst. 43, 1543-1547], it includes contributions from uncorrelated thermal agitation terms and, for defective crystalline nanoparticles (NPs), average site-occupancy factors (s.o.f.'s). The s.o.f.'s were introduced heuristically and no theoretical demonstration was provided. This paper presents in detail such a demonstration, corrects a glitch present in the original MDSE, and discusses the s.o.f.'s physical significance. Three new MDSE expressions are given that refer to distinct defective NP ensembles characterized by: (i) vacant sites with uncorrelated constant site-occupancy probability; (ii) vacant sites with a fixed number of randomly distributed atoms; (iii) self-excluding (disordered) positional sites. For all these cases, beneficial aspects and shortcomings of introducing s.o.f.'s as free refinable parameters are demonstrated. The theoretical analysis is supported by numerical simulations performed by comparing the corrected MDSE profiles and the ones based on atomistic modeling of a large number of NPs, satisfying the structural conditions described in (i)-(iii).

Large-scale oxygen order phase transitions and fast ordering kinetics at moderate temperatures in Nd2NiO4+δ electrodes.

Non-stoichiometric 214-nickelates with Ruddlesden-Popper (RP) type frameworks emerged as potential candidates for mixed electronic/ionic conductors in the intermediate temperature range. In this work we investigated structural aspects of the oxygen ion mobility diffusion mechanisms in non-stoichiometric Nd2NiO4+δ nickelates by X-ray (laboratory and synchrotron) as well by neutron diffraction. Temperature dependent synchrotron powder diffraction revealed a phase diagram of unprecedented complexity, involving a series of highly organized, 3D modulated phases related to oxygen ordering below 800 K. All phase transitionsimply translational periodicities exceeding 100 Å, and are found to be of 1st order, together with fast ordering kinetics. These surprising structural correlations, induced by the presence of interstitial oxygen atoms, suggest a collective phason-like oxygen diffusion mechanism together with dynamical contributions from the aperiodical lattice creating shallow diffusion pathways down to room temperature.

Charge fluctuations in the intermediate-valence ground state of SmCoIn5.

The microscopic mechanism of heavy band formation, relevant for unconventional superconductivity in CeCoIn5 and other Ce-based heavy fermion materials, depends strongly on the efficiency with which f electrons are delocalized from the rare earth sites and participate in a Kondo lattice. Replacing Ce3+ (4f1, J = 5/2) with Sm3+ (4f5, J = 5/2), we show that a combination of the crystal electric field and on-site Coulomb repulsion causes SmCoIn5 to exhibit a Γ7 ground state similar to CeCoIn5 with multiple f electrons. We show that with this single-ion ground state, SmCoIn5 exhibits a temperature-induced valence crossover consistent with a Kondo scenario, leading to increased delocalization of f holes below a temperature scale set by the crystal field, Tv ≈ 60 K. Our result provides evidence that in the case of many f electrons, the crystal field remains the dominant tuning knob in controlling the efficiency of delocalization near a heavy fermion quantum critical point, and additionally clarifies that charge fluctuations play a general role in the ground state of "115" materials.

BCC-Cu nanoparticles: from a transient to a stable allotrope by tuning size and reaction conditions.

Metallic copper generally adopts an FCC structure. In this work, we detect highly unusual BCC-structured Cu nanoparticles as a transient intermediate during the H2 reduction of a CuI precursor, [Cu4OtBu4], grafted onto the surface of partially dehydroxylated silica. The Cu BCC structure, assigned by in situ Cu K-edge XANES and EXAFS, as well as in situ synchrotron PXRD, converts upon heating into the most commonly found FCC allotrope. DFT calculations show that the BCC-Cu phase is in fact predicted to be more stable for small particles, and that their stability increases at lower H2 concentrations. Using this knowledge, we show that it is possible to synthesize BCC-structured Cu nanoparticles as a stable allotrope by reduction of the same grafted precursor either in 10% H2 diluted in Ar or 100% H2 at low temperature.

Dynamic magnetic crossover at the origin of the hidden-order in van der Waals antiferromagnet CrSBr.

The van-der-Waals material CrSBr stands out as a promising two-dimensional magnet. Here, we report on its detailed magnetic and structural characteristics. We evidence that it undergoes a transition to an A-type antiferromagnetic state below TN ≈ 140 K with a pronounced two-dimensional character, preceded by ferromagnetic correlations within the monolayers. Furthermore, we unravel the low-temperature hidden-order within the long-range magnetically-ordered state. We find that it is associated to a slowing down of the magnetic fluctuations, accompanied by a continuous reorientation of the internal field. These take place upon cooling below Ts ≈ 100 K, until a spin freezing process occurs at T* ≈ 40 K. We argue this complex behavior to reflect a crossover driven by the in-plane uniaxial anisotropy, which is ultimately caused by its mixed-anion character. Our findings reinforce CrSBr as an important candidate for devices in the emergent field of two-dimensional magnetic materials.

Diffraction from Nanocrystal Superlattices.

Diffraction from a lattice of periodically spaced crystals is a topic of current interest because of the great development of self-organised superlattices (SL) of nanocrystals (NC). The self-organisation of NC into SL has theoretical interest, but especially a rich application prospect, as the coherent organisation has large effects on a wide range of material properties. Diffraction is a key method to understand the type and quality of SL ordering. Hereby, the characteristic diffraction signature of an SL of NC-together with the characteristic types of disorder-are theoretically explored.

Frustration, strain and phase co-existence in the mixed valent hexagonal iridate Ba3NaIr2O9.

Using detailed synchrotron diffraction, magnetization, thermodynamic and transport measurements, we investigate the relationship between the mixed valence of Ir, lattice strain and the resultant structural and magnetic ground states in the geometrically frustrated triple perovskite iridate Ba3NaIr2O9. We observe a complex interplay between lattice strain and structural phase co-existence, which is typically not observed in this family of compounds. The low temperature magnetic ground state is characterized by the absence of long-range magnetic order, and points towards the condensation of a cluster glass state from an extended regime of short range magnetic correlations.

Effects of Structural and Microstructural Features on the Total Scattering Pattern of Nanocrystalline Materials.

Atomic- and nanometer-scale features of nanomaterials have a strong influence on their chemical and physical properties and a detailed description of these elements is a crucial step in their characterization. Total scattering methods, in real and reciprocal spaces, have been established as fundamental techniques to retrieve this information. Although the impact of microstructural features, such as defectiveness of different kinds, has been extensively studied in reciprocal space, disentangling these effects from size- and morphology-induced properties, upon downsizing, is not a trivial task. Additionally, once the experimental pattern is Fourier transformed to calculate the pair distribution function, the direct fingerprint of structural and microstructural features is severely lost and no modification of the histogram of interatomic distances derived therefrom is clearly discussed nor considered in the currently available protocols. Hereby, starting from atomistic models of a prototypical system (cadmium selenide), we simulate multiple effects on the atomic pair distribution function, obtained from reciprocal space patterns computed through the Debye scattering equation. Size and size dispersion effects, as well as different structures, morphologies, and their interplay with several kinds of planar defects, are explored, aiming at identifying the main (measurable and informative) fingerprints of these features on the total scattering pattern in real and reciprocal spaces, highlighting how, and how much, they become evident when comparing different cases. The results shown herein have general validity and, as such, can be further extended to other classes of nanomaterials.

Sifting fluctuation scattering from microtextured samples.

As the relationship of texture and microtexture to fluctuation X-ray scattering (FXS) has been clarified in detail, key progress is expected in the exploitation of FXS-based structural investigation of matter exhibiting complex order.

Signature of antiphase boundaries in iron oxide nanoparticles.

Iron oxide nanoparticles find a wide variety of applications, including targeted drug delivery and hyperthermia in advanced cancer treatment methods. An important property of these particles is their maximum net magnetization, which has been repeatedly reported to be drastically lower than the bulk reference value. Previous studies have shown that planar lattice defects known as antiphase boundaries (APBs) have an important influence on the particle magnetization. The influence of APBs on the atomic spin structure of nanoparticles with the γ-Fe2O3 composition is examined via Monte Carlo simulations, explicitly considering dipole-dipole interactions between the magnetic moments that have previously only been approximated. For a single APB passing through the particle centre, a reduction in the magnetization of 3.9% (for 9 nm particles) to 7.9% (for 5 nm particles) is found in saturation fields of 1.5 T compared with a particle without this defect. Additionally, on the basis of Debye scattering equation simulations, the influence of APBs on X-ray powder diffraction patterns is shown. The Fourier transform of the APB peak profile is developed to be used in a whole powder pattern modelling approach to determine the presence of APBs and quantify them by fits to powder diffraction patterns. This is demonstrated on experimental data, where it could be shown that the number of APBs is related to the observed reduction in magnetization.

Unravelling Magnetic Nanochain Formation in Dispersion for In Vivo Applications.

Self-assembly of iron oxide nanoparticles (IONPs) into 1D chains is appealing, because of their biocompatibility and higher mobility compared to 2D/3D assemblies while traversing the circulatory passages and blood vessels for in vivo biomedical applications. In this work, parameters such as size, concentration, composition, and magnetic field, responsible for chain formation of IONPs in a dispersion as opposed to spatially confining substrates, are examined. In particular, the monodisperse 27 nm IONPs synthesized by an extended LaMer mechanism are shown to form chains at 4 mT, which are lengthened with applied field reaching 270 nm at 2.2 T. The chain lengths are completely reversible in field. Using a combination of scattering methods and reverse Monte Carlo simulations the formation of chains is directly visualized. The visualization of real-space IONPs assemblies formed in dispersions presents a novel tool for biomedical researchers. This allows for rapid exploration of the behavior of IONPs in solution in a broad parameter space and unambiguous extraction of ​the parameters of the equilibrium structures. Additionally, it can be extended to study novel assemblies formed by more complex geometries of IONPs.

Mechanism of magnetization reduction in iron oxide nanoparticles.

Iron oxide nanoparticles are presently considered as main work horses for various applications including targeted drug delivery and magnetic hyperthermia. Several questions remain unsolved regarding the effect of size onto their overall magnetic behavior. One aspect is the reduction of magnetization compared to bulk samples. A detailed understanding of the underlying mechanisms of this reduction could improve the particle performance in applications. Here we use a number of complementary experimental techniques including neutron scattering and synchrotron X-ray diffraction to arrive at a consistent conclusion. We confirm the observation from previous studies of a reduced saturation magnetization and argue that this reduction is mainly associated with the presence of antiphase boundaries, which are observed directly using high-resolution transmission electron microscopy and indirectly via an anisotropic peak broadening in X-ray diffraction patterns. Additionally small-angle neutron scattering with polarized neutrons revealed a small non-magnetic surface layer, that is, however, not sufficient to explain the observed loss in magnetization alone.

Texture corrections for total scattering functions.

Many functional materials are today synthesized in the form of nanoparticles displaying preferred orientation effects to some small or large extent. The analysis of diffraction data of such kinds of systems is best performed in the framework of the total scattering approach that prescinds from translation symmetry assumptions. Therefore modified expressions were derived for the most common total scattering functions, in particular the Debye scattering equation (DSE) which yields the texture-averaged differential cross section as a function of atomic coordinates and texture parameters. The modified DSE encodes higher-order even spherical Bessel functions which account for the texture effect. Selection rules arising from experimental geometries and symmetries are discussed. In addition the duality of the texture effect is introduced showing the effects of texture on both the I(Q) and {\cal{G}}(r). The paper includes several definitions and appendices which are meant to be useful for those involved in the development of crystallographic computing.

Structure, Morphology, and Faceting of TiO2 Photocatalysts by the Debye Scattering Equation Method. The P25 and P90 Cases of Study.

Characterization of functional nanocrystalline materials in terms of quantitative determination of size, size dispersion, type, and extension of exposed facets still remains a challenging task. This is particularly the case of anisotropically shaped nanocrystals (NCs) like the TiO2 photocatalysts. Here, commercially available P25 and P90 titania nanopowders have been characterized by wide-angle X-ray total scattering techniques. Synchrotron data were modelled by the reciprocal space-based Debye scattering equation (DSE) method using atomistic models of NC populations (simultaneously carrying atomic and nanoscale structural features) for both anatase and rutile phases. Statistically robust descriptors are provided of size, morphology, and {101} vs. {001} facet area of truncated tetragonal bipyramids for anatase, jointly to polymorph quantification. The effects of using the proper NC shape on the X-ray diffraction pattern are analyzed in depth through DSE simulations by considering variable bipyramid aspect ratios (resulting in different {101} vs. {001} surface) and relative dispersion in a bivariate manner. We demonstrate that using prismatic NCs having equal volume and aspect ratio as bipyramids provides reasonably accurate sizes and {101} and {001} surface areas of the parent morphology.

Homogeneous nucleation of Li2O2 under Li-O2 battery discharge.

The development of high-energy lithium-oxygen batteries has significantly slowed by numerous challenges including capacity limitations due to electrode surface passivation by the discharge product Li2O2. Since the passivation rate and intensity are dependent on the deposit morphology, herein, we focus on the mechanisms governing Li2O2 formation within the porous cathode. We report evidence of homogeneous nucleation of Li2O2 crystallites and their further assembly in bulk of the electrolyte solution in DMSO, which possesses a high donor number. After careful estimation of the superoxide ion concentration distribution within a phenomenological model, it was found that the high stability of superoxide ions formed during the ORR towards disproportionation and sufficient diffusivity of (0.5-1.2) × 10-6 cm2 s-1 enabled Li2O2 nucleation and crystallization not only at the surface but also in the electrolyte, and the reaction zone spread throughout the internal space of the porous electrode. High initial supersaturation promoted the homogeneous nucleation of Li2O2 nanoplates, which instantly assembled into mesocrystals also in the solution bulk. These results were supported by operando SAXS/WAXS and morphology observations. Thus, although homogeneous nucleation is not dominant, it is important for achieving a high capacity in Li-O2 batteries.

Crystal Structure, Morphology, and Surface Termination of Cyan-Emissive, Six-Monolayers-Thick CsPbBr3 Nanoplatelets from X-ray Total Scattering.

Highly anisotropic colloidal CsPbBr3 nanoplatelets (NPLs) represent an appealing class of colloidal quantum wells with enhanced light emissivity. Strong quantum confinement imposed by the small platelet thickness and atomic flatness gives rise to enhanced oscillator strength, higher exciton binding energy, and narrow emission linewidth. While discrete thicknesses manifest themselves in discrete bandgap energies, fine-tuning of the emission energy can be achieved by compositional modulations. Here we address one of the most debated aspects of perovskite nanoplatelets: their crystal structure. Starting with the direct imaging by high-resolution electron microscopy (providing a clue on the pseudocubic faceting of the NPLs), we focus the study on X-ray total scattering techniques, based on the Debye scattering equation (DSE) approach, to obtain better atomistic insight. The nanoplatelets are six-monolayers thick and exhibit an orthorhombic structure. A thorough structure-morphology characterization unveils a specific orientation of the axial and equatorial bromides of the PbBr6 octahedra versus the NPLs thickness; we found that {010} and {101} planes of the orthorhombic CsPbBr3 lattice (Pnma space group) correspond to the six facets of the NPL, with basal planes being of {101} type. The NPLs undergo a lattice relaxation in comparison to cuboidal CsPbBr3 NCs; the major deformation is observed in the axial direction, which suggests a structural origin of the higher compliance along the b axis. The DSE-based analysis also supports a CsBr surface termination model, with half Cs sites and a half (or slightly more) Br sites vacant.

Size-Dependent Fault-Driven Relaxation and Faceting in Zincblende CdSe Colloidal Quantum Dots.

Surface chemistry and core defects are known to play a prominent role in governing the photophysical properties of nanocrystalline semiconductors. Nevertheless, investigating them in small nanocrystals remains a complex task. Here, by combining X-ray scattering techniques in the wide- and small-angle regions and using the Debye scattering equation (DSE) method of analysis, we unveil a high density of planar defects in oleate-terminated zincblende (ZB) CdSe colloidal quantum dots (QDs) and size-dependent faceting within a square-cuboid morphology. Atomistic models of faulted ZB nanocrystals, based on the probabilistic stacking of CdSe layers in cubic and hexagonal sequences, and data analysis point to the preferential location of faults near the center of nanocrystals. By finely modeling faulting and morphological effects on the X-ray scattering pattern, a relaxation of the Cd-Se bond distance parallel to the stacking direction, up to +3% (2.71 Å) with respect to the reference bulk value (2.63 Å), is detected, at the cubic/hexagonal transitions. The smallest nanocrystals show cubic {100} facets; {111} facets appear above 4 nm and progressively extend at larger sizes. These structural and morphological features likely vary depending on the synthesis conditions; nevertheless, since planar defects are nearly ubiquitous in CdSe QDs, the modeling approach here presented has a general validity. This work also points to the great potential of combining small- and wide-angle X-ray scattering and DSE-modeling techniques in gaining important knowledge on atomic-scale defects of semiconductor nanocrystals, underpinning the comprehension of the impact of structural defectiveness on the exciting properties of these QDs.

Formation and transformation of calcium phosphate phases under biologically relevant conditions: Experiments and modelling.

The experimental data on calcium phosphates formation were collected in dilute solution at constant pH (7.40) and temperature (37.0 °C) at different levels of ionic strength (IS). The evolution of the solid phase formation is described in detail using a thermodynamic-kinetic model. The thermodynamic model takes into account all relevant chemical species as well as Posner's clusters; the kinetic model, based on the discretized population balance approach, accounts for the solid formation from solution. The experimental data are consistent with an initial formation of dicalcium phosphate dihydrate (DCPD, brushite), which dominates the nucleation rate, and its rapid transformation into octacalcium phosphate (OCP) or hydroxyapatite (HA), which dominates the growth rate. Depending on the experimental conditions and, including the influence of the IS level, OCP may be further transformed into apatite. The classical nucleation theory is able to describe the experimental results very well and the solid phase growth is limited by the diffusion of Ca2+ ions. The precipitation pathway described by a complete thermodynamic-kinetic model is expected to contribute to the understating of the in vivo osteogenesis. STATEMENT OF SIGNIFICANCE: The formation mechanism of calcium phosphates under biomimetic conditions is unraveled. The formation pathway is mathematically described based on a thermodynamic-kinetic model in which (i) the nucleation stages (primary and secondary) are dominated by the formation of dicalcium phosphate dihydrate (DCPD) and (ii) the fast growth stage is limited by the diffusion of Ca2+ ions under the driving force of octacalcium phosphate (OCP), or hydroxyapatite (HA), solubility. The obtained solid phase seems correlated to the activity coefficient of phosphate ions, thus to the ionic strength and local phosphate speciation. The model, being able to highlight the details of the precipitation pathway, is expected to contribute to the understanding of the apatitic phase formation in the biomineralization-biodemineralization processes under in-vivo conditions.

Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7.

The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives rise to highly correlated magnetic phases with strong fluctuations, including spin liquids and spin ices. It is an open question how these ground states governed by local rules are affected by disorder. Here we demonstrate in the pyrochlore Tb2Hf2O7, that the vicinity of the disordering transition towards a defective fluorite structure translates into a tunable density of anion Frenkel disorder while cations remain ordered. Quenched random crystal fields and disordered exchange interactions can therefore be introduced into otherwise perfect pyrochlore lattices of magnetic ions. We show that disorder can play a crucial role in preventing long-range magnetic order at low temperatures, and instead induces a strongly fluctuating Coulomb spin liquid with defect-induced frozen magnetic degrees of freedom.Experimental studies of frustrated spin systems such as pyrochlore magnetic oxides test our understanding of quantum many-body physics. Here the authors show experimentally that Tb2Hf2O7 may be a model material for investigating how structural disorder can stabilize a quantum spin liquid phase.

Coherent Nanotwins and Dynamic Disorder in Cesium Lead Halide Perovskite Nanocrystals.

Crystal defects in highy luminescent colloidal nanocrystals (NCs) of CsPbX3 perovskites (X = Cl, Br, I) are investigated. Here, using X-ray total scattering techniques and the Debye scattering equation (DSE), we provide evidence that the local structure of these NCs always exhibits orthorhombic tilting of PbX6 octahedra within locally ordered subdomains. These subdomains are hinged through a two-/three-dimensional (2D/3D) network of twin boundaries through which the coherent arrangement of the Pb ions throughout the whole NC is preserved. The density of these twin boundaries determines the size of the subdomains and results in an apparent higher-symmetry structure on average in the high-temperature modification. Dynamic cooperative rotations of PbX6 octahedra are likely at work at the twin boundaries, causing the rearrangement of the 2D or 3D network, particularly effective in the pseudocubic phases. An orthorhombic, 3D γ-phase, isostructural to that of CsPbBr3 is found here in as-synthesized CsPbI3 NCs.