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)

Spin liquid in a single crystal of the frustrated diamond lattice antiferromagnet CoAl2O4

We study spin liquid in the frustrated diamond lattice antiferromagnet CoAl2O4 by means of single crystal neutron scattering in zero and applied magnetic field. The magnetically ordered phase appearing below TN=8 K remains nonconventional down to 1.5 K. The magnetic Bragg peaks at the q=0 positions remain broad and their profiles have strong Lorentzian contribution. Additionally, they are connected by weak diffuse streaks along the directions. These observations are explained within the spiral spin liquid model as short-range magnetic correlations of spirals populated at these finite temperatures, as the energy minimum around q=0 is flat and the energy of excited states with q=(111) is low. The agreement is only qualitative, leading us to suspect that microstructure effects are also important. Magnetic field significantly perturbs spin correlations. The 1.5 K static magnetic moment increases from 1.58 mB/Co at zero field to 2.08 mB/Co at 10 T, while the magnetic peaks, being still broad, acquire almost Gaussian profile. Spin excitations are rather conventional spin waves at zero field, resulting in the exchange parameters J1=0.92(1) meV, J2=0.101(2) meV and the anisotropy term D=-0.0089(2) meV for CoAl2O4. The application of a magnetic field leads to a pronounced broadening of the excitations at the zone center, which at 10 T appear gapless and nearly featureless

Magnetoelastic coupling in triangular lattice antiferromagnet CuCrS2

CuCrS2 is a triangular lattice Heisenberg antiferromagnet with a rhombohedral crystal structure. We report on neutron and synchrotron powder diffraction results which reveal a monoclinic lattice distortion at the magnetic transition and verify a magnetoelastic coupling. CuCrS2 is therefore an interesting material to study the influence of magnetism on the relief of geometrical frustration.Comment: 6 pages, 6 figures, 1 tabl

Cluster Model of Decagonal Tilings

A relaxed version of Gummelt's covering rules for the aperiodic decagon is considered, which produces certain random-tiling-type structures. These structures are precisely characterized, along with their relationships to various other random tiling ensembles. The relaxed covering rule has a natural realization in terms of a vertex cluster in the Penrose pentagon tiling. Using Monte Carlo simulations, it is shown that the structures obtained by maximizing the density of this cluster are the same as those produced by the corresponding covering rules. The entropy density of the covering ensemble is determined using the entropic sampling algorithm. If the model is extended by an additional coupling between neighboring clusters, perfectly ordered structures are obtained, like those produced by Gummelt's perfect covering rules.Comment: 10 pages, 20 figures, RevTeX; minor changes; to be published in Phys. Rev.

Beam-induced damage on diffractive hard X-ray optics

Beam-induced damage on diffractive hard X-ray optics is studied by means of X-ray diffraction and scanning electron microscopy

Mono- and bi-functional arenethiols as surfactants for gold nanoparticles: synthesis and characterization

Stable gold nanoparticles stabilized by different mono and bi-functional arenethiols, namely, benzylthiol and 1,4-benzenedimethanethiol, have been prepared by using a modified Brust's two-phase synthesis. The size, shape, and crystalline structure of the gold nanoparticles have been determined by high-resolution electron microscopy and full-pattern X-ray powder diffraction analyses. Nanocrystals diameters have been tuned in the range 2 ÷ 9 nm by a proper variation of Au/S molar ratio. The chemical composition of gold nanoparticles and their interaction with thiols have been investigated by X-ray photoelectron spectroscopy. In particular, the formation of networks has been observed with interconnected gold nanoparticles containing 1,4-benzenedimethanethiol as ligand

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR < 60 mL/min/1.73 m2) or eGFR reduction > 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR < 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR > 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening

Bending by faulting: A multiple scale study of copper and silver nitropyrazolates

A multiscale approach, combining structural and microstructural characterizations, was applied to tackle an uncommon and so far unsolved structural problem occurring in group 11 nitropyrazolates. To this goal, the average structure of the [Ag(4-NO2-pz)]3 and [Cu(4-NO 2-pz)]3 species was determined through ab initio X-ray powder diffraction techniques on high-resolution synchrotron data, and used to infer molecular models of randomly distributed defects within molecular stacks of trimeric molecules of D3h idealized symmetry. By cross-coupling the size and shape information on nanocrystalline coherent domains derived from tailored Debye function simulations with those obtained from scanning electron miscroscopy images on multidomain particles, the mechanism of structural disorder disrupting crystal periodicity is proposed. Such a model was further supported through the derivation of the pair distribution function, which affords local features to be sought independently from the presence of structural periodicity. Finally, the effects of stacking faults on the electrical properties of [Ag(4-NO2-pz)]3 have been experimentally evaluated

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

Soft X-ray magnetic circular dichroism in Fe and Fe

Magnetic circular dichroism (MCD) in X-ray absorption has been measured at the ${\rm L}_{2,3}$ edges of Fe in ex-situ grown Fe and ${{\rm Fe}_{0.50}{\rm Co}_{0.48}{\rm V}_{0.02}}$ films by means of the transmission method. A new approach is developed for fitting the observed transmittance, which describes the resonance lineshapes as (generalized) Fano profiles. Analytical integration of each single resonance allows a more reliable determination of the orbital and spin magnetic moments based on the MCD sum rules. The results are consistent with an increase of the Fe spin and orbital magnetic moment in Fe-Co alloys as obtained by other experiments and band structure calculations