Pair distribution function and structure factor of spherical particles

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.Comment: 7 pages, 6 figure

Nanocrystallization and Amorphization Induced by Reactive Nitrogen Sputtering in Iron and Permalloy

Thin films of iron and permalloy Ni80Fe20 were prepared using an Ar+N2 mixture with magnetron sputtering technique at ambient temperature. The nitrogen partial pressure, during sputtering process was varied in the range of 0 to 100%, keeping the total gas flow at constant. At lower nitrogen pressures RN2<33% both Fe and NiFe, first form a nanocrystalline structure and an increase in nitrogen partail pressure results in formation of an amorphous structure. At intermediate nitrogen partial pressures, nitrides of Fe and NiFe were obtained while at even higher nitrogen partial pressures, nitrides themselves became nanocrystalline or amorphous. The surface, structural and magnetic properties of the deposited films were studied using x-ray reflection and diffraction, transmission electron microscopy, polarized neutron reflectivity and using a DC extraction magnetometer. The growth behavior for amorphous film was found different as compared with poly or nanocrystalline films. The soft-magnetic properties of FeN were improved on nanocrystallization while those of NiFeN were degraded. A mechanism inducing nanocrystallization and amorphization in Fe and NiFe due to reactive nitrogen sputtering is discussed in the present article.Comment: 13 Pages, 15 Figure

Structural and magnetic properties of CoPt mixed clusters

In this present work, we report a structural and magnetic study of mixed Co58Pt42 clusters. MgO, Nb and Si matrix can be used to embed clusters, avoiding any magnetic interactions between particles. Transmission Electron Microscopy (TEM) observations show that Co58Pt42 supported isolated clusters are about 2nm in diameter and crystallized in the A1 fcc chemically disordered phase. Grazing Incidence Small Angle X-ray Scattering (GISAXS) and Grazing Incidence Wide Angle X-ray Scattering (GIWAXS) reveal that buried clusters conserve these properties, interaction with matrix atoms being limited to their first atomic layers. Considering that 60% of particle atoms are located at surface, this interactions leads to a drastic change in magnetic properties which were investigated with conventional magnetometry and X-Ray Magnetic Circular Dichro\"{i}sm (XMCD). Magnetization and blocking temperature are weaker for clusters embedded in Nb than in MgO, and totally vanish in silicon as silicides are formed. Magnetic volume of clusters embedded in MgO is close to the crystallized volume determined by GIWAXS experiments. Cluster can be seen as a pure ferromagnetic CoPt crystallized core surrounded by a cluster-matrix mixed shell. The outer shell plays a predominant role in magnetic properties, especially for clusters embedded in niobium which have a blocking temperature 3 times smaller than clusters embedded in MgO

Small Angle Scattering by Fractal Aggregates: A Numerical Investigation of the Crossover Between the Fractal Regime and the Porod Regime

Fractal aggregates are built on a computer using off-lattice cluster-cluster aggregation models. The aggregates are made of spherical particles of different sizes distributed according to a Gaussian-like distribution characterised by a mean $a_0$ and a standard deviation $\sigma$. The wave vector dependent scattered intensity $I(q)$ is computed in order to study the influence of the particle polydispersity on the crossover between the fractal regime and the Porod regime. It is shown that, given $a_0$, the location $q_c$ of the crossover decreases as $\sigma$ increases. The dependence of $q_c$ on $\sigma$ can be understood from the evolution of the shape of the center-to-center interparticle-distance distribution function.Comment: RevTex, 4 pages + 6 postscript figures, compressed using "uufiles", published in Phys. Rev. B 50, 1305 (1994

A 4-unit-cell superstructure in optimally doped YBa2Cu3O6.92 superconductor

Using high-energy diffraction we show that a 4-unit-cell superstructure, q0=(1/4,0,0), along the shorter Cu-Cu bonds coexists with superconductivity in optimally doped YBCO. A complex set of anisotropic atomic displacements on neighboring CuO chain planes, BaO planes, and CuO2 planes, respectively, correlated over ~3-6 unit cells gives rise to diffuse superlattice peaks. Our observations are consistent with the presence of Ortho-IV nanodomains containing these displacements.Comment: Corrected typo in abstrac

Exact limiting relation between the structure factors in neutron and x-ray scattering

The ratio of the static matter structure factor measured in experiments on coherent X-ray scattering to the static structure factor measured in experiments on neutron scattering is considered. It is shown theoretically that this ratio in the long-wavelength limit is equal to the nucleus charge at arbitrary thermodynamic parameters of a pure substance (the system of nuclei and electrons, where interaction between particles is pure Coulomb) in a disordered equilibrium state. This result is the exact relation of the quantum statistical mechanics. The experimental verification of this relation can be done in the long wavelength X-ray and neutron experiments.Comment: 7 pages, no figure

Molecular dynamics simulations of lead clusters

Molecular dynamics simulations of nanometer-sized lead clusters have been performed using the Lim, Ong and Ercolessi glue potential (Surf. Sci. {\bf 269/270}, 1109 (1992)). The binding energies of clusters forming crystalline (fcc), decahedron and icosahedron structures are compared, showing that fcc cuboctahedra are the most energetically favoured of these polyhedral model structures. However, simulations of the freezing of liquid droplets produced a characteristic form of ``shaved'' icosahedron, in which atoms are absent at the edges and apexes of the polyhedron. This arrangement is energetically favoured for 600-4000 atom clusters. Larger clusters favour crystalline structures. Indeed, simulated freezing of a 6525-atom liquid droplet produced an imperfect fcc Wulff particle, containing a number of parallel stacking faults. The effects of temperature on the preferred structure of crystalline clusters below the melting point have been considered. The implications of these results for the interpretation of experimental data is discussed.Comment: 11 pages, 18 figues, new section added and one figure added, other minor changes for publicatio

Surface Structure of Liquid Metals and the Effect of Capillary Waves: X-ray Studies on Liquid Indium

We report x-ray reflectivity (XR) and small angle off-specular diffuse scattering (DS) measurements from the surface of liquid Indium close to its melting point of $156^\circ$C. From the XR measurements we extract the surface structure factor convolved with fluctuations in the height of the liquid surface. We present a model to describe DS that takes into account the surface structure factor, thermally excited capillary waves and the experimental resolution. The experimentally determined DS follows this model with no adjustable parameters, allowing the surface structure factor to be deconvolved from the thermally excited height fluctuations. The resulting local electron density profile displays exponentially decaying surface induced layering similar to that previously reported for Ga and Hg. We compare the details of the local electron density profiles of liquid In, which is a nearly free electron metal, and liquid Ga, which is considerably more covalent and shows directional bonding in the melt. The oscillatory density profiles have comparable amplitudes in both metals, but surface layering decays over a length scale of $3.5\pm 0.6$ \AA for In and $5.5\pm 0.4$ \AA for Ga. Upon controlled exposure to oxygen, no oxide monolayer is formed on the liquid In surface, unlike the passivating film formed on liquid Gallium.Comment: 9 pages, 5 figures; submitted to Phys. Rev.

Diffractive point sets with entropy

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition

Law, Liberty and the Rule of Law (in a Constitutional Democracy)

In the hunt for a better--and more substantial--awareness of the “law,” The author intends to analyze the different notions related to the “rule of law” and to criticize the conceptions that equate it either to the sum of “law” and “rule” or to the formal assertion that “law rules,” regardless of its relationship to certain principles, including both “negative” and “positive” liberties. Instead, he pretends to scrutinize the principles of the “rule of law,” in general, and in a “constitutional democracy,” in particular, to conclude that the tendency to reduce the “democratic principle” to the “majority rule” (or “majority principle”), i.e. to whatever pleases the majority, as part of the “positive liberty,” is contrary both to the “negative liberty” and to the “rule of law” itself