A Formalism for Scattering of Complex Composite Structures. 1 Applications to Branched Structures of Asymmetric Sub-Units

We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural scattering in terms of three equations expressing the sub-unit scattering. The structural scattering expressions allows a composite structures to be used as sub-units within the formalism itself. This allows the scattering expressions for complex hierarchical structures to be derived with great ease. The formalism is furthermore generic in the sense that the scattering due to structural connectivity is completely decoupled from internal structure of the sub-units. This allows sub-units to be replaced by more complex structures. We illustrate the physical interpretation of the formalism diagrammatically. By applying a self-consistency requirement we derive the pair distributions of an ideal flexible polymer sub-unit. We illustrate the formalism by deriving generic scattering expressions for branched structures such as stars, pom-poms, bottle-brushes, and dendrimers build out of asymmetric two-functional sub-units.Comment: Complete rewrite generalizing the formalism to arbitrary functional sub-units and including a new Feynmann like diagrammatic interpretatio

The isotropic correlation function of plane figures: the triangle case

The knowledge of the isotropic correlation function of a plane figure is useful to determine the correlation function of the cylinders having the plane figure as right-section and a given height as well as to analyze the out of plane intensity collected in grazing incidence small-angle scattering from a film formed by a particulate collection of these cylinders. The correlation function of plane polygons can always be determined in closed algebraic form. Here we report its analytic expression for the case of a triangle. The expressions take four different forms that depend on the relative order among the sides and the heights of the triangle.Comment: 11 pages, 2 figure

Multiple Time Scales in Diffraction Measurements of Diffusive Surface Relaxation

We grew SrTiO3 on SrTiO3 (001) by pulsed laser deposition, using x-ray scattering to monitor the growth in real time. The time-resolved small angle scattering exhibits a well-defined length scale associated with the spacing between unit cell high surface features. This length scale imposes a discrete spectrum of Fourier components and rate constants upon the diffusion equation solution, evident in multiple exponential relaxation of the "anti-Bragg" diffracted intensity. An Arrhenius analysis of measured rate constants confirms that they originate from a single activation energy.Comment: 4 pages, 3 figure

Time-, Frequency-, and Wavevector-Resolved X-Ray Diffraction from Single Molecules

Using a quantum electrodynamic framework, we calculate the off-resonant scattering of a broad-band X-ray pulse from a sample initially prepared in an arbitrary superposition of electronic states. The signal consists of single-particle (incoherent) and two-particle (coherent) contributions that carry different particle form factors that involve different material transitions. Single-molecule experiments involving incoherent scattering are more influenced by inelastic processes compared to bulk measurements. The conditions under which the technique directly measures charge densities (and can be considered as diffraction) as opposed to correlation functions of the charge-density are specified. The results are illustrated with time- and wavevector-resolved signals from a single amino acid molecule (cysteine) following an impulsive excitation by a stimulated X-ray Raman process resonant with the sulfur K-edge. Our theory and simulations can guide future experimental studies on the structures of nano-particles and proteins

Structure and equation of state of interaction site models for disc-shaped lamellar colloids

We apply RISM (Reference Interaction Site Model) and PRISM (polymer-RISM) theories to calculate the site-site pair structure and the osmotic equation of state of suspensions of circular or hexagonal platelets (lamellar colloids) over a range of ratios of the particle diameter over thickness. Despite the neglect of edge effects, the simpler PRISM theory yields results in good agreement with the more elaborate RISM calculations, provided the correct form factor, characterizing the intramolecular structure of the platelets, is used. The RISM equation of state is sensitive to the number of sites used to model the platelets, but saturates when the hard spheres, associated with the interaction sites, nearly touch; the limiting equation of state agrees reasonably well with available simulation data for all densities up to the isotropic-nematic transition. When properly scaled with the second virial coefficient, the equations of state of platelets with different aspect ratios nearly collapse on a single master curve.Comment: 10 Pages, 11 Figures, Typesetted using RevTeX

A Formalism for Scattering of Complex Composite Structures. 2 Distributed Reference Points

Recently we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units.{[}C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012){]} We assumed each sub-unit has reference points associated with it. These are well defined positions where sub-units can be linked together. In the present paper, we generalize the formalism to the case where each reference point can represent a distribution of potential link positions. We also present a generalized diagrammatic representation of the formalism. Scattering expressions required to model rods, polymers, loops, flat circular disks, rigid spheres and cylinders are derived. and we use them to illustrate the formalism by deriving the generic scattering expression for micelles and bottle brush structures and show how the scattering is affected by different choices of potential link positions.Comment: Paper no. 2 of a serie

Short-range incommensurate magnetic order near the superconducting phase boundary in Fe(1+d)Te(1-x)Se(x)

We performed elastic neutron scattering and magnetization measurements on Fe(1.07)Te(0.75)Se(0.25) and FeTe(0.7)Se(0.3). Short-range incommensurate magnetic order is observed in both samples. In the former sample with higher Fe content, a broad magnetic peak appears around (0.46,0,0.5) at low temperature, while in FeTe(0.7)Se(0.3) the broad magnetic peak is found to be closer to the antiferromagnetic (AFM) wave-vector (0.5,0,0.5). The incommensurate peaks are only observed on one side of the AFM wave-vector for both samples, which can be modeled in terms of an imbalance of ferromagnetic/antiferromagnetic correlations between nearest-neighbor spins. We also find that with higher Se (and lower Fe) concentration, the magnetic order becomes weaker while the superconducting temperature and volume increase.Comment: Version as appeared in PR

Characterization of the glass transition in vitreous silica by temperature scanning small-angle X-ray scattering

The temperature dependence of the x-ray scattering in the region below the first sharp diffraction peak was measured for silica glasses with low and high OH content (GE-124 and Corning 7980). Data were obtained upon scanning the temperature at 10, 40 and 80 K/min between 400 K and 1820 K. The measurements resolve, for the first time, the hysteresis between heating and cooling through the glass transition for silica glass, and the data have a better signal to noise ratio than previous light scattering and differential thermal analysis data. For the glass with the higher hydroxyl concentration the glass transition is broader and at a lower temperature. Fits of the data to the Adam-Gibbs-Fulcher equation provide updated kinetic parameters for this very strong glass. The temperature derivative of the observed X-ray scattering matches that of light scattering to within 14%.Comment: EurophysicsLetters, in pres

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