1,651 research outputs found
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
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