The “fuzziness” of the interface is defined by the parameter σ fuzzy. The returned value is scaled to units of cm -1sr -1 ie, absolute scale. Poly-dispersion in radius and in fuzziness is provided for. Contrast (Δρ) is the difference of scattering length densities of the sphere and the surrounding The scale is equivalent to the volume fraction of spheres, each of Where the amplitude A(q) is given as the typical sphere scattering convoluted with a Gaussian to get a gradualĭrop-off in the scattering length density The scattering intensity I(q) is calculated as: This model is to calculate the scattering from spherical particles with a “fuzzy” interface. N W Ashcroft and D C Langreth, Physical Review, 156 (1967) 685-692 1D plot using the default values above (w/200 data point). While s (or ss) for the smaller spheres). The parameters of the BinaryHSModel are the following (in the names, l (or ls) stands for larger spheres The 2D scattering intensity is the same as 1D, regardless of the orientation of the q vector which is defined as Where n = the number density) is internally calculated based on The number fraction of the larger particle, ( x = n2/(n1+n2), Is for the smaller particle and 2 is for the larger. Where Sij are the partial structure factors and fi are the scattering amplitudes of the particles. Using Percus-Yevick closure, the calculation is an exact multi-component Sphere interaction between those particles. This model (binary hard sphere model) provides the scattering intensity, for binary mixture of spheres including hard The parameters were set to: Scale=1.0, Radius=60 Å, Contrast=1e-6 Å -2, and Background=0.01 cm -1.Ģ013/09//01/06 - Description reviewed by S King and P Parker. Figure 1 shows a comparison of the output of our model and the output of the NIST software.įigure 1: Comparison of the DANSE scattering intensity for a sphere with the output of the NIST SANS analysis software. Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the Fournet, Small-Angle Scattering of X-Rays, John Wiley and Sons, New York, (1955) Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for NeutronĪ Guinier and G. The returned value is scaled to units of cm -1 and the parameters of the SphereModel are the following: Parameter name The 2D scattering intensity is the same as above, regardless of the orientation of the q vector. If not, it should represent the volume fraction * a factor (by which your data might need to be Note that if your data is in absolute scale, the scale should represent the volume fraction (which is unitless) if The background level and sldXXX is the scattering length density (SLD) of the scatterer or the solvent. Where scale is a volume fraction, V is the volume of the scatterer, r is the radius of the sphere, bkg is The 1D scattering intensity is calculated in the following way (Guinier, 1955) The form factor is normalized by the particle volume as described below. This model provides the form factor, P(q), for a monodisperse spherical particle with uniform scattering lengthĭensity. We define the angle φ as the angle between the q vector and the horizontalįor information about polarised and magnetic scattering, click here. Our so-called 2D scattering intensity functions provide P(q, φ ) for an oriented system as a function of a The intensity measured on the plane of the SASĭetector will have an azimuthal symmetry around q=0. That case, the scattering intensity only depends on the length of q. Our so-called 1D scattering intensity functions provide P(q) for the case where the scatterer is randomly oriented. Point in space and the integration is done over the volume V of the scatterer.įor systems without inter-particle interference, the form factors we provide can be related to the scattering intensity Where P 0 (q) is the un-normalized form factor, ρ (r) is the scattering length density at a given To easily compare to the scattering intensity measured in experiments, we normalize the form factors by the volume of Instructions on how to use SasView itself are available separately. Validation plots for each model are also presented. We show the list of parameters available to the user. After giving a mathematical definition of each model, This software provides form factors for various particle shapes. Research and thus some content and figures in this document are originated from or shared with the NIST SANS Igor-based Many of our models use the form factor calculations implemented in a c-library provided by the NIST Center for Neutron
0 Comments
Leave a Reply. |