2.1.6.2. Sphere¶
Spheres with uniform scattering length density
| Parameter | Description | Units | Default value |
|---|---|---|---|
| scale | Source intensity | None | 1 |
| background | Source background | cm-1 | 0 |
| sld | Layer scattering length density | 10-6Å-2 | 1 |
| solvent_sld | Solvent scattering length density | 10-6Å-2 | 6 |
| radius | Sphere radius | Å | 50 |
The returned value is scaled to units of cm-1.
For information about polarised and magnetic scattering, click here.
Definition¶
The 1D scattering intensity is calculated in the following way (Guinier, 1955)
where scale is a volume fraction, \(V\) is the volume of the scatterer, \(R\) is the radius of the sphere, background is the background level and sld and solvent_sld are the scattering length densities (SLDs) of the scatterer and the solvent respectively.
Note that if your data is in absolute scale, the scale should represent the volume fraction (which is unitless) if you have a good fit. If not, it should represent the volume fraction times a factor (by which your data might need to be rescaled).
The 2D scattering intensity is the same as above, regardless of the orientation of \(\vec q\).
Our model uses the form factor calculations as defined in the IGOR package provided by the NIST Center for Neutron Research (Kline, 2006).
Validation¶
Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). Figure figure 1 shows a comparison of the output of our model and the output of the NIST software.
Figure 1: Comparison of the DANSE scattering intensity for a sphere with the output of the NIST SANS analysis software. The parameters were set to: scale = 1.0, radius = 60 Å, contrast = 1e-6 Å-2, and background = 0.01 cm-1.
Reference¶
A Guinier and G. Fournet, Small-Angle Scattering of X-Rays, John Wiley and Sons, New York, (1955)
2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.