core_multi_shell

This model provides the scattering from a spherical core with 1 to 4 concentric shell structures. The SLDs of the core and each shell are individually specified.

Parameter Description Units Default value
scale Source intensity None 1
background Source background cm-1 0.001
sld_core Core scattering length density 10-6Å-2 1
radius Radius of the core Å 200
sld_solvent Solvent scattering length density 10-6Å-2 6.4
n number of shells None 1
sld[n] scattering length density of shell k 10-6Å-2 1.7
thickness[n] Thickness of shell k Å 40

The returned value is scaled to units of cm-1 sr-1, absolute scale.

Definition

This model is a trivial extension of the CoreShell function to a larger number of shells. The scattering length density profile for the default sld values (w/ 4 shells).

../../_images/core_multi_shell_sld_default_profile.jpg

Fig. 77 SLD profile of the core_multi_shell object from the center of sphere out for the default SLDs.*

The 2D scattering intensity is the same as \(P(q)\) above, regardless of the orientation of the \(\vec q\) vector which is defined as

\[q = \sqrt{q_x^2 + q_y^2}\]

Note

Be careful! The SLDs and scale can be highly correlated. Hold as many of these parameters fixed as possible.

Note

The outer most radius (= radius + thickness) is used as the effective radius for \(S(Q)\) when \(P(Q)*S(Q)\) is applied.

For information about polarised and magnetic scattering, see the Polarisation/Magnetic Scattering documentation.

Our model uses the form factor calculations implemented in a C-library provided by the NIST Center for Neutron Research [1].

../../_images/core_multi_shell_autogenfig.png

Fig. 78 1D plot corresponding to the default parameters of the model.

Source

core_multi_shell.py \(\ \star\ \) core_multi_shell.c \(\ \star\ \) lib/sas_3j1x_x.c

References

Also see the core_shell_sphere model documentation and [2]

[1]S R Kline, J Appl. Cryst., 39 (2006) 895
[2]L A Feigin and D I Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, New York, 1987.

Authorship and Verification

  • Author: NIST IGOR/DANSE Date: pre 2010
  • Last Modified by: Paul Kienzle Date: September 12, 2016
  • Last Reviewed by: Paul Kienzle Date: September 12, 2016