broad_peak

Broad Lorentzian type peak on top of a power law decay

Parameter Description Units Default value
scale Scale factor or Volume fraction None 1
background Source background cm-1 0.001
porod_scale Power law scale factor None 1e-05
porod_exp Exponent of power law None 3
lorentz_scale Scale factor for broad Lorentzian peak None 10
lorentz_length Lorentzian screening length 50
peak_pos Peak position in q -1 0.1
lorentz_exp Exponent of Lorentz function None 2

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

Definition

This model calculates an empirical functional form for SAS data characterized by a broad scattering peak. Many SAS spectra are characterized by a broad peak even though they are from amorphous soft materials. For example, soft systems that show a SAS peak include copolymers, polyelectrolytes, multiphase systems, layered structures, etc.

The d-spacing corresponding to the broad peak is a characteristic distance between the scattering inhomogeneities (such as in lamellar, cylindrical, or spherical morphologies, or for bicontinuous structures).

The scattering intensity I(q) is calculated as

I(q)=Aqn+C1+(|qq0|ξ)m+B

Here the peak position is related to the d-spacing as q0=2π/d0.

A is the Porod law scale factor, n the Porod exponent, C is the Lorentzian scale factor, m the exponent of q, ξ the screening length, and B the flat background.

For 2D data the scattering intensity is calculated in the same way as 1D, where the q vector is defined as

q=q2x+q2y
../../_images/broad_peak_autogenfig.png

Fig. 95 1D plot corresponding to the default parameters of the model.

Source

broad_peak.py

References

None.

Authorship and Verification

  • Author: NIST IGOR/DANSE Date: pre 2010
  • Last Modified by: Paul kienle Date: July 24, 2016
  • Last Reviewed by: Richard Heenan Date: March 21, 2016