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

$I(q) = \frac{A}{q^n} + \frac{C}{1 + (|q - q_0|\xi)^m} + B$

Here the peak position is related to the d-spacing as $$q_0 = 2\pi / d_0$$.

$$A$$ is the Porod law scale factor, $$n$$ the Porod exponent, $$C$$ is the Lorentzian scale factor, $$m$$ the exponent of $$q$$, $$\xi$$ 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

$q = \sqrt{q_x^2 + q_y^2}$

Source

broad_peak.py

References

None.

Authorship and Verification

• Author: NIST IGOR/DANSE Date: pre 2010