dab

DAB (Debye Anderson Brumberger) Model

Parameter Description Units Default value
scale Scale factor or Volume fraction None 1
background Source background cm-1 0.001
cor_length correlation length 50

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

Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system is characterized by a single length scale, the correlation length, which is a measure of the average spacing between regions of phase 1 and phase 2. The model also assumes smooth interfaces between the phases and hence exhibits Porod behavior (Iq4) at large q, (qL1).

The DAB model is ostensibly a development of the earlier Debye-Bueche model.

Definition

I(q)=scaleL3(1+(qL)2)2+background

where scale is

scale=8πϕ(1ϕ)Δρ2

and the parameter L is the correlation length.

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/dab_autogenfig.png

Fig. 97 1D plot corresponding to the default parameters of the model.

Source

dab.py

References

  1. P Debye, H R Anderson, H Brumberger, Scattering by an Inhomogeneous Solid. II. The Correlation Function and its Application, J. Appl. Phys., 28(6) (1957) 679
  2. P Debye, A M Bueche, Scattering by an Inhomogeneous Solid, J. Appl. Phys., 20 (1949) 518

Source

dab.py

Authorship and Verification

  • Author:
  • Last Modified by:
  • Last Reviewed by: Steve King & Peter Parker Date: September 09, 2013
  • Source added by : Steve King Date: March 25, 2019