2.2.2. Dab¶

DAB (Debye Anderson Brumberger) Model

Parameter	Description	Units	Default value
scale	Source intensity	None	1
background	Source background	cm^-1	0
length	correlation length	Å	50

The returned value is scaled to units of cm^-1.

Scattering model class for the DAB (Debye Anderson Brumberger) Model

2.2.2.1. Definition¶

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 (I ~ q^-4) at large q (QL >> 1).

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

Definition

\[I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q \cdot L)^2)^2} + \text{background}\]

where scale is

\[\text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2\]

and the parameter L is the correlation length.

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

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

Parameter name	Units	Default value
scale	None	1.0
corr length L	Å	50.0
background	cm^-1	0.0

Figure 1: 1D plot using the default values (w/200 data point).

2.2.2.2. Reference¶

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

P Debye, A M Bueche, Scattering by an Inhomogeneous Solid, J. Appl. Phys., 20 (1949) 518

2013/09/09 - Description reviewed by King, S and Parker, P.

Home

2.2.2. Dab

2.2.2. Dab¶

2.2.2.1. Definition¶

2.2.2.2. Reference¶