MODEL

Debye-Anderson-Brumberger (DAB)

AUTHOR/MODIFICATION

Charlie Glinka 05 DEC 1998

Alan Munter 08 JULY 1999, converted to Java

APPROVED FOR DISTRIBUTION

DESCRIPTION

Calculates the scattering from a randomly distributed (i.e.
nonparticulate), 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 (Q*correlation
length >> 1). The macroscopic scattering cross-section in the
DBA model is given by

dS/dW = A/(1 + (*q***a*)^2)^2

where a is the correlation length in Å.

Resolution smeared version is also provided.

VARIABLES

Input Variables (default values):

Parameter | Variable | Value |
---|---|---|

0 | Scale | 10.0 |

1 | Radius (Å) | 40.0 |

2 | Incoherent Background (cm^{-1}) | 0.0 |

USAGE NOTES

The returned value is in units of [cm^{-1}].

The scale factor, A or Parameter[0], is treated as an independent
fitting parameter, but is, in the DBA model, related to the volume
fractions of the two phases, f1 and f2, their contrast,
(sld_1 - sld_2)^{2}, and the correlation length, a, as follows:

A = 8**p***a*^{3}*contrast*f1*f2

The surface, S, to volume, V, ratio for the system is given by

S/V = 4*f1*f2/ *a*

REFERENCES

Debye, P., Anderson, R., Brumberger, H., "Scattering by an
Inhomogeneous Solid. II. The Correlation Function and Its Application,"
J. Appl. Phys. **28 (6)**, 679 (1957).

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

TEST DATASET

This example dataset is produced by multiplying the values generated
by the Model DAB (using the default parameter values given above) by
(1 + gnoise(.05)) to simulate real data with 5% gaussian noise. The
q-range has been restricted to (0.001,0.05) Å^{-1}.