Journal of Applied Crystallography

Volume 37, Part 4 (August 2004)

research papers

J. Appl. Cryst. (2004). 37, 643-651 [ doi:10.1107/S0021889804013196 ]

Modified Porod's law estimate of the transition-layer thickness between two phases: test of triangular smoothing function

M.-H. Kim

Abstract: An analytical method to estimate the thickness of the interface between two phases from small-angle scattering (SAS) data has been developed using Porod's law modified by a triangular smoothing function. The convolution with a `top-hat' function describing a sharp density profile results in a semi-sigmoidal density profile. This analytical method allows an interfacial layer thickness to be estimated from the negative slope of a Porod plot. The interfacial layer thickness (T) obtained from this model is related to similar models, namely a linear (E) and a sigmoidal density profile ( [sigma] ) model, as follows: T = 2^1/2E = 2(6^1/2) [sigma] , where [sigma] is the standard deviation of the Gaussian function and does not represent the boundary thickness itself. The interfacial layer thickness obtained from any convolution method is a model-dependent parameter.

Keywords: small-angle scattering; transition (or interface) boundary thickness; modified Porod law; electron density profile; triangle smoothing function; phase transitions.