Finite slit-height correction for the study of systematic deviations from Porod's law

Abstract

The evaluation of the small-angle scattering of two-phase systems is greatly facilitated if Porod's law can be observed in the outer angular region. A finite width of the phase boundary as well as density fluctuations within the phases produce systematic deviations from Porod's law which can be determined and eliminated by s41-s plots in the case of pin-hole collimation and s3J-s plots in the case of an 'infinite' slit-height. Unfortunately, the study of the systematic deviations very often necessitates measurements in angular regions for which the assumption of an infinite slit height is no longer valid. However, if the lower limit of the validity of Porod's law is equal or smaller than half of the extent of the constant inner part of the slit function, a complete evaluation of the scattering is still possible. The method consists in replacing the factors s in the above-mentioned plots by appropriate expressions deduced from the slit function. In a first step, the parameters related to the slope and the intercept of this plot are obtained which, in further steps, are used to correct the integral values which are needed to compute the invariant and the length of coherence. If the slit function can be approximated by a trapezium, all correction functions can be given in analytical form. The method is applied to some earlier measurements on glassy carbons and it is shown that neglecting the effect of a finite slit height leads primarily to underestimating the values for the density fluctuations whereas the pore-size parameters and the porosity values are much less affected.