The effect of finite slit heights on the determination of systematic deviations from Porod's law

Abstract

Systematic deviations from Porod's law have often to be studied in angular regions in which the infiniteslit approximation is no longer valid. It is shown that this is not a serious limitation as long as the lower limit of the validity of Porod's law is smaller than a certain dimension of the slit height and that the method of evaluation proposed in an earlier paper [Ruland (1971). J. Appl. Cryst. 4,[70][71][72][73] can be modified to allow for the effect of finite slit heights. An example of application is given for the smallangle scattering of glassy carbons.

Examination of errors in the determination of phase boundary thickness by small-angle X-ray scattering

“…Deviations from this Porod law can occur in practice since the boundaries between the phases may not be perfectly sharp, and the electron densities within the phases contain local fluctuations. The potential utility of determining the phase boundary thickness, by examination of the deviation of observed SAXS intensity from Porod's law, was first pointed out by Ruland (1971) and has since been examined by a number of workers (Vonk, 1973;Ruland, 1974;Hashimoto, Todo, Itoi & Kawai, 1977;Todo, Hashimoto & Kawai, 1978;Hashimoto, Shibayama & Kawai, 1980;Koberstein, Morra & Stein, 1980;.…”

“…According to Ruland (1971), the observed intensity lobs(S ) can be expressed as lobs(S) = Iid(S)H 2(S) "1-I b ,…”

The two-phase structure of segmented block copoly(ether ester)

“…In view of the fact that the material exhibits only one glass transition, as indicated by differential scanning calorimetric and dynamical mechanical data, the amorphous phase has been treated as a single phase, even though it is a mixture of hard and soft segments [6][7][8][9][10][11][12][13][14]. The relative composition of this phase is found to be a critical factor in determining the glass transition temperature 27 The arrangement of the chains in the crystalline domains resembles that of the a-modification of the parent homopolymer PBT [7]. These crystalline domains are believed to exist in the form of lamellae where the short dimension coincides with the chain direction [6,7,10,14].…”

Determination of the interface distribution function of lamellar two-phase systems

“…In this case, the determination of d= and J~d can be carried out by a method described in an earlier paper (Ruland, 1974) in which the profile of the slit is approximated by a trapezoid.…”