The mean square of the electron-density gradient, (Igrad r/[ 2) in isotropic structures is shown to be proportional to the fourth moment of the SAXS intensity distribution in reciprocal space ~s4l(s)ds, as well as to the second derivative of the correlation function in the origin. In the case of two-phase structures with unsharp phase boundaries, these relations may be used to find the thickness E of the transition regions. As was shown by Ruland [J. Appl. Cryst. (1971). 4, 70-73] Ecan also be determined by analysis of the intensity in the tail of the SAXS pattern. This approach is used here to investigate the effect of E on the one-dimensional correlation function. In the application of both methods, separation of the SAXS intensity from the continuous background of liquid scattering constitutes a critical step. A procedure in which the background is represented by a curve of the type a + bs", where n is an even number, is found to work well for a number of polymers.

This gives 0~t=162.8+0.2°K for the thin film and 0M = 202 _+ 11 °K for the thick film. ConclusionsAfter the 2-beam correction for dynamical scattering is applied, the difference between the slopes for the small and large particles has become even larger. Three explanations seem to be possible, (i) the Debye temperature 0M, for the small crystallites is lower because of surface, contributions, (ii) 0M for the bigger crystallites is higher because of the inclusion of impurity atoms in the film and (iii) the temperatures of the thick film are very different from those of the thin film. For the last explanation to be possible the following conditions are required. For the thin film no radiation exchange is assumed and the beam increases the high and low temperatures by equal amounts. For the thick film beam heating and radiation exchange lead to a decrease in the temperature difference between the high and low-temperature runs. If, therefore, for the thick film the temperature difference is reduced to 111 + 16 °K and for the thin film is 172°K, the two films give the same 0M= 175°K. However, this situation is contrary to expectation because it is more likely that the thin film shows radiation exchange than that the thick film shows it. The second explanation is unlikely because both films were prepared under the same conditions. It is suggested that the first explanation is correct. This is supported by an estimate of the changes to be expected when size limitations are introduced into the Debye distribution (Schoening, 1968). Although the theoretical calculations were made for free surfaces they should give an indication of the magnitude of the effect for the gold-carbon interfaces. Comparing the B without zero-point contribution for a 35 A cubic crystal to that for an infinite crystal shows that the ratio B(small) to B(large) is about 1-14 in the present temperature range. The observed ratio of 1-26 +0.15 increases to 1.54 when dynamical corrections are made for the thick film. However, except for showing that these corrections increase the ratio, not much importance can be attached to the numerical value of the corrections. The major uncertainty arises from the use of the 2-beam approximation in estimating the dynamical influences.In their comprehensive work on polycrystalline aluminum, Horstmann & Meyer found that in the size range below 90 A, the observed intensities were, on the average, about 10% lower than those predicted by the kinematical theory. Because the difference appears to increase with angle it is possible that it is also due to a size effect.The author would like to thank Professor M. Horstmann for his comments on the manuscript and for his permission to use the apparatus during this study, the staff of the Institut f/Jr Angewandte Physik for its hospitality and the University of Hamburg for financial assistance.References BLACKMAN, M. (1939 A general procedure for determination of the crystallinity in polymers from the X-ray diffraction pattern was developed by modifying the method described by R...

No abstract

A computer procedure for slit‐height correction of X‐ray small‐angle scattering curves is described, which Ij based on direct calculation of the desmeared intensity values Ij from the equations ?i = ∑jai,jIj where ?i is the observed smeared intensity at point i and ai,jIj represents the contribution from a point j along the trace of the primary beam. However, the number of unknown Ij values is reduced by a factor 1/n (n = 3 to 5), and the equations are solved by the method of least‐squares. The performance of the method is tested on the diffraction curve of isolated spheres.

The program comprises a main program for inspection and correction of the intensity data, and a number of subroutines covering specific operations. These subroutines can be called upon in any desired sequence.