Correlation functions of amorphous multiphase systems

We give two general integral expressions for the first and second derivatives of the so-called stick probability functions which are commonly used in analyzing x-ray-scattering results. Then it is shown that by letting the length of the stick go to zero, the limit of the second derivative can be expressed in terms of an integral over the singularity lines of the surfaces which separate the different phases of the sample. In this way one has achieved the generalization of the well-known result that the limit of the second derivative is always zero when phase boundaries are smooth.