Model X-ray scattering behaviour of arrays of structured cylinders.

The model X-ray scattering behaviour of hexagonal arrays of infinitely long cylinders with various internal structures is considered by regarding the model as a function of three parameters, viz: the cylinder's scattering function, the swelling factor (Y), and the lattice interference function. The behaviour of the scattering function is considered as the cylinder's structure (electron density distribution) is systematically varied from the case of a solid cylinder to that of a thin shell. A ten stage electron density strip model is shown to be sufficient for this purpose. The effects of packing of the cylinders is examined by the use of the swelling factor (Y), and the behaviour of the diffraction pattern due to an array of solid cylinders is used to illustrate the effects of changing. The behaviour of the lattice function is examined as the numbers of lattice points in a centred hexagonal array is varied from seven to sixty-one. It is shown that the interference function due to a hexagonal array of thirty-seven points represents a reasonable approximation to the case of the interference function due to an infinite hexagonal array. The behaviour of the diffraction patterns due to a series of cylinders with various structures in a centred hexagonal array of thirty-seven components is examined as systematic changes to the various parameters are made, and explained in terms of the combined behaviour of those parameters as outlined above.