The problem of the diffraction of x-rays by small crystalline particles is discussed by the methods of Fourier analysis, and the calculation of the intensity of the x-ray scattering from a single particle is reduced to the evaluation of a simple Fourier transform. This approach leads immediately to the interference functions for the parallellepipedon and the octahedron as obtained by other authors. In addition, it makes possible the detailed discussion of the interference functions for the tetrahedron, the rhombic dodecahedron, the ellipsoid, and the elliptic cylinder. The method is shown to be applicable to any polyhedron. A simple method is also given for calculating the interference function and its integral breadth for specific directions of departure from the whole-numbered points. This is applied to obtain a partial discussion of the scattering from the tetrahexahedron and the trisoctahedron.

• Received 24 July 1939

DOI:https://doi.org/10.1103/PhysRev.56.972