The interpretation of X-ray and neutron diffraction data in accurate studies of crystal and molecular structure requires the development of a new structure factor formalism. The formalism normally employed in structure analysis fails to recognize antisymmetric features associated with nonspherical atomic charge distributions and with anharmonic components of the atomic vibration amplitudes. Both these antisymmetric features can be incorporated readily in the analysis of diffraction data by using a general formalism involving complex atomic scattering factors and complex temperature factors. Some implications of the general formalism are discussed. Relations between atomic motions and static positions are considered in terms of equilibrium and time-averaged concepts, and the case of librational motion is cited to illustrate the relation of these concepts to the type of vibrational approximation employed in data analysis. The discussion is extended to general considerations of the atomic scattering powers, and approximations in the customary handling of these quantities are noted.