Diffraction patterns were measured on a polycrystalline bcc 57 Fe foil using a Mössbauer powder diffractometer with high sensitivity. Measurements with and without a magnetic field normal to the scattering plane showed large differences in the diffracted intensities of the different nuclear resonances. These magnetic effects on diffraction intensities were interpreted successfully with a single scattering theory developed to handle isotropic and anisotropic orientation distributions of hyperfine magnetic fields. When there is coherent interference between nuclear scattering and x-ray Rayleigh scattering, an asymmetry in the coherent intensity of the three pairs of diffractions for the 57 Fe magnetic sextet ͑1,6͒, ͑2,5͒, ͑3,4͒ is predicted. This is largest in the presence of a uniaxial magnetic field, and the calculated and measured asymmetries were in good agreement. A reduced diffraction intensity for lines ͑2,5͒ and ͑3,4͒ caused by spin-flip incoherence was also measured. The effects of dynamical diffraction, if present, are shown to be small.