Relativistic Hartree–Fock X-ray and electron atomic scattering factors at high angles

An enlarged set (atomic number Z = 2 to 98) of free-atom X-ray atomic scattering (form) factors for high angles [2 ≤ (sin θ)/λ ≤ 6Å^-1] has been calculated based on those of Doyle & Turner [Acta Cryst. (1968). A24, 390-397]. Four-parameter 'exponential polynomial' fits for these are presented which give far more accurate estimates of the scattering factors at high angles than the Gaussian fits normally used. The use of the Mott formula in conjunction with these new high-angle X-ray form factors allows the calculation of improved-accuracy high-angle electron scattering factors. The use of these high-accuracy high-angle scattering factors for important applications such as Fourier charge-density analysis and computer simulation of high-resolution electron microscope (HREM) images is discussed.