Structure determination in highly absorbing crystals

If electron scattering is described by a complex crystal potential

$\text{V = ∑}{}_{\mathrm{g}}\text{(v}{}_{\mathrm{g}}\text{exp}\text{(?M}{}_{\mathrm{g}}\text{+ iv}{}_{\mathrm{g}}{}^{\mathrm{i}}\text{) exp(2πiG·r)}$

,then whenever 2v_gexp(?M_g) < v₀ⁱ, it can be expected that the diffraction conditions correspond to the case of strong absorption. It is shown that in this limit a measurement of the maximum intensity of a Bragg reflection from a single crystal is equivalent to that of the total integrated intensity measured from a polycrystalline powder, for the same reflection. The absorption is sufficiently large to average the crystal wavefield over the entire range of elastic reflectivity, and an intensity measurement becomes proportional to |F|² provided that it has been maximized by small variation of the diffraction parameters about an apparent Bragg reflection to avoid the accidental excitation of strong reflections. Atomic positions however can only be determined from |F|² under certain critical assumptions concerning the role played by the atomic form factor ?(S), which are discussed. Since it is shown that in the high absorption limit maximized intensity measurements can be expected to be kinematical-like, it is also argued that there is no physical meaning to further averaging of LEED data. It may be necessary to “smooth” the data because of accidental reflections which violate the strong absorption condition.