A new look at absorption in high-energy electron diffraction

Abstract

People seldom take absorption very seriously in electron diffraction calculations. Since the work of Hashimoto et al. it has been common practice to set the absorbative part of the potential coefficient V′g to be one tenth of the elastic part Vg. Although this may not be a bad approximation in simple metals, there is no reason why it should apply to more complicated structures. Here, Vg may be small because of interference between different atoms in the unit cell, but the same cancellation might not occur in V′g because the individual atomic contributions to Vg and V′g need not scale in the same way. In fact, the absorbative contribution increases more rapidly with atomic number than the elastic part. This effect is particularly marked in non-centrosymmetric crystals, where V′g and Vg need not have the same phase. Both V′g and Vg are now complex numbers which we write as(1)The squared modulus of the total potential coefficient now becomes(2)If g → −g, ϕ and ϕ′ change sign, so if the phase difference is non-zero the overall magnitude of the +g and −g potential coefficients are not equal. The standard assumption is that |V′g| = 0.1|Vg| and ϕg − ϕ′g = 0, which ignores corrections to the magnitude of Vg of order | V′g/Vg|.