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A band width determination using the first derivative of the band profile systematically underestimates the true Bragg angle. Corrections are proposed to compensate for the resulting offset Δa/a of the mean lattice parameters derived from as many Kikuchi band widths as possible. For dynamically simulated Kikuchi patterns, Δa/a can reach up to 8% for phases with a high mean atomic number Z, whereas for much more common low-Z materials the offset decreases linearly. A predicted offset Δa/a = f(Z) is therefore proposed, which also includes the unit-cell volume and thus takes into account the packing density of the scatterers in the material. Since Z is not always available for unknown phases, its substitution by Zmax, i.e. the atomic number of the heaviest element in the compound, is still acceptable for an approximate correction. For simulated Kikuchi patterns the offset-corrected lattice parameter deviation is Δa/a < 1.5%. The lattice parameter ratios, and the angles α, β and γ between the basis vectors, are not affected at all.1.5%. The lattice parameter ratios, and the angles , and between the basis vectors, are not affected at all.
A typical electron backscatter diffraction (EBSD) pattern usually contains more than a hundred of Kikuchi poles that formed by intersecting dozens of visible Kikuchi bands. The poles correspond to zone axes in real space or lattice planes in reciprocal space. The band widths are inversely proportional to the interplanar spacings of diffracting lattice planes, and the angle formed by the beam source and two band center-lines approximately corresponds to angle between two lattice planes. However, EBSD patterns always suffer from gnomic distortions. In addition, the band width measurement has a relative error of 5-20% due to the complex profile. Thus, an EBSD pattern always provides abundant crystallographic information but disappointingly low accuracy.