Direct Methods of Solving Crystal Structures pp 399-400 | Cite as

# Some Considerations Concerning the Physical Interpretation of Sayre’s Equation and Phase Triplets in Direct Methods

## Abstract

Despite of the permanent progress in the theory of direct methods a problem of physical interpretation of phase relations is still not clear enough. Schenk (1981) has given a graphic explanation of phase triplets and quartets on the basis of electron density considerations. Such a geometrical approach is very convenient and viseable, however it does not take into account a real process of X-ray scattering by crystal. In direct methods a crystal is considered as an ideal infinite periodic structure. Therefore, direct methods are also valid for a large perfect crystal and one can compare phase relations of direct methods with inferences of the dynamic theory of X-ray diffraction. For this purpose we use Ewald’s dynamical theory in the case of three strong coplanar beams (Ewald & Heno, 1968; Post, 1979). The condition of compatibility of the dynamical equations has the form

_{0}is a resonance error, Г ≃ e

^{2}λ

^{2}/mc

^{2}πV, V is the volume of the unit cell. Determinant (1) (except the diagonal terms) is identical to the Karle — Hauptman’s one. If we had taken more waves into consideration we would have got a determinant of a higher order. Unfortunately, ∈

_{0}cannot be measured or calculated for an unknown structure. Nevertheless, we can use the determinant (1) for some illustrations. Expansion of the latter yields the dispersion equation

## References

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