Die Methode der Abstandsverfeinerung zur Bestimmung der Atomkoordinaten idealisierter Gerüststrukturen

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Abstract
The values of bond lengths are in most instances reasonably well known and can be predicted with some certainty. The direct use of this information in structure analyses has been found particularly useful in studies of aluminosilicate structures. The interatomic distance D is a function only of the coordinates of the atoms involved and the unit-cell constants. With framework structures it is found that the number of crystallographically independent interatomic distances exceeds the number of coordinates to be determined. Therefore, given an approximate initial solution, it is possible to compute the coordinates of framework atoms by means of least-squares adjustments of interatomic distances to prescribed values. The refined coordinates found thereby define an idealized structure with respect to prescribed interatomic distances (and fixed unit-cell constants) which is called the D structure. A general computer program has been developed for these refinements. D refinement can be applied to the analysis of pseudosymmetric framework structures, i.e. the lowering of the symmetry in structure determinations. Fourier maps of the initial high-symmetry structure yield the magnitudes but not the signs of the atomic displacements from the high-symmetry positions. The probable signs of the displacements may be obtained by D refinement. Other applications of D refinement include the calculation of reasonably accurate trial coordinates and the determination of possible Si/Al distributions in aluminosilicate frameworks. We have noted that whenever D refinement has not proceeded, either the trial structure or the assumed symmetry has been incorrect.