The structure of potassium niobate at room temperature: the solution of a pseudosymmetric structure by Fourier methods

In principle, the refinement of a pseudosymmetric structure starting from an idealized high-symmetry structure is impossible by routine methods of analysis, such as least-squares, even when the atomic displacements are very small. A much more helpful approach is by a method of successive approximations. This uses first the most important displacement parameters, whose magnitudes (but not signs) can be estimated from electron-density maps or difference maps based on the ideal structure. Certain of their signs can be allotted arbitrarily, and the further analysis follows step by step until a realistic trial model is obtained in which all (or at least a large proportion of) the displacement parameters have the correct and consistent signs and very roughly correct magnitudes. At this stage, routine use of least-squares refinement becomes permissible.