Abstract: Two different kinds of phase ambiguities are intrinsic in two-wavelength x-ray powder diffraction from acentric crystal structures having pseudo-translation symmetry. In a test calculation we have solved the problem for the first time by two different phasing procedures developed originally in single-crystal structure analysis. They are the direct method of breaking enantiomorphous phase ambiguity in protein crystallography and that of breaking translational phase ambiguity for superstructures. An artificial structure was used in the test, which is based on atomic coordinates of the known structure, SHAS (C$_5$H$_6$O$_5$N$_3$K), with the atom K replaced by Rb. The arrangement of Rb atoms possesses a subperiodicity of $t=(a+b+c)/2$. Two-wavelength synchrotron x-ray powder diffraction data were simulated with $\lambda_1=0.0816$nm and $\lambda_2=0.1319$nm. Overlapped reflections were uniformly decomposed at the beginning and redecomposed afterward when the partial-structure information became available. The enantiomorphous phase ambiguity was resolved only for reflections with $h+k+l$ even. Phases of reflections with $h+k+l$ odd were derived by the direct method of solving superstructures. A fragment was then obtained, which led to the complete structure in five cycles of Fourier iteration.

Key words: two-wavelength powder diffraction, superstructures, direct methods