An inner-space approach to the structure-factor reconstruction in quasiperiodic crystals is presented. This approach is based on the representation of a quasiperiodic crystal as a higher dimensional periodic crystal (hypercrystal) whose hyperatom form factors can often be expressed as continuous functions of the inner-space components of the scattering wave vector. Thus, the reconstruction of the structure factors is reduced to a convenient parametrization of these functions (exemplified here by a Taylor series expansion) with the parameters to be determined through a fit of the experimentally measured diffraction intensities. The fitting parameters may also include locations of the hyperatoms, their chemical composition, and Debye-Waller factors. As an illustration, we applied this technique to reconstruct neutron scattering structure factors of icosahedral quasicrystal $i-{\mathrm{Al}}_{0.570}{\mathrm{Cu}}_{0.180}{\mathrm{Li}}_{0.322}$. We found consistent results with these obtained earlier using a method based on periodic approximants of quasiperiodic crystals.

• Received 27 July 1993

DOI:https://doi.org/10.1103/PhysRevB.49.6614