STRUCTURE REFINEMENT OF THE ICOSAHEDRAL QUASI-CRYSTAL AL57LI32CU11

The structure of the icosahedral quasicrystal Al57Li32Cu11 has been re fined within the superspace formalism using symmetry-adapted surface h armonics for the description of the boundaries of atomic surfaces (occ upation domains) in internal space. The refinement process has been pe rformed with a general program, QUASI, recently developed for this pur pose. Besides published neutron and X-ray diffraction data [de Boissie u, Janot, Dubois, Audier & Dubost (1991). J. Phys. Condens. Matter, 3, 1-25], experimental density and chemical composition were used as con trol parameters of the fitting. The atomic surfaces were assumed to be parallel to the internal space. No additional a priori assumption was introduced, except the limitation on the number of harmonics for desc ribing the contours of the atomic surfaces. The refinement significant ly improved previous analyses: starting with a sphere model of the ato mic surfaces based on the results of de Boissieu et al., the fit attai ned R(F) (wR(F)) values of 0.067 (0.072) and 0.068 (0.068) for X-ray r eflections and neutron data, respectively. The final model also rather satisfactorily explains the alternative X-ray data set of Van Smaalen , de Boer and Shen [Phys. Rev. B (1991), 43, 929-937], not included as data in the fitting process. Two and three harmonics are enough to de scribe the vertex and edge Al/Cu surfaces, respectively, and their sha pes approximately coincide with those suggested by de Boissieu et al. However, some significant different chemical ordering of the two surfa ces can be ascertained. On the other hand, the lithium surface is quit e complex and its description requires, at least, four harmonics. Give n the scarce number of data, this surface cannot be determined with mu ch accuracy. The presence of nonphysical short interatomic distances i n the final structural model is analysed quantitatively.