The diffraction aspect and a structural model of mullite, Al(Al_1+2xSi_1-2x)O_5-x

Diffraction patterns of various specimens of mullite were recorded using a high-power X-ray generator. The patterns consist of main reflections based on the primitive orthorhombic lattice with a = 7.6, b = 7.7 and e = 2.9 Å, and two types of subsidiary reflections. Although the patterns show no periodicity in reciprocal space, a periodic unitary intensity distribution is deduced using information from the average structure. The distribution of the sites of the removed oxygen atoms in the sillimanite-like ideal structure is obtained from the qualitative values of the unitary intensity. In order to compare the calculated value to the observed continuous intensity distribution in reciprocal space, a structural model was constructed. It contains four sorts of equivalent domains; each domain consists of about 40 000 atoms. These atoms are situated at definite positions in real space, and no partly occupied sites are specified in these models.