Refinement of the real structures of 2:1 and 3:2 mullite

In a previous investigation (Rahman, S. H., Strothenk, S., Paulmann, C. and Feustel, U., Interpretation of mullite real structure via inter-vacancy correlation vectors. J. Eur. Ceram. Soc., 1996, 16, 177–186) we showed that the real structure of 2:1 mullite can be explained with intervacancy correlation vectors and a 3D ordering scheme for the oxygen vacancies was derived. This ordering scheme is now refined by varying the frequencies of the most important 3D vectors in videographic 3D simulations, which are tested through comparison between their Fourier transforms with the experimental diffraction patterns for the planes h0l, 0kl, hk1/2, hk1/3, hk1/4 and hk1/6. The best agreement with the experimental patterns of 2:1 mullite was reached by a 3D simulation that can be described by the following sequence of the most frequent correlation vectors lmn (l=a/2, m=b/2, n=c): 〈310〉, 〈111〉, 〈022〉, 〈201〉, 〈330〉, 〈401〉, 〈131〉, 〈130〉, 〈042〉, 〈113〉, 〈060〉. The experimental single crystal diffraction patterns of 3:2 and 2:1 mullite generally show similar diffuse scattering phenomena, though the diffuse components of 3:2 mullite are slightly broadened and have weaker relative intensities. Employing videographic 3D simulations it was confirmed that the real structure of 3:2 mullite can be characterized via the same correlation vectors, but with different sequence and frequencies: 〈022〉, 〈201〉, 〈111〉, 〈310〉, 〈130〉, 〈131〉, 〈223〉, 〈330〉, 〈222〉, 〈240〉, 〈113〉. With the aid of the above-mentioned frequencies of correlation vectors the real structures of 2:1 and 3:2 mullite can be completely described and all the complicated diffuse scattering phenomena can be explained. Furthermore the dependence on direction of several physical properties e.g. thermal heat expansion can be interpreted by means of the vacancy distribution in the real structure.