Interpretation of mullite HREM images using the Potential-exchange-method

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Abstract
Multi-slice image contrast calculations using the periodic continuation theorem (supercell-model) and a new approximation developed by Hamid Rahman (1989) called the “Potential exchange method” show good agreement in the electron microscope image contrast simulation for mullite. The method can be used to calculate a non-periodic potential and is most accurate when the defects (light atom vacancies) are distributed on (100), (010) or (001) planes and accompanied with cation shifts within the unit cell.Mullite Al2[Al2 + 2xSi2−2x]O10−xis a non-stoichiometric silicate compound wherexis the number of missing oxygen atoms per average unit cell (0.17 ≤x≤ 0.59, Cameron 1977).The average structure of mullite (Fig. 1a,Pbam,a= 7.56 Å,b= 7.68 Å,c= 2.884 Å) was determined by Burnham (1963, 1964), Durovic (1969) and Saalfeld and Guse (1981).The structure analysis shows that the vacancies occur on the tetrahedral linking positions (Oc, Oc* Fig. 1b, c). The loss of the fourth coordinating oxygen atom causes the cation on the tetrahedral sites (Si/Al site) to occupy neighbouring alternative position of the second tetrahedral site denoted by Al*. This means that the contrast variation of the HREM image is mainly affected by the site occupation (cation shift Fig. 1a, b, c) within the unit cell.X-ray (h0l, 0kl,hk1/2,hk1/3andhk2/3) and electron (h0land 0kl) diffraction patterns (x= 0.25 and 0.4) show diffuse streaks and satellite reflections, indicating a modulation (ordering scheme) within the mullite structure which doubles thec-axis and has a composition-dependent, incommensurable periodicity along thea-axis (Guse and Saalfeld, 1976;

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