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Nine elastic stiffness coefficients, c ij , of a mullite single crystal (2Al 2 O 3 ⅐SiO 2 ) are measured using acoustic resonance spectroscopy. The obtained values are similar to those of the structurally related aluminosilicate phase sillimanite (Al 2 O 3 ⅐SiO 2 ). Characteristic elastic properties of the two minerals are interpreted with the help of their crystal structures and atomic force constants for sillimanite. The high longitudinal stiffness coefficients, c 33, of mullite (ϳ352 GPa) and sillimanite (ϳ388 GPa) are caused by continuous "stiff" load-bearing tetrahedral chains parallel to c-axis, while the "soft" octahedral chains have minor direct influence. They stabilize the tetrahedal chains against tilting. The lower c 33 value of mullite in comparison to the sillimanite value may be caused by a weakening of the load-bearing tetrahedral chains which are parallel to c-axis because of partial replacement of silicon by the weaker-bonded aluminum. The longitudinal stiffness coefficients perpendicular to c-axis are significantly lower, because of sequences of alternating "soft" octahedral and "stiff" tetrahedral units. Within the plane (001), the compliant octahedra exhibit stiffness-controlling influence with coefficients parallel to b-axis (c 22 Ϸ 233 GPa) being somewhat lower than parallel to a-axis (c 11 Ϸ 291 GPa). This is explained with the occurrence of compliant octahedral Al(1)-O(D) bonds, which are more effective parallel to b-axis rather than to a-axis. Because octahedra are unaffected by the aluminum to silicon substitution, c 11 and c 22 coefficients of mullite and sillimanite are very similar. Shear stiffness coefficients of mullite increase from c 55 (ϳ77 GPa) to c 66 (ϳ80 GPa) to c 44 (ϳ110 GPa), indicating increasing resistance against shear deformation within the planes (010), (001), and (100). The lattice plane of the highest shear stiffness (100) is built up of an oxygen-oxygen network, diagonally braced along ͗011͘ ("Jägerzaun"). This network with short oxygen-oxygen distances can be sheared by compression and elongation along oxygen-oxygen interaction lines only which is rather unlikely. Because of the lack of such networks in the planes (010) and (001), bending and deformation of structural units become easier, and consequently c 55 and c 66 are

Mullite is an aluminosilicate of the composition Al 2 (Al 2ϩ2x Si 2Ϫ2x)O 10Ϫx with x generally ranging between 0.2 and 0.5. XRD and 29 Si and 27 Al nuclear magnetic resonance (NMR) have been used to investigate the structure of various mullite compositions (x ϭ 0.26, 0.36, 0.42, and 0.69) as well as sillimanite (x ϭ 0) and ␥-Al 2 O 3 (x ϭ 1). 27 Al magic angle spinning (MAS) NMR of the central and satellite transitions have been used to determine the chemical shifts and quadrupole interaction parameters for the various AlO 4 and AlO 6 units. The isotropic chemical shifts of the various units are 5.9 ppm for AlO 6 , 69.1 ppm for AlO 4 (T), 55.0 ppm for AlO 4 (TЈ), and 45.7 ppm for AlO 4 (T*) where AlO 4 (T) denotes the aluminum tetrahedra in the double chains, and AlO 4 (TЈ) and AlO 4 (T*) those next to the oxygen Oc*. Quantitative numbers of the aluminum occupancy of these sites have been determined for the various powder samples. These results are in good agreement with the average structure model of mullites. NMR and XRD proved the presence of impurities of kyanite in natural sillimanite and of ␥-Al 2 O 3 in the mullites with x ϭ 0.42 and 0.69.

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