Structural Control of Elastic Constants of Mullite in Comparison to Sillimanite

Abstract

Nine elastic stiffness coefficients, cij, of a mullite single crystal (2Al2O3·SiO2) are measured using acoustic resonance spectroscopy. The obtained values are similar to those of the structurally related aluminosilicate phase sillimanite (Al2O3·SiO2). 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, c33, of mullite (∼352 GPa) and sillimanite (∼388 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 c33 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 (c22∼ 233 GPa) being somewhat lower than parallel to a‐axis (c11∼ 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, c11 and c22 coefficients of mullite and sillimanite are very similar. Shear stiffness coefficients of mullite increase from c55 (∼77 GPa) to c66 (∼80 GPa) to c44 (∼110 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 〈011〉 (“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 c55 and c66 are <c44. All three shear stiffness coefficients of mullite are slightly lower than those of sillimanite because of the reduction of the mean tetrahedral bond strength in mullite caused by partial substitution of silicon by aluminum.