Structural Control of Elastic Constants of Mullite in Comparison to Sillimanite

Abstract

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 <c 44 . 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.

The crystalline-to-amorphous transition in shock-loaded mullite Al2VI(Al2+2xSi2−2x)IVO10−x in the light of shear modulus anisotropy

“…24 While it is true that oxygen vacancies may contribute to a relative overall reduction of both longitudinal and shear stiffness in mullite as compared to sillimanite, the well documented PDFs in shocked sillimanite 31 which is devoid of oxygen vacancies clearly prove that they are not related to PDF formation. This study and previous related work 41,42 indicate that it is the interaction of all structural units in the mullite structure and less likely the effect of randomly distributed point defects such as oxygen vacancies which give rise to the anisotropy of the shear modulus in mullite. Notably the [AlO 6 ] octahedra present the softest structural units during compression of Al 2 SiO 5 polymorphs.…”

“…The elastic stiffness coefficients c ij of mullite employed in the calculation of shear modulus anisotropy are compiled in Table 1 in comparison with the sillimanite data from the literature. 41,42 Considering the close structural relationship between mullite and sillimanite the similarity between the corresponding elastic stiffness coefficients is not surprising. Mullite and sillimanite share high longitudinal stiffness coefficients c 33 caused by loadbearing continuous tetrahedral and octahedral chains extending parallel to the c-axis.…”

“…Elastic coefficients of 2/1 mullite and sillimanite41,42 single crystals at room temperature employed in the calculation of shear modulus anisotropy. Elastic stiffnesses c ij and elastic compliances s ij are given in Voigt notation (see Appendix A).…”

Structure and properties of mullite—A review

“…In directions perpendicular to c-axis only minor differences are observed in the elastic properties of both crystal species. [37][38][39] There is also a similarity with the elastic constants of the mullite-type phase Bi 2 Ga 4 O 9 , the elastic properties of which are essentially controlled by the strong octahedral chains. 55 According to Schreuer et al 39 the elastic constants of 2/1-mullite decrease almost linearly between room temperature and 1400 • C. The thermoelastic constants T ij = d log c ij /dT are within the typical range of many silicates.…”

Single and polycrystalline mullite fibres grown by laser floating zone technique

“…The same technique was used to grow the MSCs characterized in several works published by the group led by Prof. Schneider. 1,2,[6][7][8][9][10][11] The ICM method allows the production of very thin MSCs with about 0.1 mm in diameter and high aspect-ratio (ap. 800), which are more adequate for mechanical reinforcement uses.…”