Geometrical constraints on the growth of sectors in polygonal serpentine

Abstract

The structures of the serpentine minerals (Mg3Si2O5(OH)4) consist of composite layers made up of a sheet of SiO4 tetrahedra linked to a sheet of MgO2(OH)4 octahedra. The dimensions of the tetrahedral and octahedral sheets do not match exactly, and in some serpentines the layers bend to accommodate this misfit. In the tiny fibrils of chrysotile asbestos, the layers curve round forming concentric cylinders, single or multiple spirals. A rare form, polygonal serpentine, has fibrils with a polygonal cross section, made up of flat layers in sectors. The number of sectors n is almost always either 15 or 30. An ideal geometrical model for the growth of sectors is described. At each new layer added around the polygonal fibre, five more unit cells are required around the perimeter than in the previous layer; the same number of extra unit cells is required around each successive cylindrical or spiral layer in chrysotile. Single Mg octahedra are added to new layers at the edges of sectors and this determines the Miller indices of the sector boundaries. The angle between the bounding faces will not in general be exactly 360/n. Minimal misfit occurs only for polygonal microstructures with 15 or 30 sectors, the number depending on the exact cell dimensions of the flat layers. For the curved layers of chrysotile, the cell dimensions predict a better and better fit as the number of sectors increases, as would be expected for cylindrical layers.