Incommensurate Phase of Quartz: Microscopic Origin and Interaction with Defects

Silicon dioxide is well known for its extensive polymorphism1: in addition to about 20 crystalline phases, it is also easily obtained in an amorphous state which is a prototype of glass structure. With the exception of Stishovite, these phases consist of three dimensional frameworks of corner sharing SiO₄ tetrahedra, giving structures with different topological connections. Furthermore the low pressure phases (quartz, cristobalite, tridymite) present displacive transitions produced by small displacements of the SiO₄ tetrahedra, without breaking any atomic bond. In this way quartz at 846 K transforms from the low temperature α phase of trigonal symmetry to the high temperature β phase of hexagonal symmetry. Although this transition has been studied for nearly a century, it was only in 1980 that Bachheimer discovered that the α-β transition was not direct2 but occured through a new intermediate phase, later characterized as an incommensurate (inc) phase3. In an inc structure some property (atomic position, electronic or spin density …) is modulated with a period λ which is not commensurate with the lattice period a. In a diffraction experiment satellite peaks are observed in addition to the usual lattice reflections. Indeed in the inc phase of quartz satellites have been observed by diffraction experiments with neutrons3, X rays4 and electrons5: satellites are observed along the 6 equivalent <100> directions of the hexagonal reciprocal lattice at a small distance q ≃ 0.03 a * from the Bragg peaks.