Cation substitution and strain screening in framework structures: The role of rigid unit modes

We use a combination of real-space geometric algebra and reciprocal space dynamical matrix analyses to study the effect of cation substitution on the framework geometries of β-quartz, cordierite and leucite. We show that the geometric stress associated with the substitution in these framework silicates is absorbed by rigid-unit type motion of those coordination polyhedra near the substitution site. We find that the inherent flexibility of these structures enables screening of geometric stress, such that the associated energy cost is minimal and unlikely to influence substitution patterns.