Solids, intrinsic curvature

The reason that this structure forms is as follows units of octahedral W3C crystallise on one side of an interface, that separates solid W3C from Fe. The Fe atoms are drawn into the interstices of the W3C elements, with a driving force dependent on the Gaussian curvature of the interface. This is one way of looking at intrinsic curvature in solids. As will become apparent, there are other ways that link the interactions between atoms, molecules and larger aggregates to local curvature. 

How do these unconventional ideas link with the standard view of a solid as a close packed array of atoms Evidently most of the frameworks discussed above cannot be so characterised. The two-dimensional hyperbolic picture does break down for very dense structures. Thus the densest four-coordinated silicate, coesite, violates this universality (see Fig. 2.12). (Its ring size is less than that of trid5m[ ite, cristobalite, keatite or quartz, in spite of its higher density.) This polymorph is too dense for a two-dimensional description to be useful and the Aree-dimensional description takes over. The notion of intrinsic curvature is less rigid for silicates than for the other frameworks, because the Si-O-Si angle usually differs from 180 . 

---