1. Rigid Unit Modes in Framework Structures: Theory, Experiment and Applications

Structure Dynamics and Vibronic Coupling in AECuSi4O10 (AE: Ca, Sr, Ba) Compounds

“…This structural dynamic is clearly evidenced by the total-scattering structure function S(Q), where a diffuse intensity is observed at high Q values (Figure S7). 41 range order was extinguished, in fair agreement with the G(r) fitting results. This scenario is fully consistent with previous structural investigations, 24 where the unusually large value of the isotropic displacement parameter of O(1) was ascribed to the positional disorder, with a maximum vibration direction of O(1) perpendicular to the Si−O−Si bond.…”

“…This structural dynamic is clearly evidenced by the total-scattering structure function S ( Q ), where a diffuse intensity is observed at high Q values (Figure S7). Diffuse intensity is observed in BaCuSi 4 O 10 for Q > 17.5 Å, whereas faint Bragg peaks develop for both CaCuSi 4 O 10 and SrCuSi 4 O 10 . These features are related to the dynamic tilting affecting the network of rigid [SiO 4 ] 4– tetrahedra; as the ionic radius of the AE element increases, the different [SiO 4 ] 4– tetrahedra lose coherence, and the faint sharp Bragg peaks are suppressed.…”

Dynamics of silica glass: two-level tunnelling states and low-energy floppy modes

“…Whether an infinite framework of corner-linked SiO 4 tetrahedra can vibrate without the tetrahedra distorting is actually a very subtle issue. As noted above, the vibrational modes that do not involve distortions of the interatomic bonds are usually referred as 'floppy modes' in the context of network glasses [8,9] or rigid unit modes in the context of crystalline framework structures [13,[15][16][17]. In a model in which the only forces are those associated with stretching of bonds or distortions of polyhedra, the RUMs/floppy modes will have identically zero frequency [15].…”

“…In a system such as silica, where there are rigid SiO 4 tetrahedra and separate Si-O and O-O bonds, this procedure will lead to an overcounting of the number of constraints, since the rigidity of a SiO 4 tetrahedron is ensured by only nine of the ten bonds. We tend to prefer an alternative way of counting degrees of freedom, which is to associate six degrees of freedom with the rigid-body motions of a tetrahedron, and to associate three constraints with every bridging oxygen (that is, every oxygen that is part of two tetrahedra) [15,17]. The two methods of applying the Maxwell counting procedure give identical results.…”

“…In our previous paper [7] we studied floppy modes in silica glass by applying our 'rigid-unit-mode' model [13,14]. This model was developed earlier to study floppy modes in crystalline networks of corner-linked polyhedra such as SiO 4 tetrahedra, including the crystalline phases of silica [13,[15][16][17]. The rigid unit modes (RUMs) are normal-mode vibrations that can propagate without the polyhedra distorting, and are the modes of lowest energy.…”