Answer to Question #120332 in Inorganic Chemistry for Yuki

Question

What are the key features of Rigid Unit Modes that allow for NTE? (5 marks)

Answer 1

The idea behind Rigid Unit Modes models is actually a ‘simple’ model which considers polyhedra (SiO₄, WO₄, ZrO₆,etc.) linked at their corners by shared oxygens to be rigid.

In this manner, large amplitude transverse vibrations of the oxygens can occur only through coupled oscillations of the tetrahedra and octahedra forming the structure. They involve no changes in intra-unit bond distances and angles, and so have relatively large amplitudes and low frequencies.

The RUM model involves a depiction of the structures as rotating squares where the sides of squares represent rigid bonds and the vertices represent flexible hinges (eg: shared oxygens). The dotted square represents the original area of this 2D RUM. And the figure illustrates the NTE mechanism within the 2D RUM model:

A number of NTE materials have been explained through the use of RUM and QRUM models and these include: ZrW₂O₈, ZrV₂O₇, AlPO_4-17, various zeolite frameworks, beta-quartz, and Sc₂(WO₄)_3.