Negative thermal expansion in beta-quartz

Abstract 

Computer modelling and theoretical analysis are used to explain the nearly zero and slightly negative coefficients of thermal expansion in β-quartz well above the α-β phase transition temperature. Quartz was selected for study as an archetypal material with a framework structure of stiff units, namely SiO₄ tetrahedra, linked through shared oxygen atoms as very flexible hinges. The contributions of the soft mode, the Vallade mode, the TA_z phonon branch and the phonon spectrum as a whole are discussed in detail. The results fully support and illustrate a recent theory of the negative contribution to thermal expansion in framework structures. It is a geometrical effect due to the rotation of the tetrahedral units, folding together as they vibrate. The very rapid increase in the lattice parameters for about 20 K above the transition temperature is well accounted for within quasiharmonic theory, and is therefore not evidence for critical fluctuations or fluctuating patches of α ₊, α ₋ structure.