Computer modelling and theoretical analysis are used to explain the nearly
zero and slightly negative coefficients of thermal expansion in beta-quartz
well above the alpha-beta phase transition temperature. Quartz was selecte
d for study as an archetypal material with a framework structure of stiff u
nits, namely SiO4 tetrahedra, linked through shared oxygen atoms as very fl
exible 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 detai
l. The results fully support and illustrate a recent theory of the negative
contribution to thermal expansion in framework structures. It is a geometr
ical effect due to the rotation of the tetrahedral units, folding together
as they vibrate. The very rapid increase in the lattice parameters for abou
t 20 K above the transition temperature is well accounted for within quasih
armonic theory, and is therefore not evidence for critical fluctuations or
fluctuating patches of alpha(+), alpha(-) structure.