Thermodynamic stability at the ?-? quartz transition

Publisher Website
Google Scholar
Abstract
As the α-β quartz transition appears to be first order, the condition of thermodynamic stability must be violated in the process. It is shown that this is exhibited by the vanishing of an eigenvalue of the isothermal stiffness matrix c(T). This enables a relation (c 11 (T)+c 12 (T))c 33 (T)-2c 13 (T)2=0 to be deduced for the transition point, and a limiting form for the isothermal compliance matrix, such that ratios of the diverging elements can be expressed in terms of the eigenvector corresponding to the vanishing eigenvalue. This eigenvector is also related to the change of shape, on the assumption that the transition is thermodynamically reversible, and good agreement is obtained with two other independent methods of evaluating Δe 1/Δe 3. Similar relations between diverging compliances and piezoelectric coefficients are briefly discussed for the ferroelectric transition of barium titanate.