The thermodynamic theory of the growth of Dauphine twinning in quartz under stress

Abstract

The equilibrium condition is deduced for the stable coexistence, under stress, of Dauphine twins. It is shown that this condition is determined by the principle that a generalised Gibbs free energy be minimised. At equilibrium the generalised Gibbs free energy density of each twin must have the same value. If stresses are applied such that the equilibrium condition is not satisfied, this principle determines which twin will survive the resulting untwinning process. The theory is developed rigorously using finite strain theory. It is shown that, if four relations between the elements of a certain asymmetric tensor are satisfied, the stress coexistence condition is satisfied exactly, that is, to any order. The proof of this exact temperature-independent condition employs the method of the integrity basis for invariant functions of the crystal point group.