International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 1.6, pp. 174-175
Section 1.6.7.2. Spontaneous strain in BaTiO3
a
Department of Physics, University of Oxford, Parks Roads, Oxford OX1 3PU, England, and bDepartment of Earth Sciences, University of Oxford, Parks Roads, Oxford OX1 3PR, England |
As an example of the calculation of the relationship between spontaneous strain and linear birefringence, consider the high-temperature phase transition of the well known perovskite BaTiO3. This substance undergoes a transition at around 403 K on cooling from its high-temperature phase to the room-temperature phase. The phase is both ferroelectric and ferroelastic. In this tetragonal phase, there is a small distortion of the unit cell along [001] and a contraction along compared with the unit cell of the high-temperature cubic phase, and so the room-temperature phase can be expected to have a uniaxial optical indicatrix.
The elasto-optic tensor for the phase is (Table 1.6.7.1) Consider the low-temperature tetragonal phase to arise as a small distortion of this cubic phase, with a spontaneous strain given by the lattice parameters of the tetragonal phase:Therefore, the equations (1.6.7.4) for the dielectric impermeability in terms of the spontaneous strain component are given in matrix form as so that By analogy with equations (1.6.6.5) and (1.6.6.6), the induced changes in refractive index are then where is the refractive index of the cubic phase. Thus the birefringence in the tetragonal phase as seen by light travelling along is given by Thus a direct connection is made between the birefringence of the tetragonal phase of BaTiO3 and its lattice parameters via the spontaneous strain. As in the case of the linear electro-optic effect, the calculation can be repeated using equation (1.6.3.14) with the susceptibilities and to yield the relationship