Theory of the ferroelastic transition in barium sodium niobate

The tetragonal-orthorhombic phase transition of barium sodium niobate is theoretically investigated. Available structural data are examined and it is concluded that the change in space symmetry is from $P4\mathrm{}bm \left(C_{4\nu }^2\right)$ to $Ccm{2}_1 \left(C_{2\nu }^{12}\right)$, thus differing from previous assignments. The order parameter of the transition is shown to be distinct from the spontaneous shear strain characterizing the ferroelasticity of the orthorhombic phase. The symmetry properties of the order parameter are found to be described by a two-dimensional irreducible representation of $P4\mathrm{}bm$ corresponding to the $Z$ point [$\overrightarrow{\mathrm{k}}=(0,0,\frac{\pi }{c})$] of the first Brillouin zone. The free-energy expansion is constructed on this basis and the behavior of elastic constants is examined. Comparison is made to experimental data.