Disorientation angles and compatible walls for phase transition hexagonal to monoclinic phase

Orientation of compatible domain walls and magnitude of disorientation angle of a ferroelastic domain twin resulting from phase transition hexagonal to monoclinic phases is expressed in crystallographic unit-cell parameters of the low-symmetry phase. These two characteristics, the orientation of the compatible wall and the disorientation angle, depend on the spontaneous strain in two single-domain states R ₁, R ₂ from which the domain twin is formed. They have been determined for all classes of the compatible domain walls as a function of the strain-tensor components A. Authier, International Tables for Crystallography, in Physical Properties of Crystals, Chapter 3.4, Vol. D, A. Authier, ed., Kluwer Academic Publishers, Dordrecht, 2003, pp. 449–505]. If relative changes of crystal lattice are small, then the second rank symmetrical strain tensor u can be calculated from the crystallographic unit-cell parameters before and after the deformation J.L. Schlenker, G.V. Gibbs, and M.B. Boisen Jr, Strain-tensor components expressed in terms of lattice parameters, Acta. Cryst. A 34 (1978), pp. 52–54; L. Jian and C.M. Wayman, Domain boundary and domain switching in a ceramic rare-earth Orthoniobate LaNbO_{4 ,} J. Am. Ceram. Soc. 79 (1996), pp. 1642–1648]. An alternative approach expresses the disorientation angle and orientation of the compatible domain wall J. P?ívratská, Disorientation angle expressed in terms of lattice parameters, Ferroelectrics 291 (2003), pp. 197–204] in terms of the crystallographic unit-cell parameters of the low-symmetry phase.