Elastic aspects of domain quadruplets in ferroics

Coexistence of ferroelectric ferroelastic domains in some materials plays an important role in practical area of domain engineering. Here the problem is discussed theoretically from the point of view of elastic aspects. Domain quadruplets are considered, i.e., systems of four ferroelastic domains coinciding along one intersection line. Conditions at which the elastic energy of quadruplets is zero are specified; they would allow for the existence of permissible quadruplets. The problem has been solved for the species m3¯m-mxmy2z, m3¯m-2xymx¯ymz, m3¯m-3m, and m3¯m-4mm. It is shown that, in general, no mechanically compatible (stress-free) permissible quadruplets exist. The results make it possible to specify those conditions for spontaneous strain components which must be complied to allow for energetically acceptable quadruplets. These conditions are fulfilled in the orthorhombic phase of KNbO3. The theoretical approach offered in this paper can be used for specific discussions of the existence of multidomain states in thin films where some components of spontaneous strain need not play an essential role.