Features of coexistence of tetragonal and orthorhombic phases in lead-free ferroelectric solid solutions

A model of a heterophase sample with interlayers is proposed to describe coexistence of tetragonal and orthorhombic phases in lead-free perovskite-type ferroelectric solid solutions. Versions of phase coexistence are analyzed at variations of unit-cell parameters of (Ba, Ca)(Ti, Zr)${\mathrm{\text{O}}}_3$ and (K, Na)(Nb, Sb)${\mathrm{\text{O}}}_3$-(Ba, Ca)${\mathrm{\text{ZrO}}}_3$ with compositions near morphotropic phase boundaries. Large regions of the tetragonal and orthorhombic phases are split into $90^{\circ }$ and $120^{\circ }$ domains, respectively. The interlayer of the orthorhombic phase is either single-domain or split into $90^{\circ }$ domains. A complete stress relief can be achieved at an elastic matching of the polydomain/single-domain or polydomain/polydomain phases. It is shown that different phase contents in (${\mathrm{\text{Ba}}}_{0.85}{\mathrm{\text{Ca}}}_{0.15}$)$\cdot \cdot$(${\mathrm{\text{Ti}}}_{0.9}{\mathrm{\text{Zr}}}_{0.1}$)${\mathrm{\text{O}}}_3$ powder and ceramic are caused by different non-${180}^{\circ }$ domain structures in the phases. The interlayer of the orthorhombic phase plays an important role in forming the phase content in solid solutions. Agreement is shown when comparing the evaluated volume fractions of the orthorhombic phase to experimental data.