Three dimensional domain structures for domain engineered rhombohedral perovskite ferroelectric crystals

We have constructed complicated 3D geometrical structures for domain engineered (i.e. [001] _C-poled) rhombohedral (1-x)Pb(Mg _1/3Nb _2/3)O ₃-xPbTiO ₃ (PMN-PT)and(1-x)Pb(Zn _1/3Nb _2/3)O ₃-xPbTiO ₃ (PZN-PT) ferroelectric crystals. The geometric model contains all allowed domain walls in their equilibrium orientations, and it is scalable to any domain size. All four remaining domains have equal volume ratios, and the effective domain pattern symmetry is tetragonal 4mm. Optical microscopy observations of domains are fundamentally complicated by the composite effect of polarizing light going through several domain regions with different indicatrix orientations. Our geometric model can describe the interwoven domain structures observed by the polarizing microscopy on thin plates of domain engineered PMN-PT crystals as an effect of polarizing light total reflection at the domain walls. The 3D geometric model can be used to interpret domain wall observations, including the [111] _C-poled rhombohedral multi-domain structure published previously (J. Appl. Phys. 91, 7 (2002) 4474-4478). Domain structures observed at moderate field has an effective 3m symmetry with three equivalent domain variants _PS[11] _C, _PS[11] _C and _PS[1] _C.