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(Color online) PFM-style images of simulation of (a) (001)p-oriented BiFeO3 and (c) miscut BiFeO3. PFM images of (b) (001)c-oriented BiFeO3 and (d) miscut BiFeO3. In (a) and (b), there is a mixture of all four ferroelastic variants. The white regions represent two in-plane variants (r1 and r4), while the lightly- and darkly-colored regions represent the r2 and r3 variants, respectively. In the images of miscut films, (c) and (d), the dark- and light-striped regions are mixed r1/r4 domains with 71° domain walls. (Figs. 1(b) and 1(d) reprinted with permission from Jang et al. 20)
(Color online) Domain structures of miscut BiFeO3 under different energy conditions: (a) with all energy forms included, (b) with electric but not elastic energy, (c) with elastic but not electric energy, and (d) with neither elastic nor electric energy. The elastic energy drives the symmetry non-degeneracy, and only the simulations which include elastic energy term, (a) and (c), form striped domain structures consisting of only two variants.
(Color online) Schematic of ferroelastic variant formation for (a),(b) (001)c-oriented and (c),(d) miscut substrates. For an (001)c-oriented substrate, all four ferroelastic variants are degenerate under both (a) tensile and (b) compressive strain. For the miscut substrate, mismatch strain will be along the global x′1-x′2 plane, which in the local system translates to include a shear strain. A tensile strain favors in-plane variants (those tilted towards the global x′1-x′2 plane) (c), while a compressive strain favors out-of-plane variants (d).
(Color online) Domain structures of miscut BiFeO3 simulations under different substrate strains. (a) ɛ′11 = ɛ′22 =− 1.5%, (b) ɛ′11 = ɛ′22 =− 0.0%, (c) ɛ′11 = ɛ′22 =+ 1.5%. When the miscut film is sufficiently strained, two ferroelastic variants become favored and the variants line up in a striped domain structure, as seen with compressive strain with r1/r4 variants (a), and with tensile strain with r2/r3 variants (c). Under weak strain (b), all four variants are degenerate.
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