Post-perovskite phase in selected sesquioxides from density-functional calculations

We search for the existence of the post-perovskite structure in several nonmagnetic $M_2{\mathrm{O}}_3$ sesquioxides using density-functional calculations. For each material we consider the corundum, ${\mathrm{Rh}}_2{\mathrm{O}}_3$-type II, perovskite, and post-perovskite structures. The perovskite structure is unstable with respect to at least one of the other structures at all pressures for all materials. The post-perovskite structure is stable above $120\mathrm{GPa}$ in ${\mathrm{Al}}_2{\mathrm{O}}_3$, above $344\mathrm{GPa}$ in ${\mathrm{Rh}}_2{\mathrm{O}}_3$, above $136\mathrm{GPa}$ in ${\mathrm{Ga}}_2{\mathrm{O}}_3$, and above $47\mathrm{GPa}$ in ${\mathrm{In}}_2{\mathrm{O}}_3$.

Figure 1

(Color online) Crystal structure of the four polymorphs considered in this study. Smaller spheres are cations and larger spheres the anions. Corundum structure is rhombohedral and the three other structures are orthorhombic. For sake of clarity we explicitly show the $\mathrm{Me}{\mathrm{O}}_6$ octahedra for the perovskite and the post-perovskite structures.

Figure 2

(Color online) Enthalpies relative to the ${\mathrm{Rh}}_2{\mathrm{O}}_3$-type-II structure for ${\mathrm{Al}}_2{\mathrm{O}}_3$ (a), ${\mathrm{Rh}}_2{\mathrm{O}}_3$ (b), ${\mathrm{Ga}}_2{\mathrm{O}}_3$ (c), and ${\mathrm{In}}_2{\mathrm{O}}_3$ (d). For ${\mathrm{Rh}}_2{\mathrm{O}}_3$ the underestimation of the corundum to type-II transition pressure might be due to LDA. The transition to post-perovskite occurs at pressures around $360\mathrm{GPa}$. For ${\mathrm{Ga}}_2{\mathrm{O}}_3$ the post-perovskite structure is stable above $136\mathrm{GPa}$. For ${\mathrm{In}}_2{\mathrm{O}}_3$, the transition to post-perovskite occurs at about $47\mathrm{GPa}$, making ${\mathrm{In}}_2{\mathrm{O}}_3$ a good candidate for the study of post-perovskite structure in sesquioxides and for the search of a possible post-post-perovskite phase. Corundum, type-II, perovskite, and post-perovskite structures are represented by, respectively, solid circles, solid squares, open circles, and open squares. Lines are guide for the eyes.

Figure 3

(Color online) Compressibility of the lattice parameters of the post-perovskite structure, $L∕L_0$ as a function of the bulk compressibility, $V∕V_0$ in ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{In}}_2{\mathrm{O}}_3$, and $\mathrm{Mg}\mathrm{Si}{\mathrm{O}}_3$. Squares, triangles, and circles denote the $a$, $b$, and $c$ lattice parameters, respectively.

Figure 4

Pressure variation of the $g$ modes in the post-perovskite phase of ${\mathrm{In}}_2{\mathrm{O}}_3$. There are $12g$ modes that decompose as $4A_g+3B_{1g}+1B_{2g}+4B_{3g}$. Circles, down-pointing triangles, squares, and up-pointing triangles denote, respectively, $A_g$, $B_{1g}$, $B_{2g}$, and $B_{3g}$ modes.

Figure 5

Pressure variation of the $u$ modes in the post-perovskite phase of ${\mathrm{In}}_2{\mathrm{O}}_3$. (a) $A_u$ and $B_{1u}$ modes and (b) $B_{2u}$ and $B_{3u}$ modes. There are 15 optical $u$ modes that decompose as $2A_u+5B_{1u}+5B_{2u}+3B_{3u}$. Circles, down-pointing triangles, squares, and up-pointing triangles denote, respectively, $A_u$, $B_{1u}$, $B_{2u}$, and $B_{3u}$ modes. Full symbols are for the TO modes and empty symbols for the LO modes.

Figure 6

(Color online) The calculated powder Raman spectra of crystalline ${\mathrm{In}}_2{\mathrm{O}}_3$ with post-perovskite structure at several pressures.