Yttrium oxide, with the chemical formula Y₂O₃, is known to exhibit different crystal structures under various conditions. The most common and stable form of yttrium oxide is the cubic phase, often referred to as C-type or C-Y2O3. This phase is characterized by a body-centered cubic (BCC) structure, also known as bixbyite or cubic-C structure.

Structure of the cubic C-type Y₂O₃ (bixbyite). The lattice parameter is a 0 = 1.0604 nm. (a) Unit cell representation. (b) Environment of the two Y sites (the actual position of the O atoms is slightly shifted from the corners of the cubes). The small squares are structural oxygen vacancies.

The unit cell of the Y2O3cubic-Cstructure is composed of 80 atoms with a bulk lattice constant of a0=1.0604 nm.The oxygen atoms arelocated on the (48e) sites, and yttrium atoms are located on two non-equivalent cation sites, Y1(8b) and Y2(24d)(Fig. 1-a). All of the cations are six-fold coordinated: the Y1atoms aresurrounded by six neighbouring oxygens at the same distance(0.230 nm), whereas the Y2atoms have three pairs of neighbouring ox-ygens at three different distances (0.225, 0.228, and 0.236 nm). Thisstructure results in a speci?c arrangement of structural oxygen vacan-cies that form a network in the (16c) position along the body diagonaland face diagonal of the cubic cell(Fig. 1-b).

References:

[1] R.J. GABORIAUD; B. L; F Paumier. Disorder–order phase transformation in a fluorite-related oxide thin film: In-situ X-ray diffraction and modelling of the residual stress effects[J]. Thin Solid Films, 2016. DOI:10.1016/j.tsf.2015.08.030.