Figure 1
Phonon modes mixing of orthorhombic and monoclinic phases via their trilinear coupling with \({X}_{1}^{x}\) phonon. Atomic structure of cubic phases of HfO2 (A), superlattice (B), and CeO2 (C). (D) The \({X}_{1}^{x}\) mode (at the top) shows trilinear couplings between the phonon modes of the reference cubic phase, which condense in the orthorhombic (\({\Gamma }_{15}^{z},{X}_{5}^{y},{Y}_{5}^{z}\), and \({Z}_{5}^{{\prime}y}\), blue in the left column) and monoclinic (\({X}_{5}^{{\prime}y},{\Gamma }_{25}^{z},{Z}_{5}^{y}\), and \({Y}_{5}^{{\prime}z}\), red in the right column) phases. All the phonon modes are visualized in the 12-atom unit cell of high-symmetry cubic structure of HfO2.
