Pressure-Induced Phase Transformations of Quasi-2D Sr${}_3$Hf${}_2$O${}_7$

We present an $\mathit{\text{ab-initio}}$ study of the quasi-2D layered perovskite Sr${}_3$Hf${}_2$O${}_7$ com-pound, performed within the framework of the Density Functional Theory and lattice dynamics analysis. At high temperatures, this compound takes a $\mathit{\text{I4/mmm}}$ centrosym-met-ric structure (S.G. n. 139); as the temperature is lowered, the symmetry is broken into other intermediate polymorphs before reaching the ground state structure, which is the $\mathit{\text{Cmc2}}{}_1$ ferroelectric phase (S.G. n. 36). One of these intermediate polymorphs is the $\mathit{\text{Ccce}}$ structural phase (S.G. n. 68). Additionally, we have probed the $\mathit{\text{C2/c}}$ system (S.G n. 15), which was obtained by following the atomic displacements corresponding to the eigenvectors of the imaginary frequency mode localized at the $\mathbf{\Gamma }$-point of the $\mathit{\text{Ccce}}$ phase. By observing the enthalpies at low pressures, we found that the $\mathit{\text{Cmc2}}{}_1$ phase is thermodynamically the most stable. Our results show that the $\mathit{\text{I4/mmm}}$ and $\mathit{\text{C2/c}}$ phases never stabilize in the 0-20 GPa range of pressure values. On the other hand, the $\mathit{\text{Ccce}}$ phase becomes energetically more stable at around 17 GPa, surpassing the $\mathit{\text{Cmc2}}{}_1$ structure. By considering the effect of entropy and the constant-volume free energies, we observe that the $\mathit{\text{Cmc2}}{}_1$ polymorph is energetically the most stable phase at low temperature; however, at 350 K the $\mathit{\text{Ccce}}$ system becomes the most stable. By probing the volume-dependent free energies at 19 GPa, we see that $\mathit{\text{Ccce}}$ is always the most stable phase between the two structures and also throughout the studied temperature range. When analyzing the phonon dispersion frequencies, we conclude that the $\mathit{\text{Ccce}}$ system becomes dynamically stable only around 19-20 GPa, and that the $\mathit{\text{Cmc2}}{}_1$ phase, is metastable up to 30 GPa.