First-Principles Study of Piezoelectric, Elastic, and Pressure-Dependent Properties of the R₂​Ti₂​O₇​ Carpy–Galy Phase Materials

Carpy–Galy phase materials, with general formula A_nB_nO_3n+2​, are a class of layered perovskite-derived oxides with a crystal structure formed by alternating perovskite slabs and extra oxygen planes. Among them, the R₂Ti₂O₇​ (R = La, Nd, Ce, Pr) compounds have attracted attention due to their ferroelectric properties and very high Curie temperatures. In these materials, polarization arises from a combination of rotations of the TiO₆ octahedra and the broken connectivity between octahedra in the layered crystal structure. Most previous work has focused on the ferroelectric properties of these materials, with less focus on their piezoelectric and elastic properties. In this work, we use density functional theory (DFT) and density functional perturbation theory (DFPT) to calculate the full piezoelectric stress (e_ij) and strain (d_ij​) tensors, along with the elastic constants (C_ij​), for R₂Ti₂O₇​. We also explore how the application of hydrostatic pressure can tune structural distortion amplitudes and the ferroelectric and electromechanical properties. These findings advance our understanding of this family of tunable and environmentally friendly ferroelectric and piezoelectric materials.