The piezoelectric properties of tetragonal perovskites $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, and $\mathrm{K}\mathrm{Nb}{\mathrm{O}}_3$ under uniaxial strain along the [001] direction are calculated from first principles. In order to study the piezoelectric response of individual atomic sublattices, the total polarization $P$ and piezoelectric constant $d_{33}$ are decomposed into the contributions of $A$-site and $B$-site atoms. These three materials show different behaviors at the atomic scale. In $\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$, the Pb and Ti contribute almost equally to the polarization and $d_{33}$. In $\mathrm{K}\mathrm{Nb}{\mathrm{O}}_3$, most of the polarization and $d_{33}$ are contributed by the ferroelectrically active Nb. But in $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$, as the $c$ axis increases, the contribution of Ba to $d_{33}$ rises rapidly, reaching 50% of the total $d_{33}$ at $c$ = 4.30 Å. This means that the covalent bonding between Ba and O is significant and has an important impact on the piezoelectric response of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$.

Perovskite materials are considered to be promising electrolyte membrane candidates for electrochemical applications owing to their excellent proton- or oxide-ion-conducting properties. RbBiNb₂O₇ is a double-layered Dion–Jacobson perovskite oxide, with Pmc2₁ symmetry. In this study, the electronic structure and proton-diffusion properties of bulk RbBiNb₂O₇ were systematically investigated using first-principles calculations. The unique layered crystal structure of RbBiNb₂O₇ plays a crucial role in proton storage and proton conductivity. Different proton-diffusion steps in RbBiNb₂O₇ were considered, and the activation energies of the relevant diffusion steps were evaluated using the climbing image-nudged elastic band (CI-NEB) technique. The proton diffusion in RbBiNb₂O₇ presents a two-dimensional layered characteristic in the a-b plane, owing to its layered crystalline nature. According to the transition state calculations, our results show that the bulk RbBiNb₂O₇ exhibits good proton-transport behavior in the a-b plane, which is better than many perovskite oxides, such as CaTiO₃, CaZrO₃, and SrZrO₃. The proton diffusion in the Rb–O and Nb–O layers is isolated by a higher energy barrier of 0.86 eV. The strong octahedral tilting in RbBiNb₂O₇ would promote proton transport. Our study reveals the microscopic mechanisms of proton conductivity in Dion–Jacobson structured RbBiNb₂O₇, and provides theoretical evidence for its potential application as an electrolyte in solid oxide fuel cells (SOFCs).

Two-dimensional (2D) materials have potential applications in nanoscale sensors and spintronic devices. Herein, motivated by experimental synthesis of a CrI${}_3$ monolayer possessing intrinsic magnetism and a Janus MoSSe monolayer with piezoelectricity, we propose a 2D Janus Cr${}_2$I${}_3$F${}_3$ monolayer as a multifunctional material exhibiting both piezoelectricity and ferromagnetism. Using density functional theory calculations, we systematically investigated the structural stability and the electronic, magnetic, and piezoelectric properties of the Janus Cr${}_2$I${}_3$F${}_3$ monolayer. We predicted that a vertical polarization of up to −0.155 × 10${}^{-10}$ C/m is induced in the Cr${}_2$I${}_3$F${}_3$ monolayer due to the breaking of symmetry. The origination mechanism of polarization was demonstrated in terms of a local dipole moment calculated by maximally localized Wannier functions. Meanwhile, it was found that a remarkable piezoelectric response can be produced under a uniaxial strain in the basal plane. The calculated piezoelectric coefficients of the Cr${}_2$I${}_3$F${}_3$ monolayer compare favorably with those of the frequently used bulk piezoelectric materials such as $\alpha$–quartz and wurtzite AlN. Particularly, the e${}_{31}$ and d${}_{31}$ values of the Cr${}_2$I${}_3$F${}_3$ monolayer are nearly 10 times as large as that of Mo-based transition metal dichalcogenides. We also found that the magnitude of e${}_{31}$ mainly arises from the ionic contribution, while the electronic contribution can be nearly neglected. The considerable piezoelectric response combined with the intrinsic magnetism make the Janus Cr${}_2$I${}_3$F${}_3$ monolayer a potential candidate for novel multifunctional devices integrating both piezoelectric and spintronic applications.