The first-principle study on certain structural, band-structural, elastic, optical and piezoelectric properties of the Ca, Zr and Ca/Zr-doped BaTiO3

Based on the framework of density functional theory (DFT), the structure, elastic, optical, Debye temperature and piezoelectric properties of tetragonal [Formula: see text] (BT) individually doped with calcium (Ca) at barium (Ba) and zirconium (Zr) at titanium (Ti) site have been investigated by a first-principles technique. These properties of Ca and Zr (Ca/Zr) co-doped BT (BCZT) also have been investigated by the same calculation method. The effects of exchange and correlation functional on these properties are also investigated. The structural studies have demonstrated that the Ca-doped BT (BCT) exhibits the reduced volume due to radius of Ca smaller than that of Ba, while Zr-doped BT (BZT) presents the enlarged volume due to radius of Zr being larger than that of Ti. The as-calculated lattice parameters have verified the consistency of well-designed crystal structure with the experimental results. The investigations of the band structure demonstrated that the doping of Ca, Zr and Ca/Zr enlarges the band gap ([Formula: see text]) of BT in sequence. Furthermore, the [Formula: see text] values obtained via HSE06 matched well with experimental values, while those obtained by generalized gradient approximation (GGA) and local density approximation (LDA) are significantly lower. The studies of optical, Debye temperature and elastic properties show that the BCZT displays a decreased refractive index, reduced thermal conductivity and an enhanced anisotropy index. Most importantly, after the co-doping of Ca and Zr, the piezoelectric strain tensor [Formula: see text] of BCZT increases by [Formula: see text]% compared to that of BT. This work provides a theoretical guidance for improving the piezoelectric performance of BT via the doping strategy.