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To study the structural, elastic, piezoelectric and dielectric properties of wurtzite (LaN), we have used the ab initio total-energy pseudo-potential plane-wave method (PP-PW) based on density functional theory (DFT) and density functional perturbation theory (DFPT), which performed with Generalized gradient approximation (GGA) as well as local density approximation (LDA). The calculations of piezoelectric constants by mean of linear-response calculations second derivative with respect to a strain and a modification of the electric field.The compound shows a large effective piezoelectric constant (𝑑 33 ) being in the order of 66.96, and 77.260 pc/N with (GGA), and (LDA) calculations, respectively. The dielectric properties and electromechanical coupling coefficients have been calculated. Finally, our piezoelectric findings indicate that the LaN compound has a high effective piezoelectric constant value (𝑑 33 ) which allows it to be in direct competitor of zinc oxide ZnO and aluminum nitride AIN. We hope that our findings provide guidelines for the experimental realization and further research of high-performance materials appropriate for applications in different fields of study, such as biomedical engineering.

In this paper, we deal with a theoretical and predictive study of the influence of the applied pressures on the structural, elastic and piezoelectric properties of the rhombohedral BiAlO 3 perovskite (R3c space group) phase by combining both the density functional theory (DFT) and the density functional perturbation theory (DFPT) included in the ABINIT code. The results indicate a decrease in structural cell volume and the elastic constants appear to be more intense as the applied pressure increases. Due to the increase in the direct piezoelectric coefficient (e 33 ) and the decrease of the elastic constant (c 33 ), the converse piezoelectric coefficients (d 33 ) tend to improve with increased pressure applied. At a pressure of 10 GPa, the value of the direct piezoelectric constant reached 6.23 C/m 2 which becomes an indirect competitor to lead zirconate titanate (PZT). The dielectric constants and born effective charge at high pressure have been calculated. Our results agree well with the available experimental and theoretical results. Our findings, especially piezoelectricity, can help in various applications of high-pressure devices such ultrasonic transducer.