Dielectric Constants of Zr Silicates: A First-Principles Study

Abstract

Using density-functional theory, we compute the optical and static dielectric constants for a set of Zr silicates modeled by various $\mathrm{S}\mathrm{i}{\mathrm{O}}_{\mathrm{2}}$ crystals, with Zr atoms substitutional to Si, and by an amorphous structure. We then derive a microscopic scheme that relates the dielectric constants to structural units centered on Si and Zr atoms through the definition of characteristic parameters. Applied to amorphous $({\mathrm{Z}\mathrm{r}\mathrm{O}}_2{)}_x(\mathrm{S}\mathrm{i}{\mathrm{O}}_{\mathrm{2}}{)}_{1-x}$, these schemes describe the observed dependence of the dielectric constants on the Zr concentration and highlight the role of ${\mathrm{Z}\mathrm{r}\mathrm{O}}_6$ units.