Factors influencing solid-state structure—an analysis using pseudopotential radii structural maps

Abstract

Structural sorting maps using $\frac{R_{\sigma }}{R_{\pi }}$, $\frac{r_{+}}{r_{-}}$, $\frac{r_{\sigma }^A}{r_{\sigma }^B}$, and $\frac{{\chi }^A}{{\chi }^B}$ are compared for $\mathrm{AB}$, $A{B}_2$ octets and double octets, and $A{B}_2{X}_4$ spinels. With the use of $\frac{r_{+}}{r_{-}}$, the crystal ionic radii, the sorting is tolerable only if the usual restrictions of the mechanical model (radius ratio rules) are relaxed. $\frac{R_{\sigma }}{R_{\pi }}$ are poor indices for $A{B}_2$ and $A{B}_2{X}_4$, but $\frac{r_{\sigma }^A}{r_{\sigma }^B}$ and $\frac{{\chi }^A}{{\chi }^B}$ are excellent for all three systems. It is suggested that the traditional packing ideas based on size (and viewed semiquantitatively here using the $r_{\sigma }^{\xi }$) are directly related to modern charge-control aspects (via electronegativity differences) of molecular structures, and both can be viewed as very important factors in determining structural preference.