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

Abstract

Structural sorting maps using $\frac{{R}_{\ensuremath{\sigma}}}{{R}_{\ensuremath{\pi}}}$, $\frac{{r}_{+}}{{r}_{\ensuremath{-}}}$, $\frac{{r}_{\ensuremath{\sigma}}^{A}}{{r}_{\ensuremath{\sigma}}^{B}}$, and $\frac{{\ensuremath{\chi}}^{A}}{{\ensuremath{\chi}}^{B}}$ are compared for $\mathrm{AB}$, $A{B}_{2}$ octets and double octets, and $A{B}_{2}{X}_{4}$ spinels. With the use of $\frac{{r}_{+}}{{r}_{\ensuremath{-}}}$, the crystal ionic radii, the sorting is tolerable only if the usual restrictions of the mechanical model (radius ratio rules) are relaxed. $\frac{{R}_{\ensuremath{\sigma}}}{{R}_{\ensuremath{\pi}}}$ are poor indices for $A{B}_{2}$ and $A{B}_{2}{X}_{4}$, but $\frac{{r}_{\ensuremath{\sigma}}^{A}}{{r}_{\ensuremath{\sigma}}^{B}}$ and $\frac{{\ensuremath{\chi}}^{A}}{{\ensuremath{\chi}}^{B}}$ are excellent for all three systems. It is suggested that the traditional packing ideas based on size (and viewed semiquantitatively here using the ${r}_{\ensuremath{\sigma}}^{\ensuremath{\xi}}$) 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.