Assume that the rare, radioactive elements astatine and...

Assume that the rare, radioactive elements astatine and polonium form anions $\mathrm{At}^{-}$and $\mathrm{Po}^{2-}$, each of which has a radius of about $226 \mathrm{pm}$. Which of the following lattice types $\left(\mathrm{ZnS}, \mathrm{NaCl}, \mathrm{CsCl}, \mathrm{SiO}_2, \mathrm{TiO}_2, \mathrm{CaF}_2\right)$ would be expected to be adopted by: a. the astatide of each Group 1 metal ( Na through Cs); b. the astatide of each Group 2 metal ( $\mathrm{Mg}$ through Ba); $\mathbf{c}$. the polonide of each Group 2 metal ( $\mathrm{Mg}$ through $\mathrm{Ba}$ ).

Key Concepts

Crystal Lattice Types

Ionic compounds can crystallize in several different lattice structures such as the NaCl?, ZnS?, CsCl?, and CaF2?type lattices. These types differ in the spatial arrangement of the ions and the coordination numbers (i.e. how many nearest neighbors each ion has). Understanding these lattice types provides insight into how ions pack in the solid state, influencing the physical properties of the compound.

Radius Ratio Rules

The radius ratio rule is a guideline that relates the relative sizes of the cation and anion to the coordination number and the type of crystal lattice that is likely to form. By comparing the cation’s radius to the anion’s radius, one can predict whether a compound will favor tetrahedral, octahedral, or cubic (or other) coordination geometries, and hence which lattice (e.g. NaCl versus CsCl) is more appropriate.

Coordination Number

The coordination number refers to the number of oppositely charged ions immediately surrounding a given ion in a crystal lattice. It is a crucial factor in determining the crystal structure because different lattice types have characteristic coordination numbers; for example, the NaCl structure features a coordination number of 6, while the CsCl structure has a coordination number of 8, and the ZnS structure typically displays tetrahedral (coordination number 4) geometry.

Ionic Charge and Lattice Energy Considerations

Along with ionic sizes, the magnitude of the ionic charges plays an important role in determining the stability and type of lattice structure that will form. Higher charges typically lead to stronger electrostatic interactions (lattice energies) and can affect the ideal geometry and coordination number of the ion arrangement. Thus, monovalent anions and divalent anions (such as those in the astatide versus polonide examples) may result in differing lattice types even when the ionic radii are similar.

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