A binary ionic solid AZ crystallizes such that its anions form a cubic close-packed array

CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties

Problem

A binary ionic solid AZ crystallizes such that its anions form a cubic close-packed array. The cations occupy one type of interstitial site in this array. Relevant ionic radii (Shannon):

r_{\text{A}^+}=82\,\text{pm}

and

r_{\text{Z}^-}=196\,\text{pm}

. (a) Calculate the radius ratio

\dfrac{r_{\text{A}^+}}{r_{\text{Z}^-}}

to three significant figures. (b) Using accepted radius-ratio guidelines, identify the interstitial site—tetrahedral, octahedral, or cubic—that A

^{+}

ions are most likely to occupy. (c) Explain, in terms of the balance between electrostatic attraction and like-charge repulsion, why the site you selected in part (b) is preferred over the other two possibilities for this particular radius ratio. (d) State the resulting coordination numbers of A

^{+}

and Z

^{-}

ions in the adopted structure. Justify why this pair of coordination numbers is energetically more favorable than an alternative pair that would arise from a different choice of interstitial site.

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