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General Chemistry Principles, Patterns, and Applications, 2011

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Figure 12.11 The Zinc Blende Structure<br />

Zn 2+ ions occupy every other tetrahedral hole in the fcc array of S 2− ions. Each Zn 2+ ion is surrounded<br />

by four S 2− ions in a tetrahedral arrangement.<br />

E X A M P L E 3<br />

a. If all the tetrahedral holes in an fcc lattice of anions are occupied by cations, what is<br />

the stoichiometry of the resulting compound?<br />

b. Use the ionic radii given in Figure 7.9 "Ionic Radii (in Picometers) of the Most Common<br />

Oxidation States of the " to identify a plausible oxygen-containing compound with this<br />

stoichiometry <strong>and</strong> structure.<br />

Given: lattice, occupancy of tetrahedral holes, <strong>and</strong> ionic radii<br />

Asked for: stoichiometry <strong>and</strong> identity<br />

Strategy:<br />

A Use Figure 12.8 "Holes in Cubic Lattices" to determine the number <strong>and</strong> location of the tetrahedral holes<br />

in an fcc unit cell of anions <strong>and</strong> place a cation in each.<br />

B Determine the total number of cations <strong>and</strong> anions in the unit cell; their ratio is the stoichiometry of the<br />

compound.<br />

C From the stoichiometry, suggest reasonable charges for the cation <strong>and</strong> the anion. Use the data in Figure<br />

7.9 "Ionic Radii (in Picometers) of the Most Common Oxidation States of the " to identify a cation–anion<br />

combination that has a cation:anion radius ratio within a reasonable range.<br />

Solution:<br />

a. A Figure 12.8 "Holes in Cubic Lattices" shows that the tetrahedral holes in an fcc<br />

unit cell of anions are located entirely within the unit cell, for a total of eight (one near<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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