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Show that the zinc blende structure can be described as having zinc and sulfide ions each in face-centered lattices, merged so that each ion is in a tetrahedral hole of the other lattice.

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Final answer:

The zinc blende structure is characterized by sulfide ions forming an FCC lattice with zinc ions occupying half of the tetrahedral holes, resulting in a 1:1 stoichiometry and tetrahedral coordination for both ions.

Step-by-step explanation:

The zinc blende structure can be demonstrated to consist of face-centered lattices of both zinc and sulfide ions by examining the crystal geometry. In a face-centered cubic (FCC) lattice, which is also called cubic close-packed (CCP), sulfide ions are positioned at the lattice points. Each sulfide ion in the FCC lattice has tetrahedral holes, and there are two of these holes for each ion. Since zinc ions are significantly smaller than sulfide ions, they fit into these tetrahedral spaces. Specifically, the zinc ions occupy half of the tetrahedral holes, which ensures a 1:1 stoichiometry with the empirical formula ZnS. As a consequence, each zinc ion is surrounded by four sulfide ions, and each sulfide ion is similarly surrounded by four zinc ions, resulting in a tetrahedral coordination for each ion type.

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