Show that the radius of the largest sphere that can be placed in a tetrahedral interstitial site in an fcc lattice is 0.225r1, where r1 is the radius of the atoms making up the lattice. (Hint: Consider a cube with the centers of fourspheres placed at alternate corners, and visualize the tetrahedral site at the center of the cube. What is the relationship between r1 and the length of a diagonal of a face? The length of a body diagonal?)

Chemistry & Chemical Reactivity
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Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
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Chapter12: The Solid State
Section12.2: Structures And Formulas Of Ionic Solids
Problem 1RC: 1. The unit cell of silicon carbide. SiC is illustrated in the margin. In what type of unit cell are...
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Show that the radius of the largest sphere that can be placed in a tetrahedral interstitial site in an fcc lattice is 0.225r1, where r1 is the radius of the atoms making up the lattice. (Hint: Consider a cube with the centers of four
spheres placed at alternate corners, and visualize the tetrahedral site at the center of the cube. What is the relationship between r1 and the length of a diagonal of a face? The length of a body diagonal?)

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