A tetrahedral site in a closest-packed lattice is formed by fourspheres at the corners

Chapter 13, Problem 87

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A tetrahedral site in a closest-packed lattice is formed by fourspheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In sucha closest-packed arrangement the spheres are in contact, and ifthe spheres have a radius r, the diagonal of the face of the cubeis 2r. The tetrahedral hole is inside the middle of the cube. Findthe length of the body diagonal of this cube and then find theradius of the tetrahedral hole.

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