A tetrahedral site in a close-packed lattice is formed by four spheres at the co

Question

A tetrahedral site in a close-packed lattice is formed by four spheres at the comers of a regular tetrahedron. This is equivalent to placing of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a close-packed arrangement the spheres are in contact and if the spheres have a radius r. the diagonal of the face of the cube is 2r. The tetrahedral hole is inside the middle of the cube. Find the length of the body diagonal of this cube. Express your answer in terms of r. Find the radius of the tetrahedral hole. Express your answer in terms of r.

Explanation / Answer

A tetrahedral site in a close-packed lattice is formed by four spheres at the co

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