ME 2733 Chapter : Ch 3 HW Sol
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Atomic structure relates to the number of protons and neutrons in the nucleus of an atom, as well as the number and probability distributions of the constituent electrons. On the other hand, crystal structure pertains to the arrangement of atoms in the crystalline solid material. 3. 4 for the hcp crystal structure, show that the ideal c/a ratio is 1. 633. We are asked to show that the ideal c/a ratio for hcp is 1. 633. A sketch of one-third of an hcp unit cell is shown below. Consider the tetrahedron labeled as jklm, which is reconstructed as follows: The atom at point m is midway between the top and bottom faces of the unit cell--that is mh = c/2. And, since atoms at points j, k, and m, all touch one another, where r is the atomic radius. Jm = jk = 2r = a or (jm )2. + (mh )2 a2 = (jh )2 +
