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Chap 03 Solns-6E

Chap 03 Solns-6E - CHAPTER 3 THE STRUCTURE OF CRYSTALLINE...

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CHAPTER 3 THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS 3.1 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. 3.2 A crystal structure is described by both the geometry of, and atomic arrangements within, the unit cell, whereas a crystal system is described only in terms of the unit cell geometry. For example, face-centered cubic and body-centered cubic are crystal structures that belong to the cubic crystal system. 3.3 For this problem, we are asked to calculate the volume of a unit cell of aluminum. Aluminum has an FCC crystal structure (Table 3.1). The FCC unit cell volume may be computed from Equation (3.4) as V C = 16R 3 2 = (16) 0.143 x 10 -9 m ( ) 3 2 = 6.62 x 10 -29 m 3 3.4 This problem calls for a demonstration of the relationship a = 4 R 3 for BCC. Consider the BCC unit cell shown below Using the triangle NOP 11
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