The structure of crystalline solids problem solutions

3-1

CHAPTER 3

THE STRUCTURE OF CRYSTALLINE SOLIDS PROBLEM SOLUTIONS

Fundamental Concepts
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.

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Unit Cells Metallic Crystal Structures
3.2 For this problem, we are asked to calculate the volume of a unit cell of lead. Lead has an FCC crystal structure (Table 3.1). The FCC unit cell volume may be computed from Equation 3.4 as
VC = 16R 3 2 = (16) (0.175 × 10-9 m) 3( 2 ) = 1.213 × 10-28 m3

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3.3 This problem calls for a demonstration of the relationship a = cell shown below

4R for BCC. Consider the BCC unit 3

Using the triangle NOP
(NP) 2 = a 2 + a 2 = 2a 2

And then for triangle NPQ,
(NQ) 2 = (QP) 2 + ( NP) 2

But NQ = 4R, R being the atomic radius. Also, QP = a. Therefore,
(4R) 2 = a 2 + 2a 2

or a =

4R 3

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