Chap 12 Solns-6E - CHAPTER 12 STRUCTURES AND PROPERTIES OF CERAMICS PROBLEM SOLUTIONS 12.1 The two characteristics of component ions that determine the

# Chap 12 Solns-6E - CHAPTER 12 STRUCTURES AND PROPERTIES OF...

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CHAPTER 12 STRUCTURES AND PROPERTIES OF CERAMICS PROBLEM SOLUTIONS 12.1 The two characteristics of component ions that determine the crystal structure are: 1) the magnitude of the electrical charge on each ion; and 2) the relative sizes of the cations and anions. 12.2 In this problem we are asked to show that the minimum cation-to-anion radius ratio for a coordination number of four is 0.225. If lines are drawn from the centers of the anions, then a tetrahedron is formed. The tetrahedron may be inscribed within a cube as shown below.The spheres at the apexes of the tetrahedron are drawn at the corners of the cube, and designated as positions A, B, C, and D. (These are reduced in size for the sake of clarity.) The cation resides at the center of the cube, which is designated as point E. Let us now express the cation and anion radii in terms of the cube edge length, designated as a. The spheres located at positions Aand touch each other along the bottom face diagonal. Thus,AB= 2rABut(AB)2=α2+α2= 2α265 B
A ABF 66
, C A
12.5 This problem calls for us to predict crystal structures for several ceramic materials on the basis of ionic charge and ionic radii. (a) For CsI, from Table 12.3 68