Jeremy\'s Kindle for PC Fundamentals of Materials Science and Engineering: An In

Question

Jeremy's Kindle for PC Fundamentals of Materials Science and Engineering: An Integrated Approach, 4th Edition File View Go Tools Help Library 1 110096 3.6 Ceramic Crystal Structures 51 Table 3.4 lonic Radii for Several Cations and Anions for a Coordination Number of 6 Ionic Radius (nm,) 0.053 0.136 0.100 0.170 0.077 0.069 0.138 0.072 0.067 0.102 0.069 0.040 0.061 Ionic Radius (nm) 0.196 0.181 0.133 0.220 0.140 0.184 Anion Br Cl Cation 3+ Ca Fe Fe 2+ EXAMPLE PROBLEM 3.4 Computation of Minimum Cation-to-Anion Radius Ratio for a Coordination Number of 3 Show that the minimum cation-to-anion radius ratio for the coordination number 3 is 0.155 Solution For this coordination, the small cation is surrounded by three anions to form an equilateral triangle as shown here, triangle ABC; the centers of all four ions are coplanar Orc Cation This boils down to a relatively simple plane trigonometry problem. Consideration of the right trian- gle APO makes it clear that the side lengths are related to the anion and cation radii rA and rc as Anion AP = rA an Furthermore, the side length ratio AP/AO is a function of the angle as 8% Page 510f910

Explanation / Answer

The possibilities would include only the monovalent cations Cs+, K+, and Na+.

Furthermore, the coordination number for each cation must be 8, which means that 0.732 < rC/rA < 1.0

RCs+/RI- = 0.170/0.220 = 0.772

RK+/RI-    = 0.138/0.220 = 0.627

RNa+/RI- = 0.102/0.220 = 0.463

Thus, only cesium(Cs+) will form the CsCl crystal structure with iodine.

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