Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-03 GTBL042-Callister-v2 September 6, 2007 15:33

3.6 Ceramic Crystal Structures • 47

Table 3.3 Coordination Numbers and Geometries for Various Cation–Anion

Radius Ratios (rC/rA)

Coordination Cation–Anion Coordination

Number Radius Ratio Geometry

2 <0.155

3 0.155–0.225

4 0.225–0.414

6 0.414–0.732

8 0.732–1.0

Source:W. D. Kingery, H. K. Bowen, and D. R. Uhlmann,Introduction to Ceramics,2nd

edition. Copyright©c1976 by John Wiley & Sons, New York. Reprinted by permission of

John Wiley & Sons, Inc.

bound to the nucleus, which results in a decrease in ionic radius. Conversely, ionic

size increases when electrons are added to an atom or ion.

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 num-

ber 3 is 0.155.