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Unformatted text preview: o is usually r (cation) R (anion). If, however, r (anion) r (cation), then the r R ratio should be used to | v v 44 pgm 1-19-98 plm 3-21-98 MP | e-Text Main Menu | Textbook Table of Contents pg045 [R] G1 7-27060 / IRWIN / Schaffer bmb 3-31-98 MP3 Chapter 2 TABLE 2.6–1 Atomic Scale Structures The critical r R ratio for each coordination number. (Note that the drawings are not to scale.) Coordination number Critical (r/R) value (r/R) Stability range Geometry 0 < r/R < 0.155 Always possible r 2 0 3 0.155 0.155 ≤ r/R < 0.225 4 0.225 0.225 ≤ r/R < 0.414 6 0.414 0.414 ≤ r/R < 0.732 R R r R 8 r 0.732 ≤ r/R < 1 0.732 R r r 12 1 R r/R = 1 estimate the CN of the anion. Once the CN of the smaller ion is known, the CN of the larger ion can be determined based on the cation : anion ratio, or the stoichiometry of the compound. ....................................................................................................................................... EXAMPLE 2.6–1 Table 2.6–1 gives the ionic radius ratio range for CN 6 as 0.414 rR limiting values by investigating the critical geometry for CNs of 6 and 8. 0.732. Derive these Solution The geometry for the critical (minimum) r R ratio for CN 6 is shown in Table 2.6–1. If a represents the length of the edge of the cube, then when all of the ions are just touching each other r R a 2 R and R a 2 Dividing the first equation by the second equation yields r R 1 2R | v v 2 | e-Text Main Menu | Textbook Table of Contents 45 pg046 [V] G2 7-27060 / IRWIN / Schaffer Part I Fundamentals Solving for the desired quantity yields r R 2 1 0.414 Since the maximum value for CN 6 corresponds to the minimum value for CN repeat the procedure for the critical geometry for CN 8. In this case, we find r a R 3 2 and R R 8, we must a Dividing the first equation by the second and solving for r R yields r R 3 1 0.732 ......................................................................................................
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This note was uploaded on 02/25/2013 for the course PHYS 2202 taught by Professor Sowell during the Spring '10 term at Georgia Institute of Technology.

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