# 61c as r r continues to increase cns of 4 6 8 and

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Unformatted text preview: ic constant. Also called permi dielectric strength The maximum strength that a material can withstan diffraction A speciﬁc interaction o materials. Diffraction appears as reﬂe pg044 [V] G2 7-27060 / IRWIN / Schaffer Part I Fundamentals r R (a) cos 30° = R/(r + R) r/R = 0.155 Region of overlap r R 120° (b) 30° R (c) FIGURE 2.6–1 Geometry for CN 2: (a) two anions “ﬁt” but (b) a third would require overlap and (c) the minimum r R value for a CN 3 is shown to be 0.155. without forcing the anions to overlap. The repulsive force between the ions prevents this overlap. Since it is impossible for the smaller ion to have CN 3, this ratio of r R results in CNcation 2. If the radius of the cation is gradually increased while holding the radius of the anion constant, a value of r R is eventually reached for which CN 3 is possible (see Figure 2.6–1c). As r R continues to increase, CNs of 4, 6, 8, and eventually 12 become possible. The critical radius ratio for each coordination number is given in Table 2.6–1. Note that these are minimum values for each CN. Although a given CN is geometrically possible for any r R ratio greater than the value given in Table 2.6–1, it will be energetically favorable only until the minimum value of the next highest CN is reached. Thus, the maximum value of r R for CN 8 is the minimum r R value for CN 12. Examination of Appendix C shows that the radius of an anion is generally larger than the radius of the corresponding neutral atom, and the radius of a cation is usually smaller than that of the neutral atom. This behavior can be readily understood on the basis of electron-electron and electron-proton interactions. In cations, the magnitude of the electronic repulsions decreases with the loss of electrons, and the positive charge in the nucleus is able to attract the remaining electrons more closely. The result is r r 0. Using 0 the inverse argument, it can be shown that r will be greater than r . Since r R must always be less than or equal to 1, and since for most ionically bonded compounds r (cation) r (anion), the appropriate radius rati...
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