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
(a) cos 30° = R/(r + R)
r/R = 0.155 Region of
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
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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