Ionic Radii and Paulings Rules

Solving Equations (12.9) and (I2.I0) simultaneously for r+ and r, where the interionic distance in the crystal is known, yields the univalent radii. Univalent radii assume that the ions interact using a hard-spheres model such that their electron clouds do not interpenetrate with one another. For ions that are not univalent, such as Mg , a correction must be made for the compressibility because the larger the nuclear charge, the more likely the ion will be able to polarize the electron cloud of its neighbor. The correction factor, shown in Equation (12.14) can be derived from the Born constant, as demonstrated below in Equations (12.11)-(12.13). The corrected Pauling ionic radii for selected ions are listed in Table 12.5. 

Solution. Using Slater s rules to calculate 2 for the isoelectronic ions  

Example 12-5. Use Pauling s equations and the results from Example 12-4 to calculate the univalent and corrected radii of Mg and Then, use the corrected ionic radii to predict the interionic distance in MgO. 

Because of the inverse relationship between r and Z, the proportionality constant can be calculated from the univalent radius of either Na+ or F , both of which are isoelectronic with and 0 . 

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