Atomic Radii from Unit Cell Dimensions

1 Atomic Radii from Unit Cell Dimensions 

By 1920 the unit cell dimensions of 15 of the 17 alkali metal halides with the face-centered rock salt structures had been determined. The first attempt to utilize such data to estimate the size of individual ions appears to have been made by Alfred Lande [35]. He assumed that the alkali metal cations and halide anions could be regarded as spherical and concluded that the unit cell dimension a could be written 

Three years later, Wasastjema was able to present a table with more accurate radii for 16 ions, including 0 , F, Na , and Mg (Table 3) [36]. Wasastjema fixed the ratio between the radius of an alkali metal cation and the radius of the isoelectronic halide anion (for instance, the ratio between the radii of Na and F ) using polarizability data from aqueous solutions. The polarizabilities of the halide anions were first determined under the assumption that the hydrogen ions do not contribute significantly to the molar polarizabilities of dissolved hydrogen halides. The polarizabilities of the cations could then be obtained from measurements on the salts. Molar polarizabilities are roughly proportional to the ionic volumes, and Wasastjema fixed the radius ratio r+/r as the fourth root of the polarizability ratio of the two ions (Table 3). 

The radii of ions are known to increase with increasing coordination numbers. The radii in the table refer to coordination numbers equal to six 

In the 1939 edition of his classic book The Nature of the Chemical Bond, Pauling listed an extensive table of ionic radii of main-group elements obtained by fixing the radius ratios between the four isoelectronic ion pairs and Na , CP and K , Br and Rb , and I and Cs as the inverse ratio between the effective nuclear charges r+/r = [37]. The effective nuclear charge of an atom or ion is 

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