Radii Goldschmidt

Goldschmidt radii that of Cu is somewhat uncertain due to Jahn-Teller effects. 

The factor t varies from 0.8 to 1. For an ideal cubic structure t should be > 0.89 (based on the Goldschmidt radii). 

FIG. A4-1. A plot of experimentally measured electron density between adjacent F and Li nuclei in LiF. The Pauling and Goldschmidt radii of Li+ are indicated by P and G, while M denotes the actual minimum (adapted from H. Krebs, Fundamentals of Inorganic Crystal Chemistry, McGraw-Hill, New York, 1968). 

Fig. 18 Schematic of the conditions during oxide growth. The proportions are true to scale with respect to the Goldschmidt radii. Ions need several jumps to cross the entire film [53].

The sizes of polyatomic (nonglobular) ions in crystals are also expressed by their thermochemical radii according to Jenkins and coworkers [47], Circular reasoning may be involved in their determination, because these radii depend on calculated lattice energies of crystals that in turn depend on the interionic distances. The assigned uncertainties of these radii are 19 pm for univalent and divalent anions increasing to twice this amount for trivalent ones and they are listed in Table 2.8 too. A further problem with these values is the use of the Goldschmidt radii for the alkali metal counterions, r°, rather than the Shannon-Prewitt ones [43,44] appropriate for ions in solution. 

Fig. 16.2. Reduced radial distribution functions for TbFcj (left) and GdFcj (right) derived from the transform of the neutron and X-ray scattering data of fig. 16.1. The atomic spacings corresponding to several combinations of hard sphere atoms in contact with radii equal to the Goldschmidt radii are indicated by the arrows. (Gd-Cargill, 1974 Tb-Rhyne et al., 1974a).

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