The Goldschmidt Rules

On the basis of ion size and charge, Goldschmidt deduced certain principles governing trace element distribution. The principles have become known as the Goldschmidt Rules. They are  

The failure of the Goldschmidt Rules in other cases, such as accounting for the geochemical behaviour of zinc, was attributed to effects of covalent bonding (Fyfe, 1951, 1954). The rules are stated in terms of ionic radius and 

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In earlier chapters, allusions were made to die effects of covalent bonding. For example, covalent interactions were invoked to account for the intensification of absorption bands in crystal field spectra when transition metal ions occupy tetrahedral sites ( 3.7.1) patterns of cation ordering for some transition metal ions in silicate crystal structures imply that covalency influences the intracrystalline (or intersite) partitioning of these cations ( 6.8.4) and, the apparent failure of the Goldschmidt Rules to accurately predict the fractionation of transition elements during magmatic crystallization was attributed to covalent bonding characteristics of these cations ( 8.3.2). 

Important structural principles for ionic crystals, which had already been recognized in part by V. Goldschmidt, were summarized by L. Pauling in the following rules. First rule Coordination polyhedra... 

This theoretical result is completely substantiated by experiment. Goldschmidt,31 from a study of crystal structure data, observed that the radius ratio is large for fluorite type crystals, and small for those of the rutile type, and concluded as an empirical rule that this ratio is the determining factor in the choice between these structures. Using Wasastjerna s radii he decided on 0.67 as the transition ratio. He also stated that this can be explained as due to anion contact for a radius ratio smaller than about 0.74. With our radii we are able to show an even more satisfactory verification of the theoretical limit. In Table XVII are given values of the radius ratio for a large number of compounds. It is seen that the max-... 

Goldschmidt predicted from his empirical rule that calcium chloride would not have the fluorite structure, and he states that on investigation he has actually found it not to crystallize in the cubic system. Our theoretical deduction of the transition radius ratio allows us to predict that of the halides of magnesium, calcium, strontium and barium only calcium fluoride, strontium fluoride and chloride, and barium fluoride, chloride,... 

Figure 9.3 The relative abundance of the rare earth elements according to Goldschmidt and Thomassen (above) and Ida Noddack (below[57]). The Noddacks found a much higher abundance of neodymium than the Norwegian researchers, but their data were not generally accepted. Both diagrams illustrate the Oddo-Harkins rule very clearly.

Almost 20 years after Goldschmidt, Suess and Urey (1956) published a new abundance table, which in part relied on solar abundances. In addition, Suess and Urey (1956) introduced arguments based on nucleosynthesis. Their so-called semiempirical abundance rules, primarily the smooth abundance variation of odd-mass nuclei with increasing mass number, were applied to estimate abundances for elements for which analytical data from meteorites were not available or had large errors. The Suess and Urey compilation was very influential for theories of nucleosynthesis and for the development of nuclear astrophysics in general. Later compilations by Cameron (1973), Anders and Grevesse (1989), Palme and Beer (1993), and others took into account improved analytical data on meteorites and the more accurate determination of elemental abundances in the solar photosphere. Over the... 

In this case, however, the ISi jO component is at infinite dilution in a host of essentially pure YSi cO. Now we assume that Goldschmidt s first rule applies, i.e., we assume that if I and Y " " had exactly the same ionic radius then the standard free energy changes of reactions (1) and (4) would be the same. The actual difference between the standard free energy changes is assumed to be due to the work done in straining crystal and melt by introducing a cation which is not the same size as the site. This is a reasonable assumption for closed-shell ions such as Ca, Sr, and Mg " " and it also appears to work in those cases, such as the lanthanides, where crystal field effects are small (Blundy and Wood, 1994). For first row transition ions such as Co, and Cu, however,... 

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