Goldschmidt crystal radii

This distinction between electron-cloud radii and structural radii is then used to refine the system of ionic radii due to Pauling and Goldschmidt. Some further examples of anion-anion contact are discussed, and a value deduced for the crystal radius of the hydride anion. These cases of anion-anion contact argue for the Pauling tradition and against the new electron-density-minimum (EDM) radii. 

Wasastjeraa s table of radii was then revised and greatly extended by Goldschmidt by the use of empirical data.u Goldschmidt based his values on Was stjerna s values 1.33 A for F and 1.32 A for 0—, and, using data obtained from crystals that he considered to be essentially ionic in nature, he deduced from this starting point empirical values of the crystal radius for over 80 ions. His values (indicated by G) are compared with those from Table 13-3 in Table 13-4. 

Empirical crystal radius values, based on O— = 1.40 A and designed for application to the same standard crystals, are given in Table 13-5. These are in part obtained from Goldschmidt s set with suitable small corrections.18... 

Goldschmidt has classed also with the ionic crystals the C-modification of the sesqui-oxides, cubic crystals with 16 M2O3 in the unit of structure. The inter-atomic distances reported by him are 2.16-2.20 A. for scandium oxide and 2.34-2.38 A. for yttrium oxide, in good agreement with the radius sums 2.21 A. for Sc+3-0= and 2.33 A. for Y+3-0". 

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,... 

Thirdly, there is the purely structural argument from Relative Size if ions of one type are much the largest, they will effectively fix the structure since the others can pack between them. This argument, which makes no assumption whatever about electron-clouds, is often referred only to lithium iodide, but much more evidence is available. Such questions of crystal-form and isomorphism are in fact the most important applications of ionic-radius systems in chemistry and mineralogy (cp. the classical work of V. M. Goldschmidt (2)). 

According to V. M. Goldschmidt, two substances with the same basic formula and crystal structure form solid solutions in a concentration range that depends on the degree of similarity of their ionic radii. A large range of solid solutions may be expected if the radius of the larger ion does not exceed that of the smaller by more than 15% [3.73a],... 

Although the ionic radius criterion of Goldschmidt continues to serve as a useful principle of crystal chemistry, attention has been drawn to limitations of it (Bums and Fyfe, 1967b Bums, 1973). As noted earlier, the magnitude of the ionic radius and the concept of radius ratio (i.e. cation radius/anion radius) has proven to be a valuable guide for determining whether an ion may occupy a specific coordination site in a crystal structure. However, subtle differences between ionic radii are often appealed to in interpretations of trace element distributions during mineral formation. 

Goldschmidt (1937, 1954) first recognized that the distribution of trace elements in minerals is strongly controlled by ionic radius and charge. The partition coefficient of a given trace element between solid and melt can be quantitatively described by the elastic strain this element causes by its presence in the crystal lattice. When this strain is large because of the magnimde of the misfit, the partition coefficient becomes small, and the element is partitioned into the liquid. This subject is treated in detail in Chapter 2.09. 

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,... 

In such cases the mean of the two distances is taken. (We are not here referring to zinc and cadmium which show a very much larger deviation from closest packing, with axial ratios 1-856 and 1 885 respectively.) For metals which crystallize with structures of lower coordination the radii for 12-coordination have to be derived in other ways. From a study of the interatomic distances in many metals and alloys Goldschmidt found that the apparent radius of a metal atom varies with the coordination number in the following way. The relative radii for different... 

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