Hagg rules

As a final example, we may mention the NaCl-type phases formed in the V-0 systems. The V01 x phase is homogeneous in the composition range 42-57 at.% O. Lattice parameter determination in combination with density measurements evidenced that, in the structure, vacancies occur in both V and O sublattices through the entire range of composition. At the stoichiometric composition VO there are = 15% of sites vacant in each sublattice. 

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When this ratio is larger than 0.59, as in the Group 7—10 metals, the stmeture becomes more complex to compensate for the loss of metal—metal interactions. Although there are minor exceptions, the HAgg rule provides a useful basis for predicting stmeture. 

Hagg found that metals can accommodate interstitial nonmetal atoms of radius up to 59% of that of the metal atoms. Show that, in this limiting case, accommodation of the nonmetal atoms in the octahedral holes of a face-centered cubic metal lattice should result in an expansion of the unit cell dimension by 12.4%. [Hint Review the radius ratio rules in Section 4.5.]... 

Hagg et al. (48) evaluated 611 adults, they were not genotyped and thus a gene-dose effect cannot be ruled out. Although available data are conflicting, there is not clear support of sex difference in CYP2D6 activity. 

The carbides and nitrides of group 4-6 transition metals belong to the so-called Hagg compovmds (6). Hagg formulated a set of empirical rules for the crystal structures of interstitial solid solutions of transition metals. According to the rules, when the radius ratio r = rx/fmetai is less than 0.59, small atoms (such as carbon and nitrogen) occupy the interstitial sites of the simple crystal structures formed by the metal atoms. For the carbides and nitrides of Ti, V, Nb, Mo, and W, which have been extensively applied as catalysts, the radius ratios fall in between 0.491 r lr i) and 0.576 (rc/ry). They are indeed Hagg compounds (6). Table 1 summarizes the crystal structures and lattice parameters of carbides of Mo, W, V, Nb, and Ti. 

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