Relations between the structures of some nitrides and oxy-compounds

Relations between the structures of some nitrides and oxy-compounds 

The close relation between structure and composition and simple geometrical considerations is nicely illustrated by some binary and ternary nitrides. In many of these compounds there is tetrahedral coordination of the smaller metal ions in particular, there are many ternary nitrides containing tetrahedrally coordinated Li ions. From the simple theorem that not more than eight regular tetrahedra can meet at a point (p. 159) it follows, for example, that there cannot be tetrahedral coordination of Li by N in LisN, a point of some interest in view of the unexpected (and unique) structure of this compound and the apparent non-existence of other alkali nitrides of type M3N. It also follows that the limit of substitution of Be by Li in BeaN2 is reached at the composition BeLiN for example, there cannot be a compound BeLi4N2 with tetrahedrally coordinated metal atoms. 

These points are more readily appreciated if we formulate nitrides with 4 N atoms, for if all the metal atoms are 4-coordinated and all N atoms have the same coordination number this c.n. is equal to the total number of metal atoms in the 

Examples of structures in which five or seven tetrahedra meet at each point do not appear to be known, but the structures with = 3,4, 6, and 8 are well known. We see that replacement of Be by Li in BegN4 must stop at Be4Li4N4 (BeLiN) since further substitution would imply that more than eight tetrahedra must meet at each N atom. The end-member of the series would be Lij2N4 (LiaN) in which, assuming tetrahedral coordination of Li, every N would be common to 12 LiN4 tetrahedra. 

More generally we can derive the limits of substitution of a metal M by tetrahedrally coordinated Li in nitrides in the following way. Writing the formula of the ternary nitride (Li jM )3Nj, we have 

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