RESUMO
Ion radii are derived here from the characteristic (grand mean) bond lengths for (i) 135 ions bonded to oxygen in 459 configurations (on the basis of coordination number) using 177 143 bond lengths extracted from 30 805 ordered coordination polyhedra from 9210 crystal structures; and (ii) 76 ions bonded to nitrogen in 137 configurations using 4048 bond lengths extracted from 875 ordered coordination polyhedra from 434 crystal structures. There are two broad categories of use for ion radii: (1) those methods which use the relative sizes of cation and anion radii to predict local atomic arrangements; (2) those methods which compare the radii of different cations (or the radii of different anions) to predict local atomic arrangements. There is much uncertainty with regard to the relative sizes of cations and anions, giving rise to the common failure of type (1) methods, e.g. Pauling's first rule which purports to relate the coordination adopted by cations to the radius ratio of the constituent cation and anion. Conversely, type (2) methods, which involve comparing the sizes of different cations with each other (or different anions with each other), can give very accurate predictions of site occupancies, physical properties etc. Methods belonging to type (2) can equally well use the characteristic bond lengths themselves (from which the radii are derived) in place of radii to develop correlations and predict crystal properties. Extensive quantum-mechanical calculations of electron density in crystals in the literature indicate that the radii of both cations and anions are quite variable with local arrangement, suggesting significant problems with any use of ion radii. However, the dichotomy between the experimentally derived ion radii and the quantum-mechanical calculations of electron density in crystals is removed by the recognition that ion radii are proxy variables for characteristic bond lengths in type (2) relations.
RESUMO
The scarcity of nitrogen in Earth's crust, combined with challenging synthesis, have made inorganic nitrides a relatively unexplored class of compounds compared to their naturally abundant oxide counterparts. To facilitate exploration of their compositional space via a priori modeling, and to help a posteriori structure verification not limited to inferring the oxidation state of redox-active cations, we derive a suite of bond-valence parameters and Lewis acid strength values for 76 cations observed bonding to N3-, and further outline a baseline statistical knowledge of bond lengths for these compounds. Examination of structural and electronic effects responsible for the functional properties and anomalous bonding behavior of inorganic nitrides shows that many mechanisms of bond-length variation ubiquitous to oxide and oxysalt compounds (e.g., lone-pair stereoactivity, the Jahn-Teller and pseudo Jahn-Teller effects) are similarly pervasive in inorganic nitrides, and are occasionally observed to result in greater distortion magnitude than their oxide counterparts. We identify promising functional units for exploring uncharted chemical spaces of inorganic nitrides, e.g. multiple-bond metal centers with promise regarding the development of a post-Haber-Bosch process proceeding at milder reaction conditions, and promote an atomistic understanding of chemical bonding in nitrides relevant to such pursuits as the development of a model of ion substitution in solids, a problem of great relevance to semiconductor doping whose solution would fast-track the development of compound solar cells, battery materials, electronics, and more.
