Structural principles for minerals and inorganic compounds containing anion-centered tetrahedra

Several minerals and inorganic compounds contain (XA(4)) tetrahedra, with a nions, X (O2-, N3-, and F-), as central atoms and cations, A (Cu2+, Zn2+, P b2+, Bi3+, REE3+, etc.), as ligands. These tetrahedra are well defined in t hese crystal structures because the bond valences between A and X are essen tially higher than the bond valences between A and atoms from other structu ral units. According to their size, anion-centered tetrahedra may be subdiv ided into large and small tetrahedra, formed from cations with ionic radii near to 1.0 Angstrom (e.g., Pb2+, Bi3+, and REE3+) and 0.5-0.7 Angstrom (e. g., Cu2+ and Zn2+), respectively. The small anion-centered tetrahedra prefe r to link through corners, whereas the large tetrahedra prefer to link thro ugh edges. When the tetrahedra are built from both "small" and "large" cati ons, "small" cations prefer to be corners shared between lesser numbers of tetrahedra and not involved in linking tetrahedra via edges. The general cr ystal-chemical formula of minerals and compounds containing anion-centered tetrahedra may be written as A(k)'[X(n)A(m)][A(p)X(q)]X-l', where [X(n)A(m) ] (usually n less than or equal to m) is a structural unit based on anion-c entered tetrahedra (ACT) and [A(p)X(q)] (p < q) is a structural unit based on cation-centered polyhedra (CCP). A' is a cation that does not belong to anion- or cation-centered polyhedra; it is usually an interstitial cation s uch as an alkali metal; X' is an interstitial anion such as halide or S2-. Structures containing both ACT and CCP units may be ordered according to th e values of their dimensionality. In structures without CCP units, an impor tant role is played by large interstitial anions that link finite ACT units , chains, or layers into three-dimensional structures or fill cavities in A CT frameworks.