Crystal Chemical Aspects of Vanadium:  Polyhedral Geometries, Characteristic Bond Valences, and Polymerization of (VO<i>_n</i>) Polyhedra

Abstract

The distribution of bond lengths in (V 3+ O 6 ) polyhedra shows a maximum between 1.98 and 2.04 Å, and limits of 1.88 and 2.16 Å, respectively. The bond lengths in (V 4+ O n ) and (V 5+ O n ) ( n = 5, 6) polyhedra show distinct populations which allow us to define the following types of bonds: (1a) vanadyl bonds in (V 4+ O n ) polyhedra, shorter than 1.74 Å; (1b) vanadyl bonds in (V 5+ O 5 ) polyhedra, shorter than 1.76 Å; (1c) vanadyl bonds in (V 5+ O 6 ) polyhedra, shorter than 1.74 Å; (2a) equatorial bonds in (V 4+ O n ) polyhedra, in the range 1.90 to 2.12 Å; (2b) equatorial bonds in (V 5+ O 5 ) polyhedra, longer than 1.76 Å; (2c) equatorial bonds in (V 5+ O 6 ) polyhedra with one vanadyl bond, in the range 1.74 to 2.10 Å; (2d) equatorial bonds in (V 5+ O 6 ) polyhedra with two vanadyl bonds, in the range 1.80 to 2.00 Å; (3a) trans bonds in (V 4+ O 6 ) polyhedra, longer than 2.10 Å; (3b) trans bonds in (V 5+ O 6 ) polyhedra with one vanadyl bond, longer than 2.15 Å; (3c) trans bonds in (V 5+ O 6 ) polyhedra with two vanadyl bonds, longer than 2.025 Å. The average equatorial bond length in (V 4+ O n ) and (V 5+ O n ) polyhedra can be used to calculate the mean valence state of V in mixed-valent structures. We define characteristic bond valences for vanadyl, equatorial, and trans bonds in different coordinations and examine which binary linkages are possible and which linkages occur in minerals and synthetic compounds. Here, V 5+ −O−V 5+, V 5+ −O−V 4+, and V 4+ −O−V 4+ linkages between vanadyl− trans and equatorial−equatorial bonds occur often in synthetic compounds, whereas the corresponding V 4+ −O−V 4+ linkages are rare in minerals.