Partial molar volumes of metal oxides in silicate melts: Effects of Coulombic interactions

Abstract

Alkaline, alkaline earth, many 3d and most 4f modifier oxides dissolved in siliceous melts mix non-ideally with SiO₂ to produce linear, density-compositional mixing trends from which partial molar volumes of modifier oxides (V*) are determined. An analysis of these experimental data reveals that the partial molar volumes of alkali, alkaline earths, most 4f and many 3d modifier oxides partial molar volumes are accurately reproduced by: where F_C = (z⁺•z⁻)/d² (Coulomb's Law) and z indicates charge. The bond length ‘d’ is the sum of the radii of the cation (M⁺, M²⁺, M³⁺ or M⁴⁺) and oxide ion (O²⁻) observed in ionic crystals. The coefficients ‘m’ and ‘b’ are 0.325 and 1.38 Å/atom respectively. Partial molar volumes of network-forming oxides also conform to the above equation where ‘m’ = ∼3.25 and ‘b’ is 1.68 Å/atom.

Coulomb's force of attraction (F_C) is the product of the cationic field strength (z⁺/d²) and the charge on an anion, where ‘d’ is the distance separating the centers of the two charges. In silicate melts containing modifier cations, apical O atoms of Si tetrahedra are negatively charged and are displaced toward the cations due to Coulombic attraction. The resulting collapse around the cations is referred to as ‘electrostriction’. Partial molar volumes (V*) of modifier oxides are thus composed of two terms, the volume of the polyhedron of the modifier cation (V_Poly) and a volume associated with collapse of tetrahedra around the cation (V_Col): V_Col is negative for all modifier oxides and becomes increasingly negative with increased charge on the cation and with increased coordination number (CN). V_Poly is itself composed of two terms, an intrinsic volume (V_Int) and an excluded volume (V_Ex). The intrinsic volume can be calculated using cationic and O²⁻ radii evaluated from ionic crystals. V_Ex reflects the state of packing around cationic polyhedra. It is equal to 6.83 ų/atom for all modifier oxides so that the expression for V_Poly is: A linear relationship exists between V_Poly and V_Col which results in the observed linear density-composition trends from which partial molar volumes are determined. In spite of their linearity, these trends are the result of non-ideal mixing of modifier oxide and SiO₂ components in siliceous melts. Our finding that tetrahedra collapse around modifier cations differs from the traditional perspective where modifier cations were considered to occupy voids within the silicate network but otherwise had limited effect on melt structure. These results demonstrate that modifier cations affect the network substantially by causing surrounding tetrahedra to rotate, twist, tilt and flex during their collapse toward modifier cations.