Thermal Expansion of Metal Oxides in Silicate Melts: A Simple Theoretical Analysis

Abstract

The isobaric, isochemical coefficient of thermal expansion ( α) is the proportionality constant relating ∂V/V and ∂T. Noting that ∂V/V equals ∂lnV at constant pressure and composition (i.e., P and X): α=(∂VV∂T)P,X=(∂lnV∂T)P,X A polynomial expression for the temperature dependence of lnV yields direct and accurate calculation of α of melts and glasses. Using the approach, αG of Na-silicate glasses is shown to be constant between 300 and ∼650 K (P and X constant), but it increases linearly with Na2O content, indicating that α is controlled mostly by Na behaviour. Values of α for a melt or glass are necessarily (thermodynamically) related to the coefficients of thermal expansion of its ‘N’ melt components ( αN) by: α=α1θ1+α2θ2+α3θ3+⋯+αNθN where θ represents volume fraction of a component. Calculated αNa2O and αSiO2 values compare satisfactorily with reported values for melts containing ∼40–60 mole% Na2O but are less satisfactory for highly siliceous melts, implying need for refinement of α values. The Coulombic force of attraction between cation and anion is the primary determinant of the magnitude of α values of alkali and alkaline earths oxides. Their values represent a lower bound on α of 3d and 4f modifier oxides. Values larger than this lower bound likely result from a change in coordination number (CN) from higher to lower CN values of modifier cations. Experimental and molecular dynamics studies indicate that partial charges on NBO (O of Si-O-M moieties) and BO (O of Si-O-Si moieties) are about −0.96 and −0.64 respectively, thus NBOs should be incorporated into the first coordination spheres of modifier cations in preference to BOs. A simple mechanism is proposed whereby NBO-BO exchange occurs and CN of the modifier cation decreases with minimal topological adjustment or energetic cost to the melt.