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

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 = ( ∂ V V ∂ T ) P , X = ( ∂ ln V ∂ 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, α G of Na-silicate glasses is shown to be constant between 300 and ∼650 K (P and X constant), but it increases linearly with Na 2 O 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 ( α N ) by: α = α 1 θ 1 + α 2 θ 2 + α 3 θ 3 + ⋯ + α N θ N where θ represents volume fraction of a component. Calculated α Na 2 O and α SiO 2 values compare satisfactorily with reported values for melts containing ∼40–60 mole% Na 2 O 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 sphere

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