Fundamentals of Thermal Expansion Behavior

While the simple lattice vibration model works well for close packed structures, additional processes can occur in less tightly packed network structures such as those found in glasses. Bond bending can alter the positions of atoms, as can rotation about an axis. These processes can counteract the expansion of the bond length due to the increased amplitude of vibration, resulting in very low expansion coefficients. Filling of interstices inhibits these processes and tends to cause an increase in thermal expansion coefficients. 

2 Compositional Effects on Thermal Expansion Coefficients of Homogeneous Glasses 

Thermal expansion coefficients of glasses, with few exceptions, increase with increasing temperature. The data can often be expressed over a wide temperature range for the elastic material by an equation of the form  

Addition of modifier ions to silica fills the interstices, preventing bond bending, and hence increases the thermal expansion coefficient. The thermal expansion coefficients of binary alkali silicate glasses increase in the order Li Na K. The thermal expansion coefficient is virtually independent of the existence of phase separation, increasing linearly with increasing alkali oxide content for all three oxides over the 

A small mixed-alkali effect occurs in the thermal expansion coefficient of alkali silicate glasses. The deviation from additivity due to this effect has been shown to increase with increasing total alkali oxide concentration, and to be a function of the radius ratio of the larger to the smaller alkali ion present in the glass, with a maximum for the ratio for the sodium-potassium pair. The deviation from additivity is positive for radius ratios less than approximately 1.6, but is negative for larger 

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