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result in the formation of non-bridging oxygens increase the refractive index of glasses, while changes in composition which reduce the non-bridging oxygen concentration can reduce the refractive index. The refractive indices of alkali silicate glasses (Figure 10.1) thus increase with increasing alkali oxide concentration, while replacement of alkali oxides by alumina, which reduces the non-bridging oxygen concentration, can cause a reduction in the refractive index. The polarizability of the cation present increases as the field strength of the ion decreases, so that glasses containing cesium have a higher refractive index than those containing sodium. The most polarizable ions have very large electronic clouds and small oxidation numbers, e.g., T1' and Pb2+, which are used to produce very high refractive index glasses. Glasses which contain very high PbO concentrations, such as those found in unusual systems such as the PbO-Ga20, binary and the PbO-Ga203-Bi,0, ternary, have refractive indices in excess of 2.5. The density of a glass also plays a role in controlling the refractive index. Decreases in fictive temperature, which increase the density of most glasses, increase the refractive index. Since the fictive temperature is determined by the cooling rate through the glass transformation region, the refractive index is found to increase with decreasing cooling rate. This effect can be very important for optical applications, where fine annealing is essential to minimize local index variations. The refrac- tive index also increases when glasses are either reversibly or irreversibly compacted by pressure or by exposure to high energy radiation. 1.450 1 I I I 0 10 20 30 40 Mol% Alkali Oxide Figure 10.1 Effect of composition on the refractive index of alkali silicate glasses
Optical Properties 205 Thermal expansion of glasses can result in either an increase or a decrease in the refractive index. The density of a glass will decrease if it expands upon heating, which should decrease the refractive index. The polarizability of the ions, however, increases with temperature, which increases the refractive index and may therefore offset the effect of the decreasing density, Glasses with high thermal expansion coefficients and low temperature variations in polarizability are usually found in systems containing fluorine, such as the fluoride, fluorophosphate, or fluorosiIicate systems. These glasses have negative coefficients for the variation of refractive index with temperature, dnldT. Glasses with low thermal expansion coefficients and higher temperature variation of polarizability, as is the case for most silicate and borate glasses, have positive temperature coefficients of refractive index. These variations in refractive index are reversible so long as no relaxation of the density occurs during the temperature excursion.