Calculation of glass properties

Now Ernst Abbe knew exactly how to construct an excellent microscope, but unfortunately, the required lenses and prisms with specific ratios of refractive index and dispersion did not exist.

The additivity principle is a simplification and only valid within narrow composition ranges as seen in the displayed diagrams for the refractive index and the viscosity.

Subsequently, English[7] and Gehlhoff et al.[8] published similar additive glass property calculation models.

[9][10] Schott and many scientists and engineers afterwards applied the additivity principle to experimental data measured in their own laboratory within sufficiently narrow composition ranges (local glass models).

This huge pool of experimental data was not investigated as a whole, until Bottinga,[13] Kucuk,[14] Priven,[15] Choudhary,[16] Mazurin,[17] and Fluegel[18][19] published their global glass models, using various approaches.

In addition, global models can reveal and quantify non-additive influences of certain glass component combinations on the properties, such as the mixed-alkali effect as seen in the adjacent diagram, or the boron anomaly.

In the following sections (except melting enthalpy) empirical modeling techniques are presented, which seem to be a successful way for handling huge amounts of experimental data.

[20] They are often not created to obtain reliable glass property predictions in the first place (except melting enthalpy), but to establish relations among several properties (e.g. atomic radius, atomic mass, chemical bond strength and angles, chemical valency, heat capacity) to gain scientific insight.

If the desired glass property is not related to crystallization (e.g., liquidus temperature) or phase separation, linear regression can be applied using common polynomial functions up to the third degree.

[25] The disconnected peak functions approach is based on the observation that within one primary crystalline phase field linear regression can be applied[27] and at eutectic points sudden changes occur.

Basic information about the principle can be found in an article by Huff et al.[33] The combination of several glass models together with further relevant technological and financial functions can be used in six sigma optimization.

The calculation of glass properties allows "fine-tuning" of desired material characteristics, e.g., the refractive index . [ 1 ]
The mixed-alkali effect: If a glass contains more than one alkali oxide, some properties show non-additive behavior. The image shows, that the viscosity of a glass is significantly decreased. [ 11 ]
Decreasing accuracy of modern glass literature data for the density at 20 °C in the binary system SiO 2 -Na 2 O [ 12 ]
Refractive index in the system SiO 2 -Na 2 O. Dummy variables can be used to quantify systematic differences of whole dataseries from one investigator. [ 12 ]
Liquidus surface in the system SiO 2 -Na 2 O-CaO using disconnected peak functions based on 237 experimental datasets from 28 investigators. Error = 15 °C. [ 25 ]