Thoralf Johansson

Modeling of the thermal expansion behaviour of ZERODUR at arbitrary temperature profiles

Modeling of the thermal expansion behavior of ZERODUR® for the site conditions of the upcoming Extremely Large Telescopes (ELTs) allows an optimized material selection to yield the best performing ZERODUR® for the mirror substrates. The thermal expansion of glass ceramics is a function of temperature and a function of time, due to the structural relaxation behavior of the materials. The application temperature range of the upcoming ELT projects varies depending on the possible construction site between -13°C and +27°C. Typical temperature change rates during the night are in the range between 0.1°C/h and 0.3°C/h. Such temperature change rates are much smaller than the typical economic laboratory measurement rate, therefore the material behavior under these conditions can not be measured directly. SCHOTT developed a model approach to describe the structural relaxation behavior of ZERODUR®. With this model it is possible to precisely predict the thermal expansion behavior of the individual ZERODUR® material batches at any application temperature profile T(t). This paper presents results of the modeling and shows ZERODUR® material behavior at typical temperature profiles of different applications.

CTE characterization of ZERODUR® for the ELT century

This review paper summarizes the extensive investigations that have been performed at SCHOTT to achieve a deeper understanding of the CTE homogeneity of ZERODUR® within single blanks and the casted formats (boules). Especially for the upcoming Extremely Large Telescope (ELT) projects like E-ELT or TMT with at least several hundreds of mirror segments the reproducibility of the mean CTE, CTE homogeneity and axial gradient is very important while keeping the CTE quality assurance process economic at the same time. Statistics of CTE homogeneity measurements on a ZERODUR® boule suitable for an economical production of ELT mirror substrates using the improved dilatometer will be presented. It will be shown, that it is possible to achieve tight CTE specifications by utilisation of processes existing at SCHOTT, while at the same time guaranteeing a long term reproducibility. The CTE measurement is optimized for a temperature interval from 0°C to 50°C. We developed a model to extrapolate the CTE behaviour to specific temperature conditions at the telescope site.

Reshaping at High Viscosities

In the standard model of Tool-Narayanaswamy for the viscoelastic material behavior of glass, the shear modulus of elasticity is assumed to be temperature independent. The motivation is the exponential temperature dependence of the viscosity, which implies an exponential temperature dependence of the characteristic shear stress relaxation times. The usual assumption is that the decrease of the modulus of elasticity slows down significantly with increasing temperature.