Libor Švéda 1, Martina Landová 2, Martin Míka 2, Ladislav Pína 1, Radka Havlíková 1, Veronika Semencová 3 1)KFE FJFI ČVUT 2)VŠCHT Praha 3)Rigaku Innovative Technologies Europe s.r.o. Glass thermal formation - experiment vs. simulation Glass thermal formation - experiment vs. simulation

Motivation Glass forming process – brief description Metrology Simulations – theory Simulations – initial results Perspectives – metrology upgrades – simulation modifications

Motivation Thermal glass forming as a method how to obtain precise shapes Precursor to Si wafer forming Typical applications – glass: Space x-ray mirrors (large scale, low specific mass, good surface roughness) Mirrors for catadioptric systems, like the HUD display (large, low cost) Mirrors for condensors, like the sun heat sources, photomultiplyers etc. (large, low cost) – Silicon Space x-ray mirrors (excellent surface quality) Laboratory x-ray mirrors (diffraction imaging, excellent surface quality)

Glass forming process Form defined shaping Arbitrary shape High temperature form / mandrel Contact method – possible surface contamination „Freefall forming“ Shape given by physics Efficient shape modification only by temperature gradients Non-contact method F Oven G

Metrology - overview Low precision In-situ Process dynamics Very high precission On the table No process dynamics Possible contamination Effect of transportation

Metrology – in situ process dynamics intro

Metrology – in situ process dynamics curves

Form process parameters prediction

Metrology – in situ profile measurement End of formation After cool down

Metrology – on-the-table

Forming simulations - theory Heat-up process – Elastic material properties Forming process – Viscous liquid approximation at given temperature – Strong change of viscosity with temperature!!! – Problem of boundary conditions Cool-down process – Similar to forming process, except that changing temperature according to the measured temperature decay G Temperature gradient?

Simulations – input parameters DESAG D263 glass density: g/cm 3 Young modulus: 72.9 Mpa Poisson ratio: thermal coeff. of expansion: 7.2e-6 K -1 strain point: 529°C annealing point: 557°C softening point: 736°C sample size: 75x25x0.7 mm 100 x 100 x 0.4 mm temperatures used: °C Dynamic viscosity used

Simulations – viscous liquid Comsol Multiphysics simulations Viscous liquid at given temperature Velocity fields at given time Actual glass profile is obtained by integrating the velocity curves

Simulations vs. metrology process dynamics 75x25x0.75 mm glass Why?

Simulation vs. metrology fixed edges

Form process predictions - simulation

Simulation vs. metrology cool down process

Known error sources Cool down during the image acquisition Cool down process and corrections for that process Temperature gradients No definition of fixed points for forming Image distortions during the in-situ measurements, no camera fixation Lighting conditions not well defined Non existent fast non-contact profilometry (no need to transport over large distances, time gaps)

Perspectives – metrology upgrades in-situ Ronald A. Petrozzo and Stuart W. Singer Schneider Optics Hauppauge, NY -- Test & Measurement World, 10/15/2001

Perspectives – metrology upgrades on-the-table I Chromatic aberration based method Non-contact method Precision vs. measuring range vs. allowed surface slope Typical values:

Perspectives – simulation upgrades Include temperature gradients – Measure actual temperature inside the oven – Apply the temperatures to the simulation Include cool down process as a standard point Treat more precisely the glass/form interface

Conclusions First in-situ shaping measurements (full profile) Discrepancy between simulations and experiment – Experiment is non-linear x Simulation predict linear bending curve – Higher temperatures are preserved precisely (experiment) – Inoptimal metrology (experiment) – Boundary conditions not well defined (experiment + simulation) Experience gathered is used for developing new metrology methods for future experiments (including Silicon shaping)

Finito