Surface Transport in Micro-patterned Al-B-Silicate Glass

1. Surface Transport in Micro-patterned Al-B-Silicate Glass Adam Ellison Corning Inc

2. Thermal smoothing of corrugated surfaces DLarge volume DLong Distance DSmall curvature driving term CLarge flow cross section CSmall volume CShort Distance CLarge curvature driving term D Small flow cross section

3. Bulk Transport Surface Transport Scales linear with viscosity Scales to the fourth power with viscosity z x D2-D Flow CLow E to form “flow units” Point defect language: Low E Formation, Emigration Polymer language: Unlimited free volume C3-D Flow DHigh E to form “flow units” Point defect language: Large E formation , Emigration Polymer language: Low free volume

4. Origin of power four dependence on spatial frequency: The chemical energy of an atom scales with pressure (units energy/volume). Pressure scales as 1/r (radius of curvature). R in turn is proportional to d2z/dx2. This leads to a quadratic dependence of K on l. The continuity equation for flux adds an other quadratic dependence, resulting in a l4dependence

5. Cross over from bulk to surface diffusion occurs in metals, semiconductors, ceramics: l ~ 5…10 microns Cross over in glass unknown as regime below l 5…10 microns has not been measured. (Smaller periodicity hard to make with chemical (HF) etching)

6. EXPERIMENTAL APPROACH Measure decay constant, K, of periodic gratings as a function of grating wavelength, l and temperature T K = F×(2π/ l) + A× (2π/ l)2+ D× (2π/ l)3+ B× (2π/ l)4 The four terms represent contribution from viscous flow; evaporation-condensation; volume diffusion and/or evaporation-condensation; and surface diffusion, respectively. Inverse dependence on l=> viscous flow Power four dependence on l=> surface diffusion Variation with temperatue => Activation Energy

7. Compositions: Each compositions at two residual water contents. Sample # I II III IV V VI VII mol% SiO225 33.4 41.6 50 58.4 66.7 75 mol% CaO 37.5 33.3 29.2 25 20.8 16.6 12.5 mol% Al2O337.5 33.3 29.2 25 20.8 16.6 12.5 Temp. 1 (˚C) 880 886 892 899 910 925 950 Temp. 2 (˚C) 884 890 896 903 914 929 954 Temp. 3 (˚C) 892 894 900 907 922 933 958

9. AFM

10. Residual water content, sets I and II

11. Data Measurement

12. Example of Data Analysis

13. …continued

15. 7 Compositions 2 Sets 7 wave lengths 6 mm to 0.4 mm 3 Temperatures Total # Analyzed: 294 Data Sets

18. Summary • Surface transport l < 0.4 mm scales viscosity • Indication at 0.6 to 0.4 mm, for small for small l4 . . . ..contribution, needs to be confirmed. • Near surface transport activation energy in agreement ..with activation of viscous flow, when adjusted for ..changes with ..in/out diffusion of water vapor. • Concept of fragility extends to Alumina-Borate glasses.