ABSTRACT Knowing the ultimate surface morphology resulting from CO 2 laser mitigation of induced laser damage is important both for determining adequate treatment protocols, and for preventing deleterious intensification upon subsequent illumination of downstream optics. Physical effects such as evaporation, viscous flow and densification can strongly affect the final morphology of the treated site. Evaporation is a strong function of temperature and will play a leading role in determining pit shapes when the evaporation rate is large, both because of material loss and redeposition. Viscous motion of the hot molten material during heating and cooling can redistribute material due to surface tension gradients (Marangoni effect) and vapor recoil pressure effects. Less well known, perhaps, is that silica can densify as a result of structural relaxation, to a degree depending on the local thermal history. The specific volume shrinkage due to structural relaxation can be mistaken for material loss due to evaporation. Unlike evaporation, however, local density change can be reversed by post annealing. All of these effects must be taken into account to adequately describe the final morphology and optical properties of single and multiple-pass mitigation protocols. We have investigated, experimentally and theoretically, the significance of such densification on residual stress and under what circumstances it can compete with evaporation in determining the ultimate post treatment surface shape. In general, understanding final surface configurations requires taking all these factors including local structural relaxation densification, and therefore the thermal history, into account. We find that surface depressions due to densification can dominate surface morphology in the non-evaporative regime when peak temperatures are below 2100K

J D Cooke

J S Stolken

M D Feit

M J Matthews

R M Vignes

S T Yang

T F Soules

CiteSeerX

LLNL-PROC-461512
Densification and residual stress induced
by CO2 laser-based mitigation of SiO2
surfaces
M. D. Feit , M. J. Matthews, T. F. Soules, J. S.
Stolken
November 2, 2010
SPIE Laser Damage Conference
Boulder, CO, United States
September 26, 2010 through September 29, 2010
Disclaimer 
 
This document was prepared as an account of work sponsored by an agency of the United States 
government. Neither the United States government nor Lawrence Livermore National Security, LLC, 
nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or 
responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or 
process disclosed, or represents that its use would not infringe privately owned rights. Reference herein 
to any specific commercial product, process, or service by trade name, trademark, manufacturer, or 
otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the 
United States government or Lawrence Livermore National Security, LLC. The views and opinions of 
authors expressed herein do not necessarily state or reflect those of the United States government or 
Lawrence Livermore National Security, LLC, and shall not be used for advertising or product 
endorsement purposes. 
 
†This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under
Contract DE-AC52-07NA27344
*feit1@llnl.gov,  phone 925-422-4128
Densification and residual stress induced by CO2 laser-based 
mitigation of SiO2 surfaces†
M.D. Feit*, M.J. Matthews, T.F. Soules, J.S. Stolken, R.M. Vignes, S.T. Yang and J.D. Cooke
Lawrence Livermore National Laboratory, 7000 East Avenue, L-491, Livermore, CA 94551
ABSTRACT  
Knowing the ultimate surface morphology resulting from CO2 laser mitigation of induced laser damage is important both 
for determining adequate treatment protocols, and for preventing deleterious intensification upon subsequent 
illumination of downstream optics. Physical effects such as evaporation, viscous flow and densification can strongly 
affect the final morphology of the treated site.  Evaporation is a strong function of temperature and will play a leading 
role in determining pit shapes when the evaporation rate is large, both because of material loss and redeposition. Viscous 
motion of the hot molten material during heating and cooling can redistribute material due to surface tension gradients 
(Marangoni effect) and vapor recoil pressure effects. Less well known, perhaps, is that silica can densify as a result of 
structural relaxation, to a degree depending on the local thermal history.  The specific volume shrinkage due to structural 
relaxation can be mistaken for material loss due to evaporation. Unlike evaporation, however, local density change can 
be reversed by post annealing.  All of these effects must be taken into account to adequately describe the final 
morphology and optical properties of single and multiple-pass mitigation protocols. We have investigated, 
experimentally and theoretically, the significance of such densification on residual stress and under what circumstances 
it can compete with evaporation in determining the ultimate post treatment surface shape. In general, understanding final 
surface configurations requires taking all these factors including local structural relaxation densification, and therefore 
the thermal history, into account. We find that surface depressions due to densification can dominate surface 
morphology in the non-evaporative regime  when peak temperatures are below 2100K.
Keywords: fused silica, laser damage mitigation, densification, structural relaxation
1. INTRODUCTION
The potential usefulness of the (10.6 µm) CO2 laser for mitigation of the growth of already initiated laser damage in 
silica upon further laser exposure was pointed out by Milam1 et. al. in 1982. Vigorous investigation2 of this approach, 
however, didn’t begin for another 20 years when the need for damage growth mitigation became more evident. Since 
then LLNL, CEA3,4 and other laboratories5 have continued to develop laser based mitigation strategies. It is important to 
control the morphology of the surfaces resulting from such mitigation because mitigated sites modulate the incoming 
laser beam and can potentially cause deleterious downstream intensification. It has been difficult in the past to predict 
and control the final surface morphology both because of the complicated physical processes involved and incomplete 
knowledge of crucial process variables such as surface temperature.  In this paper, after a brief listing of involved 
physical processes, we point out the importance of structural relaxation and the unique properties of fused silica glass in 
contributing to the volume and morphology (and residual stress) of the mitigated material.  Both experimental and 
theoretical advances have led to a better understanding and control of the processes involved.
Historically, two types of motivation have been behind experimental developments for CO2 laser mitigation.  In the first, 
the goal is to remove laser damaged material via evaporation. Since this implies high temperatures, short pulse high peak 
power laser pulses are typically used. In the second type approach, the goal is to heal the damaged material via some 
combination of material flow and thermal annealing. This implies lower temperatures for longer times so typically 
involves longer lower peak power pulses.  In practice, however, it usually has been difficult to make these clear 
distinctions because of the unique properties of fused silica.  In particular, both the viscosity6 and the evaporation7 rate of 
silica vary by many orders of magnitude over the relatively small temperature range of practical interest.with the 
viscosity dropping and the vaporization rate increasing, so  it can be difficult to obtain significant fluid flow without the 
temperature being high enough for evaporation to set in8.
Along with evaporation/recondensation and material flow, surface morphology can also be affected by gradients in 
surface tension (Marangoni effect), by laser heating causing surface dehydration9 which affects density and viscosity, 
and by environmental10 and non-uniform structural changes11,12 due to heating/cooling history (local density and residual 
stress). 
Improvements13 in real time measurements of process temperature made it clear vaporization was unimportant in certain 
processes.  It was the realization that volume losses not due to evaporation could affect the resulting mitigated surface 
morphology (Fig. 1) that indicated the importance of understanding the origin of such effects.
Fig. 1:  (a) Apparent “crater” on surface after low temperature mitigation treatment. (b) Disappearance of “crater” after 
annealing sample in an oven.
We discuss volume loss (densification) effects here. Such densification also results in residual stress. The practical 
importance of choosing cooling programs to reduce such stresses in described14 in an accompanying paper in these 
proceedings.
2. VOLUME CHANGE DUE TO STRUCTURAL RELAXATION
Several causes of densification in fused silica have been noted in the literature ranging from response to large hydrostatic 
pressure to response to long time high energy fluence low pulse energy ultraviolet laser exposure. We consider here the 
effect of structural relaxation accompanying rapid cooling from high temperatures.  Fused silica is a material, like water, 
which can become less dense as it solidifies. The phase diagram (Fig. 2) for low OH content type I and II silicas shows15, 
16that specific volume first decreases and then increases (material becomes less dense) as the temperature is lowered at 
some rate.  At some point, the structure essentially becomes frozen in. This is characterized by the so-called fictive
temperature.  If the glass is cooled faster, a structure corresponding to a higher fictive temperature is frozen in at a 
smaller specific volume (higher density). Thus, the density of the cooled solid material can vary locally depending on the 
cooling history.
Since we now can accurately monitor both the temperature and fictive temperature distributions, it is possible to estimate 
the order of magnitude of the structural relaxation volume change by taking into account the local dilatation due to 
fictive temperature in a procedure analogous to thermoelastic stress theory17. This involves solving the elastic 
equilibrium and stress-strain equations  (Eq. 1 below) for the local displacements using Youngdahl stress functions18. 
When this is done using known physical properties15 and measured fictive temperatures12 for the conditions 
corresponding to Fig. (1), a surface depression of the right order of magnitude is found . This gives confidence that 
structural relaxation is the mechanism involved and the theoretical description can be included in a more comprehensive 
theoretical treatment of the mitigation process.
   
  
 rr  
ETf
1  2

E  rr  zz  
(1  2 )( 1)

 rr E
 1
   
ETf
1  2

E  rr   zz  
(1  2 )(  1)

 E
 1
 zz  
ETf
1  2

E  rr  zz   
(1  2 )( 1)

E zz
 1
  
 rr
r

 rz
z

 rr  
r
 0
 zz
z

 rz
r
 0
Eq.(1): Stress-strain relations (left) and elastic equlibrium conditions (right) in cylindrical coordinates. Here the ’s are 
components of the stress, ’s are components of the strain, E is Young’s modulus,  is Poisson’s ratio. The quantity ΔTf
is the change in fictive temperature from that at infinity and γ is a measured16 coefficient that  relates fictive temperature 
to dilation.
Such a comprehensive theoretical numerical description has been assembled including effects of temperature dependent 
properties such as thermal conductivity, viscoelastic relaxation, surface tension, and structural relaxation. Initial 
simulations show a complex interaction of the various physical processes. For example, Fig. 3 shows the effect of 
including or not including structural and viscous relaxation in modeling a low temperature mitigation site.  Such 
simulations are beginning to capture some of the complex observed site morphologies.  Fig. 4 shows experimental type 
III site profiles resulting from identical heating, but different linear ramp down cooling profiles. The more gradual the 
cooling, the smaller the apparent volume change.  Corresponding simulations using type II properties are qualitatively 
similar (Fig. 4b).
Fig. 2: Specific volume vs. temperature for low OH silicas 
from Brueckner15. Higher cooling rates lead to higher 
fictive temperature and higher ultimate density glass. 
Higher OH content type III silica has a shallower 
minimum and dependence of solid thermal expansion rate 
on fictive temperature.
Fig. 3: Simulated final low temperature type II mitigated 
silica surface profiles with and without structural 
relaxation. Inclusion or exclusion of structural relaxation, 
i.e. densification, changes the qualitative shape of the 
surface. This effect is most important when evaporation is 
insignificant, i.e. at low peak temperatures.
The experimental volume losses for high OH content silica shown in Fig. (4a) decrease dramatically as the cooling rate 
is slowed. This is shown quantitatively in Fig. 5 where volume loss is plotted as a function of the ramp down time. The 
volume loss is considerably larger for no ramp down, i.e. quenching. Simulations for low OH content silica shown in 
Fig.(4b) show the same trend.
Fig. 4: (a) Experimental type III site profiles in which laser power is held for 10 sec and then ramped down over 1-100 
sec. (b) Simulated type II site comparing effects of 1 sec and 10 sec ramp down in temperature.
Fig. 6 shows experimental and simulated volume losses as a function of achieved surface temperature as the laser power 
of a 400 µm beam is varied from 1.6 to 2.8 W. The theoretical curves assume activation energies of 4.5 eV for viscosity 
and 3.6 eV for evaporation. These activation energies were best estimates taken from the literature. The evident change 
in slope near 2100K indicates a changeover from structural relaxation to evaporation as the dominant mechanism 
determining volume change.
Fig. 5: Experimentally determined volume loss at surface 
as a function of cool down ramp time. The volume loss 
for quenched cooling is much larger.
Fig. 6: Comparison of experimental (points) and theoretical 
(curves) as a function of surface temperature. Only the 
incident laser power is varied in the experiment. 
Theoretical curves were calculated by a coupled thermo-
mechanical finite element model including only  structural 
relaxation or evaporative volume losses, respectively .The 
sudden increase in slope indicates the onset of evaporation.
3. SUMMARY
The surface morphology of CO2 laser mitigated fused silica sites reflects both the complex physical properties of silica 
glass and the strong temporal and spatial variations of heating and cooling during processing. While evaporation is the 
dominant volume loss mechanism at high temperatures, densification due to structural relaxation plays a significant role 
at lower temperatures and high cooling rates. The relative importance of highly temperature dependent properties such as 
viscosity (viscous flow), evaporation and densification varies with process variables.  Improved experimental diagnostics 
and measurements along with more comprehensive theoretical models are leading to improved understanding that will 
aid in designing mitigation protocols that result in desired morphologies.
                                               
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Densification and residual stress induced by CO2 laserbased mitigation of SiO2 surfaces

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Densification and residual stress induced by CO2 laserbased mitigation of SiO2 surfaces

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