OSA's Digital Library

Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 8, Iss. 11 — May. 21, 2001
  • pp: 611–616
« Show journal navigation

Densification of fused silica due to shock waves and its implications for 351 nm laser induced damage

A. Kubota, M.-J. Caturla, J. S. Stölken, and M. D. Feit  »View Author Affiliations


Optics Express, Vol. 8, Issue 11, pp. 611-616 (2001)
http://dx.doi.org/10.1364/OE.8.000611


View Full Text Article

Acrobat PDF (254 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

High-power 351 nm (3ω) laser pulses can produce damaged areas in high quality fused silica optics. Recent experiments have shown the presence of a densified layer at the bottom of damage initiation craters. We have studied the propagation of shock waves through fused silica using large-scale atomistic simulations since such shocks are expected to accompany laser energy deposition. These simulations show that the shocks induce structural transformations in the material that persist long after the shock has dissipated. Values of densification and thickness of densified layer agree with experimental observations. Moreover, our simulations give an atomistic description of the structural changes in the material due to shock waves and their relation to Raman spectra measurements.

© Optical Society of America

1. Introduction

Recent experiments by Wong et al [6

6. J. Wong, D. Haupt, J.H. Kinney, M. Stevens-Kalceft, A. Stesmans, and J. Ferreira, “Morphology, microstructure and defects in fused silica induced by high power 3ω (355 nm) laser pulses,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

] on damage sites have explored the morphology of the craters formed under laser fluence. These damage sites consist of a melted center region surrounded by fractured material. X-ray tomography of these damage sites has identified a layer of ~10 microns thick at the bottom of the crater that is 20% higher in density than the original silica. Moreover, Raman spectra taken at the damage sites have also shown an enhancement in the so-called D1 and D2 lines [7

7. S. G. Demos, L. Sheehan, and M. R. Kozlowski, “Spectroscopic investigation of SiO2 surfaces of optical materials for high power lasers,” in Laser applications in microelectronic and optoelectronic applications V, Proc. SPIE 3933, 316–320 (2000)

]. Enhancement of the D1 and D2 lines has also been observed in silica under shock compression [8

8. H. Sugiura, R. Ikeda, K. Kondo, and T. Yamadaya, “Densified silica glass after shock compression,” J. Appl. Phys. 81, 1651–1655 (1997). [CrossRef]

]. In this case the intensity of the Raman lines increases as the shock pressure increases. In these experiments increases in density up to ~10% have been measured. These values of density are lower than those observed under static compression.

The presence of the D1 and D2 lines in the Raman spectra has been associated with the existence of small rings in the silica structure. Six-silicon-member rings are the most frequent ones in amorphous SiO2. Electronic structure calculations performed by Pasquarello and Car [9

9. A. Pasquarello and R. Car, “Identification of Raman defect lines as signatures of ring structures in vitreous silica,” Phys. Rev. Letters , 80, 5145–5147 (1993). [CrossRef]

] have demonstrated that rings of size 3 and 4 are Raman active, and responsible for the appearance of these D1 and D2 lines.

We have performed molecular dynamics simulations of shock propagation in silica glass intended to aid understanding of the processes occurring in the material due to shock propagation accompanying laser energy absorption. We investigate the consequences for surrounding material in terms of changes in structure and density, and predict the response of this material under conditions that are difficult to obtain experimentally due to short time pulses and rapid changes in pressure, temperature and density.

2. Simulation model and sample characteristics

The interatomic potential used is that developed by Feuston and Garofalini [10

10. B. P. Feuston and S. H. Garofalini, “Empirical three-body potential for vitreous silica,” J. Chem. Phys. 89, 5818–5818 (1999). [CrossRef]

] This potential includes two-body and three-body terms to account for the ionic and covalent components of the Si-O bonds in SiO2. This potential was fitted to reproduce the measured neutron diffraction spectra of silica glass under normal conditions of pressure and temperature. This interatomic potential has been used previously by other authors to study densification [11

11. E. M. Vogel, M. H. Grabow, and S. W. Martin, “Role of silica densification in the performance of optical connectors”, J. of Non-Crystalline solids 204, 95–98 (1996) [CrossRef]

].

Our simulated amorphous silica (a-SiO2), starts from β-cristobalite. The dimensions of the initial simulation box are 71.6×71.6×716.0 Å. The total number of atoms in the simulation is 240,000. The system is melted at high temperature (7000K) using periodic boundary conditions for 25 ps. Then it is quenched to room temperature by a series of steps: from 6000K to 1000K, decreasing the temperature 1000K and relaxing at each intermediate step for 25 ps. Finally the temperature is decreased to 300K and relaxed for another 25ps. At 300K, a free surface is created along the shortest sides of the sample while periodic boundary conditions are used along the other two sides. Figure 1 shows the final simulation cell. The coordination of the silicon atoms is represented in this figure as gray tetrahedral. Yellow and green tetrahedra represent the 3-fold and 5-fold coordinated atoms respectively.

Fig. 1: Initial simulation set up. Colors represent coordination of silicon atoms, with grey being 4-fold corrdinated and yellow are 3-fold coordinated Si atoms.

Using this initial sample, we study the propagation of shock waves through the material over a range of different velocities. In order to generate the shock wave we select a set of atoms at one of the free surfaces and apply a velocity to them throughout the simulation. This set of atoms will correspond to a piston traveling at a fixed velocity, Up. This method has been applied by other authors to study shock propagation through crystalline materials [13

13. A. B. Belonoshko, “Atomistic simulation of shock wave-induced melting in Argon,” Science , 275, 955–957 (1997) [CrossRef] [PubMed]

, 14

14. D. H. Robertson, J.J. C. Barrett, M. L. Elert, and C. T. White, “Self-similar behavior from molecular dynamics simulations of detonations,” Shock Compression of Condensed Matter, 297–300 (1998)

].

2. Results

The shock wave velocities were extracted from the velocity profiles of the atoms as a function of depth for different times. Figure 2 shows a set of velocity profiles for the cases of piston velocities of (a) 0.75 km/s and (b) 2.5km/s at different times. Observe that for intermediate times the shape of the profile does not change in time, indicating a stable shock wave front. Only at long times, when the wave reaches the surface and bounces back (reflection we see a change in the shape of the profile due to the superposition of the two waves. In order to extract the shock velocities we have computed differences between velocity profiles at different times corresponding to a value of half of the maximum particle velocity.

The values of shock wave velocities obtained from these simulations are plotted in Figure 3. We present the results of two different system sizes, one with 240,000 atoms (squares) and another one with only 96,000 atoms (filled circles), in order to check the dependence on the size of the simulation. No significant differences in the computed shock velocities were observed as a function of system size, as can be seen in Figure 3. The results of these simulations show two different regimes in the shock wave velocities. At the low piston velocities the elastic region is observed, where the shock velocities are constant with particle velocity. At about 1km/s there is a sharp decrease in shock velocity and the start of densification regime, with increasing shock velocity as the particle velocity increases.

Fig. 2: Velocity profiles for (a) 0.75 km/s and (b) 2.5 km/s pistons at different times.

In Figure 3 we also present the experimental results measured by Sugiura et al [3

3. H. Sugiura, K. Kondo, and A. Sawaoka, “Dynamic response of fused quartz in the permanent densification region,” J. Appl. Phys. 52, 3375–3382 (1981). [CrossRef]

] in their flyer plate experiments. Our simulations are able to reproduce the transition from the elastic limit, and the agreement with the shock velocities in the densified region is remarkable. However, we are not able to reproduce the anomalous behavior observed experimentally in the elastic limit, where there is a slight increase in shock velocity as a function of particle velocity, and the measured values are below the sound velocity in silica glass.

Fig. 3: Velocities of shock waves as a function of piston velocity for two simulations (squares and filled circles) and experimental measurements (triangles)

In order to understand the structural changes occurring in the material at particle velocities between 1 km/s and 2 km/s, we have performed a detailed study of the coordination of silicon atoms and the evolution of ring distribution as the shock propagates through the material. This analysis shows that the density of five-fold coordinated silicon atoms increases dramatically in the densified silica. For the case of a 2.5 km/s shock values up to ~4.9% of 5-fold coordinated atoms are present during the first few picoseconds of shock propagation and ~1.2 % of 3-fold coordinated silicon atoms, representing 3,500% and 600% increase in concentration, respectively. Figure 4(a) shows the simulation cell after propagation of the shock wave. Observe the increase in over-coordinated silicon atoms (green) as compared to the initial lattice in Figure 1.

Our simulations show that the shocked material undergoes structural changes from the normally predominant 5–6 member ring distribution. After the shock, both the number of 3–4 member rings and the number of 7–10 member rings increase as shown in Figure 5. The small rings are more stressed than the normal structure and more prone to failure. These 3- and 4- fold rings not only have the property of being detected by Raman Spectroscopy [9

9. A. Pasquarello and R. Car, “Identification of Raman defect lines as signatures of ring structures in vitreous silica,” Phys. Rev. Letters , 80, 5145–5147 (1993). [CrossRef]

] but they also have reduced energy barriers to ring-breaking [15

15. J. K. West and L. L. Hench, “Molecular orbital models of silica rings and their vibrational spectra,” J. of the American Ceramic Society , 78, 1093–1096 (1994). [CrossRef]

] especially in the presence of gases (O2, N2). The larger rings represent the effect of already broken bonds. This is a type of “failed material” as has been seen in flyer plate experiments on fused silica [16

16. R. Feng, “Formation and propagation of failure in shocked glasses,” J. Appl. Phys. 87, 1693–1700 (2000) [CrossRef]

]. These larger rings may be considered microcrack precursors, i.e. broken bonds, which can coalesce into voids. Immediately behind the propagating shock, densification up to 60% is observed for the strongest shocks simulated.

Fig.4: Simulation (a) after shock, and (b) after relaxation showing the coordination of Si atoms. Gray are 4-fold coordinated, yellow 3-fold and green 5-fold. Movie of (a) (0.7Mb).

In order to study the type and degree of material modification that persist long after the shock wave has passed we performed relaxation simulations of the shocked glass. This relaxation consisted on the extraction of the extra heat deposited by the shock in the material, and cooling of the configuration down to room temperature. During this relaxation the number of five-fold and three-fold coordinated silicon atoms decreases dramatically, ending up with a total of only 1.7 % of 5-fold coordinated and 0.2 % of 3-fold coordinated atoms. This still represents a significant increase (1,200 %) in the concentration of 5-fold coordinated silicon atoms over the initial value. Most of the relaxation happens quickly and the number of defects reaches a saturation value during the time scale of the simulation (33ps). Therefore we do not expect any significant changes for longer times.

Fig. 5: Ring size statistics before and after shock

Interestingly, the ring distribution after the relaxation does not show such a significant recovery. In Figure 6 we show the initial (a), after shock (b) and final (c) configurations. In this case we represent only those rings of size 3 and 4 (dark rings) and those 10 or larger (yellow rings). Observe that there is no significant change in the number of these small and large rings after relaxation. This is also clear from Figure 5, where we show the ring distribution before the shock, after the shock and after relaxation. In fact, during relaxation the number of large member rings seems to grow even more, while there is a slight decrease in the number of 3 and 4 member rings.

After relaxation some degree of densification persists. For example, in the case of a 2.5km/s shock the final density is ~20%. This densification value is in agreement with those measured experimentally under shock compression [3

3. H. Sugiura, K. Kondo, and A. Sawaoka, “Dynamic response of fused quartz in the permanent densification region,” J. Appl. Phys. 52, 3375–3382 (1981). [CrossRef]

].

4. Discussion

The thickness of the densified layer obtained from these simulations is ~300 Å, for a shock pulse of 10ps. Assuming that the thickness of the densified layer scales linearly with the duration of the shock, we can extrapolate our results to a shock pulse of 3 ns, such as those in 3ω laser damage conditions of [6

6. J. Wong, D. Haupt, J.H. Kinney, M. Stevens-Kalceft, A. Stesmans, and J. Ferreira, “Morphology, microstructure and defects in fused silica induced by high power 3ω (355 nm) laser pulses,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

]. With this assumption our model predicts a densified layer of 9 microns, in good agreement with the measured 10 micron thick densified layer at the bottom of craters generated by laser irradiation. Moreover, the degree of densification is also in good agreement with recent experiments by Wong et al [6

6. J. Wong, D. Haupt, J.H. Kinney, M. Stevens-Kalceft, A. Stesmans, and J. Ferreira, “Morphology, microstructure and defects in fused silica induced by high power 3ω (355 nm) laser pulses,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

].

Our simulations also explain the presence of D1 and D2 lines in the Raman spectra by the formation of small rings that persist long after the shock (see Fig. 6). All this evidence strongly supports the hypothesis of strong shocks generated during the 3ω laser irradiation [6

6. J. Wong, D. Haupt, J.H. Kinney, M. Stevens-Kalceft, A. Stesmans, and J. Ferreira, “Morphology, microstructure and defects in fused silica induced by high power 3ω (355 nm) laser pulses,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

].

Fig. 6: Simulation (a) before, (b) after shock and (c) after relaxation showing rings of sizes 3 and 4 in magenta and the rings of size 10 and larger in yellow. Movie for shock propagation, (a) to (b) (0.7 Mb)

5. Conclusions

Acknowledgments

We gratefully acknowledge helpful discussions with Dr. J. Wong, Dr. A.M. Rubenchik, Prof. S. Garofalini and Dr. Diaz de la Rubia. This work was supported by the National Ignition Facility project at LLNL. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

References and Links

1.

W. Primak and R. Kampwirth, “The radiation compaction of vitreous silica,” J.Appl.Phys. 39,5651–5658 (1968) [CrossRef]

2.

C. Meade, R. J. Hemley, and H. K. Mao, “High-pressure X-Ray diffraction of SiO2 glass,” Phys. Rev. Lett. 69, 1387–1390 (1992) [CrossRef] [PubMed]

3.

H. Sugiura, K. Kondo, and A. Sawaoka, “Dynamic response of fused quartz in the permanent densification region,” J. Appl. Phys. 52, 3375–3382 (1981). [CrossRef]

4.

M. D. Feit, L. W. Hrubesh, A. M. Rubenchik, and J. Wong, “Scaling relations for laser damage initiation craters,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

5.

M. Runkel, A. Burnham, D. Milam, W. Sell, M. D. Feit, A. M. Rubenchik, R. Fluck, and P. Wegner, “Results of pulse-scaling experiments on rapid-growth DKDP triplers using the Optical Sciences Laser at 351 nm,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

6.

J. Wong, D. Haupt, J.H. Kinney, M. Stevens-Kalceft, A. Stesmans, and J. Ferreira, “Morphology, microstructure and defects in fused silica induced by high power 3ω (355 nm) laser pulses,” in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)

7.

S. G. Demos, L. Sheehan, and M. R. Kozlowski, “Spectroscopic investigation of SiO2 surfaces of optical materials for high power lasers,” in Laser applications in microelectronic and optoelectronic applications V, Proc. SPIE 3933, 316–320 (2000)

8.

H. Sugiura, R. Ikeda, K. Kondo, and T. Yamadaya, “Densified silica glass after shock compression,” J. Appl. Phys. 81, 1651–1655 (1997). [CrossRef]

9.

A. Pasquarello and R. Car, “Identification of Raman defect lines as signatures of ring structures in vitreous silica,” Phys. Rev. Letters , 80, 5145–5147 (1993). [CrossRef]

10.

B. P. Feuston and S. H. Garofalini, “Empirical three-body potential for vitreous silica,” J. Chem. Phys. 89, 5818–5818 (1999). [CrossRef]

11.

E. M. Vogel, M. H. Grabow, and S. W. Martin, “Role of silica densification in the performance of optical connectors”, J. of Non-Crystalline solids 204, 95–98 (1996) [CrossRef]

12.

L. Mozzi and B. E. Warren, “The structure of vitreous silica,” J. Appl. Crystl. 2, 164–168 (1969) [CrossRef]

13.

A. B. Belonoshko, “Atomistic simulation of shock wave-induced melting in Argon,” Science , 275, 955–957 (1997) [CrossRef] [PubMed]

14.

D. H. Robertson, J.J. C. Barrett, M. L. Elert, and C. T. White, “Self-similar behavior from molecular dynamics simulations of detonations,” Shock Compression of Condensed Matter, 297–300 (1998)

15.

J. K. West and L. L. Hench, “Molecular orbital models of silica rings and their vibrational spectra,” J. of the American Ceramic Society , 78, 1093–1096 (1994). [CrossRef]

16.

R. Feng, “Formation and propagation of failure in shocked glasses,” J. Appl. Phys. 87, 1693–1700 (2000) [CrossRef]

OCIS Codes
(140.3330) Lasers and laser optics : Laser damage
(160.6030) Materials : Silica

ToC Category:
Research Papers

History
Original Manuscript: April 13, 2001
Published: May 21, 2001

Citation
A. Kubota, M. -J. Caturla, J. Stolken, and Michael Feit, "Densification of fused silica due to shock waves and its implications for 351 nm laser induced damage," Opt. Express 8, 611-616 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-11-611


Sort:  Journal  |  Reset  

References

  1. W. Primak, R. Kampwirth, "The radiation compaction of vitreous silica," J. Appl. Phys. 39, 5651-5658 (1968) [CrossRef]
  2. C. Meade, R. J. Hemley, H. K. Mao, "High-pressure X-Ray diffraction of SiO2 glass," Phys. Rev. Lett. 69, 1387-1390 (1992) [CrossRef] [PubMed]
  3. H. Sugiura, K. Kondo, A. Sawaoka, "Dynamic response of fused quartz in the permanent densification region," J. Appl. Phys. 52, 3375-3382 (1981). [CrossRef]
  4. M. D. Feit , L. W. Hrubesh, A. M. Rubenchik, J. Wong, "Scaling relations for laser damage initiation craters," in Laser-Induced Damage in Optical Materials Proc. SPIE (in press )
  5. M. Runkel, A. Burnham, D. Milam, W. Sell, M. D. Feit, A. M. Rubenchik, R. Fluck, P. Wegner, "Results of pulse-scaling experiments on rapid-growth DKDP triplers using the Optical Sciences Laser at 351 nm," in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)
  6. J. Wong, D. Haupt, J.H. Kinney, M. Stevens-Kalceft, A. Stesmans, J. Ferreira, "Morphology, microstructure and defects in fused silica induced by high power 3 (355 nm) laser pulses," in Laser-Induced Damage in Optical Materials Proc. SPIE (in press)
  7. S. G. Demos, L. Sheehan, M. R. Kozlowski, "Spectroscopic investigation of SiO2 surfaces of optical materials for high power lasers," in Laser applications in microelectronic and optoelectronic applications V, Proc. SPIE 3933, 316-320 (2000)
  8. H. Sugiura, R. Ikeda, K. Kondo, T. Yamadaya, "Densified silica glass after shock compression," J. Appl. Phys. 81, 1651-1655 (1997). [CrossRef]
  9. A. Pasquarello and R. Car, "Identification of Raman defect lines as signatures of ring structures in vitreous silica," Phys. Rev. Lett. 80, 5145-5147 (1993). [CrossRef]
  10. B. P. Feuston, S. H. Garofalini, "Empirical three-body potential for vitreous silica," J. Chem. Phys. 89, 5818-5818 (1999). [CrossRef]
  11. E. M. Vogel, M. H. Grabow, S. W. Martin, "Role of silica densification in the performance of optical connectors", J. of Non-Crystalline solids 204, 95-98 (1996) [CrossRef]
  12. L. Mozzi, B. E. Warren, "The structure of vitreous silica," J. Appl. Crystl. 2, 164-168 (1969) [CrossRef]
  13. A. B. Belonoshko, "Atomistic simulation of shock wave-induced melting in Argon," Science 275, 955-957 (1997) [CrossRef] [PubMed]
  14. D. H. Robertson, J.J. C. Barrett, M. L. Elert, C. T. White, "Self-similar behavior from molecular dynamics simulations of detonations," Shock Compression of Condensed Matter, 297-300 (1998)
  15. J. K. West and L. L. Hench, "Molecular orbital models of silica rings and their vibrational spectra," J. Am. Ceramic Soc. 78, 1093-1096 (1994). [CrossRef]
  16. R. Feng, "Formation and propagation of failure in shocked glasses," J. Appl. Phys. 87, 1693-1700 (2000). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: MOV (676 KB)     
» Media 2: MOV (670 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited