MoIecuIar Dynamics AnaIysis of the Effect of Laser and Defects on the Micro-Structure of Fused SiIica

Li Li | Ming-Wen Zhang | Zhe-Zhen Zhao

Abstract—In this work,the classic molecular dynamics simulations are employed to investigate the atomic structural modification of fused silica with defects as laser irradiation.The dynamics evolution of the atomic structure of fused silica is modeled during energy deposition.The structure parameters such as pair distribution functions (PDFs),bond angle distributions (BADs),and the coordination number are given.The calculated results reveal that fused silica undergoes significant changes in terms of Si-O,Si-Si,and O-O bond lengths,Si-O-Si and O-Si-O bond angles,and the Si and O coordination numbers during laser irradiation.The effects of different surface defects on the microstructure of fused silica are discussed too.The simulation results of molecular dynamics may help to understand the role of defects in the radiation effect of fused silica.

1.Introduction

The design of high power laser facility,such as National Ignition Facility (NIF) in the USA,is constrained by the laser damage initiation and laser damage growth in the delivery optics,usually the fused silica lens[1]-[4].According to the research of past years,it is believed that one key factor influencing the damage threshold is the subsurface defect[5],[6].As laser irradiates fused silica,the laser energy is absorbed by electrons firstly,then the electrons may transfer to the conduction band from the valence band for short pulsed laser (shorter than 10 ps) or deliver energy to the lattice by collision with atoms (longer than 10 ps)[7]-[10].These result in the change of physical properties of fused silica.The pure fused silica has excellent light transmission for visible,infrared,or ultra-violet laser.The intrinsic damage threshold of pure fused silica is very high according to the theoretical calculation,for example,it is more than 100 J/cm2for 355 nm,3 ns laser[11].However,once defects appear,some positions in fused silica are easy to be developed to the damage precursors,resulting in irreversible modifications in the structural and physical properties and a lower laser induced damage threshold (LIDT) (5 J/cm2to 6 J/cm2for 355 nm laser)[12]-[15].

There are a lot of reports about the interaction of laser and fused silica with defects.Laurenceet al.experimentally investigated the distribution of laser damage precursors on fused silica surfaces for 351 nm,3 ns laser pulses at high fluency[16].Zoubiret al.studied the photo structural defects on silica resulting from exposure to intense near-infrared femtosecond radiation[17].Liet al.studied the effect of cracks and scratches on the silica surface on the laser damage threshold experimentally[18].Liet al.studied the incident laser electrical field modulation of a repaired damage site with a rim in the fused silica rear subsurface using the three dimensional finite difference time domain method[19].These above studies mainly focus on the macroscopic properties of fused silica.Sen and Dickinson investigated femtosecond laser pulses induced microscopic structural changes in smooth silica glass using ab initio molecular dynamics simulation methods[20].Suet al.studied the shock response and surface ejection behaviors of fused silica using the equilibrium molecular dynamics method[21].The effect of impurities on the microscopic structure of fused silica has been studied by us by the first-principles method[22].However,few researchers discuss the effect of subsurface defects on the microscopic structure of fused silica in detail as laser irradiation.The shortage of the first-principles method is that the number of atoms of the simulated structure is very small (＜200 atoms) for present computational ability.So the classic molecular dynamics method is chosen in this work to simulate the evolution of the microscopic structure of fused silica with defects as laser irradiation.

In this work,the evolution of the microscopic structure of fused silica with different defects is investigated by molecular dynamics simulations.The effects of laser irradiation on bond lengths (Si-O,Si-Si,and O-O),bond angles(Si-O-Si and O-Si-O),and the coordination numbers of the atoms are explored,which are the basic parameters to describe the fused silica microscopic structure.At the same time,the effect of the defect type on the microscopic structure of fused silica is studied too.Simulations in the present study are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) molecular dynamics parallel code with ReaxFFSio potential which is proven to be successful in describing the structures and energy of silicon and its various polymorphs[23],[24].

2.MateriaI and Methods

2.1.Construction of Fused SiIica Structure

The production of fused silica is under the canonical ensembles (constant NVT) system in 2 fs.The memory effect of the initial configuration has been considered.So the system was first heated up to 6000 K in 40000 steps,and in another 285000 steps it was cooled down to 300 K gradually.Further equilibration at 300 K was conducted for another 40000 steps[25].

As can be seen from the bond angle distribution (BAD) shown in Fig.1,the peaks of the bond anglesθO-Si-OandθSi-O-Siare located at 110.01° and 150.15°,respectively,which are close to the experimental data (108° forθSi-O-Siand 147° forθO-Si-O)[10],[21].From the radial functions shown in Fig.2,the bond lengths of three types (Si-Si,Si-O,and O-O) are in good consistence with the experimental data (rSi-Si=3.12 ?,rSi-O=1.61 ?,andrO-O=2.63 ?)[26].In addition,the coordination numbers of Si and O atoms are 4 and 2,respectively according to our simulated results.So all the above data have shown that the structure of fused silica is reasonable.

Fig.1.BADs of the defect free structure:(a) O-Si-O and (b) Si-O-Si.

Fig.2.Pair distribution functions (PDFs) of the defect free structure:(a) Si-Si,(b) Si-O,and (c) O-O.

2.2.Fused SiIica Structure with Defects

For the fused silica lens,surface LIDT is much lower as compared with bulk LIDT[18].During the manufacture,many tiny cracks invisible to naked eyes and extrinsic impurities may be contained in the surface layer[27].Experiments and theory have proven that these defects in the surface could lower LIDT of fused silica[28]-[30].In this work,four types of cracks were considered:Cubic shape,cone shape,hemispherical shape,and cylindrical shape.

2.3.Method of Laser Introduction

From a microscopic perspective,the laser irradiation process can be considered as the transfer of energy from photons to material atoms,which causes the change of kinetic or potential energy of the atoms in the material[31],[32].When we study the interaction of fused silica and laser by molecular dynamics methods,photons cannot be introduced directly.But the atomic kinetic energy can be increased by heating,to simulate the introduction of photons during laser irradiation.

3.ResuIts and Discussion

3.1.InfIuence of Laser Irradiation on Pure Fused SiIica Structure

The atomic structure of fused silica (including 12288 atoms) is shown in Fig.3 (a),which is constructed by the method described in subsection 2.1.The irradiation area is supposed as a rectangle shown in Fig.3 (b).

During calculations,fused silica was heated up by laser irradiation for 20000 steps.The time step is 0.35 fs,the heat flue is 100 kcal,and the heating frequency is 100 Hz.During the simulation,BADs of Si-O-Si and O-Si-O were calculated,as shown in Fig.4.It is noticed that the trends of BADs before and after heating in Fig.4 are almost the same.The peak of the Si-O-Si bond angle is at about 150° and that of O-Si-O is at about 109°.That is to say,the applied laser energy does not destroy the stable structure formed by the covalent bond of its internal structure.However,the percentages of the Si-O-Si band angle which is 150° and the O-Si-O band angle which is 109°increase remarkably,after heating.The reason can be explained that the laser energy promotes the thermal motion of the internal atoms,making the fused silica structure more ideal[27],[29].

Fig.5 shows the changes of the bond length distributions.Clearly,all the distributions of the three bond lengths are influenced by irradiation.The impact of laser irradiation is that the peaks of the bond lengths are all marginally increased while the fused silica microscopic structure is stable.This result is also due to the enhanced thermal motion of the internal atoms by the laser energy,the same as that of Fig.4.

Fig.3.Fused silica structure:(a) microscopic model and (b) sketch map of the laser irradiation area.

Fig.4.BADs before and after heating:(a) Si-O-Si and (b) O-Si-O.

Fig.5.Bond length distributions before and after heating:(a) Si-O,(b) O-O,and (c) Si-Si.

The effect of laser irradiation on the Si and O coordination numbers is also studied and the results are shown in Fig.6.The coordination numbers kept the same under laser radiation.Though the inter-atomic thermal motion in fused silica was aggravated under laser irradiation,the net structure of fused silica was not changed in the radiation condition of this work.

Fig.6.Coordination numbers before and after heating:(a) Si and (b) O.

3.2.InfIuence of Defects on Micro-Structure of Fused SiIica

3.2.1.Hemisphere Defect

In this section,the hemisphere defect is taken as an example to study the effect of defects on the fused silica micro-structure as laser irradiation.During the simulation,seven sizes of hemisphere defects are chosen includingr=0,r=4 ?,r=8 ?,r=12 ?,r=16 ?,r=20 ?,andr=24 ?,respectively,whereris the radius of the hemisphere defect.

The initial temperature of fused silica is 300 K and the laser frequency is 100 Hz.Fig.7 shows BADs of fused silica with different sizes of hemisphere defects after laser irradiation.

Fig.7.BADs of fused silica with different hemisphere defects:(a) O-Si-O and (b) Si-O-Si.

From Fig.7,it can be seen that,BADs of O-Si-O are symmetric with the peak position around 109° while Si-O-Si BADs are ranging from 120° to 180° with the peak position around 155°[29].It also can be observed,the percentages of the peaks of the O-Si-O and Si-O-Si bond angles increase with the increase of the defect area after laser irradiation.Obviously,the increase of the defect area indicates more broken Si-O-Si and O-Si-O bonds appeared.With the increase of the defect area,the number of fused silica atoms decreases and the structure becomes steadier and more perfect under the same irradiated laser energy.

Fig.8 shows the distributions of Si-Si,O-O,and Si-O bond lengths of fused silica with different hemisphere defect areas.The evolution of the maximum percentages of Si-Si,O-O,and Si-O bond lengths with the defect area is shown in Fig.8.From Fig.8,it can be seen that the evolution of the maximum percentage of the Si-Si bond length decreases monotonically with the defect area,which indicates that the distribution of the Si-Si bond length becomes disperse with the increase of the defect area.It also can be observed from Fig.8 that the Si-O and O-O bond lengths remain unchangeable firstly and then increase while the Si-Si bond length decreases immediately with the increase of the defect area.It can be explained that the Si-Si bond is the easiest to change because the Si-Si bond length is the longest one and the bond energy is the minimum.It is difficult for the Si-O and O-O bonds to change since the Si-O bond length is 1.62 ? and the O-O bond length is 2.65 ?,which are shorter than that of the Si-Si bond length (3.12 ?).

Fig.8.Bond length distributions of (a) and (b) Si-Si,(c) and (d) O-O,and (e) and (f) Si-O.

Fig.9 reveals that the coordination numbers of Si and O decrease with the increased area of the hemisphere defect.The coordination number of Si shows a greater variation than that of O,which can be attributed to the more active outer electron of Si.

Fig.9.Coordination numbers of (a) Si and (b) O.

3.2.2.Comparison of the Effects of Different Surface Defects

Next,the effects of four different defect types (cubic,cone,sphere,and cylinder) on the micro-structure of fused silica are discussed.The irradiation laser parameters are the same.The height of each surface defect ish=16.6 ?.The radii of cone,hemisphere,and cylinder defects are all 24 ?.The side length of the cubic defect in thexoy-plane is also 24 ?.The distributions of Si-O-Si and O-Si-O bond angles are shown in Fig.10.

Fig.10.BADs with different surface defects:(a) O-Si-O and (b) Si-O-Si.

From Fig.10,for each defect type,the evolution trends of the bond angles are almost similar.However,the peaks of Si-O-Si and O-Si-O bond distributions curves with the cone defect is the highest than those of the other three defects.It can be deduced that the fused silica structure with the cone effect is the steadiest one as the depths and widths of the four type defects are the same.The reason can be given by that the atom number of the structure with the cone defect is the least apparently since the sizes of these defects are the same.

From Fig.11,the coordination numbers of Si4+and O2-of fused silica with the cone defect are the highest than the other three defect structures.It indicates that after laser irradiation,the fused silica micro-structure with the cone defect is the most stable one.

Fig.11.Coordination numbers with different surface defects:(a) Si and (b) O.

4.ConcIusions

In this work,the effect of laser irradiation on the pure fused silica micro-structure was discussed firstly.The results show that the trends of the Si-O-Si and O-Si-O bond angles and all the bond length distributions of the pure fused silica structure after irradiation are almost as same as those before irradiation.The increase of the peak percentages of the Si-O-Si and O-Si-O bond angles and all the bond lengths indicates that the fused silica microscopic structure becomes more stable by irradiation.With the hemisphere defect,the influence of the defect area was then investigated,showing that a larger defect area results in a steadier micro-structure of fused silica.And among all the bonds,Si-Si is the easiest one to change.Different defects were also simulated to explore their effects on the micro-structure.By providing the atomic level details of laser-induced structural response,we hope the simulation results obtained in this paper may contribute to understanding the role of defects played in the radiation effects on fused silica.