Defect-mediated self-diffusion in calcium aluminosilicate glasses: A molecular modeling study

Journal of Non-Crystalline Solids 357 (2011) 1780–1786

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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l

Defect-mediated self-diffusion in calcium aluminosilicate glasses: A molecular modeling study Adama Tandia, Nikolay T. Timofeev, John C. Mauro ⁎, K. Deenamma Vargheese Science and Technology Division, Corning Incorporated, Corning, NY 14831, USA

a r t i c l e

i n f o

Article history: Received 15 November 2010 Received in revised form 17 December 2010 Available online 4 March 2011 Keywords: Glass; Diffusion; Modeling; Defects; Molecular dynamics

a b s t r a c t The mechanism of self-diffusion in calcium aluminosilicate glasses is investigated at the atomistic level using molecular dynamics (MD) simulations. We study nine glass compositions having the fixed ratio R = [CaO]/ [Al2O3] = 1 and the concentration of SiO2 varied from 11.8 to 76.5 mol%. The diffusion coefficient is calculated for each composition at different temperatures from 300 to 6000 K in steps of 300 K. The self-diffusivities of the various elements are found to be close to each other in magnitude, signifying the cooperative nature of the atomic movement. Network “defects” such as miscoordinated cations, non-bridging oxygen, and oxygen triclusters are also studied as a function of temperature and composition. We find that the behavior of selfdiffusion correlates well with the concentration of network defects. A model of self-diffusion in calcium aluminosilicate glasses is proposed where diffusion is considered as a defect-mediated process resulting from bond-switching reactions at high temperature. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Understanding the mechanisms of self-diffusivity in glasses is of considerable scientific and technological interest [1–4]. Here the term “self-diffusivity” refers to the mobility of cations and anions when no chemical gradients are present. The self-diffusivity of glasses and melts is commonly described in terms of the mobility of network defects, i.e., correlating with the degree of network polymerization [5]. Network polymerization is conventionally expressed in terms of the average number of nonbridging oxygen atoms (NBOs) per tetrahedrally coordinated network-forming cation. It was shown in Ref. [5] that an increase of the self-diffusivity of oxygen atoms results from an increase in the proportion of 5-coordinated Si (SiV) and Al (AlV) intermediate species in molten aluminosilicates. The role of SiV and AlV species in transport properties of aluminosilicates was discussed also in Ref. [6]. These 5coordinated Si and Al atoms can be considered as defects since both Si and Al are nominally tetrahedral in aluminosilicate glasses. In Ref. [7] the formation of SiV was experimentally observed in sodium tetrasilicate glass at room temperature under the high pressure (up to 50 GPa). The authors observed an increase of the number of SiV and a simultaneous decrease in the number of NBOs with increasing pressure. According to the scheme discussed in this work, SiV (and even SiVI) species are formed under pressurization from the bonding of NBO to silicon of adjacent tetrahedral species.

Evidence for AlV has been experimentally found in several calcium aluminosilicate (CAS) glasses [8–11]. It is the generally believed that AlV exists for the purpose of local charge balancing when the concentration of low charge cations as Ca is insufficient to neutralize the negative charge on bridging oxygen in SiIV–O–AlIV or AlIV–O–AlIV linkages. However the existence of AlV was observed even in CAS glasses where the concentration of Ca was in large excess over the one needed to provide charge compensation [10]. The presence of AlV is important for understanding the macroscopic dynamic properties of the liquid state, in particular diffusivity and viscous flow [10]. AlV is considered as the transient species facilitating the local redistribution of bridging and non-bridging oxygen and likely playing a governing role in viscous flow of aluminosilicate melts [10]. Together with highly coordinated Al, the charge balancing in aluminosilicate glasses can be provided by oxygen triclusters (i.e., oxygen atoms bonded to three network former atoms). Triclusters were studied in aluminosilicates with classical [12] and ab initio molecular dynamics simulations [13] but were detected experimentally only in calcium aluminate glasses [14]. The role of triclusters in transport properties of the glasses is not yet understood. In this paper, we model calcium aluminosilicate glasses at the atomistic level with the aim of understanding the role of glass network defects such as NBO, AlV and SiV, and oxygen triclusters in diffusive mass transfer. 2. Methodology

⁎ Corresponding author. E-mail address: [email protected] (J.C. Mauro). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.12.078

All glass compositions under study (Table 1) corresponded to the fixed ratio R = [CaO]/[Al2O3] = 1. At this ratio liquids and glasses are

A. Tandia et al. / Journal of Non-Crystalline Solids 357 (2011) 1780–1786 Table 1 Glass compositions and density values. Experimental densities for studied glass compositions were provided by Laurent Cormier [20]. Glass

CaO, mol%

Al2O3, mol%

SiO2, mol%

Density (g/cm3)]

CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

44.1 40.505 35.5 33.335 30 25 20 15 11.75

44.1 40.505 35.5 33.335 30 25 20 15 11.75

11.8 18.99 29 33.33 40 50 60 70 76.5

2.86 2.843 2.794 2.789 2.75 2.66 2.6 2.503 2.436

Table 2 Parameters of the Matsui potential.

Ca Al Si O

q (e)

A (Å)

B (Å)

C (Å3 eV1/2)

0.945 1.4175 1.890 −0.945

1.1720 0.7852 0.7204 1.8215

0.040 0.034 0.023 0.138

4.581 3.7483 5.0187 9.2241

often described as having a “fully polymerized” structure with no NBOs. However, experimental studies showed that even 1:1 compositions may contain considerable levels of NBO [15].

CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

III

D [cm2 s-1]

1.0E-04

II

1.0E-05 1.0E-06

I

1.0E-07


 −1 −6 V rij = qi qj rij –Ci Cj rij
 h

i + f Bi + Bj :exp Ai + Aj −rij = Bi + Bj :

Diffusion constant of Al

III 1.0E-04

II

CAS6 CAS7 CAS8 CAS9

1.0E-05 1.0E-06

I 1.0E-07 1.0E-08

Tg

Tg

1.0E-09

1.0E-09 5

10

15

0

20

5

c

d

Diffusion Constant of Silicon CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

III 1.0E-04

II

1.0E-06

I 1.0E-07 1.0E-08

15

20

Diffusion Constant of Calcium CAS1 CAS2 CAS2 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

1.0E-03

III 1.0E-04

II

D [cm2 s-1]

1.0E-03

1.0E-05

10

T-1 [10-4 K-1]

T-1 [10-4 K-1]

D [cm2 s-1]

CAS1 CAS2 CAS3 CAS4 CAS5

1.0E-03

1.0E-08

0

1.0E-05

I 1.0E-06 1.0E-07 1.0E-08

Tg

Tg

1.0E-09

1.0E-09 0

5

10

T

-1 [10-4 K-1]

15

20

ð1Þ

The three terms of Eq. (1) represent Coulomb, Van der Waals, and repulsion interactions, respectively. Here rij is interatomic distance between atoms i and j, f is a force constant of 0.010364 eV Å−1, and qi, Ai, Bi and Ci (Table 2) are partial charges, repulsive radii, softness parameters and Van der Waals coefficients of the ion i, respectively. To prepare the glass structure we used the simulated annealing technique. The initial random configuration is equilibrated at 6000 K using the Metropolis Monte Carlo algorithm. Then stepwise cooling to room temperature is carried out with a step of 300 K. The same Metropolis Monte Carlo algorithm is used to sample the system at each step of the cooling process. For all glass compositions the output configuration files at each temperature are used as input files for further molecular dynamics runs of 20.0 ns duration using a time step of 1.0 fs. These MD runs are used to study the self-diffusivity of Ca, Al, Si and O for different compositions and different temperatures. The total number of runs was 180 (9 compositions, 20 temperatures). Computed structural features are in good agreement with those found by Matsui [16]. All simulations are performed in the canonical (NVT) ensemble, where the total number of atoms is ~5000 and the volume V of the simulation box is taken in accordance with experimental glass

D [cm2 s-1]

1.0E-03

To describe interatomic interactions we use the potentials developed by Matsui [16], which have the form:

b

Diffusion Constant of Oxygen

a

1781

0

5

10

15

20

T-1 [10-4 K-1]

Fig. 1. Atomic diffusivities as a function of temperature: a — oxygen; b — aluminum; c — silicon; d — calcium. The Tg range shown is estimated from experimental data.

1782

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Ca diffusion constant

densities at room temperature. In our calculations we neglect the effect of temperature dependence of the simulation volume. For all 180 MD runs we calculate the mean square displacement (MSD) for each atomic constituent by 1 N 2 ∑ 〈½ri ðt Þ−ri ð0Þ 〉 N i=1

ð2Þ

where ri(t) is the position of an atom at time t. The angular brackets in (2) indicate an average over initial positions of atoms (at time t = 0). Summing over all the atoms and dividing by the number of atoms gives the mean value for the glass. From the MSD at long times the self diffusion constants D can be calculated using the Einstein equation:

1.0E-06

D (cm2 s-1)

2

MSD = 〈Δ r ðt Þ〉 =

1.0E-05

600 K

1.0E-07

1500 K 1.0E-08

1.0E-09 0

20



 1 2 〈Δ rðt Þ〉 6t t→∞

ð3Þ

60

80

D is calculated from the slope of MSD in the long time limit of the simulations. The configuration file is used after each MD run to analyze the structure of the glasses and melts. We perform a thorough coordination number analysis (CNA) taking into consideration the calculation of different specific types of atoms around each type of atom. To specify the radius of the first coordination sphere for CNA we used the position of the first minimum in the corresponding radial distribution function (RDF). For all nine compositions we apply CNA and calculate the concentration of various network defects like NBO, triclusters, AlV, SiV, AlIII, and SiIII as a function of temperature. 3. Results Fig. 1 illustrates the scaling of the diffusion coefficients of O, Al, Si and Ca atoms as a function of reciprocal temperature. The temperature range corresponds to an interval from 600 to 5000 K. All four sets of curves are characterized by three regions. The “low” temperature region (I) from 600 K to approximately 1100– 1200 K is described by a low slope and could be attributed to solid state of the glass, since Tg for some CAS glasses with R = 1 is in the range 1100–1150 K [17]. The “middle” temperature region (II) from 1100–1200 K up to approximately 1600–1700 K is characterized by the highest slope of the curves. Then at very high temperature all the curves tend to decrease in slope. This third region (III) from 1500–1600 K to 5000 K can be conditionally called “high” temperature melt. Another common feature of the diffusion curves in Fig. 1 is a noticeable dependence of self-diffusivity on glass composition in the “middle” temperature range II and subsequent coincidence of the diffusion constants at 5000 K. The weak variation of diffusion

Fig. 3. Self-diffusivity of Ca at 600 and 1500 K as a function of glass composition.

coefficients on composition at low temperatures in the region I is observed. The exception from this described common feature is Ca diffusivity, where dependence of the diffusion constant on composition at in the region I is higher than at “middle” temperatures in the region II. Fig. 2 illustrates the dependence of diffusion constants of all types of atoms on composition at the “middle” temperature 2400 K. The diffusivity of all glass constituents decreases as the composition changes from low silica to high silica content. The peculiar dependence of Ca diffusivity as a function of composition is shown at Fig. 3. At low temperature (600 K) the behavior of Ca diffusivity as a function of silica content is contrary to the behavior of Ca diffusivity at high temperature (1500 K). Diffusion in these glasses is enabled by cooperative motion of atoms. This leads to a fairly narrow distribution of self-diffusivity value of the various elements within a given composition. For example, for CAS1 (high alumina content) we observe near coincidence of diffusion constants versus temperature for O, Al and Si (Fig. 4a). Ca diffusivity in CAS1 a little bit higher but also is pretty much close to O, Al and Si diffusivities.

a

CAS1 1.0E-03 O Al Ca Si

1.0E-04

D [cm2 s-1]

D=

40

SiO2, mol %

1.0E-05 1.0E-06 1.0E-07 1.0E-08 1.0E-09 0

4

2400 K O Al Ca Si

4.0E-05

b

12

16

20

CAS9 1.0E-03

O Al Ca Si

1.0E-04

D [cm2 s-1]

D (cm2/s)

8

T-1 (10-4 K-1)

6.0E-05

2.0E-05

1.0E-05 1.0E-06 1.0E-07 1.0E-08

0.0E+00 0

20

40

60

80

100

SiO2 (mol%)

1.0E-09 0

4

8

12

16

20

T-1 (10-4 K-1) Fig. 2. Self-diffusivity of O, Al, Ca, and Si atoms at 2400 K as a function of glass composition.

Fig. 4. Self-diffusivity of O, Al, Ca, and Si atoms in CAS1 (a) and CAS9 (b) glasses.

A. Tandia et al. / Journal of Non-Crystalline Solids 357 (2011) 1780–1786

CAS Glass D(O), 2400 K

the diffusivity of O is close to that of Si when the concentration of Si is higher than Al (in the high silica glasses). Hence, the diffusivity of O depends on the relative concentration Si and Al. It could be assumed that O is moving together with Si and Al as a constituent of Si and Al-based tetrahedra. The cooperative nature of selfdiffusivity is discussed below. From the assumption that O atoms move together with Si and Al cations we can calculate diffusion coefficient of D(O) for each glass composition from Eq. (4), based on the diffusion coefficients of Si and Al for the same glass composition and taking into account their molar fractions.

5.0E-05 Calculated via (4) Molecular dynamics data 4.0E-05

D (cm2/s)

1783

3.0E-05 2.0E-05 1.0E-05

DðOÞ = ½SiO2   DðSiÞ + 2½Al2 O3   DðAlÞ

ð4Þ

0.0E+00 20

40

60

80

100

SiO2 (mol %) Fig. 5. Comparison of D(O) directly determined from MD data with D(O) calculated from (4).

In contrast, CAS9 (high silica content) exhibits considerably higher Ca diffusivity compared to the diffusivities of O, Al and Si (Fig. 4b). Other glasses are intermediate in their diffusivity behavior between CAS1 and CAS9. From Fig. 3 it is seen that diffusion constant of O is close to the diffusion constant of Al when concentration of Al is predominant (low silica glasses). Similarly,

a

Fraction of NBO versus temperature

Fraction ([NBO]/[O])

0.2

b CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

0.16 0.12 0.08 0.04

where [SiO2] and [Al2O3] are silica and alumina molar fractions, D(Si) and D(Al) are diffusion coefficients of Si and Al atoms for each glass composition. The comparison of thus calculated D(O) with the D(O) directly determined from MD data are presented at Fig. 5. The good agreement between MD diffusivity and that calculated from (4) is evidence that the diffusivity of O atoms is really an average over diffusivities of O atoms moving together with Si or Al. At first glance it is rather strange to see the diffusion coefficient of Al higher than the diffusion coefficient of O, in particular for CAS9 composition. But this observation is consistent with experimental data obtained in [19] where authors observed the same order of diffusivity: Ca N Al N O N Si. The absolute values of diffusion coefficients

Fraction of OIII (triclusters) versus temperature 0.3

Fraction ([OIII]/[O])

0

CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

0.25 0.2 0.15 0.1 0.05 0

0 0

5

10

15

0

20

5

T-1 (10-4 K-1)

d

Fraction of AlIII versus temperature 0.25

CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

0.2 0.15 0.1 0.05 0 0

5

10

15

Fraction ([AlV]/[Al])

Fraction ([AlIII]/[Al])

c

CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

0.3 0.25 0.2 0.15 0.1 0.05 0 0

5

0.06 0.04 0.02 0 15

T-1 (10-4 K-1)

20

Fraction ([SiV]/[Si])

Fraction ([SiIII]/[Si])

f CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

10

10

15

20

T-1 (10-4 K-1)

0.08

5

20

Fraction of AlV versus temperature

20

Fraction of SiIII versus temperature

0

15

0.35

T-1 (10-4 K-1)

e

10

T-1 (10-4 K-1)

Fraction of SiV versus temperature 0.1

CAS1 CAS2 CAS3 CAS4 CAS5 CAS6 CAS7 CAS8 CAS9

0.08 0.06 0.04 0.02 0 0

5

10

15

20

T-1 (10-4 K-1)

Fig. 6. Fraction of network defects as a function of composition: a — NBO; b — triclusters; c — AIII; d — AlV; e — SiIII; f — SiV.

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measured in [19] are about an order of magnitude lower than calculated results. The main conclusion is that such atoms as O, Al, and Si are moving together as one network structural unit. Since the structural units of aluminosilicate glasses are Al and Si-centered tetrahedra, we assume that the whole tetrahedra are involved in the process of self-diffusivity.

a 0.14 0.12

Fraction

0.1

4. Discussion

0.08

NBO Triclusters

0.06 0.04 0.02 0 0

20

40

60

80

SiO2, mol % Fraction of AlV versus composition at 600 K

b

Fraction

To understand the role of network defects in self-diffusivity of calcium aluminosilicate glasses we studied the process of defect formation as a function of temperature. The following network defects were detected with the help of CNA applied to the output MD files: one-coordinated oxygen (NBO); three-coordinated oxygen (triclusters); three-coordinated aluminum (AlIII); five-coordinated aluminum (AlV); three-coordinated silicon (SiIII); five-coordinated silicon (SiV). Fig. 7 (a–f) illustrate the dependence of the fraction of different defects on temperature and composition. One can observe a likeness in the behavior of defect formation (Fig. 6) and diffusion (Fig. 1) as a function of silica content. It can be seen that the rise of the oxygen defects (Fig. 6(a, b)) starts at lower temperatures for glasses with high alumina content compared to glasses with high silica content, where the noticeable rise of oxygen defects relates to higher temperatures. We can see the same tendency in Fig. 1 where the increase of diffusivity of all types of atoms in the “middle” temperature range starts at lower temperatures for high alumina glasses than for high silica glasses. Temperatures at which we observe the rapid growth of oxygen defects (1200–1500 K) are approximately the same as temperatures corresponding to the beginning of fast diffusion process. These temperatures can be attributed to the transition from solid to liquid state. It can be seen that at all temperatures the fraction of oxygen defects is highest for high alumina glasses and lowest for high silica glasses. This is consistent with the behavior of the diffusion coefficients which are also the highest for high alumina and lowest for high silica glasses. The correlation in the behavior of diffusivities and defect formation (mainly oxygen) provides evidence for self-diffusion as a defect-mediated process. Such an approach to diffusion and viscous flow was suggested by Mott [18], who treated viscous flow in terms of the motion of point defects. This work has revealed that defects play a dominant role in formation of diffusion mass transfer and viscous flow. In Ref. [10] Neuville and others discuss the role of high coordinated species, in particular AlV as a transition state in viscous flow in silicate liquids. It should be noted that only three kinds of defects exist in significant concentrations at low temperatures from 600 to 1200– 1500 K. These defects are: NBOs, oxygen triclusters, and AlV. NBOs exist at low temperatures due to the impact of Ca as a network modifier. Triclusters and AlV result from charge compensation as mentioned in the Introduction. The concentration of these defects is constant within the range of temperatures from 600 to 1200–1500 K and goes up when the temperature is higher than 1200–1500 K. The dependence of these defects on composition at 600 K is illustrated in Fig. 7. The fraction of oxygen defects decreases with the increase of silica content whereas the fraction of AlV exhibits a maximum at 35 mol% of SiO2 approximately. This is consistent with experimental data obtained in Ref. [10], where the authors also observed a maximum in AlV fraction at 35 mol% of SiO2 for the same glass composition. Other defects like AlIII, SiIII and SiV are generated from thermal energy only in a liquid state when the temperature is higher than 1200–1500 K. In order to understand the sequence of reactions leading to defect formation we visually studied the behavior of pure silica structure under the high temperature (3000 K) (Fig. 8(a–f)).

Fraction of NBO and triclusters versus composition at 600 K

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

20

40

60

80

SiO2, mol % Fig. 7. Fraction of NBO, triclusters and AlV as a function of composition at 600 K.

In Fig. 8 we track the following species: one tetrahedron (Si — light green, O — pink), another tetrahedron (Si — dark green, O — violet) and one bridging O (blue). The following stages of defect formation can be observed in Fig. 8. The initial totally polymerized network (Fig. 8a) consists of four coordinated Si and bridging oxygens. Under high temperature one Si–O bond is broken resulting in the formation of SiIII (light green) and NBO (pink), as when in Fig. 8b. SiIII moves towards bridging O (blue) and forms an oxygen tricluster OIII (Fig. 8c). Thus, SiIII is annihilated but another defect (OIII) is formed. In the same picture it is seen that the Si–O bond is broken inside another tetrahedron and another NBO (violet) is formed. In Fig. 8d it is seen that OIII disappears due to breaking of one of its Si–O bonds. This bond is different from the bond which was formed in previous step. At the same time an NBO (violet) comes back to its original Si and restores the previous bond. But this bond is broken again (Fig. 8e) and this time SiIII (dark green) is formed and the NBO (violet) is located at another tetrahedron. As a result in Fig. 8f it is seen that SiIII (dark green) moves to another location and the NBO (violet) is annihilated. The evidence for NBO annihilation is the appearance of a second bond at the violet oxygen. These pictures show that Si atoms undergo the displacement together with few O atoms as the constituents of tetrahedral network units, and this movement of network units is the result of defect formation and annihilation. The following reactions describe the observed structure transformation in SiO2 glass in terms of defect formation and annihilation under the high temperature: IV

III

III

II

I

Si ↔Si þ O

IV

4ðaÞ III

Si þ O ↔Si þ O

4ðbÞ

By analogy we can assume that the formation of OI and NBO in CAS glasses takes place due to the same reactions 4 but in CAS glasses both SiIV and AlIV kinds of tetrahedra give origin to OI and OIII defects. From the visual data we can propose the set of reactions responsible for the defect formation in CAS glasses.

A. Tandia et al. / Journal of Non-Crystalline Solids 357 (2011) 1780–1786

1785

Fig. 8. Formation of NBO and OIII: a) initial state: SiIV (dark and light green) and bridging O (violet and pink); b) Si-O bond in SiIV (light green) is broken, SiIII (light green) and NBO (pink) are formed; c) triclusters OIII (blue) is formed, one more NBO (violet) is formed; d) one of Si–O bonds in tricluster (blue) is broken, NBO (violet) annihilated with adjacent SiIII; e) Si–O bond in SiIV (violet) is broken, SiIII (dark green) and NBO (violet) are formed; f) SiIII (dark green) moved, NBO (violet) annihilated (second bond appeared).

(SiV) and oxygen triclusters OIII play an important role in the diffusion as intermediate products of chemical reactions.

For Al-network: IV

III

I

Al ↔Al þ O III

II

5ðaÞ

IV

Al þ O ↔Al þ O I

IV

III

V

O þ Al ↔Al

5ðbÞ

5. Conclusion

5ðcÞ

Our molecular dynamics study of self-diffusivity and network defect formation in CAS glasses shows that diffusion occurs via the cooperative movement of Al, Si, and O atoms. The individual atoms move as the components of network units, e.g., polytopes containing defects like NBO and AlIII (or SiIII) which react with cations and anions of adjacent tetrahedra and produce other defects such as AlV (or SiV) and OIII. Therefore we conclude that diffusion in CAS glasses is a defect-mediated process resulting from bond switching and defect formation/annihilation under the influence of thermal energy.

For Si-network: IV

III

I

III

II

IV

Si ↔O þ O

Si þ O ↔Si þ O I

IV

V

O þ Si ↔Si

6ðaÞ III

6ðbÞ 6ðcÞ

In addition to defects visually observed in SiO2 glass we consider in these reactions such defects as SiV and AlV. The formation of these defects is confirmed by MD data. The evident path of their formation is given by reaction 5(c) and 6(c). Here for convenience NBOs are designated as OI, triclusters are designated as OIII, and bridging oxygen as OII. Reactions 5 and 6, which illustrate the defect formation, help to understand the diffusion process in these glasses. Species responsible for the diffusion process are network units like Al (or Si) tetrahedron containing NBO and AlIII (or SiIII) species. These species move via switching of the bonds in accordance with reactions 6 and 7, and thus provide cooperative diffusion of atomic species (Al, Si and O). Five-coordinated cations AlV

Acknowledgements We would like to acknowledge valuable support from Amy L. Rovelstad and Phong Diep of Corning Incorporated. References [1] [2] [3] [4]

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