Physics and Chemistry of Glasses

ISSN 1753-3562

June 2009 Volume 50 Number 3

Physics andChemistry ofGlasses

European Journal of Glass Science and Technology Part B

PC50_3 cover.indd 1

29/06/2009 15:19:10

Volume 50 Number 3

June 2009

Physics and Chemistry of Glasses European Journal of Glass Science and Technology B Contents Papers

The European Journal of Glass Science and Technology is a publishing partnership between the Deutsche Glastechnische Gesellschaft and the Society of Glass Technology. Manuscript submissions can be made through Editorial Manager, see the inside back cover for more details. Regional Editors Professor J. M. Parker Professor C. Rüssel Professor L. Wondraczek Professor A. Duran Professor R. Vacher Dr A. C. Hannon Professor M. Liška Professor S. Buddhudu Abstracts Editor Professor J. M. Parker Managing Editor D. Moore Assistant Editor S. Lindley Society of Glass Technology Unit 9, Twelve O’clock Court 21 Attercliffe Road Sheffield S4 7WW, UK Tel +44(0)114 263 4455 Fax +44(0)114 263 4411 E-mail [email protected] Web http://www.sgt.org The Society of Glass Technology is a registered charity no. 237438. Advertising Requests for display rates, space orders or editorial can be obtained from the above address. Physics and Chemistry of Glasses: European Journal of Glass Science and Technology, Part B ISSN 1753-3562 (Print) ISSN 1750-6689 (Online) The journal is published six times a year at the beginning of alternate months from February. Electronic journals: peer reviewed papers can be viewed by subscribers through Ingenta Select http://www.ingentaconnect.com The editorial contents are the copyright © of the Society. Claims for free replacement of missing journals will not be considered unless they are received within six months of the publication date.

133 Reanalysis of density relaxation measurements on glasses and internal friction W. Gräfe 137 An atomic scale comparison of the reaction of Bioglass® in two types of simulated body fluid V. FitzGerald, D. M. Pickup, D. Greenspan, K. M. Wetherall, R. M. Moss, J. R. Jones & R. J. Newport Proceedings of the Sixth Conf. on Borate Glasses, Crystals and Melts

144 The mixed glass former effect on the thermal and volume properties of Na2S– B2S3–P2S5 glasses M. J. Haynes, C. Bischoff, T. Kaufmann & S. W. Martin 149 Brillouin scattering study of elastic properties of sodium borate binary glasses Y. Fukawa, Y. Matsuda, M. Kawashima, M. Kodama & S. Kojima 153 Viscosity of Bi2O3–B2O3–SiO2 melts S. Inaba, H. Tokunaga, C. Hwang & S. Fujino 156 A multi-technique structural study of the tellurium borate glass system E. R. Barney, A. C. Hannon & D. Holland 165 Electrical conductivity and viscosity of borosilicate glasses and melts D. Ehrt & R. Keding 172 Effects of rare earth oxides (La2O3, Gd2O3) on optical and thermal properties in B2O3–La2O3 based glasses S. Tomeno, J. Sasai & Y. Kondo 175 Structure–property studies of SrBr2–SrO–B2O3 glasses R. E. Youngman, L. K. Cornelius, S. E. Koval, C. L. Hogue & A. J. G. Ellison 183 Network structure of xB2O3.(22·5−x)Al2O3.7·5P2O5.70SiO2 glasses R. E. Youngman & B. G. Aitken 189 Borate glasses and glass-ceramics for near infrared luminescence J. Pisarska & W. A. Pisarski 195 Quantification of boron coordination changes between lithium borate glasses and melts by neutron diffraction L. Cormier, G. Calas & B. Beuneu 201 Developing 11B solid state MAS NMR methods to characterise medium range structure in borates N. S. Barrow, S. E. Ashbrook, S. P. Brown & D. Holland 205 Structure and the mechanism of rapid phase change in amorphous Ge2Sb2Te5 M. Takata, Y. Tanaka, K. Kato, F. Yoshida, Y. Fukuyama, N. Yasuda, S. Kohara, H. Osawa, T. Nakagawa, J. Kim, H. Murayama, S. Kimura, H. Kamioka, Y. Moritomo, T. Matsunaga, R. Kojima, N. Yamada, K. Toriumi, T. Ohshima & H. Tanaka 212 Boromolybdate glasses containing rare earth oxides Y. Dimitriev, R. Iordanova, L. Aleksandrov & K. L. Kostov 219 New geometrical modelling of B2O3 and SiO2 glass structures A. Takada 224 Packing in alkali and alkaline earth borosilicate glass systems S. Bista, A. O’Donovan-Zavada, T. Mullenbach, M. Franke, M. Affatigato & S. Feller 229 Thermal poling induced structural changes in sodium borosilicate glasses D. Möncke, M. Dussauze, E. I. Kamitsos, C. P. Ε. Varsamis & D. Ehrt 236 Conference Diary A29 Abstracts

Printed and bound by The Charlesworth Group, Wakefield, UK. Tel +44(0)1924 204830

Proc. VI Int. Conf. Borate Glasses, Himeji, Japan, 18–22 August 2008 Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B, June 2009, 50 (3), 219–223

New geometrical modelling of B2O3 and SiO2 glass structures Akira Takada1,2,3 Research Center, Asahi Glass Co. Ltd., 1150 Hazawa-cho, Yokohama 221-8755, Japan University College London, Gower Street, London W1E 6BT, UK 3 Institute of Industrial Sciences, University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan 1 2

Manuscript received 25 August 2008 Revised version received 16 January 2009 Accepted 29 January 2009

New geometrical modelling of glass structure employing ‘local oxygen packing number (LOPN)’ has been developed. This modelling enables the quantification of the variation in local structure in terms of oxygen packing. This new method was applied to analyse the structures of SiO2, B2O3 and boric acid systems. The analysis of LOPN for the SiO2 system shows that each structure can be classified into one of three different packing groups. Moreover, in terms of LOPN, the densification of silica glass is found to increase the fraction of coesite-like denser fragments taking the place of quartzlike and cristobalite-like fragments, although the packing group remains the same. B2O3 and boric acid systems can also be explained in terms of these three different packing groups. However, in contrast to the SiO2 system, most of these borate structures have characteristics of two different groups. The differences in LOPN can be related to the difference in dimensionality of packing, as exhibited by: (1) coordination numbers of cations and anions, and (2) the existence of super-structural units such as the boroxol ring, or low dimensional structures such as chain packing. It is also revealed that the local oxygen packing can differ from place to place even in one structure, and the LOPN is a more powerful tool to investigate structures than the conventional concept of overall packing density. 1. Introduction The structure of vitreous B2O3 is still the subject of controversy. The simpler random network model consists of planar BO3 triangles, as proposed by Zachariasen.(1) However, several serious objections to this model have been raised, as reviewed in the volume of proceedings(2) and papers of Johnson et al(3) and Wright et al.(4) Goubeau & Keller(5) first suggested the existence of boroxol (3-membered ring) groups in B2O3 glass, and then Krogh-Moe(6) concluded that a random three-dimensional network of BO3 triangles with a comparatively high fraction of boroxol rings gives the best explanation of the available data. From that time down to this day the boroxol ring model has been supported by other experiments.(7,8) The fraction of boroxol rings is usually defined by the fraction of boron atoms present in boroxol rings, estimated to be around 75%.(3,7–10) In contrast, most ordinary MD (molecular dynamics) studies(11–22) have failed to reproduce the existence of a high fraction of boroxol rings. A coordination dependent model with three-body terms(23,24) or a polarisable model(25) has been able to confirm the existence of boroxol rings, but their fraction was still small (around 30%), although Takada et al(26) conducted a “computer (in silico) synthesis” and synthesised a structure that has a density close to that of vitreous B2O3 and a high fraction of boroxol rings (75%). More Email [email protected]

improvements have been performed over the past few years. Takada(27) developed a hybrid MD/MC (Monte Carlo) method and produced a structure that has a 75% fraction of boroxol rings. Huang & Kieffer(28) also produced a structure with a high fraction of boroxol rings by melting from the caesium enneaborate structure. Furthermore, Ferlat et al(29) performed first principles MD calculations and showed that only a boroxol-rich model (75% boroxol fraction) can reproduce the full set of observables. It is also interesting to note that Takada(30) and Huang & Kieffer(28) investigated the effect of pressure on vitreous B2O3. The former discussed the densification mechanism, and the latter suggested thermomechanical anomalies that are analogous to those in the SiO2 system and proposed new low density crystal structures. On the other hand, many structural studies, using both experiments and computer simulations, have been performed for silica glass. The structures and properties of silica glass are reviewed in several papers(31–33) and monographs.(34,35) It should be emphasised that computer simulation has been proposing the microscopic mechanism of thermal and pressure effects on silica glass. After performing MD and MC calculations, the structural changes in glasses have mainly been investigated in terms of coordination number, bond angles, torsional angles, and ring statistics. As an extension of this approach, the author(36–38) has recently proposed the ‘structon model’ which classifies local structures

Physics and Chemistry of Glasses: European Journal of Glass Science and Technology Part B Volume 50 Number 3 June 2009

219

Proc. VI Int. Conf. on Borate Glasses, Crystals and Melts, Himeji, Japan, 18–22 August 2008

2. Geometrical modelling Useful information on glass structures has been obtained by the analysis of coordination number, bond angles, torsional angles, and ring statistics.(42,43) This method puts emphasis on chemical bonding. An alternative method is to emphasise the packing of atoms, such as in the random packing model.(39–41) This method works very well for monoatomic systems, but it is not easy to extend this model to a polyatomic system. On the other hand, by using a packing model for crystals, Dmitriev et al(44) showed that, when only the arrangement of oxygen atoms is considered, the crystal structures of SiO2 are derived from a common parent disordered BCC (body centred cubic) structure having different fractional concentrations of SiO2 molecules. This method, however, cannot be directly applied to amorphous systems. In general, crystal structures can be distinguished by symmetry. Each symmetry group holds its inherent number of surrounding atoms. When disordered structures are investigated, their symmetry group cannot be defined, but their number of surrounding atoms can be calculated by assuming a counting rule. In this study only structural information on oxygen atoms was investigated and the number of surrounding oxygen atoms around each oxygen was calculated. First, the relative arrangements of oxygen atoms in silica polymorphs were calculated and the data were projected onto BCC, FCC (face centred cubic), and HCP (hexagonal close packed) structures. The best fit showed that the number of surrounding oxygen atoms was 6 for cristobalite and 12 for stishovite. Next, a criterion of counting a surrounding number was investigated so that the surrounding numbers for cristobalite and stishovite can be reproduced as 6 and 12, and so that this criterion can also be applied to disordered systems. Finally, the following criterion was employed in this

study. A calculated surrounding number is termed ‘local oxygen packing number’ (LOPN) f = Â fi i

fi = 1

ri < r1

= (r2 - ri ) / (r2 - r1 ) =0

r1 < ri < r2 r2 < ri

where f is the LOPN, and r1 and r2 are 3·0 and 3·06 Å. The i summation is performed over all the other oxygens in the structure, each of which is a distance ri from the oxygen under consideration. The same criterion is also applied to B2O3 and boric oxide system.

3. Results 3.1 Silica system

The distributions of local oxygen packing numbers for silica polymorphs are plotted in Figure 1. The LOPNs for cristobalite, quartz, and stishovite are 6, 6 and 12, respectively. Coesite has two LOPNs; 6 and 7. The LOPN for fibrous silica (silica W)(45,46) is 3. The enigmatic structure of fibrous silica is comprised of one-dimensional chains. The LOPN varies from 3 to 12 as silica structure changes from one-dimensional to three-dimensional and the packing density increases. The distributions of LOPNs for silica glass are plotted in Figure 2. For details of the silica glass simulation and its structure the author’s previous paper(47) should be referred to. The LOPNs for an as-quenched glass and glasses decompressed from 25 and 40 GPa load are shown in Figure 2(a). The LOPNs for glasses under compressions of 25 and 40 GPa are also shown in Figure 2(b). The LOPNs for the as-quenched glass are 6 and 7 as for coesite, but the average LOPN for the glass is 6·1 and this value is closer to that of quartz and cristobalite (6·0) than that of coesite (6·5). Hence this as-quenched silica glass has a LOPN distribution which mixes features of quartz, cristobalite, and coesite. When this silica glass is compressed, its LOPN shifts to larger values (denser packing) and its average value approaches that of stishovite as the pressure increases. After decompression the densified glass has a larger average LOPN than that of the as-quenched glass. The

fraction

into four structural units, and explains temperature induced structural changes in SiO2, BeF2, and GeO2 glasses. On the other hand, there is another conventional approach called ‘random close packing (RCP) of hard spheres’ which was advanced by Bernal,(39) Scott,(40) and Finney.(41) RCP modelling has only been used for model glasses and simple metallic glasses. Elliot(42) reviews this sort of geometrical modelling in his book. In conclusion, there have been many studies on structural modelling, but no type of approach can cover the full variety of structural changes in crystals and glasses. In this study, new geometrical modelling of glasses is reported. One new parameter, named “local oxygen packing number (LOPN)”, is defined and applied to investigate crystal and glass structures of B2O3 and SiO2. Finally, several similarities and dissimilarities in local structure among crystals and glasses are discussed.

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

fibrous cristobalite quartz coesite stishovite 3 4 5 6 7

8 9 10 local packing number 11

12

Figure.1 Distributions of local oxygen packing numbers for silica polymorphs

220 Physics and Chemistry of Glasses: European Journal of Glass Science and Technology Part B Volume 50 Number 3 June 2009

Proc. VI Int. Conf. on Borate Glasses, Crystals and Melts, Himeji, Japan, 18–22 August 2008 0.9 0.8 0.6

0.8

decompress from 25GPa

0.7

0.4 0.3 0.2 0.1 0

enneaborate

0.4 0.3 0.1

4 5 6 7 8

0 13

0.4

3 4 5 6 7


(a)

(a)

P=25GPa

0.35

12

0.8

0.3

glass

0.7

0.25

P=40GPa

0.2 0.15

0.6 fraction

fraction

crystal- II

0.5

0.2


0.1 0.05 0

crystal- I

0.6

decompress from 40GPa

0.5

fraction

fraction

0.7

P=0

4 5 6 7 8

0.5

enneaborate

0.4 0.3 0.2

9 10 11 local packing number 12 (b)

0.1 13

Figure 2. Distributions of local oxygen packing numbers for silica glass. As-quenched, decompressed from 25GPa load, and decompressed from 40GPa load. Compressed under 25GPa load, and compressed under 40GPa load distributions of LOPN are broadened, ranging from 6 to 9. The average LOPNs for two densified glasses are 7·0 and 7·1 and are larger than that of coesite (6·5). To sum up, the effect of densification on silica glass is the transformation of an oxygen packing state from quartz-like and cristobalite-like to coesite-like through a denser packing like that of stishovite.

3.2 B2O3 system The distributions of LOPNs for two B2O3 crystals, one borate crystal, and one B2O3 glass are plotted in Figure 3. For details of the B2O3 glass simulation and its structure the author’s previous paper(27) should be referred to. Three crystals; B2O3-I (low pressure form), B2O3-II (high pressure form) and caesium enneaborate (Cs2O.9B2O3) have different average LOPN values of 5·7, 9·3 and 4·3 respectively. B2O3-I is comprised of BO3 units. One-third of oxygen atoms have a higher value of LOPN (6·6) than that of the other atoms (5·3), because the former are located at sites where two chains cross each other and the packing is denser than that for the latter two-thirds. B2O3-II is comprised of 4-fold coordinated BO4 units. One-third of oxygen atoms are two-fold coordinated and the others are three fold-coordinated. The former and the latter have the LOPNs of 8 and 10. Caesium enneaborate crystal is comprised of two kinds of basic unit; the triborate group (containing a six-membered ring, but with one of the boron atoms coordinated tetrahedrally with

0

3 4 5 6 7

8 9 10 local packing number 11 (b)

12

Figure 3. Distributions of local oxygen packing numbers for B2O3-I, B2O3-II, Cs2O.9B2O3 crystals, and B2O3 glass. (a) B2O3-I, B2O3-II, and Cs2O.9B2O3. (b) B2O3 glass and Cs2O.9B2O3 oxygen atoms) and the boroxol group. The oxygen atoms surrounding 4-fold coordinated boron atoms have the higher LOPN value of 5 than that (4) of the oxygens coordinated to only 3-fold coordinated boron. B2O3 glass a LOPN distribution which mixes features of caesium enneaborate and B2O3-I. The oxygen atoms in boroxol rings are responsible for the LOPN value of 4, and oxygen atoms in independent BO3 units are responsible for the other larger values. To investigate the relation of LOPN with local structure in more detail, four crystal structures of boric acid, which are similar to B2O3, were analysed. The distributions of LOPNs for four boric acids are plotted in Figure 4. The structure of orthoboric acid, H3BO3, is built up by B(OH)3 molecules which form endless layers. Its LOPN value of 4 is the same with that of caesium enneaborate. In caesium enneaborate the oxygen in boroxol rings is responsible for the LOPN value of 4, but H3BO3 has no boroxol rings. It is interesting to note that both structures have a common feature, that they are comprised of planar structural units, either boroxol rings or a layered structure. A key to explain the LOPN value of 4 seems to be the planarity of the structure. The structure of orthorhombic metaboric acid, HBO2-III, is also layered. It is comprised of trimeric HBO2 molecules which form a boroxol ring. Its LOPN values are 4


221


1

HBO2- III HBO2- II HBO2- I H3BO3

0.9

fraction

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

3

4

5

6

7 8 9 local packing number

10

11

12

Figure 4. Distributions of local oxygen packing numbers for H3BO3, HBO2-I, HBO2-II, and HBO2-III and 5. The oxygens inside and outside the ring are responsible for the former and the latter, respectively. The structure of cubic metaboric acid, HBO2-I, forms a three-dimension network of BO4 tetrahedra. Its LOPN values are 7 and 8. The oxygen atoms with the LOPN value of 7 have 2-fold coordination which is the same as one-third of the oxygen atoms in B2O3-II. The other two-thirds of oxygen atoms with the LOPN value of 8 have an additional hydrogen bonding. This hydrogen bonding seems to attract one additional oxygen atom and increase the LOPN value from 7 to 8. The structure of monoclinic metaboric acid, HBO2-II, consists of endless zigzag chains of composition [B3O4(OH) (OH2)]. Two-thirds of the boron atoms are in triangular and one-third in tetrahedral configuration. Its structure is comprised of chains like those found in B2O3-I crystal, and triborate groups like those found in caesium enneaborate. Its LOPNs are 4, 5, 6 and 7. The oxygen atoms which are located in an environment like that of enneaborate and HBO2-I are responsible for the LOPN values of 4 and 5, and 7, respectively. The environment of the oxygen atoms with a LOPN value of 6 is similar to that of B2O3-I, but the degree of distortion of the chains is different. This difference in the distortion enables the LOPN value of HBO2-II (6·0) to be different from those of B2O3-I (5·3 and 6·6). It is interesting to note that most structures of both B2O3 and boric oxide crystals are comprised of two local fragments with different LOPNs, in contrast to those of all the SiO2 crystals except coesite.

4. Discussion Structures in silica, B2O3 and boric acid systems are compared in terms of LOPN in Table 1. The analysis of LOPN for oxygen in the silica system showed that each structure can be classified into one of three different packing groups. The first group contains stishovite. The LOPN of stishovite has a value of 12 which corresponds to denser packing structures such as FCC, HCP and icosahedron. The other crystals with lower density have smaller oxygen packing in terms of

Table 1. Classification of structures in terms of local oxygen packing number Dimensionality of packing

Group-1 Group-2 Group-3 three-dimensional three-dimensional planar-like or denser packing less dense packing chain-like packing

Name of system stishovite B2O3-II LOPN 10–12 (local oxygen packing number)

cristobalite, quartz, coesite silica glass B2O3-I, B2O3-II, Cs2O.9B2O3 B2O3 glass HBO2-I, HBO2-II, HBO2-III 5–9

fibrous silica

Cs2O.9B2O3 B2O3 glass H3BO3, HBO2-II, HBO2-III 3–4

LOPN. The second group contains quartz, cristobalite and coesite. Their occupation fraction is almost half compared with stishovite. Silica glass also belongs to the second group. Silica glass originally has the mixed features of quartz, cristobalite and coesite, but in its densified structure the fraction of coesite-like denser packing increases. The third group contains fibrous silica which is comprised of one-dimensional chains. In conclusion, one-dimensional or two-dimensional structures with less dense packing belong to the third group, although no two-dimensional planar structure of silica has been observed yet, in contrast to borate and boric acid systems. B2O3 and boric acid systems can also be explained in terms of three packing groups. B2O3-II is in both the first and the second packing group. In contrast with stishovite, for which all the oxygen atoms are threefold coordinated, B2O3-II has both two-fold and threefold coordinated oxygen atoms. The fragments with different coordination number belong to different packing groups. B2O3-I belongs to the second group alone. Caesium enneaborate seems to be a mixture of the second and the third group, because there are two types of oxygen atoms; those bonded to 4-fold coordinated boron and those in boroxol rings. The latter belongs to the third group due to the planarity of the boroxol ring. B2O3 glass also has a mixed character of the second and the third group due to the mixture of independent BO3 units and boroxol rings. The boric acid system has similar features to the B2O3 system, but the existence of hydrogen bonding produces a variety of combinations of LOPNs. Although the LOPN for densified B2O3 glass has not been analysed in this study, it is speculated that densification would transform the fragments in the second group into those in the third, because the decompressed glass still kept the 3-fold coordinated states, but the fraction of boroxol rings decreased significantly, as found in the previous study.(30) The common feature in all systems investigated in this study is that all the systems can be classified into three groups depending on the manner of packing of oxygen atoms. Moreover, a common relation between the dimensionality of structure and the LOPN value is revealed, that is to say the lower dimensionality a

222 Physics and Chemistry of Glasses: European Journal of Glass Science and Technology Part B Volume 50 Number 3 June 2009


structure has, the smaller value of LOPN its structure has. On the other hand, the structural difference between the SiO2 and B2O3 systems is analysed as follows. All the silica crystals and glass can be classified into an individual group (1, 2 or 3). In contrast, B2O3-II crystal and B2O3 glass are in two different groups. The former is a mixture of two structural fragments with 2-fold and 3-fold coordinated oxygen atoms. The latter can be regarded to be an assembly of two-dimensional-like fragments comprised of boroxol rings, and three-dimensional-like fragments comprised of independent BO3 units. This difference is assumed to be due to the more complex and diverse chemical bonding of B–O than that of Si–O. Finally, the advantage of the concept of LOPN is that it can distinguish the difference in local structural environment very simply even for amorphous structures. Moreover, this new method, which is complementary to traditional methods such as bond length, bond angle, torsional angle, ring statistics, can provide new information on crystal and amorphous structures. In the previous papers,(36–38) the author developed ‘structon’ analysis, focusing on the local structural units in terms of chemical bonds. This structon can be named ‘chemical structon.’ In contrast, the structure fragments defined by the LOPN in this study can be named ‘physical structon’, because the focus here is on physical packing states. The applications of LOPN analysis to B2O3–SiO2, silicate, and borate systems is in progress. They will be published elsewhere.

5. Conclusions New geometrical modelling of glass structure employing ‘local oxygen packing number (LOPN)’ has been developed. This modelling enables the quantification of the variation in local structure in terms of oxygen packing. This new method was applied to analyse the structures of SiO2, B2O3 and boric acid systems. The analysis of LOPN for the SiO2 system showed that each structure could be classified into one of three different packing groups. Moreover, in terms of LOPN, the densification of silica glass was found to increase the fraction of coesite-like denser fragments, taking the place of quartz-like and cristobalite-like fragments. B2O3 and boric acid systems can also be explained in terms of these three different packing groups. However, in contrast to the SiO2 system, most of these borate structures have characteristics of two different groups. The differences in LOPN can be related to the difference in dimensionality of packing, as exhibited by: (1) coordination numbers of cations and anions, and (2) the existence of superstructural units such as the boroxol ring, or low dimensional structures such as chain packing. It is also revealed that the local oxygen packing can differ from place to place even in one structure, and the LOPN is a more powerful tool to

investigate structures than the conventional concept of overall packing density.

References 1. Zachariasen, W. H. J. Am. Chem. Soc., 1932, 54, 3841. 2. Pye, L. D., Frechette, V. D. & Kreidl, N. J. (Eds.), Borate Glasses: Structure, properties, Applications, 1978, Plenum Press, New York. 3. Johnson, P. A. V., Wright, A. C. & Sinclair, R. N. J. Non-Cryst. Solids, 1982, 50, 281. 4. Wright, A. C., Vedishcheva, N. M. & Shakhmatkin, B. A. J. Non-Cryst. Solids, 1995, 192&193, 92. 5. Goubeau, J. & Keller, H. Z. Anorg. Chem., 1953, 272, 303. 6. Krogh-Moe, J. J. Non-Cryst. Solids, 1969, 1, 269. 7. Jellison, G. E. Jr, Panek, L. W., Bray, L. W. & Rouse, G. B. Jr J. Chem. Phys., 1977, 66, 802. 8. Hannon, A. C., Grimley, R. A., Hulme, A. C., Wright, A. C. & Sinclair, R. N. J. Non-Cryst. Solids, 1994, 177, 299. 9. Youngman, R. E. & Zwanziger, J. W. J. Non-Cryst. Solids., 1994, 168, 293. 10. Joo, C., Zwanziger, U. W. & Zwanziger, J. W. Solid State NMR, 2000, 16, 77. 11. Soules, T. F. J. Chem. Phys., 1980, 73, 4032. 12. Soules, T. F. J. Chem. Phys., 1979, 71, 4570. 13. Soules, T. F. & Varshneya, A. K. J. Am. Ceram. Soc., 1981, 64, 145. 14. Soppe, W., van der Marel, C., van Gunsteren, W. F. & den Hartog, H. W. J. Non-Cryst. Solids, 1988, 103, 201. 15. Soppe, W. & den Hartog, H. W. J. Phys. C, 1988, 21, L689. 16. Soppe, W. & den Hartog, H. W. J. Non-Cryst. Solids, 1989, 108, 260. 17. Amini, M., Mitra, S. K. & Hockney, R. W. J. Phys. C., 1981, 14, 3689. 18. Abramo, M. C. & Pizzimneti, G. J. Non-Cryst. Solids, 1986, 85, 233. 19. Xu, Q., Kawamura, K. & Yokokawa, T. J. Non-Cryst. Solids, 1988, 104, 206. 20. Hirao, K. & Soga, N. J. Am. Ceram. Soc., 1985, 68, 515. 21. Inoue, H., Aoki, N. & Yasui, I. J. Am. Ceram. Soc., 1987, 70, 622. 22. Vehoef, A. H. & den Hartog, H. W. J. Non-Cryst. Solids, 1992, 146, 267. 23. Takada, A., Catlow, C. R. A. & Price, G. D. J. Phys.: Condens. Matter, 1995, 7, 8659. 24. Takada, A., Catlow, C. R. A. & Price, G. D. J. Phys.: Condens. Matter, 1995, 7, 8693. 25. Maranas, J. K., Chen, Y., Stillinger, D. K. & Stillinger, F. H. J. Chem. Phys., 2001, 115, 6578. 26. Takada, A., Catlow, C. R. A. & Price, G. D. Phys. Chem. Glasses, 2003, 44, 147. 27. Takada, A. Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B, 2006, 47, 493. 28. Huang, L. & Kieffer, J. Phys. Rev. B, 2006, 45, 4435. 29. Ferlat, G., Charpentier, T., Seitsonen, A. P., Takada, A., Lazzeri, M., Cormier L., Calas, G. & Mauri, F. Phys. Rev. Lett., 2008, 101, 065504. 30. Takada, A. Phys. Chem. Glasses, 2004, 45, 156. 31. Brückner, R. J. Non-Cryst. Solids, 1970, 5, 123. 32. Tomozawa, M. in Silicon-Based Materials and Devices, Ed. H. S. Nalwa, Vol. 1, 2001, Academic Press, New York, p.127. 33. Takada, A. & Cormack, A. N. Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B, 2008, 49, 127. 34. Pacchini, G. (ed.) Defects in SiO2 and Related Dielectrics, 2000, Academic Press, Dordrecht. 35. Devine, R. A. B., Durand, J.-P. & Dooryhee, E. (Eds.) Structure and Imperfections in Amorphous and Crystalline Silicon Dioxide, 2000, John Wiley & Sons, Chichester. 36. Takada, A., Richet, P., Catlow, C. R. A. & Price, G. D. Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B, 2007, 48, 182. 37. Takada, A., Richet, P., Catlow, C. R. A. & Price, G. D. J. Non-Cryst. Solids, 2007, 353, 1892. 38. Takada, A., Richet, P., Catlow, C. R. A. & Price, G. D. J. Non-Cryst. Solids, 2008, 354, 181. 39. Bernal, J. D. in Liquids: Structure, Properties, Solid Interactions, Ed. T.J. Hughel, Elsevier, Amsterdam, p.25. 40. Scott, G. D. & Kilgour, D. M. J. Phy. D, 1969, 2, 263. 41. Finney, J. L. Proc. Roy. Soc. A, 1970, 319, 479. 42. Elliot, S. R. Physics of Amorphous Materials (second edition), 1990, Longman, Essex, Chapter 3. 43. Hobb, L. W., Jesurum, C. E. & Berger, C. E., in Structure and Imperfections in Amorphous and Crystalline Silicon Dioxide (eds.) R. A. B. Devine, J.-P. Durand & E. Dooryhee, 2000, John Wiley & Sons, Chichester, p.3. 44. Dmitriev, V., Torgashev, V., Toledano, P. & Salje, E. K. H. Europhys. Lett., 1997, 37, 553. 45. Weiss, A. & Weiss, A. Naturwissenschaften, 1954, 41, 12. 46. Weiss, A. & Weiss, A. Z. Anorg. Chem., 1954, 276, 95. 47. Takada, A., Richet, P., Catlow, C. R. A. & Price, G. D. J. Non-Cryst. Solids, 2004, 345&346, 224.


223