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Behavior of the packing densities of alkali germanate glasses
Journal of Non-Crystalline Solids 248 (1999) 11±18
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Behavior of the packing densities of alkali germanate glasses U. Hoppe
*
Department of Physics, Rostock University, D-18051 Rostock, Germany Received 27 April 1998; received in revised form 26 January 1999
Abstract Packing densities are more suitable than the mass densities for structural studies. A comparison of the corresponding data on alkali germanate glasses with those of alkali borate glasses corroborates the suggestion of the formation of GeO5 and/or GeO6 units in systems Me2 Ox GeO2 1ÿx in that range of composition where the maximum packing density occurs. The packing densities of both the alkali germanate and borate glasses strongly obey a common behavior while the data of the related crystals are widely spread. Simple structural rules like those used for the borate glasses are suggested for an explanation of the germanate anomaly. However, a speci®c characteristic of some germanate crystals is the occurrence of three-fold coordinated O sites accompanied by clusters of GeO6 units. There is no evidence for a signi®cant role of such clusters in the glass structures though minor indications for such features were detected by Raman spectroscopy. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 61.43.F
1. Introduction The anomalous behavior of some properties of alkali germanate glasses is commonly related to the conversion of the network of GeO4 tetrahedra forming the structure of vitreous (v-)GeO2 into a mixture of GeO4 and GeO6 units in glasses Me2 Ox GeO2 1ÿx of low modi®er content [1]. A change of the Ge±O coordination would explain the maxima in the behavior of the mass densities [2] and of the viscosities [3] at x of 0:15 . . . 0:20. However, dierent positions and heights of the maxima of the mass densities, q, make this explanation of the `germanate anomaly' somewhat questionable. In the case of the alkali systems, where the modi®er cations are either lighter or
* Tel.: +49-381 498 1731; fax: +49-381 498 1726; e-mail: [email protected]
heavier than the Ge atoms, q is not well suited for any structural comparisons. In structural considerations, it may be, therefore, more suitable to use the packing density rather than the mass density. In this way, the data of the mass densities of the alkali germanate glasses may also give clear evidence for the change of the Ge±O coordination state of a fraction of the Ge atoms, as well, if they are compared by means of the packing density. The examination of this behavior is the main topic of the present study. Some experimental methods indicate the conversion of GeO4 tetrahedra into larger structural units almost conclusively. Neutron diraction experiments of high real-space resolution [4±6] show a clear shoulder on the long-distance side of the Ge± O nearest-neighbor peak in the radial distribution function. These larger distances are attributable to Ge±O bonds in GeO5 and/or GeO6 units [6]. Furthermore, the total Ge±O coordination numbers,
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 1 0 5 - 2
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U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
NGeO , [4±6] follow well that behavior which was predicted by Raman spectroscopy [7] and O1s Xray photoelectron spectroscopy (XPS) [8]. It was observed that up to 18 mol% Me2 O content, nonbridging oxygen atoms (ONB ) do not occur but only bridging oxygen atoms (OB ) [7,8] are found. Beyond this composition and up to 33 mol% Me2 O the ONB fraction reaches that quantity which is typical for silicate glasses being formed of only tetrahedral units. The incorporation of all the O atoms in Ge± O±Ge bridges (NOGe 2) inevitably results in an increase of NGeO with NGeO 4 + y where y is equal to n(Me2 O)/n(2GeO2 ). Hereinafter, for simplicity, the maximum of NGeO is set at 20 mol% Me2 O (y 0.5). Beyond this composition NGeO returns to four with NGeO 5 ÿ y which is reached at 33 mol% Me2 O (y 1). At present, no clear indication of a signi®cant role of three-fold coordinated oxygen sites in this process exists. Their occurrence would increase even more the NGeO or it would compensate for small fractions of ONB . Such oxygen sites are found in some of the crystal structures, among them in rutile-like GeO2 [9]. A few of such sites are detected in structural models which are generated by molecular dynamics (MD) simulations [10]. Thus, the exact structural situation might be more complicated than described by the model given in Refs. [7,8]. In this paper we will not stress small improvements of this model. In the preceding paper [6] it is shown that detailed knowledge which would characterize the exact distribution of the coordination state of all the Ge and O atoms is dicult to obtain by experimental methods. Here we plan to compare the behavior of the packing densities with that of the related crystals and with that of the borate glasses in a more approximate and simpli®ed way. The behavior of the packing densities only sheds a little more light on the structural situation but it is a simple approach. It raises the same questions about the mechanisms of the network reconstruction in alkali gemanate glasses which are still under debate in the literature. 2. Calculation of the packing densities The mass density, q, of a glassy material is an integral expression of the network characteristics,
of coordination numbers and the way of linking (connectivities) between the structural units. Furthermore, this value is in¯uenced by the mass number and the dimension of the various types of atoms. Hence, in case of the alkali germanate systems, q is not well suited for any structural comparisons. The number density of atoms may be a good alternative. Here we suggest using the packing density, qp , which is dierent from the number density and also takes into account the dierent dimensions of the types of atoms. The packing density is calculated according to , X X 3 ci Ai 1 qp 4p=3 ci ri qNav i
i
where ci is the molar fraction, Ai the mass number of the atoms of type i and Nav is the Avogadro number. The arbitrariness in the choice of the ionic radii, ri , taken here from Refs. [11,12] allows only qualitative discussions. The data of the mass density used in the calculations are taken from Refs. [2,13] for the alkali germanate glasses, from Refs. [14±16] for the alkali borate glasses and from Ref. [17] for the lithium silicate system. The radii used are the following: Li ± 59 pm, Na ± 100 pm, K ± 138 pm, Rb ± 161 pm, Cs ± 174 pm, O2ÿ ± 135 pm, B3 ± 1 pm, Si4 ± 26 pm, Ge4 ± 39 pm. The radii of the B3 and Ge4 cations are ®xed according to three- or four-fold coordination, respectively. Slightly larger radii of the higher coordinated Ge or B sites are not taken into account. The spheres of the small B3 and Ge4 cations play only a minor role in ®lling the space if compared with the role of the oxygen anions. The large spheres of the O2ÿ may partially overlap if they are members of the same structural unit. Since we do not plan to discuss the absolute values of qp but only tendencies occurring with an increasing alkali content the use of qp is justi®ed. 3. Results Figs. 1 and 2 show the behavior of the packing densities of the alkali germanate and borate glasses as a function of composition. As the uni®ed measure of the Me2 O content the molar ratio, y, with y n(Me2 O)/n(A2 Ov ) is used. Me is the alkali metal
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
13
Fig. 1. Packing densities of alkali germanate glasses with modi®er atoms Li ± squares, Na ± circles, K ± triangles, Rb ± plus signs, Cs ± ´ signs. The mass densities used in the calculations were taken from Ref. [13] (®lled marker) and all the other from Ref. [2]. The dashed line is a guide to the eye.
and A is the network former atom with the valency v. The plots in each ®gure allow detailed considerations in the interval up to y 0.8. The dashed lines are guides to the eye. The solid line in Fig. 2 accentuates the behavior of the packing density of the lithium silicate system which appears quite dierent from that of both other groups, the alkali germanate and borate systems. Since the packing densities, qp , have been calculated without corrections for overlapping of the O2ÿ spheres which share in common structural units the densities of those alkali systems appear largest in units that possess the shortest O±O distances. These systems are the alkali borate glasses. Corrections for overlapping are not planned because they are complex. These shortcomings do not limit the qualitative value of the dependencies of qp on the alkali content. 4. Discussion The packing densities, qp , of the alkali systems of the germanate and borate glasses increase rather
drastically up to molar ratios, y, of about 0.5 (Figs. 1 and 2). Beyond this composition the values of qp decrease, but less rapidly than found in the increase. The maximum positions and extents of the increase are similar for both groups of glasses. This ®nding corroborates the concept of an increase of the Ge±O coordination state [7,8] (cf. Section 1). In the case of the borate systems, the change of the B±O coordination number is shown beyond any doubt as, for example, frequently has been obtained by NMR [18]. The behavior of the NAO s of both groups of glasses is compared in Fig. 3 represented by the data of Ueno et al. [5] and those from Ref. [18]. The lines denote the structural behavior of the simple models. That for the germanate glasses was outlined earlier. In case of the borate glasses the increase of NBO up to y of 0.5 is the same for the same reason which is the lack of ONB in the glass structure. The subsequent decrease of NBO seems to follow a rule slightly dierent from that of NGeO which will be discussed later.
14
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
Fig. 2. Packing densities of alkali borate glasses with modi®er atoms Li ± squares, Na ± circles, K ± triangles, Rb ± plus signs, Cs ± ´ signs. The mass densities used in the calculations were taken from Ref. [14] (®lled squares) and all the other from Refs. [15,16]. The dashed line is a guide to the eye. The ®lled squares which follow the solid line belong to the data of a lithium silicate system [17]. In this case the values of the abscissa have to be understood as a molar ratio n(Me2 O)/n(2SiO2 ).
Fig. 3. Ge±O and B±O coordination numbers in alkali borate and germanate glasses versus composition. The data are taken from Refs. [4,18], respectively. The dashed lines correspond to the idealized behavior discussed in the text.
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
The packing density of the lithium silicate system [17] is shown in Fig. 2 as an example of a simpler structural behavior with invariable building units, the SiO4 tetrahedra, in a network which undergoes a continuous degradation process. The authors [17] paid much care to the suppression of phase separation in the samples with y < 0.4 by rapid quenching. Starting from vitreous SiO2 the packing density increases moderately and reaches a constant level at about y 1. This behavior can be explained by the simple concept of ®lling up the network holes by modi®er cations [19]. This process seems to ®nish at the molar ratio y 1. Except for the clear indications for the change of the Ge±O coordination state, one should pay some attention to other facts: The maximum positions of the packing densities and of the A±O coordination numbers are nearly the same for both the alkali germanate and borate glasses. The phenomenon of the change of the structural units AOn has similar characteristics and limitations. Thus,
15
one might expect a similar underlying mechanism. A comparison with the related crystals may help to clarify the structural behavior. The packing densities of the related crystals are compared with those of the glasses (cf. Fig. 4). From Figs. 1 and 2 it is observed that the packing densities of the glasses obey a stronger common rule than the related crystals. The packing densities of some of the crystals even miss the range of the ®gures, e.g., the packing density of the rutile-like GeO2 [9] clearly exceeds 60%. The densities, and thus, the glass structures with dierent alkali modi®ers follow well a common behavior. On the other hand, the data points of all the crystals are widely spread. This may be due to the additional constraints of symmetry which become eective only in the crystals. Most of the crystal structures of equal stoichiometry, thus, with equal mixtures of AOn groups but with unlike alkali oxide dier in their connectivity pattern. In two crystals, Na4 Ge9 O20 [20] and Na2 B4 O7 [21], even the numbers NAO
Fig. 4. Packing densities of alkali germanate and borate crystals with the alkali atoms Li ± squares, Na ± circles, K ± triangles, Cs ± ´ signs. The asterisks in the left plot mark the packing densities of two polymorphs of GeO2 . The dashed lines are the same as those shown in Figs. 1 and 2. They illustrate the behavior of the packing densities of the glasses. Note, the data of some of the crystals miss the range of the ®gure.
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U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
dier from those in structures of the same stoichiometry (Li4 Ge9 O20 [22] and Li2 B4 O7 [23], K2 B4 O7 [24]). Thus, it is not simple to obtain the characteristics of the glass structures by considering those of the related crystal structures. Here only the common features of the crystals are taken into account whereby Na4 Ge9 O20 [20] and Na2 B4 O7 [21] are excluded. The behavior common to all the crystals is characterized brie¯y. Most of the rules have been well known. Initial structures for the alkali borate glasses were given by Beekenkamp [25]: (a) So far as possible the O atoms are found in OB positions. (b) BO4 tetrahedra cannot bind to each other. (c) The ONB occur only in BO3 triangles. In addition, when approaching y 0.5, pairs of BO4 units become possible. In this way, the recent observations of NBO are well described. Larger superstructural units [26,27] are not essential to understand the enormous alterations of the packing densities and the change of the B±O coordination numbers. A modi®ed version of these rules can explain the anomalous behavior of the alkali germanate glasses, as well. Thus: (a) The oxygen atoms tend to occupy OB sites. (b) Assuming that the formation of GeO5 is possible, additional units of GeO4 can have four GeO5 neighbors and a GeO5 unit can link to one GeO5 unit. In the case of GeO6 additional units, a GeO4 can have only two GeO6 neighbors at maximum. A GeO6 octahedron cannot form pairs with GeO6 units. (c) The ONB s do not participate in GeO5 or GeO6 units. These rules are similar with those introduced earlier [7,8]. The additional allowance of GeO5 units suggested in Ref. [6] does not alter the explanation of the phenomenon.
The density maxima, especially those of the germanate systems (Fig. 1), are located slightly below y 0.5. Thus, the disorder in the arrangement of the dierent GeOn units in the glass structure limits the increase of the packing density and the NGeO s just before the maximum of the idealized model is reached. Following the rules given above, the behavior at y 0.5 would require an ordered variant of network connectivity which is only possible in the crystals, i.e. K2 Ge4 O9 [28] for the alkali germanates or Li2 B4 O7 [23], K2 B4 O7 [24] for the alkali borates. Besides that a slight deviation is found in the behavior of the packing densities at y of about 0.2 (Figs. 1 and 2) whose origin is not clear. The decrease of NGeO beyond y 0.5 can be explained as follows: GeO4 units which possess more than one ONB are not suitable for links with GeO5 or GeO6 units. This is still possible for the BO3 triangles in the borate systems. They can have two ONB and one link with a BO4 group using the third vertex. In Table 1 the number of groups and their connectivities are given for the important compositions of the rules stated above. The dashed lines in Fig. 3 illustrate the corresponding behavior of NGeO and NBO . Now some attention should be paid to the origin of the changes of the various AOn groups. Dierent from Si4 cations, the radius ratio of Ge4 and O2ÿ allows the formation of GeO5 and GeO6 units rather easily, which polyhedra more eectively ®ll the space than GeO4 tetrahedra [29]. For the B atoms the same eect would lead to BO4 tetrahedra instead of BO3 triangles. But in v-GeO2 and v-B2 O3 the networks are formed of GeO4 and
Table 1 Connectivities of the structural units in alkali germanate and borate glasses at important limiting compositions according to an idealized formation of links Molar ratio n(Me2 O)/n(A2 Ov ) 0.5 0.5 0.5 1.0 1.8
a
a a
Enlarged group ± number of links with equal other
Standard group ± number of links with equal other
Ratio of groups NAO
BO4 GeO5 GeO6
1 1 0
3 4 6
BO4
0
4
BO3 GeO4 GeO4 (GeO4 )ÿ (BO3 )2ÿ
1 1 0.33 0 0.25
0 0 2 3 0
The number of minus signs in the exponent indicates the number of ONB in these units Molar ratios with types of links which are also known in crystal structures.
a
3 4 2 0 1
3.5 4.5 4.5 4.0 3.2
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
BO3 units [30,31], respectively, and as a common characteristic all the oxygen atoms occupy bridging positions. Similarly with vitreous silica the packing density of vitreous germania lies even below that of the cristobalite-like form [32] with 47.5%. Obviously, the strong preference for the two-fold coordination of all the O atoms characterizes the structural behavior in the glasses. With additions of alkali oxide the role of the oxygens as OB s with NOA 2 can be maintained if this process is accompanied by an increase of the AOn units. Also such a behavior increases the packing eciency. Since at the molar ratio y of about 0.5 some unfavorable structures must occur, the process of the formation of larger units is not only terminated but it is turned in the opposite direction. These structural features include the incorporation of ONB in the GeO5 and/or GeO6 (BO4 ) units or the formation of clusters of these units. Obviously, ONB s overcompensate the formal charge of the Ge4 cations in ®ve- and six-fold coordinated Ge sites. The ONB s destroy the symmetry of the negative countercharge. Any neighboring alkali cations cannot balance these charges. Consequently, except for the formation of GeO5 pairs the higher coordinated Ge sites must be surrounded by GeO4 tetrahedra. Sucient space for the alkali cations is in the vicinity of the neighboring GeO4 units. Such a behavior is shown by the crystal structures, for example by that of K2 Ge4 O9 [28]. A partial shift of electron charge from the GeO6 to the GeO4 units along the bonds might stabilize such arrangements. A second questionable alternative is the formation of clusters of GeO5 and/or GeO6 (BO4 ) units. In this case, due to the need for charge compensation, the formation of three-fold coordinated oxygen sites is required. Such structures are known in several crystalline germanates, i.e. in rutile-like GeO2 [9] and in Na4 Ge9 O20 [20]. But structural disorder in the glasses should destabilize such clusters. The behaviors of the packing densities and the NGeO s stand in contrast to the frequent formation of such clusters. Recently, from the large NGeO s observed by X-ray diraction and EXAFS on sol±gel derived germanate glasses the existence of clusters formed with up to four GeO6
17
units is suggested [33]. Evidence for such clusters was already found in the Raman spectra of the series of alkali germanate glasses (Me Li,Na,K) and in comparisons to the related crystals [7]. On the whole, the Raman spectra demonstrate a structural behavior in accordance with the simple model [7,8] outlined in Section 1. But the spectra of the K germanate glasses, to a minor extent also those of the Na germanate glasses, show two small additional lines which are typical of the crystal Na4 Ge9 O20 [20]. This crystal contains clusters formed with four GeO6 units connected by threefold coordinated oxygen sites. A maximum of these features was detected [7] at molar ratios y of 0.5. A quantitative estimation of this small contribution of clusters was not possible. The use of spectroscopy mostly includes the comparison with spectra of the related crystals. As already shown in Ref. [7], the dierent types of oxygen sites, if not only OB and ONB species exist, complicate the comparisons of the germanate systems. The Raman spectra [34] and the 17 O NMR [35] spectra of rutile-like GeO2 cannot re¯ect a common oxygen site which would be characteristic for the GeO6 unit. This crystal [9] is formed of GeO6 units with three-fold coordinated O atoms. Consequently, the arguments of Refs. [34,35] for the full or partial absence of GeO6 units in alkali germanate glasses are not conclusive. 5. Conclusions The comparison of the packing densities of the alkali germanate glasses with those of alkali borate glasses corroborates the suggestion of the formation of GeO5 and/or GeO6 units in systems Me2 Ox GeO2 1ÿx in order to explain the anomalous behavior of the mass densities. The packing densities of the alkali germanate and borate glasses strongly obey a common behavior while the data of the related crystals are widely spread. Simple rules are suggested for explaining the germanate anomaly. These are the preference of the oxygen atoms for OB positions and the preference of the Ge atoms for units larger than GeO4 tetrahedra. Since ONB s are not suitable for incorporation in GeO5 and/or GeO6 sites the fraction of these units
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U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
decreases beyond x 0.20. However, a speci®c of some germanate crystals is the occurrence of clusters of GeO6 units accompanied by three-fold coordinated oxygen sites. The role of such clusters in the glass structures is not clear. Minor indications for such features were detected by Raman spectroscopy. Acknowledgements Financial support of the BMBF is gratefully acknowledged (Grant 03-KR5ROK-9). References [1] A.O. Ivanov, K.S. Evstropiev, Dokl. Akad. Nauk SSSR 145 (1962) 797. [2] M.K. Murthy, J. Ip, Nature 201 (1964) 285. [3] J.E. Shelby, J. Am. Ceram. Soc. 57 (1974) 436. [4] M. Ueno, M. Misawa, K. Suzuki, Physica B 120 (1983) 347. [5] P. Armand, M. Beno, A.J.G. Ellison, G.S. Knapp, D.L. Price, M.-L. Saboungi, Europhys. Lett. 29 (1995) 549. [6] U. Hoppe, R. Kranold, H.-J. Weber, A.C. Hannon, this issue, p. 1. [7] H. Verweij, J.H.J.M. Buster, J. Non-Cryst. Solids 34 (1979) 81. [8] B.M.J. Smets, T.P.A. Lommon, J. Non-Cryst. Solids 46 (1981) 21. [9] W.H. Baur, A.A. Khan, Acta Crystallogr. B 27 (1971) 2133. [10] T. Nanba, Y. Miura, S. Inoue, J. Takada, in: Proceedings of XVII International Congress on Glass, vol. 2, Chinese Ceramic Soc., Beijing, 1995, pp. 194±199. [11] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. B 26 (1970) 1046.
[12] R.D. Shannon, Acta Crystallogr. A 32 (1976) 751. [13] G.S. Henderson, M.E. Fleet, Trans. Am. Cryst. Assoc. 27 (1991) 251. [14] M. Shibata, C. Sanchez, H. Patel, S. Feller, J. Stark, G. Sumcad, J. Kasper, J. Non-Cryst. Solids 85 (1986) 29. [15] S. Takeuchi, T. Yamate, M. Kunugi, J. Soc. Mater. Sci. Jpn. 14 (1965) 225. [16] M. Kunugi, A. Konishi, S. Takeuchi, T. Yamate, J. Soc. Mater. Sci. Jpn. 21 (1972) 978. [17] A.M. Peters, F.M. Alamgir, S.W. Messer, S.A. Feller, K.L. Loh, Phys. Chem. Glasses 35 (1994) 212. [18] P.J. Bray, S.A. Feller, G.E. Jellison Jr, Y.H. Yun, J. NonCryst. Solids 38&39 (1980) 93. [19] B.E. Warren, H. Krutter, O. Morningstar, J. Am. Ceram. Soc. 19 (1936) 202. [20] N. Ingri, G. Lundgren, Acta Chem. Scand. 17 (1963) 617; M.E. Fleet, Acta Crystallogr. C 46 (1990) 1202. [21] J. Krogh-Moe, Acta Crystallogr. B 30 (1974) 578. [22] H. V ollenkle, A. Wittmann, H. Nowotny, Mh. Chem. 102 (1971) 361. [23] J. Krogh-Moe, Acta Crystallogr. 15 (1962) 190. [24] J. Krogh-Moe, Acta Crystallogr. B 28 (1972) 3089. [25] P. Beekenkamp, Philips Res. Rep. Suppl. 4 (1966) 1. [26] J. Krogh-Moe, Phys. Chem. Glasses 6 (1965) 46. [27] A.C. Wright, N.M. Vedishcheva, B.A. Shakhmatkin, J. Non-Cryst. Solids 192&193 (1995) 92. [28] H. V ollenkle, A. Wittmann, Mh. Chem. 102 (1971) 1245. [29] J.V. Smith, in: Geometrical and Structural Crystallography, Wiley, New York, 1982, 129 pp. [30] J.A.E. Desa, A.C. Wright, R.N. Sinclair, J. Non-Cryst. Solids 99 (1988) 276. [31] P.A.V. Johnson, A.C. Wright, R.N. Sinclair, J. Non-Cryst. Solids 50 (1982) 281. [32] H.J. Seifert, H. Nowotny, E. Hauser, Mh. Chem. 102 (1971) 1006. [33] K. Kamiya, M. Tatsumi, J. Matsuoka, H. Nasu, Phys. Chem. Glasses 39 (1998) 9. [34] G.S. Henderson, M.E. Fleet, J. Non-Cryst. Solids 134 (1991) 259. [35] R. Hussin, D. Holland, R. Dupree, J. Non-Cryst. Solids 232 (1998) 440.
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Behavior of the packing densities of alkali germanate glasses U. Hoppe
*
Department of Physics, Rostock University, D-18051 Rostock, Germany Received 27 April 1998; received in revised form 26 January 1999
Abstract Packing densities are more suitable than the mass densities for structural studies. A comparison of the corresponding data on alkali germanate glasses with those of alkali borate glasses corroborates the suggestion of the formation of GeO5 and/or GeO6 units in systems Me2 Ox GeO2 1ÿx in that range of composition where the maximum packing density occurs. The packing densities of both the alkali germanate and borate glasses strongly obey a common behavior while the data of the related crystals are widely spread. Simple structural rules like those used for the borate glasses are suggested for an explanation of the germanate anomaly. However, a speci®c characteristic of some germanate crystals is the occurrence of three-fold coordinated O sites accompanied by clusters of GeO6 units. There is no evidence for a signi®cant role of such clusters in the glass structures though minor indications for such features were detected by Raman spectroscopy. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 61.43.F
1. Introduction The anomalous behavior of some properties of alkali germanate glasses is commonly related to the conversion of the network of GeO4 tetrahedra forming the structure of vitreous (v-)GeO2 into a mixture of GeO4 and GeO6 units in glasses Me2 Ox GeO2 1ÿx of low modi®er content [1]. A change of the Ge±O coordination would explain the maxima in the behavior of the mass densities [2] and of the viscosities [3] at x of 0:15 . . . 0:20. However, dierent positions and heights of the maxima of the mass densities, q, make this explanation of the `germanate anomaly' somewhat questionable. In the case of the alkali systems, where the modi®er cations are either lighter or
* Tel.: +49-381 498 1731; fax: +49-381 498 1726; e-mail: [email protected]
heavier than the Ge atoms, q is not well suited for any structural comparisons. In structural considerations, it may be, therefore, more suitable to use the packing density rather than the mass density. In this way, the data of the mass densities of the alkali germanate glasses may also give clear evidence for the change of the Ge±O coordination state of a fraction of the Ge atoms, as well, if they are compared by means of the packing density. The examination of this behavior is the main topic of the present study. Some experimental methods indicate the conversion of GeO4 tetrahedra into larger structural units almost conclusively. Neutron diraction experiments of high real-space resolution [4±6] show a clear shoulder on the long-distance side of the Ge± O nearest-neighbor peak in the radial distribution function. These larger distances are attributable to Ge±O bonds in GeO5 and/or GeO6 units [6]. Furthermore, the total Ge±O coordination numbers,
0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 1 0 5 - 2
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U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
NGeO , [4±6] follow well that behavior which was predicted by Raman spectroscopy [7] and O1s Xray photoelectron spectroscopy (XPS) [8]. It was observed that up to 18 mol% Me2 O content, nonbridging oxygen atoms (ONB ) do not occur but only bridging oxygen atoms (OB ) [7,8] are found. Beyond this composition and up to 33 mol% Me2 O the ONB fraction reaches that quantity which is typical for silicate glasses being formed of only tetrahedral units. The incorporation of all the O atoms in Ge± O±Ge bridges (NOGe 2) inevitably results in an increase of NGeO with NGeO 4 + y where y is equal to n(Me2 O)/n(2GeO2 ). Hereinafter, for simplicity, the maximum of NGeO is set at 20 mol% Me2 O (y 0.5). Beyond this composition NGeO returns to four with NGeO 5 ÿ y which is reached at 33 mol% Me2 O (y 1). At present, no clear indication of a signi®cant role of three-fold coordinated oxygen sites in this process exists. Their occurrence would increase even more the NGeO or it would compensate for small fractions of ONB . Such oxygen sites are found in some of the crystal structures, among them in rutile-like GeO2 [9]. A few of such sites are detected in structural models which are generated by molecular dynamics (MD) simulations [10]. Thus, the exact structural situation might be more complicated than described by the model given in Refs. [7,8]. In this paper we will not stress small improvements of this model. In the preceding paper [6] it is shown that detailed knowledge which would characterize the exact distribution of the coordination state of all the Ge and O atoms is dicult to obtain by experimental methods. Here we plan to compare the behavior of the packing densities with that of the related crystals and with that of the borate glasses in a more approximate and simpli®ed way. The behavior of the packing densities only sheds a little more light on the structural situation but it is a simple approach. It raises the same questions about the mechanisms of the network reconstruction in alkali gemanate glasses which are still under debate in the literature. 2. Calculation of the packing densities The mass density, q, of a glassy material is an integral expression of the network characteristics,
of coordination numbers and the way of linking (connectivities) between the structural units. Furthermore, this value is in¯uenced by the mass number and the dimension of the various types of atoms. Hence, in case of the alkali germanate systems, q is not well suited for any structural comparisons. The number density of atoms may be a good alternative. Here we suggest using the packing density, qp , which is dierent from the number density and also takes into account the dierent dimensions of the types of atoms. The packing density is calculated according to , X X 3 ci Ai 1 qp 4p=3 ci ri qNav i
i
where ci is the molar fraction, Ai the mass number of the atoms of type i and Nav is the Avogadro number. The arbitrariness in the choice of the ionic radii, ri , taken here from Refs. [11,12] allows only qualitative discussions. The data of the mass density used in the calculations are taken from Refs. [2,13] for the alkali germanate glasses, from Refs. [14±16] for the alkali borate glasses and from Ref. [17] for the lithium silicate system. The radii used are the following: Li ± 59 pm, Na ± 100 pm, K ± 138 pm, Rb ± 161 pm, Cs ± 174 pm, O2ÿ ± 135 pm, B3 ± 1 pm, Si4 ± 26 pm, Ge4 ± 39 pm. The radii of the B3 and Ge4 cations are ®xed according to three- or four-fold coordination, respectively. Slightly larger radii of the higher coordinated Ge or B sites are not taken into account. The spheres of the small B3 and Ge4 cations play only a minor role in ®lling the space if compared with the role of the oxygen anions. The large spheres of the O2ÿ may partially overlap if they are members of the same structural unit. Since we do not plan to discuss the absolute values of qp but only tendencies occurring with an increasing alkali content the use of qp is justi®ed. 3. Results Figs. 1 and 2 show the behavior of the packing densities of the alkali germanate and borate glasses as a function of composition. As the uni®ed measure of the Me2 O content the molar ratio, y, with y n(Me2 O)/n(A2 Ov ) is used. Me is the alkali metal
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
13
Fig. 1. Packing densities of alkali germanate glasses with modi®er atoms Li ± squares, Na ± circles, K ± triangles, Rb ± plus signs, Cs ± ´ signs. The mass densities used in the calculations were taken from Ref. [13] (®lled marker) and all the other from Ref. [2]. The dashed line is a guide to the eye.
and A is the network former atom with the valency v. The plots in each ®gure allow detailed considerations in the interval up to y 0.8. The dashed lines are guides to the eye. The solid line in Fig. 2 accentuates the behavior of the packing density of the lithium silicate system which appears quite dierent from that of both other groups, the alkali germanate and borate systems. Since the packing densities, qp , have been calculated without corrections for overlapping of the O2ÿ spheres which share in common structural units the densities of those alkali systems appear largest in units that possess the shortest O±O distances. These systems are the alkali borate glasses. Corrections for overlapping are not planned because they are complex. These shortcomings do not limit the qualitative value of the dependencies of qp on the alkali content. 4. Discussion The packing densities, qp , of the alkali systems of the germanate and borate glasses increase rather
drastically up to molar ratios, y, of about 0.5 (Figs. 1 and 2). Beyond this composition the values of qp decrease, but less rapidly than found in the increase. The maximum positions and extents of the increase are similar for both groups of glasses. This ®nding corroborates the concept of an increase of the Ge±O coordination state [7,8] (cf. Section 1). In the case of the borate systems, the change of the B±O coordination number is shown beyond any doubt as, for example, frequently has been obtained by NMR [18]. The behavior of the NAO s of both groups of glasses is compared in Fig. 3 represented by the data of Ueno et al. [5] and those from Ref. [18]. The lines denote the structural behavior of the simple models. That for the germanate glasses was outlined earlier. In case of the borate glasses the increase of NBO up to y of 0.5 is the same for the same reason which is the lack of ONB in the glass structure. The subsequent decrease of NBO seems to follow a rule slightly dierent from that of NGeO which will be discussed later.
14
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
Fig. 2. Packing densities of alkali borate glasses with modi®er atoms Li ± squares, Na ± circles, K ± triangles, Rb ± plus signs, Cs ± ´ signs. The mass densities used in the calculations were taken from Ref. [14] (®lled squares) and all the other from Refs. [15,16]. The dashed line is a guide to the eye. The ®lled squares which follow the solid line belong to the data of a lithium silicate system [17]. In this case the values of the abscissa have to be understood as a molar ratio n(Me2 O)/n(2SiO2 ).
Fig. 3. Ge±O and B±O coordination numbers in alkali borate and germanate glasses versus composition. The data are taken from Refs. [4,18], respectively. The dashed lines correspond to the idealized behavior discussed in the text.
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
The packing density of the lithium silicate system [17] is shown in Fig. 2 as an example of a simpler structural behavior with invariable building units, the SiO4 tetrahedra, in a network which undergoes a continuous degradation process. The authors [17] paid much care to the suppression of phase separation in the samples with y < 0.4 by rapid quenching. Starting from vitreous SiO2 the packing density increases moderately and reaches a constant level at about y 1. This behavior can be explained by the simple concept of ®lling up the network holes by modi®er cations [19]. This process seems to ®nish at the molar ratio y 1. Except for the clear indications for the change of the Ge±O coordination state, one should pay some attention to other facts: The maximum positions of the packing densities and of the A±O coordination numbers are nearly the same for both the alkali germanate and borate glasses. The phenomenon of the change of the structural units AOn has similar characteristics and limitations. Thus,
15
one might expect a similar underlying mechanism. A comparison with the related crystals may help to clarify the structural behavior. The packing densities of the related crystals are compared with those of the glasses (cf. Fig. 4). From Figs. 1 and 2 it is observed that the packing densities of the glasses obey a stronger common rule than the related crystals. The packing densities of some of the crystals even miss the range of the ®gures, e.g., the packing density of the rutile-like GeO2 [9] clearly exceeds 60%. The densities, and thus, the glass structures with dierent alkali modi®ers follow well a common behavior. On the other hand, the data points of all the crystals are widely spread. This may be due to the additional constraints of symmetry which become eective only in the crystals. Most of the crystal structures of equal stoichiometry, thus, with equal mixtures of AOn groups but with unlike alkali oxide dier in their connectivity pattern. In two crystals, Na4 Ge9 O20 [20] and Na2 B4 O7 [21], even the numbers NAO
Fig. 4. Packing densities of alkali germanate and borate crystals with the alkali atoms Li ± squares, Na ± circles, K ± triangles, Cs ± ´ signs. The asterisks in the left plot mark the packing densities of two polymorphs of GeO2 . The dashed lines are the same as those shown in Figs. 1 and 2. They illustrate the behavior of the packing densities of the glasses. Note, the data of some of the crystals miss the range of the ®gure.
16
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
dier from those in structures of the same stoichiometry (Li4 Ge9 O20 [22] and Li2 B4 O7 [23], K2 B4 O7 [24]). Thus, it is not simple to obtain the characteristics of the glass structures by considering those of the related crystal structures. Here only the common features of the crystals are taken into account whereby Na4 Ge9 O20 [20] and Na2 B4 O7 [21] are excluded. The behavior common to all the crystals is characterized brie¯y. Most of the rules have been well known. Initial structures for the alkali borate glasses were given by Beekenkamp [25]: (a) So far as possible the O atoms are found in OB positions. (b) BO4 tetrahedra cannot bind to each other. (c) The ONB occur only in BO3 triangles. In addition, when approaching y 0.5, pairs of BO4 units become possible. In this way, the recent observations of NBO are well described. Larger superstructural units [26,27] are not essential to understand the enormous alterations of the packing densities and the change of the B±O coordination numbers. A modi®ed version of these rules can explain the anomalous behavior of the alkali germanate glasses, as well. Thus: (a) The oxygen atoms tend to occupy OB sites. (b) Assuming that the formation of GeO5 is possible, additional units of GeO4 can have four GeO5 neighbors and a GeO5 unit can link to one GeO5 unit. In the case of GeO6 additional units, a GeO4 can have only two GeO6 neighbors at maximum. A GeO6 octahedron cannot form pairs with GeO6 units. (c) The ONB s do not participate in GeO5 or GeO6 units. These rules are similar with those introduced earlier [7,8]. The additional allowance of GeO5 units suggested in Ref. [6] does not alter the explanation of the phenomenon.
The density maxima, especially those of the germanate systems (Fig. 1), are located slightly below y 0.5. Thus, the disorder in the arrangement of the dierent GeOn units in the glass structure limits the increase of the packing density and the NGeO s just before the maximum of the idealized model is reached. Following the rules given above, the behavior at y 0.5 would require an ordered variant of network connectivity which is only possible in the crystals, i.e. K2 Ge4 O9 [28] for the alkali germanates or Li2 B4 O7 [23], K2 B4 O7 [24] for the alkali borates. Besides that a slight deviation is found in the behavior of the packing densities at y of about 0.2 (Figs. 1 and 2) whose origin is not clear. The decrease of NGeO beyond y 0.5 can be explained as follows: GeO4 units which possess more than one ONB are not suitable for links with GeO5 or GeO6 units. This is still possible for the BO3 triangles in the borate systems. They can have two ONB and one link with a BO4 group using the third vertex. In Table 1 the number of groups and their connectivities are given for the important compositions of the rules stated above. The dashed lines in Fig. 3 illustrate the corresponding behavior of NGeO and NBO . Now some attention should be paid to the origin of the changes of the various AOn groups. Dierent from Si4 cations, the radius ratio of Ge4 and O2ÿ allows the formation of GeO5 and GeO6 units rather easily, which polyhedra more eectively ®ll the space than GeO4 tetrahedra [29]. For the B atoms the same eect would lead to BO4 tetrahedra instead of BO3 triangles. But in v-GeO2 and v-B2 O3 the networks are formed of GeO4 and
Table 1 Connectivities of the structural units in alkali germanate and borate glasses at important limiting compositions according to an idealized formation of links Molar ratio n(Me2 O)/n(A2 Ov ) 0.5 0.5 0.5 1.0 1.8
a
a a
Enlarged group ± number of links with equal other
Standard group ± number of links with equal other
Ratio of groups NAO
BO4 GeO5 GeO6
1 1 0
3 4 6
BO4
0
4
BO3 GeO4 GeO4 (GeO4 )ÿ (BO3 )2ÿ
1 1 0.33 0 0.25
0 0 2 3 0
The number of minus signs in the exponent indicates the number of ONB in these units Molar ratios with types of links which are also known in crystal structures.
a
3 4 2 0 1
3.5 4.5 4.5 4.0 3.2
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
BO3 units [30,31], respectively, and as a common characteristic all the oxygen atoms occupy bridging positions. Similarly with vitreous silica the packing density of vitreous germania lies even below that of the cristobalite-like form [32] with 47.5%. Obviously, the strong preference for the two-fold coordination of all the O atoms characterizes the structural behavior in the glasses. With additions of alkali oxide the role of the oxygens as OB s with NOA 2 can be maintained if this process is accompanied by an increase of the AOn units. Also such a behavior increases the packing eciency. Since at the molar ratio y of about 0.5 some unfavorable structures must occur, the process of the formation of larger units is not only terminated but it is turned in the opposite direction. These structural features include the incorporation of ONB in the GeO5 and/or GeO6 (BO4 ) units or the formation of clusters of these units. Obviously, ONB s overcompensate the formal charge of the Ge4 cations in ®ve- and six-fold coordinated Ge sites. The ONB s destroy the symmetry of the negative countercharge. Any neighboring alkali cations cannot balance these charges. Consequently, except for the formation of GeO5 pairs the higher coordinated Ge sites must be surrounded by GeO4 tetrahedra. Sucient space for the alkali cations is in the vicinity of the neighboring GeO4 units. Such a behavior is shown by the crystal structures, for example by that of K2 Ge4 O9 [28]. A partial shift of electron charge from the GeO6 to the GeO4 units along the bonds might stabilize such arrangements. A second questionable alternative is the formation of clusters of GeO5 and/or GeO6 (BO4 ) units. In this case, due to the need for charge compensation, the formation of three-fold coordinated oxygen sites is required. Such structures are known in several crystalline germanates, i.e. in rutile-like GeO2 [9] and in Na4 Ge9 O20 [20]. But structural disorder in the glasses should destabilize such clusters. The behaviors of the packing densities and the NGeO s stand in contrast to the frequent formation of such clusters. Recently, from the large NGeO s observed by X-ray diraction and EXAFS on sol±gel derived germanate glasses the existence of clusters formed with up to four GeO6
17
units is suggested [33]. Evidence for such clusters was already found in the Raman spectra of the series of alkali germanate glasses (Me Li,Na,K) and in comparisons to the related crystals [7]. On the whole, the Raman spectra demonstrate a structural behavior in accordance with the simple model [7,8] outlined in Section 1. But the spectra of the K germanate glasses, to a minor extent also those of the Na germanate glasses, show two small additional lines which are typical of the crystal Na4 Ge9 O20 [20]. This crystal contains clusters formed with four GeO6 units connected by threefold coordinated oxygen sites. A maximum of these features was detected [7] at molar ratios y of 0.5. A quantitative estimation of this small contribution of clusters was not possible. The use of spectroscopy mostly includes the comparison with spectra of the related crystals. As already shown in Ref. [7], the dierent types of oxygen sites, if not only OB and ONB species exist, complicate the comparisons of the germanate systems. The Raman spectra [34] and the 17 O NMR [35] spectra of rutile-like GeO2 cannot re¯ect a common oxygen site which would be characteristic for the GeO6 unit. This crystal [9] is formed of GeO6 units with three-fold coordinated O atoms. Consequently, the arguments of Refs. [34,35] for the full or partial absence of GeO6 units in alkali germanate glasses are not conclusive. 5. Conclusions The comparison of the packing densities of the alkali germanate glasses with those of alkali borate glasses corroborates the suggestion of the formation of GeO5 and/or GeO6 units in systems Me2 Ox GeO2 1ÿx in order to explain the anomalous behavior of the mass densities. The packing densities of the alkali germanate and borate glasses strongly obey a common behavior while the data of the related crystals are widely spread. Simple rules are suggested for explaining the germanate anomaly. These are the preference of the oxygen atoms for OB positions and the preference of the Ge atoms for units larger than GeO4 tetrahedra. Since ONB s are not suitable for incorporation in GeO5 and/or GeO6 sites the fraction of these units
18
U. Hoppe / Journal of Non-Crystalline Solids 248 (1999) 11±18
decreases beyond x 0.20. However, a speci®c of some germanate crystals is the occurrence of clusters of GeO6 units accompanied by three-fold coordinated oxygen sites. The role of such clusters in the glass structures is not clear. Minor indications for such features were detected by Raman spectroscopy. Acknowledgements Financial support of the BMBF is gratefully acknowledged (Grant 03-KR5ROK-9). References [1] A.O. Ivanov, K.S. Evstropiev, Dokl. Akad. Nauk SSSR 145 (1962) 797. [2] M.K. Murthy, J. Ip, Nature 201 (1964) 285. [3] J.E. Shelby, J. Am. Ceram. Soc. 57 (1974) 436. [4] M. Ueno, M. Misawa, K. Suzuki, Physica B 120 (1983) 347. [5] P. Armand, M. Beno, A.J.G. Ellison, G.S. Knapp, D.L. Price, M.-L. Saboungi, Europhys. Lett. 29 (1995) 549. [6] U. Hoppe, R. Kranold, H.-J. Weber, A.C. Hannon, this issue, p. 1. [7] H. Verweij, J.H.J.M. Buster, J. Non-Cryst. Solids 34 (1979) 81. [8] B.M.J. Smets, T.P.A. Lommon, J. Non-Cryst. Solids 46 (1981) 21. [9] W.H. Baur, A.A. Khan, Acta Crystallogr. B 27 (1971) 2133. [10] T. Nanba, Y. Miura, S. Inoue, J. Takada, in: Proceedings of XVII International Congress on Glass, vol. 2, Chinese Ceramic Soc., Beijing, 1995, pp. 194±199. [11] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. B 26 (1970) 1046.
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