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Medium range order in glass and the `germanate anomaly' effect
20 June 2002
Chemical Physics Letters 359 (2002) 246–252 www.elsevier.com/locate/cplett
Medium range order in glass and the ‘germanate anomaly’ effect Y.D. Yiannopoulos, C.P.E. Varsamis, E.I. Kamitsos
*
Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vass. Constantinou Ave., Athens 11635, Greece Received 30 January 2002; in final form 18 April 2002
Abstract The origin of extrema in the property-composition curves of germanate glasses has been a much debated issue. Using density and structural data for K- and Rb-germanate glasses we find that the short-range order structure alone cannot reproduce the maximum in density. By combining short- and medium-range order structures we calculate the dependence of density on composition in remarkably good agreement with experiment. The results show that the maximum in density can be traced to the coexistence of germanate octahedral units with compact three-membered rings of tetrahedral units. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The physical properties of alkali germanate glasses, xM2 O–ð1 xÞGeO2 (x ¼ mole fraction of the alkali oxide modifier, M2 O), deviate markedly from those of silicate glasses. While density and refractive index of alkali silicates are monotonically increasing functions of alkali content, they show a maximum at 10–20 mol% M2 O in germanate glasses. The presence of extrema in the composition dependence of physical properties in germanate glasses is known as the ‘germanate anomaly’ effect. Despite the long-term interest for its explanation [1–3], this effect continues to be a matter of controversy.
*
Corresponding author. Fax: +301-7273-794. E-mail address: [email protected] (E.I. Kamitsos).
The traditional explanation of the ‘germanate anomaly’ is based on a change of Ge coordination from four to six at small alkali oxide contents; a process thought to cause compaction of glass structure [1–3]. Early spectroscopic studies [4–9] have supported the conversion of GeØ4 tetrahedral units (Ø ¼ oxygen atom bridging two Ge atoms) into octahedral GeØ2 units in the 6 composition range 0 6 x 6 0:20 as follows: þ GeØ4 þ M2 O ! GeØ2 6 2M
ð1Þ
In the above scheme GeØ4 denotes the building unit of GeO2 glass, and the germanate octahedron GeØ2 6 is charge compensated by two alkali metal ions, Mþ . Germanate glasses with high M2 O contents were rarely considered in early investigations [4–9]; nevertheless, it was proposed that increasing metal oxide content above the extremum in physical properties leads to formation of non-bridging oxygen (NBO) atoms in germanate
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tetrahedra, and, thus, to network de-polymerization and expansion [1–3]. We may express the sequence of such modifications of the germanate network by the general reaction scheme: GeØ4 þ
4i ð4iÞ M2 O ! GeØi O4i ð4 iÞMþ 2 ð2Þ
with i ¼ 4, 3, 2, 1 and 0. Following the silicate nomenclature, we denote by Qi the complex in the right-hand side of Eq. (2) which involves a germanate tetrahedron with i bridging oxygens (BOs) and (4 i) NBOs, and (4 i) Mþ ions for charge compensation. In line with this notation, we may þ denote by Q6 the structural entity GeØ2 6 2M formed in Eq. (1). The original interpretation of the ‘germanate anomaly’ [1–9] was questioned by Henderson and Fleet [10]. They proposed formation of Qi tetrahedral units with NBOs without a change in Ge coordination, and associated the maximum in density with the creation of three-membered rings of tetrahedral Q4 units [10]. Recent studies of alkali germanate glasses suggest either the coexistence [11–14] or the sequential activation [15–18] of the two modification mechanisms, i.e., creation i of GeØ2 6 octahedral (Eq. (1)) and Q tetrahedral units with NBOs (Eq. (2)). New attempts to elucidate the structural origin of the property-composition trends in germanate glasses are based on a redistribution of the free volume [19], or on the increase of Ge coordination [20–22]. We have studied Rb- and K-germanate glasses by Raman and infrared spectroscopy as a function of metal oxide content to reveal the factors controlling glass properties. While these detailed vibrational studies of glass structure have been reported elsewhere [23–25], Fig. 1 summarizes the short-range order (SRO) structures in terms of mole fractions of the germanate units in the two glass-forming systems. It is evident that addition of M2 O to GeO2 up to ca. 25 mol% leads to parallel transformation of Q4 tetrahedral into Q3 tetrahedral and Q6 octahedral units. Above x ¼ 0:25 and up to ca. x ¼ 0:35 the conversion of Q4 and Q6 into Q3 prevails. For high alkali contents (x > 0:4) the creation of Qi tetrahedral with two- (Q2 , 1 3 þ GeØ2 O2 2 2M ) and three-NBOs (Q , GeØO3
Fig. 1. Mole fractions of octahedral GeØ2 6 units, X6 , and of germanate tetrahedral units Qi with (4 i) non-bridging oxygen atoms, Xi , as a function of alkali oxide content in glasses xM2 O–ð1 xÞGeO2 , M ¼ K (a) and M ¼ Rb (b). Lines are drawn as guides to the eye.
3Mþ ) dominates and causes the progressive depolymerization of the glass network. Preliminary results have highlighted the importance of both short- and medium-range order structures in determining dynamic, e.g. electrical conductivity, as well as static properties, e.g. density, in germanate glasses [26,27]. In this Letter we present a comparative study of density in Rb- and K-germanate glasses on the basis of their structure, and propose a new structural model for the quantitative description of the ‘germanate anomaly’ in density.
2. Results Reported density data for Rb- and K-germanate glasses [3,11,28–32] have been collected and are shown by solid symbols in Fig. 2 versus mole fraction of alkali metal oxide. The density data,
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although originating from different laboratories, manifest clearly the ‘germanate anomaly’ in both systems. It is observed that the alkali content at which density attains its maximum value depends on the alkali metal, as found also for the index of refraction [3]. According to the existing models, structural compaction is achieved when the content in GeØ2 octahedral is maximized [1–9], or 6 when three-membered rings of Q4 tetrahedral are formed [10] and lead to a decrease of the average size of voids in glass [19]. Since structural data are now available for Rb- and K-germanate glasses [23–25], it becomes feasible to test the existing models in predicting the composition dependence of density. Feller and co-workers have shown that the density, dðxÞ, of silicate and borate glasses is re-
Fig. 2. Composition dependence of density in glasses xM2 O–ð1 xÞGeO2 , M ¼ K (a) and M ¼ Rb (b). Experimental density (solid symbols) is compared with results of fitting Eq. (3) to the data with composition independent molar volumes of the germanate units (open circles), or with composition dependent molar volume of Q4 species (solid lines).
lated to the local polyhedra constituting their short-range order structure as follows: P Mi Xi ðxÞ dðxÞ ¼ Pi ; ð3Þ i Vi Xi ðxÞ where Mi is the molar mass, Vi is the effective molar volume, and Xi (x) is the mole fraction of the ith local polyhedron at composition x [21,22]. The SRO structural units found to build up the structure of K- and Rb-germanate glasses (Fig. 1) are given in Table 1 for the composition ranges of available density data. We now use the SRO structure and Eq. (3) to simulate the composition dependence of the experimental density in K- and Rb-germanate glasses. The results of the nonlinear least squares fitting of Eq. (3) to density data with composition independent volumes Vi as fitting parameters, as for silicate and borate glasses [21,22], are shown in Fig. 2 by the open symbols. It is found that for alkali contents above ca. 15 mol% M2 O the simulated and experimental data compare quite well, but below this composition the agreement is very poor. Similar results can be reproduced from density data reported recently by Kiczenski et al. [21]. Therefore, it appears that the SRO structures alone are not adequate to describe the non-monotonic density profile in germanate glasses, suggesting the necessity for incorporating structures beyond the SRO range. We note that in the range 0 6 x < 0:15, where simulated and experimental data do not compare well, the tetrahedral units Q4 are the majority structural species (Fig. 1), and that there is spectroscopic evidence for their redistribution in ring arrangements smaller than those in glassy GeO2 [10,23–25]. This suggests that there are Q4 -controlled medium-range order (MRO) structures which change with composition, and, therefore, the effective volume of Q4 would vary also with composition, i.e. V4 ¼ V4 ðxÞ. Thus, we now fit Eq. (3) to density data assuming a composition dependent volume of Q4 , but composition independent volumes V3 , V2 and V6 as fitting parameters. We find in the process of fitting that an exponential decay of V4 ðxÞ with composition x V4 ðxÞ ¼ A1 þ A2 expðx=A3 Þ
ð4Þ
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Table 1 Short-range order structural units, effective molar volumes ðViÞ, and effective densities (di ) in K- and Rb-germanate glasses. Q4L and Q4S are germanate tetrahedra, Q4 , arranged in large and small rings, respectively Structural units (M ¼ K, Rb)
K-germanates 3
4
Q (GeØ4 ¼ GeO2 ) Q3 (GeØ3 O Mþ ) þ Q2 (GeØ2 O2 2 2M ) 2 6 þ Q (GeØ6 2M ) Q4L (GeØ4 ¼ GeO2 ) Q4S (GeØ4 ¼ GeO2 )
Rb-germanates
Vi ðcm /mol)
di (g/cm )
Vi (cm3 /mol)
di (g/cm3 )
29 1 45.6 0.1 66.3 0.2 70 2 29 1 19.4 0.5
3.7 0.2 3.33 0.01 3.00 0.01 2.8 0.01 3.7 0.2 5.4 0.1
29 1 50.8 0.1 – 77 2 29 1 23.1 0.5
3.7 0.2 3.90 0.01 – 3.8 0.1 3.7 0.2 4.5 0.1
can describe remarkably well the density-composition profiles as shown by the continuous lines in Fig. 2. The adjustable parameters A1 , A2 and A3 , as well as V3 ; V2 and V6 , are determined from the best
3
fit of density. V4 ðxÞ is shown in Fig. 3a versus composition in the two systems and exhibits a faster decay in Rb-containing glasses. The effective molar volumes, Vi , of the local structural units are given in Table 1 and depicted in Fig. 3b as a function of the nominal negative charge per germanate unit. In K-glasses the effective volumes of germanate tetrahedra vary linearly with the number of charge-compensating K þ ions. Also, volumes Vi in Rb-glasses are found to be larger than those in K-glasses, as expected from the size difference of the charge-balancing alkali ions. Thus, very reasonable effective volumes Vi have resulted from the best fit of density.
3. Discussion and conclusions
Fig. 3. (a) Composition dependence of the effective molar volume of Q4 units, V4 ðxÞ, in glasses xM2 O–ð1 xÞGeO2 (M ¼ K, Rb); and (b) Effective molar volume of germanate tetrahedral (solid symbols) and octahedral units (open symbols) as a function of the nominal negative charge per germanate unit. Straight lines are least square fits to volume data of germanate tetrahedral units, with V4 denoting the molar volume of Q4 in GeO2 glass.
We find in this work that the combination of SRO and MRO structures in germanate glasses can lead to a successful quantification of the effect of composition on density. The variation of MRO structure with composition was quantified through the composition dependence of the effective molar volume of Q4 species, V4 ðxÞ, and this result is exploited here to shed light on the MRO structures in germanate glasses. We recall spectroscopic evidence for a redistribution of Q4 -based formations from large (L) rings in GeO2 glass (x ¼ 0) into small (S) rings at larger alkali contents, x [10,23– 25]. Noting by V4L and V4S the effective volume of Q4 units in L and S rings Eq. (4) gives V4L ¼ A1 þ A2 , and V4S ¼ A1 , while the parameter A3 controls the decay of V4 ðxÞ due to transformation of large into small rings. Denoting now by X4L ðxÞ and X4S ðxÞ the fractions of Q4 units in L and S rings one can write
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X4 ðxÞ ¼ X4L ðxÞ þ X4S ðxÞ;
ð5aÞ
X4 ðxÞV4 ðxÞ ¼ X4L ðxÞV4L þ X4S ðxÞV4S :
ð5bÞ
Eqs. (5a) and (5b) lead easily to the following expressions for X4L ðxÞ and X4S ðxÞ: X4L ðxÞ ¼ X4 ðxÞ
V4 ðxÞ V4S ; V4L V4S
ð6aÞ
X4S ðxÞ ¼ X4 ðxÞ
V4L V4 ðxÞ : V4L V4S
ð6bÞ
From the above expressions the fractions X4L ðxÞ and X4S ðxÞ can be calculated now in terms of the total fraction of units Q4 , X4 ðxÞ, and the effective volumes V4 ðxÞ, V4L and V4S obtained from best fitting the density. The results are shown in Fig. 4 and demonstrate for the first time a systematic variation of MRO structure in germanate glasses. Thus, the population of large rings, X4L ðxÞ, is found to decrease continuously with alkali content, while the fraction of small rings, X4S ðxÞ, increases with x and passes through a maximum value at ca. x ¼ 0:15–0:20. We consider now the relative contribution of the structure-building units on the overall glass density in terms of their effective densities (Table 1). The results show that Q6 octahedral units exhibit lower (M ¼ K), or comparable (M ¼ Rb), effective density than units QL4 in GeO2 glass. This shows that Q6 units alone are not the key factor causing the ‘anomaly’ in density, in contrast with the widely accepted model [1–9]. The only units found to exhibit a definite increase in density compared to g-GeO2 , and thus being capable of introducing compaction in the structure, are the small rings (QS4 ) of Q4 units. This is in agreement with previous propositions based on infrared and Raman studies of germanate glasses [10,23–25]. In view of the crucial role that MRO plays on the density ‘anomaly’ we discuss now the nature of Q4 -rings in germanate glasses. The similarities in the Raman spectra of g-GeO2 and its crystalline quartz phase suggest that six-membered rings of Q4 units constitute the dominant MRO structure in g-GeO2 , as shown schematically in Fig. 5a [33,34]. The smallest Q4 -based rings formed in germanates are the three-membered rings in crys-
Fig. 4. Fractions of Q4 germanate tetrahedral units in large, X4L (x), and small, X4S ðxÞ, ring formations in xM2 O–ð1 xÞGeO2 glasses, M ¼ K (a) and M ¼ Rb (b). X4 ðxÞ is the total fraction of Q4 germanate units as determined by spectroscopy (see Fig. 1).
tals M2 O–4GeO2 (M ¼ Na; K; Rb) having the stoichiometry of the x ¼ 0:20 glass [35]. The structure of these crystals consists of GeØ2 6 octahedral each being linked by corners to six three-membered rings (Ge3 Ø9 ) of Q4 units [35]. Formation of this type of arrangement of GeØ2 6 with Q4 in three-membered rings (denoted by Q6 =Q4S ) requires mole fractions: X6 ¼ 0:25 and X4 ¼ 0:75 ð¼ X4S ). This crystalline structure shows that the presence of three-membered rings of Q4 is intrinsically consistent with formation of GeØ2 6 units. This notion is in perfect agreement with the present results which show that formation of GeØ2 (Fig. 1) parallels the formation of small 6 rings of Q4 (Fig. 4). Arrangement of these units in Q6 =QS4 -type MRO structures like in crystals would require X6 =X4S ¼ 1=3. The most probable glass composition to support formation of Q6 =Q4S -type
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structure. Thus, the strong tendency of Q6 and Q4S structures to form and coexist in alkali germanate glasses appears to be a key element for the appearance of the maximum in density. In summary, density simulations in alkali germanate glasses have shown that even a detailed knowledge of SRO structures is inadequate to reproduce the composition dependence of density. When the density-composition model combined SRO with MRO structures an excellent agreement was obtained with experimental density. It was shown that MRO modifications involve a change in the size of Q4 rings towards more compact smaller rings, most probably the three-membered rings encountered in corresponding crystals. The findings of this work show that the maximum in density originates from the co-formation of threemembered rings with germanate octahedral units. The present results may provide a new basis for explaining ‘anomalies’ in other germanate properties, and in particular those exhibiting two extrema like the glass transition temperature and the activation energy for ion transport. Fig. 5. Two dimensional representations of atomic arrangements in germanate glasses as suggested from the analysis of density data. Six-membered rings of GeØ4 tetrahedra form the most probable MRO structure in GeO2 glass (a). In alkali germanate glasses three-membered rings of GeØ4 are linked to octahedral GeØ2 6 units to form a new MRO structure (b), and this is combined with larger rings of GeØ4 tetrahedra and nonbridging oxygen-containing tetrahedra to form the glass structure.
arrangements is the x ¼ 0:20 composition. The data in Fig. 1 give X6 ¼ 0:15 for M ¼ K and X6 ¼ 0:17 for M ¼ Rb. Thus, utilization of all GeØ2 units in Q6 =Q4S -type MRO structures 6 would require X4S ¼ 0:45 for M ¼ K and X4S ¼ 0:51 for M ¼ Rb. We find from fitting the density (Fig. 4) that X4S ¼ 0:42 for M ¼ K and X4S ¼ 0:59 for M ¼ Rb at x ¼ 0:20. This good agreement between required and found X4S values suggests that, when the chemical composition permits, Q6 units would link with Q4 -based three-membered rings to form arrangements like the one illustrated schematically in Fig. 5b. Such MRO arrangements would combine in a complex way, and in proportions determined by alkali content, with larger rings of Q4 units and with Q2 =Q1 tetrahedral to form the glass
Acknowledgements This work was financially supported by the Greek General Secretariat for Research and Technology (Grant PENED99/ED44).
References [1] A.O. Ivanov, K.S. Evstropiev, Dokl. Chem. Akad. Nauk, SSSR 145 (1962) 797. [2] E.F. Riebling, J. Chem. Phys. 39 (1963) 1889. [3] M.K. Murthy, J. Ip, Nature 201 (1964) 285. [4] M.K. Murthy, E.M. Kirby, Phys. Chem. Glasses 5 (1964) 144. [5] H. Verweij, J.H.J.M. Buster, J. Non-Cryst. Solids 34 (1979) 81. [6] K. Kamiya, S. Sakka, Phys. Chem. Glasses 20 (1979) 60. [7] B.M.J. Smets, T.P.A. Lommen, J. Non-Cryst. Solids 46 (1981) 21. [8] A.D. Cox, P.W. McMillan, J. Non-Cryst. Solids 44 (1981) 257. [9] M. Ueno, M. Misawa, K. Susuki, Physica B 120 (1983) 347. [10] G.S. Henderson, M.E. Fleet, J. Non-Cryst. Solids 134 (1991) 259.
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[11] W.C. Huang, H. Jain, M.A. Marcus, J. Non-Cryst. Solids 180 (1994) 40. [12] X. Lu, H. Jain, W.C. Huang, Phys. Chem. Glasses 37 (1996) 201. [13] D.L. Price, A.J.G. Ellison, M.L. Saboungi, R.Z. Hu, T. Egami, W.S. Howells, Phys. Rev. B 55 (1997) 11249. [14] K. Kamiya, M. Tatsumi, H. Nasu, Phys. Chem. Glasses 39 (1998) 9. [15] R. Hussin, D. Holland, R. Dupree, J. Non-Cryst. Solids 232–234 (1998) 440. [16] U. Hoppe, R. Kranold, H.-J. Weber, A.C. Hannon, J. Non-Cryst. Solids 248 (1999) 1. [17] T. Nanba, J. Kieffer, Y. Miura, J. Non-Cryst. Solids 277 (2000) 188. [18] A. Karthikeyan, R.M. Almeida, J. Non-Cryst. Solids 281 (2001) 152. [19] H.-J. Weber, J. Non-Cryst. Solids 243 (1999) 220. [20] S.K. Lee, M. Tatsumisago, T. Minami, Phys. Chem. Glasses 36 (1995) 225. [21] T.J. Kiczenski, C. Ma, E. Hammarsten, D. Wilkerson, M. Affatigato, S.A. Feller, J. Non-Cryst. Solids 272 (2000) 57. [22] S.A. Feller, N. Lower, M. Affatigato, Phys. Chem. Glasses 42 (2001) 240, and references therein.
[23] E.I. Kamitsos, Y.D. Yiannopoulos, M.A. Karakassides, G.D. Chryssikos, H. Jain, J. Phys. Chem. 100 (1996) 11755. [24] E.I. Kamitsos, Y.D. Yiannopoulos, C.P. Varsamis, H. Jain, J. Non-Cryst. Solids 222 (1997) 59. [25] Y.D. Yiannopoulos, Ph.D. Thesis, Athens University, Athens, Greece, 2000. [26] H. Jain, W.C. Huang, E.I. Kamitsos, Y.D. Yiannopoulos, J. Non-Cryst. Solids 222 (1997) 361. [27] Y.D. Yiannopoulos, C.P. Varsamis, E.I. Kamitsos, J. NonCryst. Solids 293–295 (2001) 244. [28] M.K. Murthy, L. Long, J. Ip, J. Am. Ceram. Soc. 51 (1968) 661. [29] A.M. Efimov, E.K. Mazurina, V.A. Kharyuzov, M.V. Proskuryakov, Fiz. Khim. Stekla 2 (1976) 151. [30] S. Sakka, K. Kamiya, J. Non-Cryst. Solids 49 (1982) 103. [31] K.S. Evstropiev, V.K. Pavlovskii, Inorg. Mater. 3 (1967) 592. [32] J.N. Mundy, G.L. Jin, Solid State Ionics 24 (1987) 263. [33] F.L. Galeener, Phys. Rev. B 19 (1979) 4292. [34] D.A. McKeown, C.I. Merzbacher, J. Non-Cryst. Solids 183 (1995) 61. [35] M. Goreaud, B. Raveau, Acta Crystallogr. B 32 (1976) 1536.
Chemical Physics Letters 359 (2002) 246–252 www.elsevier.com/locate/cplett
Medium range order in glass and the ‘germanate anomaly’ effect Y.D. Yiannopoulos, C.P.E. Varsamis, E.I. Kamitsos
*
Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vass. Constantinou Ave., Athens 11635, Greece Received 30 January 2002; in final form 18 April 2002
Abstract The origin of extrema in the property-composition curves of germanate glasses has been a much debated issue. Using density and structural data for K- and Rb-germanate glasses we find that the short-range order structure alone cannot reproduce the maximum in density. By combining short- and medium-range order structures we calculate the dependence of density on composition in remarkably good agreement with experiment. The results show that the maximum in density can be traced to the coexistence of germanate octahedral units with compact three-membered rings of tetrahedral units. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The physical properties of alkali germanate glasses, xM2 O–ð1 xÞGeO2 (x ¼ mole fraction of the alkali oxide modifier, M2 O), deviate markedly from those of silicate glasses. While density and refractive index of alkali silicates are monotonically increasing functions of alkali content, they show a maximum at 10–20 mol% M2 O in germanate glasses. The presence of extrema in the composition dependence of physical properties in germanate glasses is known as the ‘germanate anomaly’ effect. Despite the long-term interest for its explanation [1–3], this effect continues to be a matter of controversy.
*
Corresponding author. Fax: +301-7273-794. E-mail address: [email protected] (E.I. Kamitsos).
The traditional explanation of the ‘germanate anomaly’ is based on a change of Ge coordination from four to six at small alkali oxide contents; a process thought to cause compaction of glass structure [1–3]. Early spectroscopic studies [4–9] have supported the conversion of GeØ4 tetrahedral units (Ø ¼ oxygen atom bridging two Ge atoms) into octahedral GeØ2 units in the 6 composition range 0 6 x 6 0:20 as follows: þ GeØ4 þ M2 O ! GeØ2 6 2M
ð1Þ
In the above scheme GeØ4 denotes the building unit of GeO2 glass, and the germanate octahedron GeØ2 6 is charge compensated by two alkali metal ions, Mþ . Germanate glasses with high M2 O contents were rarely considered in early investigations [4–9]; nevertheless, it was proposed that increasing metal oxide content above the extremum in physical properties leads to formation of non-bridging oxygen (NBO) atoms in germanate
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tetrahedra, and, thus, to network de-polymerization and expansion [1–3]. We may express the sequence of such modifications of the germanate network by the general reaction scheme: GeØ4 þ
4i ð4iÞ M2 O ! GeØi O4i ð4 iÞMþ 2 ð2Þ
with i ¼ 4, 3, 2, 1 and 0. Following the silicate nomenclature, we denote by Qi the complex in the right-hand side of Eq. (2) which involves a germanate tetrahedron with i bridging oxygens (BOs) and (4 i) NBOs, and (4 i) Mþ ions for charge compensation. In line with this notation, we may þ denote by Q6 the structural entity GeØ2 6 2M formed in Eq. (1). The original interpretation of the ‘germanate anomaly’ [1–9] was questioned by Henderson and Fleet [10]. They proposed formation of Qi tetrahedral units with NBOs without a change in Ge coordination, and associated the maximum in density with the creation of three-membered rings of tetrahedral Q4 units [10]. Recent studies of alkali germanate glasses suggest either the coexistence [11–14] or the sequential activation [15–18] of the two modification mechanisms, i.e., creation i of GeØ2 6 octahedral (Eq. (1)) and Q tetrahedral units with NBOs (Eq. (2)). New attempts to elucidate the structural origin of the property-composition trends in germanate glasses are based on a redistribution of the free volume [19], or on the increase of Ge coordination [20–22]. We have studied Rb- and K-germanate glasses by Raman and infrared spectroscopy as a function of metal oxide content to reveal the factors controlling glass properties. While these detailed vibrational studies of glass structure have been reported elsewhere [23–25], Fig. 1 summarizes the short-range order (SRO) structures in terms of mole fractions of the germanate units in the two glass-forming systems. It is evident that addition of M2 O to GeO2 up to ca. 25 mol% leads to parallel transformation of Q4 tetrahedral into Q3 tetrahedral and Q6 octahedral units. Above x ¼ 0:25 and up to ca. x ¼ 0:35 the conversion of Q4 and Q6 into Q3 prevails. For high alkali contents (x > 0:4) the creation of Qi tetrahedral with two- (Q2 , 1 3 þ GeØ2 O2 2 2M ) and three-NBOs (Q , GeØO3
Fig. 1. Mole fractions of octahedral GeØ2 6 units, X6 , and of germanate tetrahedral units Qi with (4 i) non-bridging oxygen atoms, Xi , as a function of alkali oxide content in glasses xM2 O–ð1 xÞGeO2 , M ¼ K (a) and M ¼ Rb (b). Lines are drawn as guides to the eye.
3Mþ ) dominates and causes the progressive depolymerization of the glass network. Preliminary results have highlighted the importance of both short- and medium-range order structures in determining dynamic, e.g. electrical conductivity, as well as static properties, e.g. density, in germanate glasses [26,27]. In this Letter we present a comparative study of density in Rb- and K-germanate glasses on the basis of their structure, and propose a new structural model for the quantitative description of the ‘germanate anomaly’ in density.
2. Results Reported density data for Rb- and K-germanate glasses [3,11,28–32] have been collected and are shown by solid symbols in Fig. 2 versus mole fraction of alkali metal oxide. The density data,
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although originating from different laboratories, manifest clearly the ‘germanate anomaly’ in both systems. It is observed that the alkali content at which density attains its maximum value depends on the alkali metal, as found also for the index of refraction [3]. According to the existing models, structural compaction is achieved when the content in GeØ2 octahedral is maximized [1–9], or 6 when three-membered rings of Q4 tetrahedral are formed [10] and lead to a decrease of the average size of voids in glass [19]. Since structural data are now available for Rb- and K-germanate glasses [23–25], it becomes feasible to test the existing models in predicting the composition dependence of density. Feller and co-workers have shown that the density, dðxÞ, of silicate and borate glasses is re-
Fig. 2. Composition dependence of density in glasses xM2 O–ð1 xÞGeO2 , M ¼ K (a) and M ¼ Rb (b). Experimental density (solid symbols) is compared with results of fitting Eq. (3) to the data with composition independent molar volumes of the germanate units (open circles), or with composition dependent molar volume of Q4 species (solid lines).
lated to the local polyhedra constituting their short-range order structure as follows: P Mi Xi ðxÞ dðxÞ ¼ Pi ; ð3Þ i Vi Xi ðxÞ where Mi is the molar mass, Vi is the effective molar volume, and Xi (x) is the mole fraction of the ith local polyhedron at composition x [21,22]. The SRO structural units found to build up the structure of K- and Rb-germanate glasses (Fig. 1) are given in Table 1 for the composition ranges of available density data. We now use the SRO structure and Eq. (3) to simulate the composition dependence of the experimental density in K- and Rb-germanate glasses. The results of the nonlinear least squares fitting of Eq. (3) to density data with composition independent volumes Vi as fitting parameters, as for silicate and borate glasses [21,22], are shown in Fig. 2 by the open symbols. It is found that for alkali contents above ca. 15 mol% M2 O the simulated and experimental data compare quite well, but below this composition the agreement is very poor. Similar results can be reproduced from density data reported recently by Kiczenski et al. [21]. Therefore, it appears that the SRO structures alone are not adequate to describe the non-monotonic density profile in germanate glasses, suggesting the necessity for incorporating structures beyond the SRO range. We note that in the range 0 6 x < 0:15, where simulated and experimental data do not compare well, the tetrahedral units Q4 are the majority structural species (Fig. 1), and that there is spectroscopic evidence for their redistribution in ring arrangements smaller than those in glassy GeO2 [10,23–25]. This suggests that there are Q4 -controlled medium-range order (MRO) structures which change with composition, and, therefore, the effective volume of Q4 would vary also with composition, i.e. V4 ¼ V4 ðxÞ. Thus, we now fit Eq. (3) to density data assuming a composition dependent volume of Q4 , but composition independent volumes V3 , V2 and V6 as fitting parameters. We find in the process of fitting that an exponential decay of V4 ðxÞ with composition x V4 ðxÞ ¼ A1 þ A2 expðx=A3 Þ
ð4Þ
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Table 1 Short-range order structural units, effective molar volumes ðViÞ, and effective densities (di ) in K- and Rb-germanate glasses. Q4L and Q4S are germanate tetrahedra, Q4 , arranged in large and small rings, respectively Structural units (M ¼ K, Rb)
K-germanates 3
4
Q (GeØ4 ¼ GeO2 ) Q3 (GeØ3 O Mþ ) þ Q2 (GeØ2 O2 2 2M ) 2 6 þ Q (GeØ6 2M ) Q4L (GeØ4 ¼ GeO2 ) Q4S (GeØ4 ¼ GeO2 )
Rb-germanates
Vi ðcm /mol)
di (g/cm )
Vi (cm3 /mol)
di (g/cm3 )
29 1 45.6 0.1 66.3 0.2 70 2 29 1 19.4 0.5
3.7 0.2 3.33 0.01 3.00 0.01 2.8 0.01 3.7 0.2 5.4 0.1
29 1 50.8 0.1 – 77 2 29 1 23.1 0.5
3.7 0.2 3.90 0.01 – 3.8 0.1 3.7 0.2 4.5 0.1
can describe remarkably well the density-composition profiles as shown by the continuous lines in Fig. 2. The adjustable parameters A1 , A2 and A3 , as well as V3 ; V2 and V6 , are determined from the best
3
fit of density. V4 ðxÞ is shown in Fig. 3a versus composition in the two systems and exhibits a faster decay in Rb-containing glasses. The effective molar volumes, Vi , of the local structural units are given in Table 1 and depicted in Fig. 3b as a function of the nominal negative charge per germanate unit. In K-glasses the effective volumes of germanate tetrahedra vary linearly with the number of charge-compensating K þ ions. Also, volumes Vi in Rb-glasses are found to be larger than those in K-glasses, as expected from the size difference of the charge-balancing alkali ions. Thus, very reasonable effective volumes Vi have resulted from the best fit of density.
3. Discussion and conclusions
Fig. 3. (a) Composition dependence of the effective molar volume of Q4 units, V4 ðxÞ, in glasses xM2 O–ð1 xÞGeO2 (M ¼ K, Rb); and (b) Effective molar volume of germanate tetrahedral (solid symbols) and octahedral units (open symbols) as a function of the nominal negative charge per germanate unit. Straight lines are least square fits to volume data of germanate tetrahedral units, with V4 denoting the molar volume of Q4 in GeO2 glass.
We find in this work that the combination of SRO and MRO structures in germanate glasses can lead to a successful quantification of the effect of composition on density. The variation of MRO structure with composition was quantified through the composition dependence of the effective molar volume of Q4 species, V4 ðxÞ, and this result is exploited here to shed light on the MRO structures in germanate glasses. We recall spectroscopic evidence for a redistribution of Q4 -based formations from large (L) rings in GeO2 glass (x ¼ 0) into small (S) rings at larger alkali contents, x [10,23– 25]. Noting by V4L and V4S the effective volume of Q4 units in L and S rings Eq. (4) gives V4L ¼ A1 þ A2 , and V4S ¼ A1 , while the parameter A3 controls the decay of V4 ðxÞ due to transformation of large into small rings. Denoting now by X4L ðxÞ and X4S ðxÞ the fractions of Q4 units in L and S rings one can write
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X4 ðxÞ ¼ X4L ðxÞ þ X4S ðxÞ;
ð5aÞ
X4 ðxÞV4 ðxÞ ¼ X4L ðxÞV4L þ X4S ðxÞV4S :
ð5bÞ
Eqs. (5a) and (5b) lead easily to the following expressions for X4L ðxÞ and X4S ðxÞ: X4L ðxÞ ¼ X4 ðxÞ
V4 ðxÞ V4S ; V4L V4S
ð6aÞ
X4S ðxÞ ¼ X4 ðxÞ
V4L V4 ðxÞ : V4L V4S
ð6bÞ
From the above expressions the fractions X4L ðxÞ and X4S ðxÞ can be calculated now in terms of the total fraction of units Q4 , X4 ðxÞ, and the effective volumes V4 ðxÞ, V4L and V4S obtained from best fitting the density. The results are shown in Fig. 4 and demonstrate for the first time a systematic variation of MRO structure in germanate glasses. Thus, the population of large rings, X4L ðxÞ, is found to decrease continuously with alkali content, while the fraction of small rings, X4S ðxÞ, increases with x and passes through a maximum value at ca. x ¼ 0:15–0:20. We consider now the relative contribution of the structure-building units on the overall glass density in terms of their effective densities (Table 1). The results show that Q6 octahedral units exhibit lower (M ¼ K), or comparable (M ¼ Rb), effective density than units QL4 in GeO2 glass. This shows that Q6 units alone are not the key factor causing the ‘anomaly’ in density, in contrast with the widely accepted model [1–9]. The only units found to exhibit a definite increase in density compared to g-GeO2 , and thus being capable of introducing compaction in the structure, are the small rings (QS4 ) of Q4 units. This is in agreement with previous propositions based on infrared and Raman studies of germanate glasses [10,23–25]. In view of the crucial role that MRO plays on the density ‘anomaly’ we discuss now the nature of Q4 -rings in germanate glasses. The similarities in the Raman spectra of g-GeO2 and its crystalline quartz phase suggest that six-membered rings of Q4 units constitute the dominant MRO structure in g-GeO2 , as shown schematically in Fig. 5a [33,34]. The smallest Q4 -based rings formed in germanates are the three-membered rings in crys-
Fig. 4. Fractions of Q4 germanate tetrahedral units in large, X4L (x), and small, X4S ðxÞ, ring formations in xM2 O–ð1 xÞGeO2 glasses, M ¼ K (a) and M ¼ Rb (b). X4 ðxÞ is the total fraction of Q4 germanate units as determined by spectroscopy (see Fig. 1).
tals M2 O–4GeO2 (M ¼ Na; K; Rb) having the stoichiometry of the x ¼ 0:20 glass [35]. The structure of these crystals consists of GeØ2 6 octahedral each being linked by corners to six three-membered rings (Ge3 Ø9 ) of Q4 units [35]. Formation of this type of arrangement of GeØ2 6 with Q4 in three-membered rings (denoted by Q6 =Q4S ) requires mole fractions: X6 ¼ 0:25 and X4 ¼ 0:75 ð¼ X4S ). This crystalline structure shows that the presence of three-membered rings of Q4 is intrinsically consistent with formation of GeØ2 6 units. This notion is in perfect agreement with the present results which show that formation of GeØ2 (Fig. 1) parallels the formation of small 6 rings of Q4 (Fig. 4). Arrangement of these units in Q6 =QS4 -type MRO structures like in crystals would require X6 =X4S ¼ 1=3. The most probable glass composition to support formation of Q6 =Q4S -type
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structure. Thus, the strong tendency of Q6 and Q4S structures to form and coexist in alkali germanate glasses appears to be a key element for the appearance of the maximum in density. In summary, density simulations in alkali germanate glasses have shown that even a detailed knowledge of SRO structures is inadequate to reproduce the composition dependence of density. When the density-composition model combined SRO with MRO structures an excellent agreement was obtained with experimental density. It was shown that MRO modifications involve a change in the size of Q4 rings towards more compact smaller rings, most probably the three-membered rings encountered in corresponding crystals. The findings of this work show that the maximum in density originates from the co-formation of threemembered rings with germanate octahedral units. The present results may provide a new basis for explaining ‘anomalies’ in other germanate properties, and in particular those exhibiting two extrema like the glass transition temperature and the activation energy for ion transport. Fig. 5. Two dimensional representations of atomic arrangements in germanate glasses as suggested from the analysis of density data. Six-membered rings of GeØ4 tetrahedra form the most probable MRO structure in GeO2 glass (a). In alkali germanate glasses three-membered rings of GeØ4 are linked to octahedral GeØ2 6 units to form a new MRO structure (b), and this is combined with larger rings of GeØ4 tetrahedra and nonbridging oxygen-containing tetrahedra to form the glass structure.
arrangements is the x ¼ 0:20 composition. The data in Fig. 1 give X6 ¼ 0:15 for M ¼ K and X6 ¼ 0:17 for M ¼ Rb. Thus, utilization of all GeØ2 units in Q6 =Q4S -type MRO structures 6 would require X4S ¼ 0:45 for M ¼ K and X4S ¼ 0:51 for M ¼ Rb. We find from fitting the density (Fig. 4) that X4S ¼ 0:42 for M ¼ K and X4S ¼ 0:59 for M ¼ Rb at x ¼ 0:20. This good agreement between required and found X4S values suggests that, when the chemical composition permits, Q6 units would link with Q4 -based three-membered rings to form arrangements like the one illustrated schematically in Fig. 5b. Such MRO arrangements would combine in a complex way, and in proportions determined by alkali content, with larger rings of Q4 units and with Q2 =Q1 tetrahedral to form the glass
Acknowledgements This work was financially supported by the Greek General Secretariat for Research and Technology (Grant PENED99/ED44).
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