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A neutron diffraction, isotopic substitution study of the structure of Li2O·2SiO2 glass
Journal of Non-Crystalline Solids 232±234 (1998) 721±727
A neutron diraction, isotopic substitution study of the structure of Li2Oá2SiO2 glass J. Zhao b
a,* ,
P.H. Gaskell a, M.M. Cluckie a, A.K. Soper
b
a Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK ISIS Science Division, Daresbury Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UK
Abstract The structure of Li2 Oá2SiO2 glass has been studied in detail by neutron diraction with isotopic substitution of Li. The ®rst Si±O and O±O distances are 0:163 0:001 and 0:266 0:001 nm, respectively. Li is found in a relatively wellde®ned tetrahedral site, with 3:2 0:2 oxygen atoms at 0:197 0:001 nm and a further 0:8 0:5 in a broad tail extending to about 0.22. The Li±Li ®rst neighbour distance in a silicate glass has been measured directly, for the ®rst time, and the value of 0:310 0:002 nm yields strong evidence for a non-random distribution of the Li ions in the glass. The short- and medium-range structure exhibit considerable similarity to those of crystalline (c-) lithium disilicate. Ó 1998 Elsevier Science B.V. All rights reserved.
1. Introduction While diraction gives a maximum amount of structural information for monoatomic systems, the technique suers from the problem that for multi-component systems, uncertainties arise due to the overlap of coordination shells. A determination of the structure associated with weakly bonded cations requires chemically speci®c techniques, and the extended X-ray absorption ®ne structure (EXAFS) has proved useful in the studies of alkali silicate glasses [1]. The technique is suitable for relatively heavy elements, but the information obtained is the most accurate for the ®rst coordination shell. Neutron diraction, with isotopic
* Corresponding author. Present address: Advanced Laser and Fusion Tech. Inc., 189 Deveault Street Unit 7, Hull, Que., Canada J8Z 1S7. Tel.: 1 819 7700477; fax: 1 819 7703862; e-mail: [email protected].
0022-3093/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 8 ) 0 0 5 5 4 - 7
substitution, is a very powerful technique for obtaining the structure around network modifying cations [2±6], provided suitable isotopes are available. Li-containing silicate glasses have been studied previously [7±10], but the information available so far is still inadequate to establish a complete structural picture. Uhlig et al. [8] used isotopic substitution in their neutron scattering study of silicate glasses, but concentrated mainly on an examination of the silicate `framework'. Here we emphases the local structure surrounding Li, and the distribution of Li ions within the framework. Despite the fact that 6 Li has a high neutron absorption cross-section rabs 940 barns [11]), the large dierence between the coherent scattering lengths of 6 Li b 2:0 10ÿ15 m and 7 Li b ÿ2:22 10ÿ15 m [11] makes it possible to obtain good signal contrast from isotopic substitution. First- and second-order dierences are obtained from measurements involving three
722
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
dierent Li isotopic compositions, giving information on the local environment of Li from ®rst-order dierence data, and the Li±Li distribution function from the second-order dierence. Information on local and medium-range order are then examined in detail.
2. Experimental details and data analysis Three Li2 Oá2SiO2 glasses were prepared. The starting materials were melted in a covered Pt/Rh crucible at 1200°C for 30 min. To ensure homogeneity, the glasses obtained were subsequently crushed and re-melted twice at 1200°C for 30 min. The resulting glasses were clear with no sign of phase separation. The isotopic contents of the samples were analysed using laser ionic mass analysis (LIMA). The results show that the 6 Li enriched sample contains 87.8 1.0% 6 Li and 12.2 1.0% 7 Li. The 7 Li enriched sample contains essentially pure 7 Li isotope, while the third sample contains an equal mixture of the two (mix Li). Atomic absorption analysis indicates approximately 1% loss of Li2 O due to volatilisation during sample preparation for the 7 Li-containing glass, but problems in estimating the 6 Li2 O concentration prevented accurate analysis of the composition of the 6 Li and mix Li glasses. The compositions of all of the glasses are assumed to be identical to that of the 7 Li-containing glass. The number density of the sample is 8:30 0:02 10ÿ5 nmÿ3 . The neutron diraction measurements were carried out using the SANDALS diractometer at ISIS (Daresbury Rutherford Appleton Laboratory, UK). A relatively thin ¯at geometry was used to optimise the scattered intensity and minimise the adverse eects of the high absorption of 6 Li. The sample container was made of null Ti±Zr alloy and its inner thickness was 2 mm. The corrected dierential scattering cross-section, dr=dX, for the system can be expressed in terms of the `self-scattering' and the `distinct-scattering', i.e. 1 dr X 2 XX ci bi ci cj bi bj Sij Q ÿ 1 ; N dX i i j6i
1
where Q 4p sin h=k; k is the incident neutron wavelength, 2h the scattering angle, N the total number of atoms, ci and bi are the atomic concentration and the coherent neutron scattering length of species i, respectively, and Sij Q the partial structure factor relating species i and j. The dierence, DLi Q, between the distinct scattering functions for two samples, diering only in their isotopic contents, gives a weighted sum of the Li-centred partial correlation functions: DLi Q W1 SLiO Q ÿ 1 W2 SLiSi Q ÿ 1 W3 SLiLi Q ÿ 1;
2
ÿ W1 2cLi cO bO bLi ÿ b0Li ; ÿ W2 2cLi cSi bSi bLi ÿ b0Li ;
3
ÿ W3 c2Li b2Li ÿ b02 Li ;
4
b0Li
are the scattering lengths for Li where bLi and in the two samples concerned. With three isotopically substituted samples containing 6 Li, 7 Li and an equal mixture of the two, mix Li, two sets of ®rst-order dierence are obtained and subtraction of the two yields a second-order dierence function D2Li Q which, in the absence of systematic errors, contains only the Li±Li correlations, 2 1 6 5 D2Li Q c2Li bLi ÿ7 bLi SLiLi Q ÿ 1; 2 where 6 bLi and 7 bLi are the average neutron scattering lengths of lithium in the 6 Li- and 7 Li-containing samples. The dierence in neutron scattering lengths of the Li isotopes is large. The maximum dierence in the scattering length of Li in this experiment, 6 bLi ÿ7 bLi , is 3.92 fm, giving a weighting factor 2 c2Li 6 bLi ÿ7 bLi =2, of 0.38 fm2 . The expected D2Li signal intensity is twice that of the Ca±Ca distribution in an experiment on a CaO±SiO2 glass [6], where D2Ca 0:18 fm2 . The real-space distributions are obtained by Fourier transformation of the Q-space data. The total reduced correlation function, G r, is given by 2 G r p
QZmax
Q S Q ÿ 1 sin Qr dQ: 0
6
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
3. Results 3.1. Total functions The experimental structure factors for the three samples, S Q, are shown in the upper part of Fig. 1. The total reduced radial distribution functions, G r, shown in Fig. 2 were obtained by Fourier transformation of the reciprocal space data using a Lorch modi®cation function, to reduce the scattered intensity smoothly to zero at Qmax 400 nmÿ1 . The two well-de®ned peaks at 0:163 0:001 and 0:266 0:001 nm in G r correspond respectively to the dominant Si±O and O±O correlations. The O±Si±O bond angle is 109.4°. In G r, the ®rst Li±O peak lies between the Si±O and O±O peaks. There are distinct dierences in this region for the three samples due to the dierent scattering contributions from the Li-centred par-
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tial distribution functions. Speci®cally, Li±O correlations give a positive contribution in the 6 Li sample and a negative contribution in 7 Li sample. The contribution of the Li±O partial in the mix Li sample is very small as the average scattering length of Li in this sample is close to zero. Parameters for the various coordination shells were obtained by ®tting the experimental G r with a series of Gaussian functions folded with the cosine transform of the Lorch window function. Applying the ®tting procedure to the three sets of data gives a measure of the consistency of the experiment. The ®ts are also shown in Fig. 2 and the coordination parameters obtained are given in Table 1. 3.2. First-order dierences The ®rst-order dierence Q-space data, DLi Q, are also shown in Fig. 1. Fourier transformation
Fig. 1. Total structure factors and ®rst- and second-order dierence data for Li2 O á 2SiO2 glass. The curves are displaced vertically for clarity. From top to bottom: The experimental S Q for 7 Li, mix Li and 6 Li glasses; the ®rst-order dierence function DLi Q and the second-order dierence function D2Li Q (multiplied by a factor of 5). The points in D2Li Q are data taken from the unsmoothed total functions.
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J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
Fig. 2. Reduced radial distribution functions obtained by Fourier transformation of the data shown in Fig. 1. A Lorch modi®cation was used, with Qmax 400 nmÿ1 for the total function, G r; Qmax 250 nmÿ1 for GLi r and Qmax 100 nmÿ1 for GLiLi r. The dotted lines are Gaussian ®ts to the experimental data and the curves are displaced vertically for clarity.
Table 1 Comparison of the coordination parameters for Li2 O á 2SiO2 glass, as obtained in this study and from other experiments Si±O
O±O
r (nm)
r (nm)
N
References
0.163 0.001 0.161 0.1625(1) 0.1624
0.007 0.001 0.0074(1) 0.0061
3.9 0.2 3.8 3.80(2) 3.9
[8] [9] [10]
0.010 0.001
4.4 0.2
0.0108(1) 0.010
4.815(2) 4.4
0.266 0.001 0.264 0.2655(1) 0.265
Si±Si
0.304 0.001 0.308
0.013 0.001
3.0
Li±O
0.197 0.001 0.220 0.005 0.194 0.1963(3)
0.012 0.001 0.016 0.002
3.2 0.2 0.8 0.5 4.0 2.16(9)
Li±Li
0.310 0.005 0.32 0.42
0.0108(4) 0.028 0.005
41 1.8
Here, r is the average interatomic distances and r the standard deviation of the distribution containing N atoms.
[8] [9] [10] [8]
[8] [9]
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
of DLi Q gives a weighted sum of the reduced partial radial distribution functions, GLi r, as shown in Fig. 2. The peak at 0:197 0:001 nm in GLi r corresponds to the ®rst Li±O neighbour shell. It can be seen that the distribution of Li±O distances is asymmetric and in order to ®t this peak with Gaussian functions as above, the oxygen coordination number is found to be 3:2 0:2 in a narrow distribution r 0:012 0:001 nm with a further 0:8 0:5 atoms in a broad tail at around 0.22 nm. Beyond the ®rst peak, two prominent features are seen at 0.3 and 0.5 nm. This region comprises a series of overlapping features de®ning the broad second and higher coordination shells. Similar features have been seen in all of the oxide glasses previously examined by this technique (see, for example [2±6]), indicating the existence of a reasonably well-de®ned medium-range structure, possibly with considerable similarities for the dierent oxide glass systems. The atomic density ¯uctuations persist to about 1 nm, which again indicates that the organisation, even the around weakly bonded cations, extends throughout the medium-range structure. 3.3. Second-order dierence The Li±Li partial distribution function, GLiLi r, shown at the bottom of Fig. 2, is obtained directly by Fourier transformation of D2Li Q (Fig. 1). The random error associated with this weak signal is about 20% and so that any features beyond about 100 nmÿ1 should be ignored. In addition, GLiLi r is subject to systematic errors (errors in composition, neutron scattering lengths, etc.) as well as random errors. While the peak at 0.12 nm is an artefact, the peak at 0.31 nm most likely corresponds to the Li±Li distribution. Fitting the data gave an estimated coordination number of 4 1 at an average distance of 0:31 0:005 nm and a further 1.8 in a broad tail extending to 0.42 nm. 4. Discussion 4.1. Environment of Si and O A useful approach in interpreting the structure of glasses is to compare the results with similar pa-
725
rameters for the equivalent crystalline phase and, in this case, similarities between the glassy and crystalline phases [12,13] are evident. The Si±O bond length and the O±Si±O bond angle are (not surprisingly) almost identical to those found in crystalline (c-) Li2 Si2 O5 . The breadth of the Si±O peak, as measured by the r value of 7 10ÿ3 nm, is greater than that for a-SiO2 rSi±O 5 10ÿ3 nm [14]. This is due to the dierence between the bridging and non-bridging Si±O distances is disilicates. The average Si±O distance is also larger than in a-SiO2 . A number of workers have argued that the distribution of nearest neighbour distances in narrower in glasses, than in crystals, re¯ecting the possibility that the removal of the constrains imposed by translational periodicity and lattice symmetry allows the average local structure to become better de®ned. For example, Greaves et al. [15] ®nd that Si K-edge X-ray absorption spectroscopy data suggest that the variance in the Si±O ®rst neighbour distances `is far smaller in the glass than in the crystal with the same stoichiometry'. For a-Li2 Si2 O5 , the value of r for the Si±O distribution, as quoted by Greaves et al. is 2:2 2:2 10ÿ3 nm ± a value that is not supported by this work r 7 10ÿ3 nm. For comparison, the values of r for the Si±O distribution in c-Li2 Si2 O5 are 5:4 10ÿ3 and 3:2 10ÿ3 nm for the stable and metastable forms, respectively. 4.2. Environment of Li The average Li±O bond length of 0:197 0:001 nm compares well with those found in crystalline lithium disilicates, 0.194 nm in the stable phase [12] and 0.2 nm in the metastable phase [13]. The coordination number of 3:2 0:2 corresponding to the narrow component of the Li±O distribution is less than that expected for a tetrahedral arrangement but the asymmetric Li±O distribution in GLi r suggests a further 0:8 0:5 atoms at longer distances. In crystalline lithium disilicates, there are three non-bridging and one bridging oxygen atom around each Li ion. It seems reasonable to assume a 4-fold site for Li, probably a distorted tetrahedron, similar to that in the crystals, and it is possible that the average distance between Li
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J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
and the bridging oxygens in the glass is longer and less well de®ned. In c-Li2 Si2 O5 , the Li±O(bridging) distance is about 0.014 nm longer than the Li± O(non-bridging) distance. Again, narrowing of the ®rst neighbour distribution in the glass, as suggested by EXAFS data [15], is not observed for the Li±O distances (ignoring the broad tail). Our value for the glass, r 0:012 0:001 nm, is larger than the value for the crystal 9 10ÿ3 nm in both the stable and metastable phases). In earlier work, the coordination number for Li has been variably estimated in the range from 2 to 4. Uhlig et al. [8] reported a coordination number of 4 for Li(rLi±O 0.194 nm) in a Li disilicate glass, whereas Hannon et al. [9] obtained a coordination number of 2 for Li in a glass of similar composition, suggesting a simple pairing of lithium atoms between two non-bridging oxygens. The bond valence approach has been a very useful method for checking and interpreting bond lengths and coordination numbers in crystals [16±18]. In any coordination shell, the sum of bond valences involving the central atom and its neighbours should equal its atomic valence. There is no reason to believe that the atoms in a glass should behave dierently. Taking account of the disorder and assuming a Gaussian distribution of distances, the bond valence in an amorphous system can be expressed as s exp
ÿ
R ÿ R0 B
exp
r2 ; 2B2
7
where R0 and B are atom-dependent constants, R is the mean bond length and r the standard deviation of the distribution. With the empirical constantsPR0 0:1292 nm and B 0:048 nm for Li [16], s 0:98, the value expected for monovalent Li, provided the distribution of 0.8 O atoms at 0.22 nm is included in the calculation. This result supports 4-fold coordination for lithium, but without the further 0.8 atoms, the bond valence sum would only be 0.86. Any deviation of the individual bond lengths from their average value increases the average bond length due to the non-linearity of the bond length±bond valence relationship [19]. This oers one explanation of the observed elongation of
the average cation±oxygen bonds in glasses when compared with their crystalline counterparts. 4.3. Li±Li distance The Li±Li correlations in both the stable and metastable c-Li2 Si2 O5 , have a short pair in the region 0.250±0.266 nm, followed by a main distribution of four neighbours around 0.3 nm. Due to the random and systematic errors and the relatively poor spatial resolution (D2Li Q was truncated at 100 nmÿ1 ), it is not possible to say with any certainty whether a short Li±Li pair also exists in the glass. Nonetheless, the peak at 0.31 nm in GLi r, can be related to the main Li±Li distribution in the crystals. In c-Li2 Si2 O5 , there are both edge- and corner-sharing LiO4 tetrahedra: Two adjacent LiO4 tetrahedra share a common edge and also share corners with other LiO4 tetrahedra. The Li±O±Li bond angle ranges from 83° to 132°, giving an average value of 101.5°. In the glass, the Li±O distance observed is 0:197 0:001 nm and Li±Li ®rst neighbour distance of 0:31 0:005 nm corresponds to an average Li±O±Li bond angle of 103.8°. The present experimental results therefore show strong evidence for a non-random distribution of alkali ions. The ordering around the weakly bonded network modifying ions is likely to re¯ect to a certain degree, the ordering beyond the short-range in the glass. Conversely, models that assume the Li atoms to be completely randomly distributed in the glass suggest an average Li±Li distance of about 0.4 nm, where a minimum occurs in the experimental data. There is little agreement with models for alkali silicates produced by inserting ions into a simulated SiO2 network [20,21], which yield, for example, Li±O ®rst coordination numbers in the region of 8±9, with only one non-bridging oxygen in the ®rst shell and a very broad distribution of cation±cation and cation±oxygen distances. Experimental data for the Ca±Ca correlations in a calcium metasilicate glass and Ni±Ni correlations in a mixed Ni/ Ca metasilicate glass have also shown evidence for a non-random distribution of cations and the results all suggest that similar medium-range order exists in the glasses and in their crystalline counterparts [4±6].
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
5. Conclusions The local order around the Si and O atoms in glassy Li2 Si2 O5 shows considerable similarities to that of the corresponding c-Li2 Si2 O5 . The ®rst-order dierence data give detailed information on the local environment of Li , showing that this ion is in a relatively well-de®ned tetrahedral site with some distortion ± possibly due to longer Li± O(bridging) distances forming a broad high-r tail to the Li±O distribution. The second-order dierence measurement allows the Li±Li correlation in the present silicate glass to be directly obtained for the ®rst time. There is clear evidence for a non-random distribution of the Li ions in the glass. The results strongly indicate the existence of medium-range structure, with considerable similarity to that for the corresponding crystalline phases.
Acknowledgements Thanks are due to Ken Fyles and Helen McPhail of the Pilkington Technology Centre, Lancs. UK for help with the sample preparation and M.A. Farnworth, M. Cottam and B.W. Shaw, also of the Pilkington Technology Centre, for the sample composition analysis. References [1] G.N. Greaves, S.J. Gurman, C.R.A. Catlow, A.V. Chadwick, B. Dobson, C.M.B. Henderson, Philos. Mag. A 64 (1991) 1059.
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[2] C.A. Yarker, P.A.V. Johnson, A.C. Wright, J. Wong, R.B. Greegor, F.W. Lytle, R.N. Sinclair, J. Non-Cryst. Solids 79 (1985) 117. [3] P.H. Gaskell, M.C. Eckersley, J. Zhao, P. Chieux, Riv. Staz. Speriment. Vetro 5 (1990) 21. [4] P.H. Gaskell, J. Zhao, G. Calas, L. Galoisy, in: L.D. Pye, W.C. LaCourse, H.J. Stevens (Eds.), The Physics of NonCrystalline Solids, Taylor and Francis, London, 1992, p. 53. [5] P.H. Gaskell, M.M. Cluckie, J. Zhao, P.D. Beattie, P. Levitz, in: Proceedings of the Second International Conference on the Fundamentals of Glass Science and Technology, Venice, Italy, 1993. [6] P.H. Gaskell, M.C. Eckersley, A.C. Barnes, P. Chieux, Nature 350 (1991) 675. [7] Z. Xu, J.F. Stebbins, Solid State Nucl. Magn. Reson. 5 (1995) 103. [8] H. Uhlig, M.J. Homann, H.-P. Lamparter, F. Aldinger, R. Bellissent, S. Steeb, J. Am. Ceram. Soc. 79 (1996) 2833. [9] A.C. Hannon, B. Vessal, J.M. Parker, J. Non-Cryst. Solids 150 (1992) 97. [10] M. Misawa, D.L. Price, K. Suzuki, J. Non-Cryst. Solids 37 (1979) 85. [11] V.F. Sears, Methods of Experimental Physics, Part A, vol. 23, Academic Press, London, 1987, p. 521. [12] F. Liebau, Acta Crystallogr. 14 (1961) 389. [13] R.I. Smith, R.A. Howie, A.R. West, Acta Crystallogr. C 46 (1990) 363. [14] R.N. Sinclair, A.C. Wright, J. Non-Cryst. Solids 57 (1983) 447. [15] G.N. Greaves, S.J. Gurman, C.R.A. Catlow, A.V. Chadwick, S. Houde-Walter, C.M.B. Henderson, B.R. Dobson, Philos. Mag. A 64 (1991) 1059. [16] I.D. Brown, in: M. O'Keee, A. Navrotsky (Eds.), Structure and Bonding in Crystals II, Academic Press, London, 1981. [17] M. O'Keee, Struct. Bonding 71 (1989) 162. [18] N.E. Brese, M. O'Keee, Acta Crystallogr. B 47 (1991) 192. [19] I.D. Brown, R.D. Shannon, Acta Crystallogr. B 32 (1973) 266. [20] J.H. Lee, S.R. Elliott, Phys. Rev. B 50 (1994) 5981. [21] A. Alavi, L.J. Alvarez, S.R. Elliott, I.R. McDonald, Philos. Mag. B 65 (1992) 489.
A neutron diraction, isotopic substitution study of the structure of Li2Oá2SiO2 glass J. Zhao b
a,* ,
P.H. Gaskell a, M.M. Cluckie a, A.K. Soper
b
a Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK ISIS Science Division, Daresbury Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, UK
Abstract The structure of Li2 Oá2SiO2 glass has been studied in detail by neutron diraction with isotopic substitution of Li. The ®rst Si±O and O±O distances are 0:163 0:001 and 0:266 0:001 nm, respectively. Li is found in a relatively wellde®ned tetrahedral site, with 3:2 0:2 oxygen atoms at 0:197 0:001 nm and a further 0:8 0:5 in a broad tail extending to about 0.22. The Li±Li ®rst neighbour distance in a silicate glass has been measured directly, for the ®rst time, and the value of 0:310 0:002 nm yields strong evidence for a non-random distribution of the Li ions in the glass. The short- and medium-range structure exhibit considerable similarity to those of crystalline (c-) lithium disilicate. Ó 1998 Elsevier Science B.V. All rights reserved.
1. Introduction While diraction gives a maximum amount of structural information for monoatomic systems, the technique suers from the problem that for multi-component systems, uncertainties arise due to the overlap of coordination shells. A determination of the structure associated with weakly bonded cations requires chemically speci®c techniques, and the extended X-ray absorption ®ne structure (EXAFS) has proved useful in the studies of alkali silicate glasses [1]. The technique is suitable for relatively heavy elements, but the information obtained is the most accurate for the ®rst coordination shell. Neutron diraction, with isotopic
* Corresponding author. Present address: Advanced Laser and Fusion Tech. Inc., 189 Deveault Street Unit 7, Hull, Que., Canada J8Z 1S7. Tel.: 1 819 7700477; fax: 1 819 7703862; e-mail: [email protected].
0022-3093/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 8 ) 0 0 5 5 4 - 7
substitution, is a very powerful technique for obtaining the structure around network modifying cations [2±6], provided suitable isotopes are available. Li-containing silicate glasses have been studied previously [7±10], but the information available so far is still inadequate to establish a complete structural picture. Uhlig et al. [8] used isotopic substitution in their neutron scattering study of silicate glasses, but concentrated mainly on an examination of the silicate `framework'. Here we emphases the local structure surrounding Li, and the distribution of Li ions within the framework. Despite the fact that 6 Li has a high neutron absorption cross-section rabs 940 barns [11]), the large dierence between the coherent scattering lengths of 6 Li b 2:0 10ÿ15 m and 7 Li b ÿ2:22 10ÿ15 m [11] makes it possible to obtain good signal contrast from isotopic substitution. First- and second-order dierences are obtained from measurements involving three
722
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
dierent Li isotopic compositions, giving information on the local environment of Li from ®rst-order dierence data, and the Li±Li distribution function from the second-order dierence. Information on local and medium-range order are then examined in detail.
2. Experimental details and data analysis Three Li2 Oá2SiO2 glasses were prepared. The starting materials were melted in a covered Pt/Rh crucible at 1200°C for 30 min. To ensure homogeneity, the glasses obtained were subsequently crushed and re-melted twice at 1200°C for 30 min. The resulting glasses were clear with no sign of phase separation. The isotopic contents of the samples were analysed using laser ionic mass analysis (LIMA). The results show that the 6 Li enriched sample contains 87.8 1.0% 6 Li and 12.2 1.0% 7 Li. The 7 Li enriched sample contains essentially pure 7 Li isotope, while the third sample contains an equal mixture of the two (mix Li). Atomic absorption analysis indicates approximately 1% loss of Li2 O due to volatilisation during sample preparation for the 7 Li-containing glass, but problems in estimating the 6 Li2 O concentration prevented accurate analysis of the composition of the 6 Li and mix Li glasses. The compositions of all of the glasses are assumed to be identical to that of the 7 Li-containing glass. The number density of the sample is 8:30 0:02 10ÿ5 nmÿ3 . The neutron diraction measurements were carried out using the SANDALS diractometer at ISIS (Daresbury Rutherford Appleton Laboratory, UK). A relatively thin ¯at geometry was used to optimise the scattered intensity and minimise the adverse eects of the high absorption of 6 Li. The sample container was made of null Ti±Zr alloy and its inner thickness was 2 mm. The corrected dierential scattering cross-section, dr=dX, for the system can be expressed in terms of the `self-scattering' and the `distinct-scattering', i.e. 1 dr X 2 XX ci bi ci cj bi bj Sij Q ÿ 1 ; N dX i i j6i
1
where Q 4p sin h=k; k is the incident neutron wavelength, 2h the scattering angle, N the total number of atoms, ci and bi are the atomic concentration and the coherent neutron scattering length of species i, respectively, and Sij Q the partial structure factor relating species i and j. The dierence, DLi Q, between the distinct scattering functions for two samples, diering only in their isotopic contents, gives a weighted sum of the Li-centred partial correlation functions: DLi Q W1 SLiO Q ÿ 1 W2 SLiSi Q ÿ 1 W3 SLiLi Q ÿ 1;
2
ÿ W1 2cLi cO bO bLi ÿ b0Li ; ÿ W2 2cLi cSi bSi bLi ÿ b0Li ;
3
ÿ W3 c2Li b2Li ÿ b02 Li ;
4
b0Li
are the scattering lengths for Li where bLi and in the two samples concerned. With three isotopically substituted samples containing 6 Li, 7 Li and an equal mixture of the two, mix Li, two sets of ®rst-order dierence are obtained and subtraction of the two yields a second-order dierence function D2Li Q which, in the absence of systematic errors, contains only the Li±Li correlations, 2 1 6 5 D2Li Q c2Li bLi ÿ7 bLi SLiLi Q ÿ 1; 2 where 6 bLi and 7 bLi are the average neutron scattering lengths of lithium in the 6 Li- and 7 Li-containing samples. The dierence in neutron scattering lengths of the Li isotopes is large. The maximum dierence in the scattering length of Li in this experiment, 6 bLi ÿ7 bLi , is 3.92 fm, giving a weighting factor 2 c2Li 6 bLi ÿ7 bLi =2, of 0.38 fm2 . The expected D2Li signal intensity is twice that of the Ca±Ca distribution in an experiment on a CaO±SiO2 glass [6], where D2Ca 0:18 fm2 . The real-space distributions are obtained by Fourier transformation of the Q-space data. The total reduced correlation function, G r, is given by 2 G r p
QZmax
Q S Q ÿ 1 sin Qr dQ: 0
6
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
3. Results 3.1. Total functions The experimental structure factors for the three samples, S Q, are shown in the upper part of Fig. 1. The total reduced radial distribution functions, G r, shown in Fig. 2 were obtained by Fourier transformation of the reciprocal space data using a Lorch modi®cation function, to reduce the scattered intensity smoothly to zero at Qmax 400 nmÿ1 . The two well-de®ned peaks at 0:163 0:001 and 0:266 0:001 nm in G r correspond respectively to the dominant Si±O and O±O correlations. The O±Si±O bond angle is 109.4°. In G r, the ®rst Li±O peak lies between the Si±O and O±O peaks. There are distinct dierences in this region for the three samples due to the dierent scattering contributions from the Li-centred par-
723
tial distribution functions. Speci®cally, Li±O correlations give a positive contribution in the 6 Li sample and a negative contribution in 7 Li sample. The contribution of the Li±O partial in the mix Li sample is very small as the average scattering length of Li in this sample is close to zero. Parameters for the various coordination shells were obtained by ®tting the experimental G r with a series of Gaussian functions folded with the cosine transform of the Lorch window function. Applying the ®tting procedure to the three sets of data gives a measure of the consistency of the experiment. The ®ts are also shown in Fig. 2 and the coordination parameters obtained are given in Table 1. 3.2. First-order dierences The ®rst-order dierence Q-space data, DLi Q, are also shown in Fig. 1. Fourier transformation
Fig. 1. Total structure factors and ®rst- and second-order dierence data for Li2 O á 2SiO2 glass. The curves are displaced vertically for clarity. From top to bottom: The experimental S Q for 7 Li, mix Li and 6 Li glasses; the ®rst-order dierence function DLi Q and the second-order dierence function D2Li Q (multiplied by a factor of 5). The points in D2Li Q are data taken from the unsmoothed total functions.
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Fig. 2. Reduced radial distribution functions obtained by Fourier transformation of the data shown in Fig. 1. A Lorch modi®cation was used, with Qmax 400 nmÿ1 for the total function, G r; Qmax 250 nmÿ1 for GLi r and Qmax 100 nmÿ1 for GLiLi r. The dotted lines are Gaussian ®ts to the experimental data and the curves are displaced vertically for clarity.
Table 1 Comparison of the coordination parameters for Li2 O á 2SiO2 glass, as obtained in this study and from other experiments Si±O
O±O
r (nm)
r (nm)
N
References
0.163 0.001 0.161 0.1625(1) 0.1624
0.007 0.001 0.0074(1) 0.0061
3.9 0.2 3.8 3.80(2) 3.9
[8] [9] [10]
0.010 0.001
4.4 0.2
0.0108(1) 0.010
4.815(2) 4.4
0.266 0.001 0.264 0.2655(1) 0.265
Si±Si
0.304 0.001 0.308
0.013 0.001
3.0
Li±O
0.197 0.001 0.220 0.005 0.194 0.1963(3)
0.012 0.001 0.016 0.002
3.2 0.2 0.8 0.5 4.0 2.16(9)
Li±Li
0.310 0.005 0.32 0.42
0.0108(4) 0.028 0.005
41 1.8
Here, r is the average interatomic distances and r the standard deviation of the distribution containing N atoms.
[8] [9] [10] [8]
[8] [9]
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
of DLi Q gives a weighted sum of the reduced partial radial distribution functions, GLi r, as shown in Fig. 2. The peak at 0:197 0:001 nm in GLi r corresponds to the ®rst Li±O neighbour shell. It can be seen that the distribution of Li±O distances is asymmetric and in order to ®t this peak with Gaussian functions as above, the oxygen coordination number is found to be 3:2 0:2 in a narrow distribution r 0:012 0:001 nm with a further 0:8 0:5 atoms in a broad tail at around 0.22 nm. Beyond the ®rst peak, two prominent features are seen at 0.3 and 0.5 nm. This region comprises a series of overlapping features de®ning the broad second and higher coordination shells. Similar features have been seen in all of the oxide glasses previously examined by this technique (see, for example [2±6]), indicating the existence of a reasonably well-de®ned medium-range structure, possibly with considerable similarities for the dierent oxide glass systems. The atomic density ¯uctuations persist to about 1 nm, which again indicates that the organisation, even the around weakly bonded cations, extends throughout the medium-range structure. 3.3. Second-order dierence The Li±Li partial distribution function, GLiLi r, shown at the bottom of Fig. 2, is obtained directly by Fourier transformation of D2Li Q (Fig. 1). The random error associated with this weak signal is about 20% and so that any features beyond about 100 nmÿ1 should be ignored. In addition, GLiLi r is subject to systematic errors (errors in composition, neutron scattering lengths, etc.) as well as random errors. While the peak at 0.12 nm is an artefact, the peak at 0.31 nm most likely corresponds to the Li±Li distribution. Fitting the data gave an estimated coordination number of 4 1 at an average distance of 0:31 0:005 nm and a further 1.8 in a broad tail extending to 0.42 nm. 4. Discussion 4.1. Environment of Si and O A useful approach in interpreting the structure of glasses is to compare the results with similar pa-
725
rameters for the equivalent crystalline phase and, in this case, similarities between the glassy and crystalline phases [12,13] are evident. The Si±O bond length and the O±Si±O bond angle are (not surprisingly) almost identical to those found in crystalline (c-) Li2 Si2 O5 . The breadth of the Si±O peak, as measured by the r value of 7 10ÿ3 nm, is greater than that for a-SiO2 rSi±O 5 10ÿ3 nm [14]. This is due to the dierence between the bridging and non-bridging Si±O distances is disilicates. The average Si±O distance is also larger than in a-SiO2 . A number of workers have argued that the distribution of nearest neighbour distances in narrower in glasses, than in crystals, re¯ecting the possibility that the removal of the constrains imposed by translational periodicity and lattice symmetry allows the average local structure to become better de®ned. For example, Greaves et al. [15] ®nd that Si K-edge X-ray absorption spectroscopy data suggest that the variance in the Si±O ®rst neighbour distances `is far smaller in the glass than in the crystal with the same stoichiometry'. For a-Li2 Si2 O5 , the value of r for the Si±O distribution, as quoted by Greaves et al. is 2:2 2:2 10ÿ3 nm ± a value that is not supported by this work r 7 10ÿ3 nm. For comparison, the values of r for the Si±O distribution in c-Li2 Si2 O5 are 5:4 10ÿ3 and 3:2 10ÿ3 nm for the stable and metastable forms, respectively. 4.2. Environment of Li The average Li±O bond length of 0:197 0:001 nm compares well with those found in crystalline lithium disilicates, 0.194 nm in the stable phase [12] and 0.2 nm in the metastable phase [13]. The coordination number of 3:2 0:2 corresponding to the narrow component of the Li±O distribution is less than that expected for a tetrahedral arrangement but the asymmetric Li±O distribution in GLi r suggests a further 0:8 0:5 atoms at longer distances. In crystalline lithium disilicates, there are three non-bridging and one bridging oxygen atom around each Li ion. It seems reasonable to assume a 4-fold site for Li, probably a distorted tetrahedron, similar to that in the crystals, and it is possible that the average distance between Li
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and the bridging oxygens in the glass is longer and less well de®ned. In c-Li2 Si2 O5 , the Li±O(bridging) distance is about 0.014 nm longer than the Li± O(non-bridging) distance. Again, narrowing of the ®rst neighbour distribution in the glass, as suggested by EXAFS data [15], is not observed for the Li±O distances (ignoring the broad tail). Our value for the glass, r 0:012 0:001 nm, is larger than the value for the crystal 9 10ÿ3 nm in both the stable and metastable phases). In earlier work, the coordination number for Li has been variably estimated in the range from 2 to 4. Uhlig et al. [8] reported a coordination number of 4 for Li(rLi±O 0.194 nm) in a Li disilicate glass, whereas Hannon et al. [9] obtained a coordination number of 2 for Li in a glass of similar composition, suggesting a simple pairing of lithium atoms between two non-bridging oxygens. The bond valence approach has been a very useful method for checking and interpreting bond lengths and coordination numbers in crystals [16±18]. In any coordination shell, the sum of bond valences involving the central atom and its neighbours should equal its atomic valence. There is no reason to believe that the atoms in a glass should behave dierently. Taking account of the disorder and assuming a Gaussian distribution of distances, the bond valence in an amorphous system can be expressed as s exp
ÿ
R ÿ R0 B
exp
r2 ; 2B2
7
where R0 and B are atom-dependent constants, R is the mean bond length and r the standard deviation of the distribution. With the empirical constantsPR0 0:1292 nm and B 0:048 nm for Li [16], s 0:98, the value expected for monovalent Li, provided the distribution of 0.8 O atoms at 0.22 nm is included in the calculation. This result supports 4-fold coordination for lithium, but without the further 0.8 atoms, the bond valence sum would only be 0.86. Any deviation of the individual bond lengths from their average value increases the average bond length due to the non-linearity of the bond length±bond valence relationship [19]. This oers one explanation of the observed elongation of
the average cation±oxygen bonds in glasses when compared with their crystalline counterparts. 4.3. Li±Li distance The Li±Li correlations in both the stable and metastable c-Li2 Si2 O5 , have a short pair in the region 0.250±0.266 nm, followed by a main distribution of four neighbours around 0.3 nm. Due to the random and systematic errors and the relatively poor spatial resolution (D2Li Q was truncated at 100 nmÿ1 ), it is not possible to say with any certainty whether a short Li±Li pair also exists in the glass. Nonetheless, the peak at 0.31 nm in GLi r, can be related to the main Li±Li distribution in the crystals. In c-Li2 Si2 O5 , there are both edge- and corner-sharing LiO4 tetrahedra: Two adjacent LiO4 tetrahedra share a common edge and also share corners with other LiO4 tetrahedra. The Li±O±Li bond angle ranges from 83° to 132°, giving an average value of 101.5°. In the glass, the Li±O distance observed is 0:197 0:001 nm and Li±Li ®rst neighbour distance of 0:31 0:005 nm corresponds to an average Li±O±Li bond angle of 103.8°. The present experimental results therefore show strong evidence for a non-random distribution of alkali ions. The ordering around the weakly bonded network modifying ions is likely to re¯ect to a certain degree, the ordering beyond the short-range in the glass. Conversely, models that assume the Li atoms to be completely randomly distributed in the glass suggest an average Li±Li distance of about 0.4 nm, where a minimum occurs in the experimental data. There is little agreement with models for alkali silicates produced by inserting ions into a simulated SiO2 network [20,21], which yield, for example, Li±O ®rst coordination numbers in the region of 8±9, with only one non-bridging oxygen in the ®rst shell and a very broad distribution of cation±cation and cation±oxygen distances. Experimental data for the Ca±Ca correlations in a calcium metasilicate glass and Ni±Ni correlations in a mixed Ni/ Ca metasilicate glass have also shown evidence for a non-random distribution of cations and the results all suggest that similar medium-range order exists in the glasses and in their crystalline counterparts [4±6].
J. Zhao et al. / Journal of Non-Crystalline Solids 232±234 (1998) 721±727
5. Conclusions The local order around the Si and O atoms in glassy Li2 Si2 O5 shows considerable similarities to that of the corresponding c-Li2 Si2 O5 . The ®rst-order dierence data give detailed information on the local environment of Li , showing that this ion is in a relatively well-de®ned tetrahedral site with some distortion ± possibly due to longer Li± O(bridging) distances forming a broad high-r tail to the Li±O distribution. The second-order dierence measurement allows the Li±Li correlation in the present silicate glass to be directly obtained for the ®rst time. There is clear evidence for a non-random distribution of the Li ions in the glass. The results strongly indicate the existence of medium-range structure, with considerable similarity to that for the corresponding crystalline phases.
Acknowledgements Thanks are due to Ken Fyles and Helen McPhail of the Pilkington Technology Centre, Lancs. UK for help with the sample preparation and M.A. Farnworth, M. Cottam and B.W. Shaw, also of the Pilkington Technology Centre, for the sample composition analysis. References [1] G.N. Greaves, S.J. Gurman, C.R.A. Catlow, A.V. Chadwick, B. Dobson, C.M.B. Henderson, Philos. Mag. A 64 (1991) 1059.
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[2] C.A. Yarker, P.A.V. Johnson, A.C. Wright, J. Wong, R.B. Greegor, F.W. Lytle, R.N. Sinclair, J. Non-Cryst. Solids 79 (1985) 117. [3] P.H. Gaskell, M.C. Eckersley, J. Zhao, P. Chieux, Riv. Staz. Speriment. Vetro 5 (1990) 21. [4] P.H. Gaskell, J. Zhao, G. Calas, L. Galoisy, in: L.D. Pye, W.C. LaCourse, H.J. Stevens (Eds.), The Physics of NonCrystalline Solids, Taylor and Francis, London, 1992, p. 53. [5] P.H. Gaskell, M.M. Cluckie, J. Zhao, P.D. Beattie, P. Levitz, in: Proceedings of the Second International Conference on the Fundamentals of Glass Science and Technology, Venice, Italy, 1993. [6] P.H. Gaskell, M.C. Eckersley, A.C. Barnes, P. Chieux, Nature 350 (1991) 675. [7] Z. Xu, J.F. Stebbins, Solid State Nucl. Magn. Reson. 5 (1995) 103. [8] H. Uhlig, M.J. Homann, H.-P. Lamparter, F. Aldinger, R. Bellissent, S. Steeb, J. Am. Ceram. Soc. 79 (1996) 2833. [9] A.C. Hannon, B. Vessal, J.M. Parker, J. Non-Cryst. Solids 150 (1992) 97. [10] M. Misawa, D.L. Price, K. Suzuki, J. Non-Cryst. Solids 37 (1979) 85. [11] V.F. Sears, Methods of Experimental Physics, Part A, vol. 23, Academic Press, London, 1987, p. 521. [12] F. Liebau, Acta Crystallogr. 14 (1961) 389. [13] R.I. Smith, R.A. Howie, A.R. West, Acta Crystallogr. C 46 (1990) 363. [14] R.N. Sinclair, A.C. Wright, J. Non-Cryst. Solids 57 (1983) 447. [15] G.N. Greaves, S.J. Gurman, C.R.A. Catlow, A.V. Chadwick, S. Houde-Walter, C.M.B. Henderson, B.R. Dobson, Philos. Mag. A 64 (1991) 1059. [16] I.D. Brown, in: M. O'Keee, A. Navrotsky (Eds.), Structure and Bonding in Crystals II, Academic Press, London, 1981. [17] M. O'Keee, Struct. Bonding 71 (1989) 162. [18] N.E. Brese, M. O'Keee, Acta Crystallogr. B 47 (1991) 192. [19] I.D. Brown, R.D. Shannon, Acta Crystallogr. B 32 (1973) 266. [20] J.H. Lee, S.R. Elliott, Phys. Rev. B 50 (1994) 5981. [21] A. Alavi, L.J. Alvarez, S.R. Elliott, I.R. McDonald, Philos. Mag. B 65 (1992) 489.