Infrared spectroscopic investigation of structure and crystallization of aluminosilicate glasses

Infrared spectroscopic investigation of structure and crystallization of aluminosilicate glasses

310 Journal of Non-Crystalline Solids 119 (1990) 310-317 North-Holland INFRARED S P E C T R O S C O P I C I N V E S T I G A T I O N O F S T R U C T ...

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310

Journal of Non-Crystalline Solids 119 (1990) 310-317 North-Holland

INFRARED S P E C T R O S C O P I C I N V E S T I G A T I O N O F S T R U C T U R E AND CRYSTALLIZATION O F AEUMINOSILICATE G L A S S E S Krystyna E. LIPINSKA-KALITA Regional Laboratory of Physicochemical Analyses and Structural Research, Jagiellonian University, 30-060 Krakbw, ul. Karasia 3, Poland Received 8 September 1989 Revised manuscript received 28 November 1989

Fourier transform infrared (FTIR) absorption spectra have been measured for a series of potassium aluminosilicate glasses. The influence of preparation temperature, atmosphere, composition and crystallization of the studied glasses on their structure is discussed. Systematic changes are observed in the frequency and intensity characteristics of the spectral bands with variations in iron content for these glasses. The S7Fe MiSssbauer spectroscopy was used to find the correlation between the coordination number and the valence state of Fe 2+ and Fe 3+ cations. The phase composition of samples undergoing crystallization was confirmed using X-ray diffraction (XRD) and scanning electron microscopy (SEM). On the basis of F T I R spectra and other considerations, a structural model is proposed to describe potassium aluminosilicate glasses containing iron oxides. It is found that the analyzed glasses have three-dimensional network structures, with silicon and aluminium in tetrahedral coordination. However, iron exhibits a variety of bonding geometries. Glass structures, intermediate between very highly ordered network forming units and crystallites regions, are also discussed.

1. Introduction In recent years growing interest has developed in the study of silicate glasses containing iron oxides. These glasses exhibit semiconductor properties and are also of importance in other applications such as glass metal composites and as solar energy absorbers [1-3]. The vibrational spectra of oxide glasses contain a significant amount of encoded information potentially useful for determining glass structures and interpreting physical properties of glasses. In previous studies of silicate glasses, it has been suggested that specific vibrational bands are characteristic for the network-forming units (silica tetrahedra) and for the extent to which these units are polymerized. Several studies indicated that specific bands are characteristic of Si-O bridging or Si-O non-bridging bonds [4-6]. Vibrational spectra of aluminosilicate glasses were compared to crystalline materials of the same composition to determine structural units that may exist in the glass structure [7-12].

In this work F T I R absorption spectra have been measured for a series of potassium aluminosilicate glasses in order to study the influence of preparation temperature, atmosphere and the addition of iron oxides on the structure of these glasses, as well as the impact of the effect of heat treatment on the course of crystallization. This paper presents the results of a F T I R spectroscopic study of glasses and partly crystalline materials in the system K 2 0 - F e O / F e 2 0 3 - A I 2 O3-SIO 2 and discusses the models for the behaviour of A13+, Fe 2÷ and Fe 3+ cations in the glass structure. This study is also concerned with the hypothesis regarding changes in the glass structure with respect to changes in composition.

2. Experimental Aluminosilicate glass samples of basic composition 65SIO2, 17A1203, xFe203 and 8 K 2 0 (in wt%), where x = 0-10 wt% Fe203, were prepared with high purity dried silica gel, aluminium hydroxide,

0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

K.E. Lipinska-Kalita / Structure and crystallization of aluminosilicate glasses

iron oxalate and potassium carbonate powders. This composition is close to that of natural basalts and other raw materials used in the production of artificial light aggregates. The components were weighed and then were thoroughly ground. Mixes were loaded into alumina crucibles, heated at 700-900 ° C for several hours to decarbonate and then melted at different temperatures (14001600°C) in a furnace with a controlled argon atmosphere or in air (at 1400°C) and quenched by removing from the furnace and allowed to air cool. Melting and cooling conditions were the same for all samples. Quenched glass compositions were checked by wet chemical analyses (SiO 2, A1203) [32], flame photometry (K20) [32], polarography and amperometric titration ( F e E + + F e 3+ and Fe E+) [17], M~Sssbauer spectroscopy (FeE+/Fe 3+) [15]. The K20 loss was limited to less than 10% of the amount present in starting materials ( - 8 wt%). No systematic differences were observed between K20 lOSS in glasses melted at 1400°C and 1600°C (argon). The discrepancy between analyzed and nominal composition of all the glasses was less than 2 wt%. Therefore, the compositions of all the glasses have been expressed by the nominal compositions. Fourier transform infrared (FTIR) absorption spectra of the glasses were measured in the 1001300 cm -1 region using a Digilab FTS system, with a resolution of 2 c m - ] on the KBr pelletized disks. The D R O N diffractometer was used in Xray studies of powder samples. The differential thermal analysis (DTA) was carried out by a Mettler thermoanalyzer at a heating rate of 10 o C / m i n . The MiSssbauer spectra were accumulated at room temperature using the conventional constant acceleration spectrometer. 57Co in chromium matrix served as a source [15].

3. Results

The F T I R absorption spectra of glasses composed of 65SIO2, 17A1203, 10Fe203, 8K20 (wt%) and synthesized in an argon atmosphere at temperatures from 1400 to 1600°C are shown in fig. 1. All these glasses have the same basic composition

Grasses ,

311

Si O= -AtzO=-FeOI Fe=O=.-K=O

!T 2/\oo% I

100

I

300

500 400

I

I

800

I

I

1200

I

¢m "1

Fig. 1. FTIR absorption spectra of glasses of the same basic composition with different Fe2+/Fe 3+ ratios synthesized at various temperaturesin an argon atmosphere.

but different F e 2 + / F e 2+ ratios. Infrared absorption spectra for different glasses show great similarity in their general shape and no new bands are observed. The influence of preparation conditions and of composition of the studied glasses on the valence state and on coordination number of iron cations was determined by MiSssbauer spectroscopy [15]. Table 1 lists relative populations of Fe3+tet, Fe~ct3+ and Fe2~- cations in a series of glasses synthesized at different temperatures under argon atmosphere. It can be observed (fig. 2) that the addition of iron oxides to the potassium aluminosilicate glasses causes a general shift of the existing infrared absorption bands toward lower wavenumbers and introduces new weak absorption bands. F T I R spectroscopy was also used for studying the crystallization process in potassium aluminosilicate glasses synthesized at various temperatures and containing different amounts of iron oxides.

312

K.E. Lipinska-Kalita / Structure and crystallization of aluminosificate glasses SiO=-AhO=- Fe O/Fe=Oi-K=O

SiO 2-At~O3-FeO/Fe=Oa-K20

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100

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I

300

I

I

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I

I

8OO

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I

120O

I

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Fig. 2. FTIR absorption spectra of ( A - D ) glasses with different iron oxides content synthesized in air (1400°C) and (E)

co"c i ,00

potassium feldspar glass.

300

~O0

eOO'

'200

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Fig. 3. FTIR absorption spectra of basic glass and the progress of its crystallization. I n o r d e r to f o l l o w t h e c o u r s e o f c r y s t a l l i z a t i o n , glass s a m p l e s w e r e a n n e a l e d for v a r i o u s l e n g t h s o f t i m e at d i f f e r e n t t e m p e r a t u r e s . T h e p r o g r e s s o f c r y s t a l l i z a t i o n h a s b e e n t r a c e d b y m e a s u r i n g inf r a r e d s p e c t r a o f glasses w i t h a s e q u e n c e o f h e a t treatments. Figure 3 illustrates the spectral changes

a n d fig. 4 s h o w s t h e e x a m p l e s o f t h e X - r a y diff r a c t o g r a m s at v a r i o u s a n n e a l i n g t e m p e r a t u r e s for o n e o f t h e a n a l y z e d glasses (10 wt% o f Fe203). T h i s s a m p l e c o n t a i n s b o t h glass a n d m a g n e t i t e

Table 1 Relative populations of Fe3+ , Fe,3o~ and Fe2+ cations in glass matrix and magnetite for glasses synthesized in an argon atmosphere (wt%) [15] Melting temperature (°C)

1400 1450 1500 1520 1600

Fet3e+

Fe~c+

Fe2+

Fe 2+ ~Fe

Fe 3+ VFe

magnetite

glass matrix

magnetite

glass matrix

magnetite

glass matrix

whole material

glass matrix

9.5 7.2 7,6 6.6 -

6.7 6.0 6.7 5.7 5.5

10.2 10.5 8.8 9.0 -

12.8 12.0 11.3 8.9 6.2

10.2 10.5 8.8 9.0 -

50.7 53.9 56.9 60.9 41.2 a) 47.1

0.61 0.64 0.66 0.70 0.88

0.28 0.25 0.24 0.19 0.12

") MOssbaner spectrum has been described with 4 quadrupole doublets; 2 doublets come from Fe2+ indicating that Fe~+ have two structurally different octahedral-like sites.

K.E. Lipinska.Kalita / Structure and crystallization of aluminosificate glasses

.

.gl?

M

I lit

60*

Ill

t,l

ttt

I I,II

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lift

t II

I1 Ill

t,O*

lilt|

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10*

Fig. 4. X-ray diffraction pattern of basic glass and the progress of its crystallization (M, magnetite; H, hematite; Sk, potassium feldspar; Mu, muLlite).

phases. The crystallization temperature of this glass was found to be 1300°C with the differential termal analysis (DTA) method.

4. Discussion

4.1. Band assignment

Vibrational spectra of silicate glasses characteristically consist of a few broad bands, the frequencies of which are related to the network forming units (silica tetrahedra) and to the extent to which these units are polymerized. Most models for the structure of silicate glasses assume that various anionic units exist in the glass structure (SiOz, Si2O2- and SiO 2- with 0, 1, 2 non-bridging oxygens). The vibrations of these different anionic units give rise to specific vibration frequencies and these frequencies are relatively independent of glass composition [4-6,13,14].

313

Below, a summary is given of those spectral assignments which are most reasonable in the light of experimental results obtained in this study. The assignments of vibrational bands were carried out taking account of the generally acceptable fact that the frequency of a stretching mode is higher than that of a bending mode. The most intense broad absorption bands of the alkali aluminosilicate glasses lie ,in the 9001200 cm-1 region Which has been associated with the cooperative antisymmetric stretching motion of silica tetrahedra containing bridging (i.e, S i - O Si bond) and non-bridging (i.e. S i - O 7 bonding) oxygens. The second strongest region of absorption usually lies between 400-500 cm-1, and can be assigned to cooperative O - S i - O and O - S i - O bending vibrations (involving mostly O anions). All glasses show one or more weak absorption bands lying between 600 and 800 cm-1 which are the consequence of their polymerized structure but the choice of a suitable nomenclature to describe them has given some difficulty. Some or all of them have been assigned to (i) activation of the total symmetric stretching mode of the component tetrahedra, or (ii) symmetric stretching motions across the T - O - T bridging oxygen involving mostly T cations (where T represents a tetrahedrally coordinated ion, either Si 4÷ or AI 3+ and FeS+). It should be emphasized that the AIO 4 tetrahedra in aluminosilicate glasses must be considered to couple with SiO4 tetrahedra in the same way as SiO4 tetrahedra couple with each other. Thus, the vibrations of aluminosilicate glasses will include stretching and bending modes of both S i - O - S i as well as S i - O - A I ( F e ) bonds. 4.2. Glass spectra

F T I R absorption spectra of glasses having the same basic composition (65SIO 2, 17A1203, 10Fe203, 8 K 2 0 (wt%)) but different FeE+/Fe 3+ ratios show great similarity in their general shape (fig. 1). However, the general tendency is observed that the centre of gravity of the high frequency bands shifts to lower frequencies with increase in the synthesis temperature. Simultaneously, the width at half maximum amplitude of these bands

314

K.E. Lipinska-Kalita / Structure and crystallization of aluminosilicate glasses

increases with the increase of synthesis temperature. These changes are in accordance with the resuits obtained by Mrssbauer spectroscopy [15]. It should b e mentioned that magnetite has been found in some glasses (table 1). The dimensions of magnetite particles are at least of the order of 200 A, because smaller grains are non-distinguishible in Mt~ssbauer spectra taken at room temperature without an external magnetic field (cf. ref. [16]). With an increase in the synthesis temperature of glasses, the amount of magnetite decreases and for glasses prepared at temperatures > 1550 ° C magnetite was not detected. Simultaneously, the iron concentration increases in the glass matrix. It is worth noticing that the Fe 2+ content in the glass matrix increases with an increase of the sample preparation temperature [15,17]. The above takes place at the expense of b o t h Fet3e+ and Fe~t+ cations. M~ssbauer spectra of the studied glasses indicates that Fe 2÷ cations occupy network-modifying sites and, thus, would act to depolymerize the glass network. It can be concluded that increasing content of the Fe z+ cations in the glass matrix should produce additional non-bridging oxygens and thus cause a broadening and shifting of the bands in the high-frequency region of F T I R spectra to lower frequencies. The addition of iron oxides (0-10 wt% Fe203) to the potassium aluminosilicate glasses introduces a new weak absorption band. It can be seen from fig. 2 that this new absorption band (730 cm-~) in the glass spectra increases in intensity relative to the dominant 780 cm -1 band with increasing Fe203 content. It appears that this band may be related to the existence of Fe 3+ cations in tetrahedral coordination. This conclusion is in agreement with the results obtained from 57Fe Mt~ssbauer spectroscopy [15]. It was found that Fe 2+ ions are only octahedrally coordinated, while Fe 3+ ions are present both in tetrahedral and octahedral coordination. It can be observed (fig. 2) that the F T I R high and medium frequency bands shift continuously to lower frequency with corresponding changes in composition. These shifts are due to increasing Fe203 content and probably result from changes in the mean tetra-

hedral cation population of the glass and reflect the effect of substituting Fe 3÷ for Si 4+ which changes T - O bond strengths and T - O - T bond angles (where T = Fe 3+, AI 3+, Si 4+) throughout the network. Aluminium cations may exist in both tetrahedral and octahedral coordination in silicate glasses. Substitution of A13+ into alkali silicate glasses produces non-bridging oxygens, if the A13 ÷ enters network-modifying sites. Aluminium does not produce non-bridging oxygens, if it enters network-forming sites. The fraction of AI atoms in octahedral coordination in a glass is affected by its alkali composition [5,10,18.19]. There is no direct evidence in the presented spectra that glasses under consideration contain higher than fourfold coordinated aluminium (lack of diagnostic bands for A106). Therefore, we assume that most of the A13+ ions enter as network-forming cations and occupy tetrahedral coordination sites throughout the analyzed glass series. It appears from the above discussion that most of the A13÷ ions substitute for tetrahedrally coordinated Si 4+ ions in the glass network, and are charge balanced by K +, Fe 2+ and some Fe 3+ ions. For frequencies less than 400 cm-1, there is no structure in the spectra of all analyzed glasses. The low frequency bands, which represent complicated motions of the silicate network and motions of modifier cations (K +, Fe 2+ and some Fe3+), lose their distinctive character in amorphous materials. The result is that all the low frequency bands are not resolved. The examination of the F T I R absorption spectra of the potassium aluminosilicate glasses analyzed here leads to the conclusion that the network of these glasses consists of the SiO4, A104 and Fe3+O4 tetrahedra as the most fundamental units, with K ÷, Fe 2+ and some Fe 3+ ions present in charge balancing positions.

4.3. Comparisons of spectra of the parent glass and crystallized samples The structure of amorphous materials is frequently investigated by measuring vibrational spectra and assigning their characteristics to the bands derived from some model compounds [7-

315

K.E. Lipinska-Kalita / Structure and crystallization of alurninosilicate glasses

12]. There are similarities in the position of the principal vibrational bands of the glasses and of the stoichiometrically identical crystalline materials, which make it possible to identify local structures in the glass [10-12,18]. Generally, the bands in the glass spectra are broader, some are shifted in frequency and some have changed intensity compared with the corresponding bands of the materials with analogous compositions and known structures. Comparison of the glass spectra with the spectra of partially crystallized materials (of the same composition and known structures) obtained by crystallization of considered glasses as well as final comparisons with the spectra of model compounds permit conclusions to be made about glass structure. The infrared spectra of glass samples after heat treatment at 1000°C from 2 h to 120 h (fig. 3) did not show any resolvable change. The spectrum of the glass after 120 h at 1000°C exhibits only a very slightly modified lineshape in the 500-800 cm -1 region. As seen in fig. 4, the long time annealing (120 h) at a temperature 1000 ° C caused an increase of the quantity of magnetite. Since it appeared that the driving force for the crystallization is rather weak at this temperature, the glass sample was annealed at higher temperature. After annealing at l l 0 0 ° C for 30 h, some new bands developed in the 400-800 cm -1 spectral region. The sharp bands can be seen first as shoulders on the broad glass bands. These new bands subsequently increased in intensity with increasing annealing time to 70 h (fig. 3, D). The development of crystallization is also reflected in the X-ray patterns in which two additional crystalline phases are seen: hematite and potassium feldspar (fig. 4). Comparing the spectra of the partly crystallized glass sample (after 70 h at 1100 o C) with those of crystalline potassium feldspar permits conclusions to be made about origin of these new bands (fig. 5). The observed spectrum of the partially crystallized glass sample (70 h at l l 0 0 ° C ) seems to be a superposition of the crystalline feldspar bands on the characteristic glass spectrum. Annealing at higher temperatures 12001250°C) results in a remarkable growth of new bands at 340 and 560 cm-1. The spectra E, F, G in fig. 3 differ mainly in the intensity of the 340

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?20 0

KAiSiaOI 2

I

J

I

~oo

600

soo

I ~ooo

em-I

I

I

~2oo

~oo

Fig. 5. FTIR absorption spectra of (1) partially crystallized glass (70 h at llO0°C) and (2) crystallinepotassium feldspar. and 560 cm-1 bands. Detailed comparison of the spectra of glass samples after 120 h at 1 2 5 0 ° C with hematite and mullite spectra (fig. 6) shows that bands at 340 cm - ] and 560 cm -1 may be

26O

I/I 100

I 300

I

I I &O0

I

I 800

I

I 1200

l crn-I

Fig. 6. FTIR absorption spectra of partially crystallized glass (120 h at 1250°C), crystallinemullite and crystallinehematite.

316

K.E. Lipinska-Kafita / Structure and crystallization of aluminosificate glasses

assigned to hematite. As is seen in the X-ray diffractograms (fig. 4) the long time annealing (120 h) at a temperature of 1250°C causes a complete transformation of magnetite into hematite and crystallization of mullite is also observed. The spectra of glasses heat-treated at 1350°C and 1400°C (H, I, K. in fig. 3) are identical with the spectrum of the basic glass. As is readily seen, annealing at temperatures higher than the crystallization temperature causes a decrease in the hematite content due to dissolution of this phase. X-ray diffractograms show a complete transformation of hematite to magnetite. Quantitative Xray analysis indicated an increase in mullite content from 6 wt% (5 h at 1300°C) to 9 wt% (for the sample heated for 5 h at 1350 o C). The process of crystallization was also observed with the scanning electron microscope and X-ray microprobe [15]. We suggest that the appearance and the growth of the new bands may be due to microstructural changes occurring after heat treatment. As already stated [18,20,21], the vibrational spectra often show that the early crystallizing phases, although metastable, are structurally similar to the parent glass, whereas the thermodynamically stable phases exhibit structural rearrangement. This structural similarity is particularly useful in studying the crystallization of analyzed glasses. It should be noted that FTIR absorption spectra of all partially crystallized glass samples are similar to the parent glass spectrum. On the other hand, the partly crystalline glass sample which contains potassium feldspar (beginning of crystallization) has an infrared spectrum that seems to be a superposition of the bands from the crystalline feldspar vibrations on the parent glass spectrum. Taking into account the above considerations, one can conclude that the network of the studied potassium aluminosilicate glasses contains the same structural units as are present in vitrified potassium feldspar. The R D F studies have indicated that the network structure of vitreous potassium feldspar is predominantly composed of sixmembered rings of tetrahedra [22,23]. On the basis of FTIR spectra and other considerations, a structural model for iron containing potassium aluminosilicate glasses is proposed. It

can be inferred that the three-dimensional network structure of these glasses has tetrahedra of SiO4, A104 and Fe3+O4 which share vertices and form six-membered tings (as present in vitreous feldspar). The K ÷, Fe 2+ and some Fe 3+ act as charge balancing cations for the tetrahedral units. In addition it was shown that the early crystallizing phases (incipient nuclei or crystallites) are structurally similar to the parent glass. The conclusion drawn from the available spectra is that in the examined glasses there presumably exists a local (nanostructural) arrangement, similar to that in the vitreous potassium feldspar. The local arrangement may compose precursor structures for subsequent crystallization. Many different expressions ('clustered', 'microheterogeneous' 'domain', 'paracrystalline' structure etc.) have been previously used to describe this local arrangement [11,24]. These expresions show the difficulty in defining a disordered structure in the intermediate scale between the basic structural units, tetrahedra or tings of tetrahedra, and the scale of crystallites. A more precise and detailed investigation of isostructural glasses will be needed to provide a better understanding of the spectra of the corresponding aluminosilicate glasses [25-28]. Aluminogermanate and gallogermanate compositions have frequently been used for modelling the physical properties and structures of aluminosilicate glasses [29-31] and seem to be a good candidates for further studying isostructural materials.

5. Conclusions

FTIR spectroscopic data of glasses and partially crystallized glass samples indicate that potassium aluminosilicate glasses, containing iron oxides, have three-dimensional network structures consisting of interlinked SiO4, A104 and Fe3+O4 tetrahedra as their most fundamental units with K ÷, Fe 2+ and some Fe 3+ ions acting as charge balancing cations. It appears that these structures are dominated by six-membered tings of tetrahedra. The glass structure intermediate between network forming units and the crystallites regions seems to be similar to the local structures of vitreous feldspar.

K.E. la'pinska-Kalita / Structure and crystallization of aluminosilicate glasses

The influence of preparation conditions (temperature and atmosphere) and of composition of the studied glasses on the valence state and on coordination number of iron cations was determined by MiSssbauer spectroscopy. It was found that Fe 3+ cations are present in both tetra- and octahedral coordination sites, while Fe 2÷ cations occupy only network modifying sites and thus act to depolymerize the network of the studied glasses. The author is grateful to E. GiSrlich for bringing the problem of glass structure to her attention and for helpful discussions as the work progressed.

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[11] W.B. White, J. Non-Cryst. Solids 49 (1982) 321. [12] W.M. Risen Jr., J. Non-Cryst. Sofids 76 (1985) 97. [13] W.L. Konijnendijk and J.M. Stevels, J. Non-Cryst. Solids 21 (1976) 447. [14] D. Virgo, B.O. Mysen and I. Kushiro, Science 208 (1980) 1371. [15] K.E. Lipinska-Kalita and E. GSrlich Jr., J. Non-Cryst. Solids 107 (1988) 73. [16] S. Morup, Phys. Scripta 25 (1982) 713. [17] K.E. Lipinska-Kalita and J. Zarebski, Chem. Anal .33 (1988) 61. [18] T. Furukawa and W.B. White, J. Non-Cryst. Solids 38&39 (1980) 87. [19] N. Iwamoto, N. Umesaki, S. Goto, T. Hanada and N. Soga, J. Non-Cryst. Solids 70 (1985) 177. [20] T. Furukawa, S.A. Brawer and W.B. White, J. Mater. Sci. 13 (1978) 268. [21] T. Furukawa and W.B. White, Phys. Chem. Glasses 20 (1979) 69. [22] M. Taylor and G. Brown Jr, Geochim. Cosmochim. Acta 43 (1979) 61. [23] G.S. Henderson, M.E. Fleet and G.M. Bancroft, J. NonCryst. Solids 68 (1984) 333. [24] J. Zarzycki, J. Non-Cryst. Solids 52 (1982) 31. [25] K.E. Lipinska-Kalita, PhD thesis, The Academy of Mining and Metallurgy, Krakow, Poland (1988). [26] K.E. Lipinska-Kalita, J. Non-Cryst. Solids 119 (1990) 41. [27] K.E. Lipinska-Kalita and E. GiSrlich, in: Proc. 11th Int. Conf. on Raman Spectroscopy, eds. R.J.H. Clark and D.A. Long, (Wiley, Chichester, 1988) p. 523. [28] K.E. Lipinska-Kalita, D.J. Mowbray and W. Hayes, J. Molec. Struct. 219 (1990) 107. [29] N. Kinomura, M. Koizumi and S. Kume, J. Geophys. Res. 76 (1971) 2035. [30] C. Capobianco and A. Navrotsky, Am. Mineral. 67 (1982) 718. [31] I. Kushiro, Geoehim. Cosmochim. Acta 87 (1983) 1415. [32] H.M. K~ster, Die Chemische Silikatanalyse (Springer, Berlin, 1979).