- Email: [email protected]
Phase diagram of the TeO2GeO2 system
Mat. Res. Bull. Vol. Ii, pp. 1397-1404, 1976. Printed in the United States.
P e r g a m o n Press, Inc.
PHASE DIAGRAM OF THE TeO2-GeO 2 SYSTEM
Yo Dimitriev, Eo Kaschieva, E. Gurov Higher Institute of Chemical Technology Darvenitsa, S o f i a - 56, Bulgaria
(Received September 16, 1976; Communicated by N. B. Hannay)
ABSTRACT The TeO~-GeO 2 phase diagram has been investigated by X-ray p~ase analysis, DTA and electron ~icroscopy. A eutectic at 67 mol% TeO 2 and 685 -~ lO C has been found. There is evidence-of microscopic phase separation in some glasses° Introduction The presence of significant structural differences between TeOo and the traditional glass formers (SIC2, B20~, GeO 2 and PoO~) determine the special place of that oxide ~n the group 8fJglass formers. As already stated in previous works (1. 2),-that difference makes it possible to suggest that a trend towards separation is probable in the simultaneous melting of TeO 2 and some of the above oxides. The above has been demonstrated for the TeO2-B203 system (1, 2). The purpose of this paper is to check whether similar phenomena may be detected in the TeO2-GeO 2 system, too. Me tho d o f In_ves.ti~ation The phase eguilibrium in the TeO~-GeO~ system was determined with the a~d of DTA and X-ray a~alys~s. DTA was performed on a non-standard thermal analyser EPP-09, specially redesigned for the purpose with a -2 mV to +3 mV range of the scale and lO ° C/min heating rate. Gold -platinum crucibles were used, up to 55 mol% TeO 2, and after that composition, in a direction of the increase in the GeO 2 content, quartz ones. The X-ray phase analysis was performed on powder samples with a URC-50-IM diffractometer (Cu K~ radiation, Ni filter). Electron microscopic observations with a Karl Zeiss (Jena) D2 microscope were carried out on microseparation. To this end, carbon-platinum replicas of freshly fractured surfaces, treated with 2% hydrofluoric acid for 10 sec, were prepared. 1397
1398
Y. DIM/TRIEV, et al
Vol. Ii, No. II
The investigations embraced three types of samples | glasses; batches melted and cooled slowly to different temperatures, annealed to achieve equilibrium and quenched rapidly after that, and solid-state reactions@ The batches were prepar@d in amounts of 50 g each from GeO 2 (lab@lied 'for analysis' DDR) and TeO 2 (labelled 'for analysis', USSR). Melting was done in an electrlc furnace in air for 1/2 hour from 900oc to 12OOOC, depending on the composition. Porcelain, platinum and quartz crucibles were tested. The effect of the material of which the crucibles were made on the structure and the colouring of the samples, obtained in them, was assessed. It was found that the crystallization ability of the samples was enhanced in porcelain crucibles, while an intensive colouration was observed in the platinum ones which ranged from yellowish-brown to blue. Using the quartz crucibles, these phenomena were less clearly ?xpresse d, which is in line with our preference for them (Fig.l).
PIG. i Effect of the crucible material ( a - quartz, b porcelain, c - platinum) on the microstructure of a quenched 30TeO2,7OGeO 2 sample. Replica electron micrographs X 12 000 Results and Discussion It is found that compositions from 15 mol% to 1OO mol% GeO % are obtained as stable glasses and between 10 mol% to 15 tool2 as glass plus crystals from the conventional rates of cooling applied. According to data by Imaoka (3), the region of glass-formation for that system is from 7.1 to 35.6 mol% GeO2, while Vogel (4) found values from 10.2 to 1OO mol% GeO 2. The chemical analysis of the batches melted is done in relation to TeOo content. The values found differ from those of the TeO 2 amount introduced by about 1-3 %. Since no data have been obtained on the content of GeO2, the results are expressed in the initial synthetic compositions.
Vol. Ii, No. Ii
T H E T e O z-GeO z S Y S T E M
The exothermic effects are seen on the DTA curves of the glasses which we assume to be due to crystallization processes. The first corresponds to the release of GeO2, and the second, to that of TeOp. This assumption has been confirmed b~ studying the crystallization products, following isothermic _ treatment from 1 to 8 hrs in the 350 u to 600 ° C temperature range. The onset of the pre-crystallization endothermic effect marks the glass transition temperature (T~), while the maximum of the same effect~is interpreted as a softening temperature. Depending on the composition, these par a~.eters varYoWithin the_following limits, from 310 C tQ 340 u C for T~ and from 330 ° C to 380 U C for the soTtening temperature° The crystallization temperatures (Tc) also differ in accordance with the composition and as seen in Fig. 2, increase in a direction towards GeO 2 .
i
1399
365 ~,, 495
0 X tu
680 3
,,
oL
_
0 Z I.u
6BO -
68o
r700
695 685
,/-----_.,,_
7
685
970
With the exception of the ini685 985 tial components, no other crystal compounds are detected° The most probable course of the liquidus line (T l) is 682 100.5 plotted on the basis of the X-ray data 10 and the values of the endothermic ef690 fects of the thermograms (Fig. 3). In the area, rich in TeO 2, it slopes gently, and for this reason the precise esFIG. 2 tablishment of the eutectic point is rendered difficult. According to our DTA thermograms of data, it corresponds to the composition lasses : of 67 mol% TeO 2 and Te = 685 _+ iO ° C. l) 70 TeO 2, 30 Ge02; After this composition an endothermic 2~ 45 TeO~, 55 GeO2; effect appears nearly at 970-1OO5 ° C (3) 20 TeO~, 80 GeO2; with variation of the composition. T 1 DTA thermograms of rises steeply and after that a flattening batches ' or 'S' shape of the liquidus is observed. 4) 90 TeO ~, iO Ge02; Visual observations of quenched melts ;, 30 Ge02; show that they are opaque, but a macro67 TeO' , ;, 33 GeO2; scopic liquid phase separation is not 45 TeO ~, 55 Ge02; distinct. For the time being it is im30 TeO ~, 70 GeO~; possible to state whether there exists 20 TeO:3, 80 GeO~; a liquid phase separation of a monoteclO TeO:3, 90 GeO 2. tic type, with the exception of the observed metastable ~mmiscibilityo The presence of a fine-scale phase structure is established with the aid of electron microscopic observations. It appears in the cooling process. Similar effects have been observed by Vogel, too (4).
l
Ioe°
1400
Y. DlhiITRIEV, et al
C •
1200 1100 1000 900 //Metastoble /
800
/
700 600
/; Te 02*GeO 2(t)
5OO
• •
~00 300 200
+
i
10 Te 0 2
~L* G e 0 2 ( t ) Two L;quids ~ o O D O %O o .
•
•
•
o
•
•
•
+ 4. 4, 4.
t
,
,
i
i
i
20 30 40 .50 60 ?0 80 90 100 re•l%
GeO2
FIG. 3 Phase diagram of the TeO.2-Ge02 system, +, • - exothermzc effects of glasses| o, - endethermic effects of batches! m - exothermic effects GeO2(h) --~ GeO2(t) transition
Vol. ii, No. II
The most stable glasses are obtained in the region of compositions around the eutect, in which microheterogeneities also appear at slow cooling (Fig. 4). To a certain extent this is a confirmation of an idea, put forward by Roy for the first time (5). In his opinion, the occurrence of a metastable phase separation may be expected around the stable immiscibility region and below some liquidus curve s o In general, to elucidate the mechani~n of the phase separation in glass systems and the causes for immiscibility in them, various models may be applied and some of the latter are the object of intensive development ( 6 - 13).
It is not our intention to dwell on a detailed interpretation, using one or another thesis; we shall only note that the microseparation of that system proceeds quickly. Owing to this, if the cooling rate is varied, it is possible to fix different degrees of metastable equilibrium and microheterogeneities for the same composition, without carrying out any additional ther. mal treatment. It is difficult to observe immiscibility in highcrystallization compositions; instead, a crystallization is at hand, as shown in Fig. 5. . Several conclusions, may be drawn about the hexagonal GeOo(h) to tetragonal GeOo(t)" transition. As is known, GeO2(h) is act transformed into G@O2(t), irrespective of the fact that the latter is a stable polymorphic form up to 1033 ° C• This transit.ion may be achieved solely by the introduction of c a t a lysts (K01, LiCe3) (14). In such a case the detection of Ge02(t) in the TeO2-GeO 2 system at relatively low temperatures (650 ° 800 ° C) is an indication of the catalyzing effect of the other component, TeO 2 (Fig. 6). It is also found that with the change of the compositions in a direction to GeO2, the temperature limit of GeO2(h) stability shifts towards the higher temperatures. Returning again to binary glasses of the TeO2-GeO 2 system, and to their structure in particular, it may b~ noted from the investigations presented that no other conclusions may be drawn than about the already mentioned liquid phase separation. Still, the presence of indirect evidence offers possibilities
Vol. II, No. ii
T H E TeOz-GeO Z S Y S T E M
FIG. 4 Replica electron micrographs of 67 TeOp, 33 GeO 2 samples : (a) etched for lO sec with TO% hydrofluoric acid; (b) untreated sample
~
~
ill
,%
FIG. 5 Replica micrographs of samples : (a) 90 TeO Teo2'lO2 GeOp, crystals of TeO 2 X 2000 (b) lO ,90 GeO2, crystals of GeO 2 X 6000
1401
1402
Y. D I M I T R I E V , .e,t al
Vol. 11, No. 11
for certain assumptions concerning the kind of the basic structural units. -39 Z~.
1.62
A "
2s
,,o?
A
,..?
V: JL
"ll)l l' J')/L
i
2?
.3.10 ~,
2,0
2s
23
II
2~
~9
rll All
~?
~5
..
63,39
~3
. g ? oroeFes (e)
PTG. 6
X-ray diffractogram of the composition 50 TeO~, 50 GeO 2 (GeO~/t/- m, TeO 2 - .).- (a) batch after thermal treatment at 670 ° C for 3 hrs; (b) melt supercooled to 67000, treated for 3 hrs at that temperature; (c) melt supercooled to 780oc, treated for 3 hrs According to X-ray structural data by Zarzycki (15), melts and glasses from GeO~ are built up by Ge0 A tetrahedra, hence they are similar to ~he hexagonal modificdtion. On the other hand, it is known that the crystal TeO 2 (paratellurite) is built up by trigonal bipyramids TeO 4 (14) which are transformed into trigonal pyramids TeO 3 in the tellurite ones(17,18). In such a case, on the basis of the shown presence of GeOo(t) at low temperatures in certain compositions, a hypothesis may be evolved about the participation of its GeO 6 polyhedra, along with GeO¢ in the structure of the corresponding glasses. It is most probable that similar structural units form mainly in the compositions, located in the centre of the system, where a sufficient number of TeO 3 groups may form (by analogy with some tellurites). In that case, oxygen ions will be released at the formation of the germanate polyhedra. Naturally, special experiments should be carried out to verify such a contention. Conclusion ~rom the investigations carried out it is found that no chemical interaction takes place between GeO 2 and TeO 2. The phase diagram is of a eutectic type. In some samples super-
Vol. II, No. II
THE TeOz-GeO Z SYSTEM
1403
cooled to glass, 4mmiscibility is observed. These compositions are in the primary phase areas of Ge02. The addition of TeO 2 to GeO 2 to a large extent activates arid at the same time considerably lowers the temperature of the GeO2(h) to GeO2(t) transition. ~rences
i. Y.Dimitriev, E.Kaschieva, paper, Conference of TNTM, 9thlOtb May (1974) 2. Y. ~imitriev, E. Easchleva, J. Mat. Solo 10, 1419 (1975) 3o M. Imaoka, Advances in GlassTechnology, p. i, 149, Plenum Press, New York (1962) 4. W. Vogel, H. BUrger, G. Winterstein, C. Ludwig, W. Jaekel, Silikattechnik 25, 209 (1974) 5- R. Roy, J. Amer. Ceram. 8oc. 45, 670 (1960) 6. E. M. Levin, J. Amer. Cemam. Soc. 50, 29 (1967) 7. R. A. McOurrie, R. W. Douglas, Phys. Chem. Glasses, 8, 132 (1967) 8. J. W. Cahn, R. J. Charles, Phys. Chem. Glasses, 6, 181
(1965) 9. R. Jo Charles, Phys. Chem. Glasses, 10, 169 (1969) iO. J. Zarzycki, Disc. Faraday Soc. 50, 122 (1970) ii. W. Haller, D. H. Blackburn, J. H° 31mmons, J. Amer. Ceram. Soc. 57, 120 (1974) 12. P. ~. James, J. Mat. Sci. i0, 1802 (1975) 15. E. A. Porai-Koshits, Phisika i Chimia Stekla i, 385 (1976) 14. Y. Kotera, M. Yonemura, Trans. Paraday 8oc. 59, 147 (1963) 15. J. Zarzycki, Verres Refract. ill, 3 (1957) 16. O. Lindquist, Ac~a Chem. Scando 22, 977 (1968) 17. K. Hancke, Naturwiss. 53, 275 (1966) 18. Jo Zemann, Z. Kristallogro 127, 319 (1968)
P e r g a m o n Press, Inc.
PHASE DIAGRAM OF THE TeO2-GeO 2 SYSTEM
Yo Dimitriev, Eo Kaschieva, E. Gurov Higher Institute of Chemical Technology Darvenitsa, S o f i a - 56, Bulgaria
(Received September 16, 1976; Communicated by N. B. Hannay)
ABSTRACT The TeO~-GeO 2 phase diagram has been investigated by X-ray p~ase analysis, DTA and electron ~icroscopy. A eutectic at 67 mol% TeO 2 and 685 -~ lO C has been found. There is evidence-of microscopic phase separation in some glasses° Introduction The presence of significant structural differences between TeOo and the traditional glass formers (SIC2, B20~, GeO 2 and PoO~) determine the special place of that oxide ~n the group 8fJglass formers. As already stated in previous works (1. 2),-that difference makes it possible to suggest that a trend towards separation is probable in the simultaneous melting of TeO 2 and some of the above oxides. The above has been demonstrated for the TeO2-B203 system (1, 2). The purpose of this paper is to check whether similar phenomena may be detected in the TeO2-GeO 2 system, too. Me tho d o f In_ves.ti~ation The phase eguilibrium in the TeO~-GeO~ system was determined with the a~d of DTA and X-ray a~alys~s. DTA was performed on a non-standard thermal analyser EPP-09, specially redesigned for the purpose with a -2 mV to +3 mV range of the scale and lO ° C/min heating rate. Gold -platinum crucibles were used, up to 55 mol% TeO 2, and after that composition, in a direction of the increase in the GeO 2 content, quartz ones. The X-ray phase analysis was performed on powder samples with a URC-50-IM diffractometer (Cu K~ radiation, Ni filter). Electron microscopic observations with a Karl Zeiss (Jena) D2 microscope were carried out on microseparation. To this end, carbon-platinum replicas of freshly fractured surfaces, treated with 2% hydrofluoric acid for 10 sec, were prepared. 1397
1398
Y. DIM/TRIEV, et al
Vol. Ii, No. II
The investigations embraced three types of samples | glasses; batches melted and cooled slowly to different temperatures, annealed to achieve equilibrium and quenched rapidly after that, and solid-state reactions@ The batches were prepar@d in amounts of 50 g each from GeO 2 (lab@lied 'for analysis' DDR) and TeO 2 (labelled 'for analysis', USSR). Melting was done in an electrlc furnace in air for 1/2 hour from 900oc to 12OOOC, depending on the composition. Porcelain, platinum and quartz crucibles were tested. The effect of the material of which the crucibles were made on the structure and the colouring of the samples, obtained in them, was assessed. It was found that the crystallization ability of the samples was enhanced in porcelain crucibles, while an intensive colouration was observed in the platinum ones which ranged from yellowish-brown to blue. Using the quartz crucibles, these phenomena were less clearly ?xpresse d, which is in line with our preference for them (Fig.l).
PIG. i Effect of the crucible material ( a - quartz, b porcelain, c - platinum) on the microstructure of a quenched 30TeO2,7OGeO 2 sample. Replica electron micrographs X 12 000 Results and Discussion It is found that compositions from 15 mol% to 1OO mol% GeO % are obtained as stable glasses and between 10 mol% to 15 tool2 as glass plus crystals from the conventional rates of cooling applied. According to data by Imaoka (3), the region of glass-formation for that system is from 7.1 to 35.6 mol% GeO2, while Vogel (4) found values from 10.2 to 1OO mol% GeO 2. The chemical analysis of the batches melted is done in relation to TeOo content. The values found differ from those of the TeO 2 amount introduced by about 1-3 %. Since no data have been obtained on the content of GeO2, the results are expressed in the initial synthetic compositions.
Vol. Ii, No. Ii
T H E T e O z-GeO z S Y S T E M
The exothermic effects are seen on the DTA curves of the glasses which we assume to be due to crystallization processes. The first corresponds to the release of GeO2, and the second, to that of TeOp. This assumption has been confirmed b~ studying the crystallization products, following isothermic _ treatment from 1 to 8 hrs in the 350 u to 600 ° C temperature range. The onset of the pre-crystallization endothermic effect marks the glass transition temperature (T~), while the maximum of the same effect~is interpreted as a softening temperature. Depending on the composition, these par a~.eters varYoWithin the_following limits, from 310 C tQ 340 u C for T~ and from 330 ° C to 380 U C for the soTtening temperature° The crystallization temperatures (Tc) also differ in accordance with the composition and as seen in Fig. 2, increase in a direction towards GeO 2 .
i
1399
365 ~,, 495
0 X tu
680 3
,,
oL
_
0 Z I.u
6BO -
68o
r700
695 685
,/-----_.,,_
7
685
970
With the exception of the ini685 985 tial components, no other crystal compounds are detected° The most probable course of the liquidus line (T l) is 682 100.5 plotted on the basis of the X-ray data 10 and the values of the endothermic ef690 fects of the thermograms (Fig. 3). In the area, rich in TeO 2, it slopes gently, and for this reason the precise esFIG. 2 tablishment of the eutectic point is rendered difficult. According to our DTA thermograms of data, it corresponds to the composition lasses : of 67 mol% TeO 2 and Te = 685 _+ iO ° C. l) 70 TeO 2, 30 Ge02; After this composition an endothermic 2~ 45 TeO~, 55 GeO2; effect appears nearly at 970-1OO5 ° C (3) 20 TeO~, 80 GeO2; with variation of the composition. T 1 DTA thermograms of rises steeply and after that a flattening batches ' or 'S' shape of the liquidus is observed. 4) 90 TeO ~, iO Ge02; Visual observations of quenched melts ;, 30 Ge02; show that they are opaque, but a macro67 TeO' , ;, 33 GeO2; scopic liquid phase separation is not 45 TeO ~, 55 Ge02; distinct. For the time being it is im30 TeO ~, 70 GeO~; possible to state whether there exists 20 TeO:3, 80 GeO~; a liquid phase separation of a monoteclO TeO:3, 90 GeO 2. tic type, with the exception of the observed metastable ~mmiscibilityo The presence of a fine-scale phase structure is established with the aid of electron microscopic observations. It appears in the cooling process. Similar effects have been observed by Vogel, too (4).
l
Ioe°
1400
Y. DlhiITRIEV, et al
C •
1200 1100 1000 900 //Metastoble /
800
/
700 600
/; Te 02*GeO 2(t)
5OO
• •
~00 300 200
+
i
10 Te 0 2
~L* G e 0 2 ( t ) Two L;quids ~ o O D O %O o .
•
•
•
o
•
•
•
+ 4. 4, 4.
t
,
,
i
i
i
20 30 40 .50 60 ?0 80 90 100 re•l%
GeO2
FIG. 3 Phase diagram of the TeO.2-Ge02 system, +, • - exothermzc effects of glasses| o, - endethermic effects of batches! m - exothermic effects GeO2(h) --~ GeO2(t) transition
Vol. ii, No. II
The most stable glasses are obtained in the region of compositions around the eutect, in which microheterogeneities also appear at slow cooling (Fig. 4). To a certain extent this is a confirmation of an idea, put forward by Roy for the first time (5). In his opinion, the occurrence of a metastable phase separation may be expected around the stable immiscibility region and below some liquidus curve s o In general, to elucidate the mechani~n of the phase separation in glass systems and the causes for immiscibility in them, various models may be applied and some of the latter are the object of intensive development ( 6 - 13).
It is not our intention to dwell on a detailed interpretation, using one or another thesis; we shall only note that the microseparation of that system proceeds quickly. Owing to this, if the cooling rate is varied, it is possible to fix different degrees of metastable equilibrium and microheterogeneities for the same composition, without carrying out any additional ther. mal treatment. It is difficult to observe immiscibility in highcrystallization compositions; instead, a crystallization is at hand, as shown in Fig. 5. . Several conclusions, may be drawn about the hexagonal GeOo(h) to tetragonal GeOo(t)" transition. As is known, GeO2(h) is act transformed into G@O2(t), irrespective of the fact that the latter is a stable polymorphic form up to 1033 ° C• This transit.ion may be achieved solely by the introduction of c a t a lysts (K01, LiCe3) (14). In such a case the detection of Ge02(t) in the TeO2-GeO 2 system at relatively low temperatures (650 ° 800 ° C) is an indication of the catalyzing effect of the other component, TeO 2 (Fig. 6). It is also found that with the change of the compositions in a direction to GeO2, the temperature limit of GeO2(h) stability shifts towards the higher temperatures. Returning again to binary glasses of the TeO2-GeO 2 system, and to their structure in particular, it may b~ noted from the investigations presented that no other conclusions may be drawn than about the already mentioned liquid phase separation. Still, the presence of indirect evidence offers possibilities
Vol. II, No. ii
T H E TeOz-GeO Z S Y S T E M
FIG. 4 Replica electron micrographs of 67 TeOp, 33 GeO 2 samples : (a) etched for lO sec with TO% hydrofluoric acid; (b) untreated sample
~
~
ill
,%
FIG. 5 Replica micrographs of samples : (a) 90 TeO Teo2'lO2 GeOp, crystals of TeO 2 X 2000 (b) lO ,90 GeO2, crystals of GeO 2 X 6000
1401
1402
Y. D I M I T R I E V , .e,t al
Vol. 11, No. 11
for certain assumptions concerning the kind of the basic structural units. -39 Z~.
1.62
A "
2s
,,o?
A
,..?
V: JL
"ll)l l' J')/L
i
2?
.3.10 ~,
2,0
2s
23
II
2~
~9
rll All
~?
~5
..
63,39
~3
. g ? oroeFes (e)
PTG. 6
X-ray diffractogram of the composition 50 TeO~, 50 GeO 2 (GeO~/t/- m, TeO 2 - .).- (a) batch after thermal treatment at 670 ° C for 3 hrs; (b) melt supercooled to 67000, treated for 3 hrs at that temperature; (c) melt supercooled to 780oc, treated for 3 hrs According to X-ray structural data by Zarzycki (15), melts and glasses from GeO~ are built up by Ge0 A tetrahedra, hence they are similar to ~he hexagonal modificdtion. On the other hand, it is known that the crystal TeO 2 (paratellurite) is built up by trigonal bipyramids TeO 4 (14) which are transformed into trigonal pyramids TeO 3 in the tellurite ones(17,18). In such a case, on the basis of the shown presence of GeOo(t) at low temperatures in certain compositions, a hypothesis may be evolved about the participation of its GeO 6 polyhedra, along with GeO¢ in the structure of the corresponding glasses. It is most probable that similar structural units form mainly in the compositions, located in the centre of the system, where a sufficient number of TeO 3 groups may form (by analogy with some tellurites). In that case, oxygen ions will be released at the formation of the germanate polyhedra. Naturally, special experiments should be carried out to verify such a contention. Conclusion ~rom the investigations carried out it is found that no chemical interaction takes place between GeO 2 and TeO 2. The phase diagram is of a eutectic type. In some samples super-
Vol. II, No. II
THE TeOz-GeO Z SYSTEM
1403
cooled to glass, 4mmiscibility is observed. These compositions are in the primary phase areas of Ge02. The addition of TeO 2 to GeO 2 to a large extent activates arid at the same time considerably lowers the temperature of the GeO2(h) to GeO2(t) transition. ~rences
i. Y.Dimitriev, E.Kaschieva, paper, Conference of TNTM, 9thlOtb May (1974) 2. Y. ~imitriev, E. Easchleva, J. Mat. Solo 10, 1419 (1975) 3o M. Imaoka, Advances in GlassTechnology, p. i, 149, Plenum Press, New York (1962) 4. W. Vogel, H. BUrger, G. Winterstein, C. Ludwig, W. Jaekel, Silikattechnik 25, 209 (1974) 5- R. Roy, J. Amer. Ceram. 8oc. 45, 670 (1960) 6. E. M. Levin, J. Amer. Cemam. Soc. 50, 29 (1967) 7. R. A. McOurrie, R. W. Douglas, Phys. Chem. Glasses, 8, 132 (1967) 8. J. W. Cahn, R. J. Charles, Phys. Chem. Glasses, 6, 181
(1965) 9. R. Jo Charles, Phys. Chem. Glasses, 10, 169 (1969) iO. J. Zarzycki, Disc. Faraday Soc. 50, 122 (1970) ii. W. Haller, D. H. Blackburn, J. H° 31mmons, J. Amer. Ceram. Soc. 57, 120 (1974) 12. P. ~. James, J. Mat. Sci. i0, 1802 (1975) 15. E. A. Porai-Koshits, Phisika i Chimia Stekla i, 385 (1976) 14. Y. Kotera, M. Yonemura, Trans. Paraday 8oc. 59, 147 (1963) 15. J. Zarzycki, Verres Refract. ill, 3 (1957) 16. O. Lindquist, Ac~a Chem. Scando 22, 977 (1968) 17. K. Hancke, Naturwiss. 53, 275 (1966) 18. Jo Zemann, Z. Kristallogro 127, 319 (1968)