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The microstructure of some glasses and melts
Journal of Non-Crystalline Solids 49 (1982) 143-156 North-Holland Publishing Company
143
P a r t I1. Microstructure f o r m a t i o n
THE MICROSTRUCTURE OF SOME GLASSES AND MELTS E.A. P O R A I - K O S H I T S , V.V. G O L U B K O V , A.P. T I T O V and T.N. V A S I L E V S K A Y A The Grebenshchikov Institute of Silicate Chemistry of the Academy of Sciences of the USSR, nab. Makarova 2, 199164 Leningrad, USSR
Application of SAXS and MAXS techniques has revealed that with a sudden increase in temperature regions of inhomogeneity of about 20,~ in size appear in vitreous B203, which disappear during prolonged isothermal heating. For two-component glasses the pseudophase structure was found and studied and an approximate estimation of the composition of small inhomogeneity regions was made for alkali borate glasses. It is shown that the pseudophase structure of these glasses appears in the melts even at 950°C. Structural changes were found to take place in alkali borate melts at the liquidus temperatures; these changes are supposed to be due to the existence of borate complexes in the melts. The behaviour of supercritical fluctuations in potassium borosilicate glasses near the immiscibility region was studied.
I. Introduction Sixty years ago Lebedev suggested the crystallite hypothesis of glass structure [1]. T o d a y only the valuable idea of the structural inhomogeneity of all inorganic glasses has retained importance. This inhomogeneity evidently has some connection (see section 4) with the crystalline state of solids. Fifty years ago the famous hypothesis of a three-dimensional unregulated spatial atomic (ionic) framework was introduced by Zachariasen [2]. A few years later this hypothesis was corroborated by X-ray investigations by Warren et al. [3-6] which were carried out with the help of the radial distribution function method. In 1935 H~igg [7] published a paper in which he explained the glass formation of inorganic substances by the existence of some large and irregular fragments in them which prevented the crystallization of the glass. The same year Zachariasen reported [8] that he agreed with the existence of such irregular fragments in glass and showed that they were consistent with his hypothesis. The small angle X-ray method (SAXS), which is capable of revealing some characteristic features of glass structure in the "middle" order and of describing them in detail, was applied to glass only twenty three years later [9]. The present paper illustrates the possibilities of this method today and examines the main types of submicroheterogeneous structure which can exist in glassy substances as well as the dependence of this structure on the composition of the glass and its heat treatment. The authors would like to report on the 0 0 2 2 - 3 0 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
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E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
progress of our knowledge of submicroheterogeneous structure for one-, twoand three-component glasses preserving, though with some modifications, the main ideas of the classical hypotheses concerning glass substances. By means of X-ray scattering at small (SAXS) and mean (MAXS) angles (from 6' to 400'), we studied: (1) thermal density fluctuations (tdf) in one-component vitreous boron oxide in the glass transition range; (2) thermal concentrational fluctuations (tcf) in alkali borate glasses and the submicroheterogeneous (supermolecular, pseudophase) structure of some twocomponent glasses; (3) alkali borate melts; and (4) supercritical fluctuations in potassium borosilicate glasses having the metastable immiscibility region. The scattering intensity was measured on a small-angle apparatus with a high-temperature attachment which permitted the study of the structural changes in glasses and melts at temperatures up to 1000°C. The samples of glass were made either by grinding and polishing the plates or by melting the glass between mica plates. The glasses were studied in the temperature range from room temperature to the glass softening temperature which, in the case of the alkali borate glasses, was higher by 150-200°C than the glass transition temperature. The melts were studied in a cuvette made in the form of flat-parallel plate of quartz glass, 0.1 mm thick. A ring made from quartz glass, which served as a wall, was pasted to the plate using a high-temperature cement. A vertical beam was used in this case.
2. Structural changes of vitreous 13203 in the glass transition range As shown earlier [10], the structural inhomogeneity of one-component glasses, such as B203, GeO and SiO2, is related to thermal density fluctuations which cause scattering, the intensity of which depends slightly on the scattering angle within the whole interval (from 6' to 400'): the intensity increases only slightly with angle, and this is most visible for the quartz glass for which at an angle of 400' the intensity is a factor of 1.5 larger than that at an angle of 6'-20'. According to the thermodynamic theory of thermal density fluctuations the level of this scattering denoted by Ip(0), is proportional to the temperature T and isothermal compressibility fir: Is(0 ) =
p2krBrV,
(1)
where p is the mean electron density of the sample; k, the Boltzman constant; T, the absolute temperature; V, the scattering volume. Expression (1) is valid for gases, liquids and glasses. The isothermal compressibility fir calculated according to eq. (1) coincides with the one determined from data of ultrasonic and optical measurements [11]. In ref. 10 the temperature dependence of Ip(0) was studied, the scattering
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intensity being measured in the region of mean scattering angles (at 400') as it permitted avoiding the influence of surface effects and "device" background. The measurements confirmed the linear temperature dependence of Ip(O) above a certain temperature TO below which the structural part of tdf and Ip(0) accordingly remained constant in the range from room temperature to TO, independently of isothermal treatment of the sample within this interval. The value of TO was also independent of the thermal treatment schedule (heating and cooling at different rates or holding at any temperature near Tg). Hence it was concluded that there exists a temperature point of freezing of the structure of thermal density fluctuations in one-component glasses. This conclusion was in some contradiction with the generally accepted definition of the glass transition temperature Tg. It was for this reason that in the present work we studied the same temperature dependence of scattering intensity but in the wide angular region from 20' to 400'. Samples of vitreous B203 were chosen for the investigation as they permitted working at comparatively low temperatures, the scattering intensity being sufficiently high in order that very accurate measurements might be obtained in comparatively short calculation times: the accuracy was ± 0.3-0.5% at each point during the measurements for 400 s. The samples of vitreous B203 were remelted in vacuum for 1 - 2 h at 900--1000°C to remove gases, and were then quenched and heated to the softening temperature between two mica plates under a load, which permitted glass plates of optimum thickness to be obtained. To take into account the surface effects, samples were prepared by pressing a drop of the melt between two steel plates. The samples obtained by the first method (between mica plates) were isolated from the action of atmospheric moisture. They were heated for 500 h at 220°C in order to guarantee the attainment of equilibrium structure. For the same reason (and also as a check) some samples were also heated at higher temperatures, namely at 240°C for 70 h. This additional heating did not affect the scattering curves. The samples were then placed in the high-temperature attachment of the small-angle X-ray apparatus to study the temperature dependence of scattering intensity within the angular region from 6' to 400'. Fig. 1 shows the scattering curves of the BzO3 samples at temperatures from 240°C to 365°C within the whole range of scattering angles. It should be noted first of all that at high temperatures (above 285°C) the shape of the curves is independent of the temperature; with increasing temperature the scattering intensity increases almost uniformly at all angles. However, in the temperature range 240-260°C a significant change occurs in the shape of the curves: the scattering intensity increases noticeably at small angles (from 50' to 200'), whereas it does not change at angles from 200' to 400'; the shape of the curves changes from the anomalous form to the form acquired at higher temperatures. To study the kinetics of structural changes in the low-temperature region, the temperature of the sample heated at 240°C was sharply increased to 285°C, and the sample was subjected to this temperature for 80 min, the intensity being measured every 10 rain. Fig. 2 shows the results of this
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E.A. Porai-Koshits et aL / The microstructure of some glasses and melts
370 °C
~
30
260
J
,
4,'
i
too
'1
2oo
t
J
2oo 4,'
Fig. 1. Scattering curves for the B203 sample at different temperatures. Fig. 2. Scattering curves for different times of heating after the temperature was raised from 240 ° to 285°C.
experiment. It can be seen that the final (equilibrium) shape of the curves appears only after 70-80 min of heating at 285°C; before this time the intensity at small angles (20'-150') grows rapidly and during the period of heating from 20 to 40 min it even exceeds the characteristic values of the equilibrium state of the structure. The slope of intensity curves in the region of small scattering angles permits an estimate to be made of the change of gyration radius at this peculiar "flash" of fluctuations. The radius of gyration, estimated using the Guinier plot, first increases to 19,~ and then decreases to 9,~. Hence it follows that when choosing a certain kind of correlation function we can determine the correlation length, i.e. the parameter characterizing the distance at which the correlation of the electron density is realized. At any rate, with a sharp increase in the temperature regions of inhomogeneity may appear in the sample and for some time the sample grows considerably more inhomogeneous than at the equilibrium state corresponding to this temperature. On the other hand, the intensity of scattering at a certain angle can be assumed to be equal to the square of the amplitude of Fourier-decomposition component of the electron density with the wavelength A = X/~, where ¢p is the scattering angle, and ~ is the wavelength of X-ray irradiation. Then the increase of SAXS intensity can be regarded as an increase of intensity of the long wave fluctuations. Assuming the validity of eq. (1), the increase of Ip(0) on isothermal treatment at 285°C (fig. 2) can be explained merely by the increase of the isothermal compressibility fir [the level Ip(0) was determined approximately by extrapolation of the intensity curves to the zero scattering angle and its
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E,A. Porai-Koshits et al. / The microstructure of some glasses and melts
maximum value was about a factor of one and a half as high as the value of the equilibrium state of the structure, fig. 3]. Fig. 4 gives the experimental temperature dependences of scattering intensity for two samples for angles of 400' (curve 1) and 50' (curve2), the samples being heated for 480 h at 220°C. It can be seen that in the first case (for a scattering angle of 400') the plot reproduces the result obtained in ref. l0 for the temperature point of freezing of tdf structure; for the given sample this point is equal to Tg = 256°C. In the second case, however (for an angle of 50') the course of the curve differs significantly from that for the large angles. In the temperature range above 270-280°C the intensity really grows linearly with increasing temperatures but below this range a sharp decrease of intensity takes place up to 245-250°C (it should be remembered that the plot represents only the equilibrium values of intensity). This sharp decrease of intensity is consistent (as noted above) with the decrease of isothermal compressibility fir which does not influence the linearlity of the plot above 270-280°C. Below 245°C the thermal density fluctuations become frozen in this case too (curve 2). The course of curves 1 and 2 for increasing temperature is the same as that characteristic of decreasing temperature. It should be noted that the intensities of scattering for the samples heated for 70 h at 240°C and for 480 h at 220°C coincide within the limits of experimental error ( - 0.5%) which is mainly due to the measurements of sample thickness by X-ray absorption; the points lie so well on the curves that the error in the determination of samples thickness can be assumed to be within the limits of statistical accuracy of the measurement of scattering intensity. Thus at temperature TO only the short wave fluctuations become frozen (curve l) which was really observed in ref. 10, whereas the freezing of the long wave fluctuations takes place not at the point TO ~ 225°C determined by the
2oo
2a:-~c
lgo. i
t,mln
t
.
J
.
.
.
.
L
,
,
,
i
]
Fig. 3. Dependence of Ip(0) on the time of isothermal heating at 285°C after the temperature was raised from 240°C. Fig. 4. Temperature dependence of scattering intensity at angles of 400' and 50': The square symbols refer to sample no. l ; the open symbols to sample no. 2.
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continuation of the straight-line part of the curve (dashed line) but somewhat earlier, near 240°C (curve2). During the "defreezing" of this part of the fluctuations an increase of the isothermal compressibility fir occurs with increasing temperature which, according to SAXS data, leads to the development of submicroheterogeneous structure (fig. 2) a considerable part of which then disappears as a result of isothermal heating.
3. Thermal coneentrational fluctuations and the pseudophase structure of twocomponent glasses
Tcf only appear for two and multicomponent glasses for small (to 5-10%) concentrations of one of the components. If this component is distributed statistically randomly in the glass matrix, it will cause the appearance of additional intensity that is independent of scattering angle. The value of this intensity is proportional to the component concentration and to the square of the number of electrons in the scattering centre which can be represented by both a single ion and a complex connected with it. Fig. 5 shows the concentrational dependences of scattering intensities found by tdf and tcf, Ipc(0 ) = lp(0) + It(0), for alkali silicate and alkali borate glasses as well as by tdf, Ip(0), for vitreous B203 and SiOz (dashed horizontal lines) [12,13]. The increase of intensity at small concentrations of R20 is due to scattering by concentrational fluctuations. For alkali silicate glasses a considerable increase of intensity is observed with increasing order number of the ion: at an R20 content of about 5% the value of/pc(0) increases from 0.66 e.u./A 3 for potassium silicate glasses to 4.5 e.u./A 3 for cesium silicate glasses. In alkali borate glasses this increase is considerably smaller. Hence it can be concluded that in alkali silicate glasses additional scattering is mainly caused by the
__a~_
t /
B20~
Fig. 5. Dependenceof intensityIpc(0) on the R20 concentrationin alkali borate and alkalisilicate glasses.
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electrons of alkali ions, whereas in alkali borate glasses it is not single ions that scatter but complexes composed of B203 and the alkali ions connected with them so that the electrons of the alkali ion are only part of the effective number of scattering electrons of the whole complex. Let us also note that in this case the appearance of the maxima in the curves at 2-3% R20 is evidence of the fact that even for small concentrations the alkali ions and complexes are distributed not statistically randomly but are grouped in submicroheterogeneous regions forming a pseudophase structure [13]. The pseudophase structure is a common feature of all the two-component glasses studied by us, including those containing alkali ions and those formed by two glass forming oxides [10,13]. Attention is drawn to the nearness in size of inhomogeneity regions in these systems; in alkali borate glasses the radii of inhomogeneity regions are 10-15 A, in alkali silicate glasses 20-30 ~,, and in borosilicate and borogermate glasses 10-12 .~. In this case the sizes of inhomogeneity regions grow with increasing temperature only in alkali silicate glasses, and the values of the mean square difference between the electron densities of the inhomogeneity regions and the matrix, ((Ap) 2) = (p~ -- p2) 2 w l w 2, decrease [12], that is the regions seem to "disappear" and the glass homogenizes. In alkali borate glasses the sizes of the regions practically do not change with increasing temperature, and the values of ((Ap) 2) increase [13]. For these glasses the increase of ((Ap)Z) is due to the difference between the thermal expansion coefficients of the matrix (composed mainly of B203) and the inhomogeneity regions containing alkali ions: the electron density of inhomogeneity regions is higher and the thermal expansion coefficient is lower than in the matrix which is related to the structural transformations in the short-range order caused by alkali ions [13]. The maximum values of ((A0)2) in the glasses of alkali borate systems and accordingly the maximum degree of glass inhomogeneity can be observed, as can be seen in fig. 5, at 2-3% R20. The decrease in values of ((Ap) 2) with a further increase of R20 content can be explained by the merging of small regions into larger ones [13] which leads ultimately to the formation of a qualitatively new matrix in which separate complexes can formally be considered as structural elements. Thus this analysis leads us to the conclusion analogous to the one drawn from the analysis of the/~c(0) dependence on the R 20 concentration. In ref. 13 an approximate estimation was made of the composition of small inhomogeneous regions (or complexes) in sodium borate glasses for which the relative molecular content of B203 and N a 2 0 (B203/Na20) appeared to be equal to 6-7. Analogous estimations of the B203/R20 ratio in a separate complex were made for all low-alkali borate glasses investigated. This ratio increases with transition from Li20 to Cs20 in the following way: for lithium silicate glasses it is equal to 4-5; for sodium borate glasses, 6-7; for potassium-, rubidium- and cesium-borate glasses, about 8-9. It is the increase of this ratio that may be the explanation of the fact that the electrons of the isolated alkali ion do not show up noticeably in scattering by concentrational fluctuations.
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In borosilicate and borogermanate glasses the maximum degree of inhomogeneity is observed for approximately equal components content [10].
4. The structure of molten alkali borate glasses
As shown above, the sizes (radii R) and the "geometry" of the structure of small inhomogeneity regions of alkali borate glasses remained unchanged with an increase of temperature to that exceeding T~ by 150-200°C, and the increase of scattering intensity (with the unchanged form of scattering curves) was explained by the change of thermal expansion coefficient of the matrix compared with that of the regions of inhomogeneity. The next stage was a study of the melts of these glasses in the range up to 950°C, namely the study of the influence of the temperature and concentration of alkali ions on the structure of R20-B203 (R = Li, Na, K, Rb, Cs) melts and the establishment of the relation between the structures of the melt and the glass. The technique used was mainly the same as in the case of glasses. In order to control the chemical composition of the samples at high temperatures, the X-ray analysis was performed with a microanalyzer "Camebax" that did not reveal noticeable diffusion of alkali ions into the quartz cuvette during the experiment. All data obtained were related to equilibrium structures as the temperature and concentrational dependences of scattering intensity were reversible and the intensities were independent of the heating time. Here and in the following, when referring to melts, we mean that samples are at temperatures exceeding the liquidus temperature TL for a given composition. Some results of the study of the structure of molten alkali borate glasses are given below on an example of glasses of the Na20-B:O 3 system; analogous results were obtained for all other systems. In the sodium borate system the melts of eight compositions were studied: from 1.5 to 26.7 mol% Na20 (by analysis). The curves of scattering intensity in the angular region from 6' to about 300' showed, for all melts containing from 5 to 16 mol% Na20, the existence of small inhomogeneity regions (R ~ 1015 .A), the sizes of which, like the glasses, did not depend on temperature. Unlike the glasses, the parameter ((Ap) 2) was also independent of temperature. It is obvious that the pseudophase structure of the glasses already exists in the melts, even at high temperatures (up to 950°C). With increasing Na20 concentration from 16 to 20 mol% the regions of inhomogeneity are formed by complexes with the B203/Na20 ratio of 4-5 (instead of 6-7 in the glasses containing less than 16% Na20); by merging these regions begin to occupy the greater part of the volume thus turning into the qualitatively new matrix. Somewhat different is the case of the low-alkali melts (to approximately 4-5% Na20 ). Here sharp changes in values of the sizes (R) and the parameter ((Ap) 2) are observed at temperatures of 700-800°C. This is exemplified in fig. 6 which shows the temperature dependences of R (the upper curve) and
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
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((Ap) 2) (the lower curves) for glasses containing 3% and 6.4% Na20. It can be seen that the structural changes in the glasses occurring with increasing temperature and with transition to the melt influence the concentrational dependences of R and ((Ap) 2) only for minimal concentrations of Na20. It is natural that tdf and tcf are present in all melts. The intensity of scattering by these fluctuations, Ip¢(0), is determined by eq. (1) and grows linearly with temperature. The structural changes taking place in the melts show up most vividly in the temperature dependences of Ip¢(0). Fig. 7 shows these dependences for the samples of vitreous B203 (in this case the intensity was measured as in ref. 10 at a scattering angle of 400') and for sodium borate glasses of three compositions. Unlike the strict linear dependence of Ipc(0 ) on the temperature for vitreous B203 in the range from TOto 1000°C, the temperature dependences for all alkali borate glasses show inflexions: at high temperatures (above a certain temperature Tx) the slope of the curve is usually smaller than at temperatures below Tx. In the latter case a general tendency is observed for a decrease of the slope with increasing N a 2 0 concentration in the glass which, according to eq. (1), is evidence of the decrease of isothermal compressibility fir. It is true that for some compositions (for example, with 6.4 and 9.4% N a 2 0 ) after the passage of the melt through the temperature Tx the slope remains unchanged or increases slightly which indicates a small increase of isothermal compressibility. More detailed analysis and the possible explanation of these changes in the slopes are given in ref. 1 4 a n d here we confine ourselves to stating the fact of the presence of some structural transformations in glasses at temperature T~. In addition to this, as in the glasses containing more than 6% N a 2 0 the pseudophase structure remains almost unchanged at these transformations, they are apparently due to the change in the short-range order. The nearness of temperature T~ at which the inflections occur to the liquidus f
4bI "~.t~. 44
~"~ 2.0
40+
~ IS e~O
T~
I ~00
, ~:*,C
do
;~
ak
~'c
Fig. 6. Temperature dependences of the sizes of inhomogeneity regions (a) and values of ((Ap)2) × 104 (b) for sodium borate glasses and melts of two compositions. Fig. 7. Temperature dependencesof scattering intensity by thermal density and concentrational fluctuations in glasses and melts of the sodium borate system.
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E.A. Porai-Koshits et a L /
The microstructure of some glasses and melts
temperature TL is notable. Fig. 8 gives a comparison of these temperatures. For all glasses containing from 5 to 16% Na20 the values of T~ (the vertical columns) lie well on the liquidus curve which is evidence of structural re-
.t4_ 700
,/
600
Fig. 8. Comparison between the temperatures of inflexions in the curves for/pc(0) (dashed line) and the liquidus temperatures (solid line).
arrangements in the regions of inhomogeneity (or in the complexes) occurring at the intersection of this curve. Exceptions are again low-alkali glasses. The temperature Tx of 720-750°C for these glasses corresponds to the temperature of the melts containing 12-13% Na20. This confirms the correctness of tentative calculations made in ref. 13 in the determination of the compositions of small inhomogeneity regions in low-alkali glasses for which the composition of the regions is close to that of the glass containing 14-16% Na20. It can also be expected that the structural rearrangements in these regions will occur at the same temperatures as in the glasses of the corresponding compositions. However, the rearrangements at temperature Tx refer to those of the fluctuation structure at merely unchanged parameters of the pseudophase structure. The compositions at which these rearrangements take place enable the similarity of the complexes present in the melts and crystals to be indicated (T~ ~ TL): these complexes can be, for example, tetraborate groups for glasses with large Na20 content and nineborate groups for low-alkali melts. Such an assumption is tempting but it of course needs further proof. As mentioned above, analogous results with some insignificant peculiarities were obtained for other alkali borate melts containing ions of Li, K, Rb and Cs.
5. Supercriticai fluctuations in potassium borosiUcate glasses The potassium borosilicate system possessing a region of immiscibility was chosen because of its rather low critical point which, according to data presented in ref. 15 is equal to 620°C for the critical composition 4 K 2 0 36 B203 60 SiO2. In this case the viscosity of the glass was sufficiently high so that the samples in the form of flat-parallel polished plates retained their form even at temperatures of 640-650°C. This permitted the structure of one-phase
E.A. Porai-Koshits et a L /
The microstructure of some glasses and melts
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glasses to be studied in a temperature range above the boundary temperature of the inhomogeneity region. The main criterion of the one-phase structure of glass was independence of X-ray scattering at small angles, of the heating time. The absence of two-phase structure was also checked with the aid of electron microscopic patterns of the fractures heated in the apparatus. The patterns of the samples heated at lower temperatures at which the SAXS intensity depended on the heating time show distinctly the two-phase structure. The compositions of the studied samples are given in table 1 in molar percentage. Let us note first that in all the glasses investigated, both outside the immiscibility cupola and within it, no pseudophase structure with submicroheterogeneous regions of inhomogeneity of 10-20-30 A was observed characteristic of the two-component glasses mentioned in section 3. Fig. 9 shows the SAXS curves of sample no. 3 obtained at temperatures from 580 ° to 645°C. Despite the fact that the SAXS intensity grows with decreasing temperature with its approach to the spinodal temperature, the sizes of inhomogeneity regions determined by the Guinier plot remained nearly the same at all temperatures and were equal t o - 3 7 0 A (the radius of gyration). According to papers refs. 16 and 17 the sizes of the inhomogeneity regions in sodium borosilicate glasses were equal to 300-400 A and were very dependent on the temperature in the narrow region (about 2°C) near the immiscibility cupola. In lead aluminoborate glasses the sizes of the regions were considerably smaller and changed strongly from 30 ,~ to 100 ,~ with a decrease of temperature from 800°C to approximately 700°C. Lithium borate glasses behave similarly: the sizes of the regions increase from 20 ~, to 100 ~, with a decrease of temperature from 650-700°C to the temperature of the immiscibility cupola. These sizes are apparently related to a certain extent with the viscosity of the glasses and cannot be considered as the major sign of supercritical fluctuations. For potassium borosilicate glass No. 3 the sharp increase of SAXS intensity with decreasing temperature (fig. 9) can be explained by the growth of parameter ~(Ap)2). Fig. 10 shows the temperature dependence of this parameter for glass no. 3 (the upper curve). With a decrease of temperature from the maximal
Table 1 Composition of the samples studied No. of sample
SiO 2
B203
K 20
To
1 2 3 4 5
60.0 60.3 63.2 56.14 68.7
36.24 34,4 33,3 39,0 28.35
3.76 5.3 3.51 4.86 2.95
620 595 575 583 560
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E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
(in the given case from 650-680°C) to 580°C we observe a rapid growth of ((Ap) 2) values to the binodal temperature and even somewhat lower after the intersection of the binodal cupola (the tentative values of binodal (Tb) and
6Jg
1
,
Fig. 9. SAXS curves of the sample of potassium borosilicate glass no. 3 at different temperatures.
spinodal (T~) temperatures for sample no. 3 are given in fig. 10). At lower temperatures (in the range from Tb to T~) the values of ((Ap) 2) change very little even after prolonged isothermal treatment. If the samples are cooled from temperatures within this range to room temperature, the values of ((Ap) 2) decrease monotonically to zero (the upper solid curve), i.e. the structure decomposes gradually and ceases its existence - the glass becomes homogeneous. If the samples are held isothermally below T~, the SAXS intensity increases (the vertical direct line with the points corresponding to the heating for a different time) as the glass begins to decompose into two phases and on cooling it remains two-phase even at room temperature (the upper dashed curve).
Fig. 10. Temperature dependence of the values of ((Ap)2) for potassium borosilicate glasses: 1 glass no. 3; 2, glass no. 2 (dashed lines show the dependences during the isothermal heating and cooling after this heating).
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
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Thus on cooling sample no. 3 from 650°C to 580°C and even to Ts the changes in intensity and ~(Ap) 2) are related to the development of supercritical concentrational fluctuations, the more so as they are independent of neither the isothermal heating nor the direction of heating (cooling and heating). Analogous results were also obtained for the other glasses. In the temperature region from T b to T~ the supercritical fluctuations remain unchanged and at temperatures below Ts they start to transform into a phase-separated structure. On rapid cooling from temperatures exceeding the spinodal temperature Ts the supercritical fluctuations decompose. Let us note that supercritical fluctuations are observed not only for the glasses of critical composition but also for those the compositions of which differ from the critical. In this case the supercritical fluctuations are observed on approaching the spinodal temperature.
6. Conclusions
The results given above illustrate the real existence in glass of H~igg's "fragments" and the possibilities of studying them by SAXS and MAXS methods. None of these results pretends to be complete in the study of the nature of "fragments" and structural transformations in glasses occurring in the regions of submicroscopic (of the order of tens and hundreds of angstroms) size. Thus, for example, the details of the "flash" process of thermal density fluctuations in vitreous boron oxide that leads to the transitory formation of inhomogeneity regions are not clear although primary data on the kinetics of this process have been obtained (see section 2); primary information about the existence of "pseudophase" structure in molten alkali borate glasses (section 4), about the sensitivity of this structure to the liquidus temperature and about the relation between this structure and some complexes existing in the corresponding crystals needs more extended and detailed checking; the new and somewhat unexpected data concerning the development of supercritical fluctuations in potassium borosilicate glasses (section5) also requires further precision. However, the fact of the existence of a submicroheterogeneous pseudophase and fluctuation structure in some glasses and melts seems to be certain. The present authors believe that the possibilities involved in the study of these structures (H~igg's fragments in the Zachariasen's random network), of the mechanism and kinetics of their formation illustrated above are important (and may be decisive) for the understanding of the glass formation process and the development of the general theory of the glassy state. References
[1] A.A. Lebedev,Trudy GOI 2 (1921) 1. [2] W.H. Zachariasen, J. Am. Chem. Soc. 54 (1932) 3841. [3] B.E. Warren, H. Krutter and O. Momingstar, J. Am. Ceram. Soc. 19 (1936) 202. [4] B.E. Warren and J. Biscoe,J. Am. Ceram. Soc. 21 (1938) 259.
156 {5] [6] [7] [8] [9] [10] [I 1] [12] [13] [14] [15] [16]
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
B.E. Warren and J. Biscoe, J. Am. Ceram. Soc. 21 (1938) 287. B.E. Warren, C.S. Robinson and J. Biscoe, J. Am. Ceram. Soc. 22 (1939) 180. G. H~igg, J. Chem. Phys. 3 (1935) 42. W.H. Zachariasen, J. Chem. Phys. 3 (1935) 162. E.A. Porai-Koshits and N.S. Andreev, Nature 182 (1958) 335. V.V. Golubkov, T.N. Vasilevskaya and E.A. Porai-Koshits, J. Non-Crystalline Sollids 2 (1980) 99. J.A. Bucaro and H.D. Dardy, J. Appl. Phys. (1974) 2121. E.A. Porai-Koshits, V.V. Golubkov and A.P. Titov, Tenth Int. Congr. on Glass (Kyoto, Japan) 12 (1974) 1. V.V. Golubkov, A.P. Titov, T.N. Vasilevskaya and E.A. Porai-Koshits, Fiz. Khim. Stekla 4 (1978) 633. A.P. Titov, V.V. Golubkov, E.A. Porai-Koshits, Fiz. Khim. Stekla 7 (1981) 544. F.J. Galakhov, V.I. Averianov, V.T. Vavilonova and M.P. Areshev, Fiz. Khim. Stekla 7 (1981) 38. A. Sarkar, G.R. Srinivasan, P.B. Macedo and V. Volterra, Phys. Rev. Lett. 29 (1972) 631.
143
P a r t I1. Microstructure f o r m a t i o n
THE MICROSTRUCTURE OF SOME GLASSES AND MELTS E.A. P O R A I - K O S H I T S , V.V. G O L U B K O V , A.P. T I T O V and T.N. V A S I L E V S K A Y A The Grebenshchikov Institute of Silicate Chemistry of the Academy of Sciences of the USSR, nab. Makarova 2, 199164 Leningrad, USSR
Application of SAXS and MAXS techniques has revealed that with a sudden increase in temperature regions of inhomogeneity of about 20,~ in size appear in vitreous B203, which disappear during prolonged isothermal heating. For two-component glasses the pseudophase structure was found and studied and an approximate estimation of the composition of small inhomogeneity regions was made for alkali borate glasses. It is shown that the pseudophase structure of these glasses appears in the melts even at 950°C. Structural changes were found to take place in alkali borate melts at the liquidus temperatures; these changes are supposed to be due to the existence of borate complexes in the melts. The behaviour of supercritical fluctuations in potassium borosilicate glasses near the immiscibility region was studied.
I. Introduction Sixty years ago Lebedev suggested the crystallite hypothesis of glass structure [1]. T o d a y only the valuable idea of the structural inhomogeneity of all inorganic glasses has retained importance. This inhomogeneity evidently has some connection (see section 4) with the crystalline state of solids. Fifty years ago the famous hypothesis of a three-dimensional unregulated spatial atomic (ionic) framework was introduced by Zachariasen [2]. A few years later this hypothesis was corroborated by X-ray investigations by Warren et al. [3-6] which were carried out with the help of the radial distribution function method. In 1935 H~igg [7] published a paper in which he explained the glass formation of inorganic substances by the existence of some large and irregular fragments in them which prevented the crystallization of the glass. The same year Zachariasen reported [8] that he agreed with the existence of such irregular fragments in glass and showed that they were consistent with his hypothesis. The small angle X-ray method (SAXS), which is capable of revealing some characteristic features of glass structure in the "middle" order and of describing them in detail, was applied to glass only twenty three years later [9]. The present paper illustrates the possibilities of this method today and examines the main types of submicroheterogeneous structure which can exist in glassy substances as well as the dependence of this structure on the composition of the glass and its heat treatment. The authors would like to report on the 0 0 2 2 - 3 0 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
144
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
progress of our knowledge of submicroheterogeneous structure for one-, twoand three-component glasses preserving, though with some modifications, the main ideas of the classical hypotheses concerning glass substances. By means of X-ray scattering at small (SAXS) and mean (MAXS) angles (from 6' to 400'), we studied: (1) thermal density fluctuations (tdf) in one-component vitreous boron oxide in the glass transition range; (2) thermal concentrational fluctuations (tcf) in alkali borate glasses and the submicroheterogeneous (supermolecular, pseudophase) structure of some twocomponent glasses; (3) alkali borate melts; and (4) supercritical fluctuations in potassium borosilicate glasses having the metastable immiscibility region. The scattering intensity was measured on a small-angle apparatus with a high-temperature attachment which permitted the study of the structural changes in glasses and melts at temperatures up to 1000°C. The samples of glass were made either by grinding and polishing the plates or by melting the glass between mica plates. The glasses were studied in the temperature range from room temperature to the glass softening temperature which, in the case of the alkali borate glasses, was higher by 150-200°C than the glass transition temperature. The melts were studied in a cuvette made in the form of flat-parallel plate of quartz glass, 0.1 mm thick. A ring made from quartz glass, which served as a wall, was pasted to the plate using a high-temperature cement. A vertical beam was used in this case.
2. Structural changes of vitreous 13203 in the glass transition range As shown earlier [10], the structural inhomogeneity of one-component glasses, such as B203, GeO and SiO2, is related to thermal density fluctuations which cause scattering, the intensity of which depends slightly on the scattering angle within the whole interval (from 6' to 400'): the intensity increases only slightly with angle, and this is most visible for the quartz glass for which at an angle of 400' the intensity is a factor of 1.5 larger than that at an angle of 6'-20'. According to the thermodynamic theory of thermal density fluctuations the level of this scattering denoted by Ip(0), is proportional to the temperature T and isothermal compressibility fir: Is(0 ) =
p2krBrV,
(1)
where p is the mean electron density of the sample; k, the Boltzman constant; T, the absolute temperature; V, the scattering volume. Expression (1) is valid for gases, liquids and glasses. The isothermal compressibility fir calculated according to eq. (1) coincides with the one determined from data of ultrasonic and optical measurements [11]. In ref. 10 the temperature dependence of Ip(0) was studied, the scattering
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
145
intensity being measured in the region of mean scattering angles (at 400') as it permitted avoiding the influence of surface effects and "device" background. The measurements confirmed the linear temperature dependence of Ip(O) above a certain temperature TO below which the structural part of tdf and Ip(0) accordingly remained constant in the range from room temperature to TO, independently of isothermal treatment of the sample within this interval. The value of TO was also independent of the thermal treatment schedule (heating and cooling at different rates or holding at any temperature near Tg). Hence it was concluded that there exists a temperature point of freezing of the structure of thermal density fluctuations in one-component glasses. This conclusion was in some contradiction with the generally accepted definition of the glass transition temperature Tg. It was for this reason that in the present work we studied the same temperature dependence of scattering intensity but in the wide angular region from 20' to 400'. Samples of vitreous B203 were chosen for the investigation as they permitted working at comparatively low temperatures, the scattering intensity being sufficiently high in order that very accurate measurements might be obtained in comparatively short calculation times: the accuracy was ± 0.3-0.5% at each point during the measurements for 400 s. The samples of vitreous B203 were remelted in vacuum for 1 - 2 h at 900--1000°C to remove gases, and were then quenched and heated to the softening temperature between two mica plates under a load, which permitted glass plates of optimum thickness to be obtained. To take into account the surface effects, samples were prepared by pressing a drop of the melt between two steel plates. The samples obtained by the first method (between mica plates) were isolated from the action of atmospheric moisture. They were heated for 500 h at 220°C in order to guarantee the attainment of equilibrium structure. For the same reason (and also as a check) some samples were also heated at higher temperatures, namely at 240°C for 70 h. This additional heating did not affect the scattering curves. The samples were then placed in the high-temperature attachment of the small-angle X-ray apparatus to study the temperature dependence of scattering intensity within the angular region from 6' to 400'. Fig. 1 shows the scattering curves of the BzO3 samples at temperatures from 240°C to 365°C within the whole range of scattering angles. It should be noted first of all that at high temperatures (above 285°C) the shape of the curves is independent of the temperature; with increasing temperature the scattering intensity increases almost uniformly at all angles. However, in the temperature range 240-260°C a significant change occurs in the shape of the curves: the scattering intensity increases noticeably at small angles (from 50' to 200'), whereas it does not change at angles from 200' to 400'; the shape of the curves changes from the anomalous form to the form acquired at higher temperatures. To study the kinetics of structural changes in the low-temperature region, the temperature of the sample heated at 240°C was sharply increased to 285°C, and the sample was subjected to this temperature for 80 min, the intensity being measured every 10 rain. Fig. 2 shows the results of this
146
E.A. Porai-Koshits et aL / The microstructure of some glasses and melts
370 °C
~
30
260
J
,
4,'
i
too
'1
2oo
t
J
2oo 4,'
Fig. 1. Scattering curves for the B203 sample at different temperatures. Fig. 2. Scattering curves for different times of heating after the temperature was raised from 240 ° to 285°C.
experiment. It can be seen that the final (equilibrium) shape of the curves appears only after 70-80 min of heating at 285°C; before this time the intensity at small angles (20'-150') grows rapidly and during the period of heating from 20 to 40 min it even exceeds the characteristic values of the equilibrium state of the structure. The slope of intensity curves in the region of small scattering angles permits an estimate to be made of the change of gyration radius at this peculiar "flash" of fluctuations. The radius of gyration, estimated using the Guinier plot, first increases to 19,~ and then decreases to 9,~. Hence it follows that when choosing a certain kind of correlation function we can determine the correlation length, i.e. the parameter characterizing the distance at which the correlation of the electron density is realized. At any rate, with a sharp increase in the temperature regions of inhomogeneity may appear in the sample and for some time the sample grows considerably more inhomogeneous than at the equilibrium state corresponding to this temperature. On the other hand, the intensity of scattering at a certain angle can be assumed to be equal to the square of the amplitude of Fourier-decomposition component of the electron density with the wavelength A = X/~, where ¢p is the scattering angle, and ~ is the wavelength of X-ray irradiation. Then the increase of SAXS intensity can be regarded as an increase of intensity of the long wave fluctuations. Assuming the validity of eq. (1), the increase of Ip(0) on isothermal treatment at 285°C (fig. 2) can be explained merely by the increase of the isothermal compressibility fir [the level Ip(0) was determined approximately by extrapolation of the intensity curves to the zero scattering angle and its
147
E,A. Porai-Koshits et al. / The microstructure of some glasses and melts
maximum value was about a factor of one and a half as high as the value of the equilibrium state of the structure, fig. 3]. Fig. 4 gives the experimental temperature dependences of scattering intensity for two samples for angles of 400' (curve 1) and 50' (curve2), the samples being heated for 480 h at 220°C. It can be seen that in the first case (for a scattering angle of 400') the plot reproduces the result obtained in ref. l0 for the temperature point of freezing of tdf structure; for the given sample this point is equal to Tg = 256°C. In the second case, however (for an angle of 50') the course of the curve differs significantly from that for the large angles. In the temperature range above 270-280°C the intensity really grows linearly with increasing temperatures but below this range a sharp decrease of intensity takes place up to 245-250°C (it should be remembered that the plot represents only the equilibrium values of intensity). This sharp decrease of intensity is consistent (as noted above) with the decrease of isothermal compressibility fir which does not influence the linearlity of the plot above 270-280°C. Below 245°C the thermal density fluctuations become frozen in this case too (curve 2). The course of curves 1 and 2 for increasing temperature is the same as that characteristic of decreasing temperature. It should be noted that the intensities of scattering for the samples heated for 70 h at 240°C and for 480 h at 220°C coincide within the limits of experimental error ( - 0.5%) which is mainly due to the measurements of sample thickness by X-ray absorption; the points lie so well on the curves that the error in the determination of samples thickness can be assumed to be within the limits of statistical accuracy of the measurement of scattering intensity. Thus at temperature TO only the short wave fluctuations become frozen (curve l) which was really observed in ref. 10, whereas the freezing of the long wave fluctuations takes place not at the point TO ~ 225°C determined by the
2oo
2a:-~c
lgo. i
t,mln
t
.
J
.
.
.
.
L
,
,
,
i
]
Fig. 3. Dependence of Ip(0) on the time of isothermal heating at 285°C after the temperature was raised from 240°C. Fig. 4. Temperature dependence of scattering intensity at angles of 400' and 50': The square symbols refer to sample no. l ; the open symbols to sample no. 2.
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
148
continuation of the straight-line part of the curve (dashed line) but somewhat earlier, near 240°C (curve2). During the "defreezing" of this part of the fluctuations an increase of the isothermal compressibility fir occurs with increasing temperature which, according to SAXS data, leads to the development of submicroheterogeneous structure (fig. 2) a considerable part of which then disappears as a result of isothermal heating.
3. Thermal coneentrational fluctuations and the pseudophase structure of twocomponent glasses
Tcf only appear for two and multicomponent glasses for small (to 5-10%) concentrations of one of the components. If this component is distributed statistically randomly in the glass matrix, it will cause the appearance of additional intensity that is independent of scattering angle. The value of this intensity is proportional to the component concentration and to the square of the number of electrons in the scattering centre which can be represented by both a single ion and a complex connected with it. Fig. 5 shows the concentrational dependences of scattering intensities found by tdf and tcf, Ipc(0 ) = lp(0) + It(0), for alkali silicate and alkali borate glasses as well as by tdf, Ip(0), for vitreous B203 and SiOz (dashed horizontal lines) [12,13]. The increase of intensity at small concentrations of R20 is due to scattering by concentrational fluctuations. For alkali silicate glasses a considerable increase of intensity is observed with increasing order number of the ion: at an R20 content of about 5% the value of/pc(0) increases from 0.66 e.u./A 3 for potassium silicate glasses to 4.5 e.u./A 3 for cesium silicate glasses. In alkali borate glasses this increase is considerably smaller. Hence it can be concluded that in alkali silicate glasses additional scattering is mainly caused by the
__a~_
t /
B20~
Fig. 5. Dependenceof intensityIpc(0) on the R20 concentrationin alkali borate and alkalisilicate glasses.
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
149
electrons of alkali ions, whereas in alkali borate glasses it is not single ions that scatter but complexes composed of B203 and the alkali ions connected with them so that the electrons of the alkali ion are only part of the effective number of scattering electrons of the whole complex. Let us also note that in this case the appearance of the maxima in the curves at 2-3% R20 is evidence of the fact that even for small concentrations the alkali ions and complexes are distributed not statistically randomly but are grouped in submicroheterogeneous regions forming a pseudophase structure [13]. The pseudophase structure is a common feature of all the two-component glasses studied by us, including those containing alkali ions and those formed by two glass forming oxides [10,13]. Attention is drawn to the nearness in size of inhomogeneity regions in these systems; in alkali borate glasses the radii of inhomogeneity regions are 10-15 A, in alkali silicate glasses 20-30 ~,, and in borosilicate and borogermate glasses 10-12 .~. In this case the sizes of inhomogeneity regions grow with increasing temperature only in alkali silicate glasses, and the values of the mean square difference between the electron densities of the inhomogeneity regions and the matrix, ((Ap) 2) = (p~ -- p2) 2 w l w 2, decrease [12], that is the regions seem to "disappear" and the glass homogenizes. In alkali borate glasses the sizes of the regions practically do not change with increasing temperature, and the values of ((Ap) 2) increase [13]. For these glasses the increase of ((Ap)Z) is due to the difference between the thermal expansion coefficients of the matrix (composed mainly of B203) and the inhomogeneity regions containing alkali ions: the electron density of inhomogeneity regions is higher and the thermal expansion coefficient is lower than in the matrix which is related to the structural transformations in the short-range order caused by alkali ions [13]. The maximum values of ((A0)2) in the glasses of alkali borate systems and accordingly the maximum degree of glass inhomogeneity can be observed, as can be seen in fig. 5, at 2-3% R20. The decrease in values of ((Ap) 2) with a further increase of R20 content can be explained by the merging of small regions into larger ones [13] which leads ultimately to the formation of a qualitatively new matrix in which separate complexes can formally be considered as structural elements. Thus this analysis leads us to the conclusion analogous to the one drawn from the analysis of the/~c(0) dependence on the R 20 concentration. In ref. 13 an approximate estimation was made of the composition of small inhomogeneous regions (or complexes) in sodium borate glasses for which the relative molecular content of B203 and N a 2 0 (B203/Na20) appeared to be equal to 6-7. Analogous estimations of the B203/R20 ratio in a separate complex were made for all low-alkali borate glasses investigated. This ratio increases with transition from Li20 to Cs20 in the following way: for lithium silicate glasses it is equal to 4-5; for sodium borate glasses, 6-7; for potassium-, rubidium- and cesium-borate glasses, about 8-9. It is the increase of this ratio that may be the explanation of the fact that the electrons of the isolated alkali ion do not show up noticeably in scattering by concentrational fluctuations.
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E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
In borosilicate and borogermanate glasses the maximum degree of inhomogeneity is observed for approximately equal components content [10].
4. The structure of molten alkali borate glasses
As shown above, the sizes (radii R) and the "geometry" of the structure of small inhomogeneity regions of alkali borate glasses remained unchanged with an increase of temperature to that exceeding T~ by 150-200°C, and the increase of scattering intensity (with the unchanged form of scattering curves) was explained by the change of thermal expansion coefficient of the matrix compared with that of the regions of inhomogeneity. The next stage was a study of the melts of these glasses in the range up to 950°C, namely the study of the influence of the temperature and concentration of alkali ions on the structure of R20-B203 (R = Li, Na, K, Rb, Cs) melts and the establishment of the relation between the structures of the melt and the glass. The technique used was mainly the same as in the case of glasses. In order to control the chemical composition of the samples at high temperatures, the X-ray analysis was performed with a microanalyzer "Camebax" that did not reveal noticeable diffusion of alkali ions into the quartz cuvette during the experiment. All data obtained were related to equilibrium structures as the temperature and concentrational dependences of scattering intensity were reversible and the intensities were independent of the heating time. Here and in the following, when referring to melts, we mean that samples are at temperatures exceeding the liquidus temperature TL for a given composition. Some results of the study of the structure of molten alkali borate glasses are given below on an example of glasses of the Na20-B:O 3 system; analogous results were obtained for all other systems. In the sodium borate system the melts of eight compositions were studied: from 1.5 to 26.7 mol% Na20 (by analysis). The curves of scattering intensity in the angular region from 6' to about 300' showed, for all melts containing from 5 to 16 mol% Na20, the existence of small inhomogeneity regions (R ~ 1015 .A), the sizes of which, like the glasses, did not depend on temperature. Unlike the glasses, the parameter ((Ap) 2) was also independent of temperature. It is obvious that the pseudophase structure of the glasses already exists in the melts, even at high temperatures (up to 950°C). With increasing Na20 concentration from 16 to 20 mol% the regions of inhomogeneity are formed by complexes with the B203/Na20 ratio of 4-5 (instead of 6-7 in the glasses containing less than 16% Na20); by merging these regions begin to occupy the greater part of the volume thus turning into the qualitatively new matrix. Somewhat different is the case of the low-alkali melts (to approximately 4-5% Na20 ). Here sharp changes in values of the sizes (R) and the parameter ((Ap) 2) are observed at temperatures of 700-800°C. This is exemplified in fig. 6 which shows the temperature dependences of R (the upper curve) and
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
151
((Ap) 2) (the lower curves) for glasses containing 3% and 6.4% Na20. It can be seen that the structural changes in the glasses occurring with increasing temperature and with transition to the melt influence the concentrational dependences of R and ((Ap) 2) only for minimal concentrations of Na20. It is natural that tdf and tcf are present in all melts. The intensity of scattering by these fluctuations, Ip¢(0), is determined by eq. (1) and grows linearly with temperature. The structural changes taking place in the melts show up most vividly in the temperature dependences of Ip¢(0). Fig. 7 shows these dependences for the samples of vitreous B203 (in this case the intensity was measured as in ref. 10 at a scattering angle of 400') and for sodium borate glasses of three compositions. Unlike the strict linear dependence of Ipc(0 ) on the temperature for vitreous B203 in the range from TOto 1000°C, the temperature dependences for all alkali borate glasses show inflexions: at high temperatures (above a certain temperature Tx) the slope of the curve is usually smaller than at temperatures below Tx. In the latter case a general tendency is observed for a decrease of the slope with increasing N a 2 0 concentration in the glass which, according to eq. (1), is evidence of the decrease of isothermal compressibility fir. It is true that for some compositions (for example, with 6.4 and 9.4% N a 2 0 ) after the passage of the melt through the temperature Tx the slope remains unchanged or increases slightly which indicates a small increase of isothermal compressibility. More detailed analysis and the possible explanation of these changes in the slopes are given in ref. 1 4 a n d here we confine ourselves to stating the fact of the presence of some structural transformations in glasses at temperature T~. In addition to this, as in the glasses containing more than 6% N a 2 0 the pseudophase structure remains almost unchanged at these transformations, they are apparently due to the change in the short-range order. The nearness of temperature T~ at which the inflections occur to the liquidus f
4bI "~.t~. 44
~"~ 2.0
40+
~ IS e~O
T~
I ~00
, ~:*,C
do
;~
ak
~'c
Fig. 6. Temperature dependences of the sizes of inhomogeneity regions (a) and values of ((Ap)2) × 104 (b) for sodium borate glasses and melts of two compositions. Fig. 7. Temperature dependencesof scattering intensity by thermal density and concentrational fluctuations in glasses and melts of the sodium borate system.
152
E.A. Porai-Koshits et a L /
The microstructure of some glasses and melts
temperature TL is notable. Fig. 8 gives a comparison of these temperatures. For all glasses containing from 5 to 16% Na20 the values of T~ (the vertical columns) lie well on the liquidus curve which is evidence of structural re-
.t4_ 700
,/
600
Fig. 8. Comparison between the temperatures of inflexions in the curves for/pc(0) (dashed line) and the liquidus temperatures (solid line).
arrangements in the regions of inhomogeneity (or in the complexes) occurring at the intersection of this curve. Exceptions are again low-alkali glasses. The temperature Tx of 720-750°C for these glasses corresponds to the temperature of the melts containing 12-13% Na20. This confirms the correctness of tentative calculations made in ref. 13 in the determination of the compositions of small inhomogeneity regions in low-alkali glasses for which the composition of the regions is close to that of the glass containing 14-16% Na20. It can also be expected that the structural rearrangements in these regions will occur at the same temperatures as in the glasses of the corresponding compositions. However, the rearrangements at temperature Tx refer to those of the fluctuation structure at merely unchanged parameters of the pseudophase structure. The compositions at which these rearrangements take place enable the similarity of the complexes present in the melts and crystals to be indicated (T~ ~ TL): these complexes can be, for example, tetraborate groups for glasses with large Na20 content and nineborate groups for low-alkali melts. Such an assumption is tempting but it of course needs further proof. As mentioned above, analogous results with some insignificant peculiarities were obtained for other alkali borate melts containing ions of Li, K, Rb and Cs.
5. Supercriticai fluctuations in potassium borosiUcate glasses The potassium borosilicate system possessing a region of immiscibility was chosen because of its rather low critical point which, according to data presented in ref. 15 is equal to 620°C for the critical composition 4 K 2 0 36 B203 60 SiO2. In this case the viscosity of the glass was sufficiently high so that the samples in the form of flat-parallel polished plates retained their form even at temperatures of 640-650°C. This permitted the structure of one-phase
E.A. Porai-Koshits et a L /
The microstructure of some glasses and melts
153
glasses to be studied in a temperature range above the boundary temperature of the inhomogeneity region. The main criterion of the one-phase structure of glass was independence of X-ray scattering at small angles, of the heating time. The absence of two-phase structure was also checked with the aid of electron microscopic patterns of the fractures heated in the apparatus. The patterns of the samples heated at lower temperatures at which the SAXS intensity depended on the heating time show distinctly the two-phase structure. The compositions of the studied samples are given in table 1 in molar percentage. Let us note first that in all the glasses investigated, both outside the immiscibility cupola and within it, no pseudophase structure with submicroheterogeneous regions of inhomogeneity of 10-20-30 A was observed characteristic of the two-component glasses mentioned in section 3. Fig. 9 shows the SAXS curves of sample no. 3 obtained at temperatures from 580 ° to 645°C. Despite the fact that the SAXS intensity grows with decreasing temperature with its approach to the spinodal temperature, the sizes of inhomogeneity regions determined by the Guinier plot remained nearly the same at all temperatures and were equal t o - 3 7 0 A (the radius of gyration). According to papers refs. 16 and 17 the sizes of the inhomogeneity regions in sodium borosilicate glasses were equal to 300-400 A and were very dependent on the temperature in the narrow region (about 2°C) near the immiscibility cupola. In lead aluminoborate glasses the sizes of the regions were considerably smaller and changed strongly from 30 ,~ to 100 ,~ with a decrease of temperature from 800°C to approximately 700°C. Lithium borate glasses behave similarly: the sizes of the regions increase from 20 ~, to 100 ~, with a decrease of temperature from 650-700°C to the temperature of the immiscibility cupola. These sizes are apparently related to a certain extent with the viscosity of the glasses and cannot be considered as the major sign of supercritical fluctuations. For potassium borosilicate glass No. 3 the sharp increase of SAXS intensity with decreasing temperature (fig. 9) can be explained by the growth of parameter ~(Ap)2). Fig. 10 shows the temperature dependence of this parameter for glass no. 3 (the upper curve). With a decrease of temperature from the maximal
Table 1 Composition of the samples studied No. of sample
SiO 2
B203
K 20
To
1 2 3 4 5
60.0 60.3 63.2 56.14 68.7
36.24 34,4 33,3 39,0 28.35
3.76 5.3 3.51 4.86 2.95
620 595 575 583 560
154
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
(in the given case from 650-680°C) to 580°C we observe a rapid growth of ((Ap) 2) values to the binodal temperature and even somewhat lower after the intersection of the binodal cupola (the tentative values of binodal (Tb) and
6Jg
1
,
Fig. 9. SAXS curves of the sample of potassium borosilicate glass no. 3 at different temperatures.
spinodal (T~) temperatures for sample no. 3 are given in fig. 10). At lower temperatures (in the range from Tb to T~) the values of ((Ap) 2) change very little even after prolonged isothermal treatment. If the samples are cooled from temperatures within this range to room temperature, the values of ((Ap) 2) decrease monotonically to zero (the upper solid curve), i.e. the structure decomposes gradually and ceases its existence - the glass becomes homogeneous. If the samples are held isothermally below T~, the SAXS intensity increases (the vertical direct line with the points corresponding to the heating for a different time) as the glass begins to decompose into two phases and on cooling it remains two-phase even at room temperature (the upper dashed curve).
Fig. 10. Temperature dependence of the values of ((Ap)2) for potassium borosilicate glasses: 1 glass no. 3; 2, glass no. 2 (dashed lines show the dependences during the isothermal heating and cooling after this heating).
E.A. Porai-Koshits et al. / The microstructure of some glasses and melts
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Thus on cooling sample no. 3 from 650°C to 580°C and even to Ts the changes in intensity and ~(Ap) 2) are related to the development of supercritical concentrational fluctuations, the more so as they are independent of neither the isothermal heating nor the direction of heating (cooling and heating). Analogous results were also obtained for the other glasses. In the temperature region from T b to T~ the supercritical fluctuations remain unchanged and at temperatures below Ts they start to transform into a phase-separated structure. On rapid cooling from temperatures exceeding the spinodal temperature Ts the supercritical fluctuations decompose. Let us note that supercritical fluctuations are observed not only for the glasses of critical composition but also for those the compositions of which differ from the critical. In this case the supercritical fluctuations are observed on approaching the spinodal temperature.
6. Conclusions
The results given above illustrate the real existence in glass of H~igg's "fragments" and the possibilities of studying them by SAXS and MAXS methods. None of these results pretends to be complete in the study of the nature of "fragments" and structural transformations in glasses occurring in the regions of submicroscopic (of the order of tens and hundreds of angstroms) size. Thus, for example, the details of the "flash" process of thermal density fluctuations in vitreous boron oxide that leads to the transitory formation of inhomogeneity regions are not clear although primary data on the kinetics of this process have been obtained (see section 2); primary information about the existence of "pseudophase" structure in molten alkali borate glasses (section 4), about the sensitivity of this structure to the liquidus temperature and about the relation between this structure and some complexes existing in the corresponding crystals needs more extended and detailed checking; the new and somewhat unexpected data concerning the development of supercritical fluctuations in potassium borosilicate glasses (section5) also requires further precision. However, the fact of the existence of a submicroheterogeneous pseudophase and fluctuation structure in some glasses and melts seems to be certain. The present authors believe that the possibilities involved in the study of these structures (H~igg's fragments in the Zachariasen's random network), of the mechanism and kinetics of their formation illustrated above are important (and may be decisive) for the understanding of the glass formation process and the development of the general theory of the glassy state. References
[1] A.A. Lebedev,Trudy GOI 2 (1921) 1. [2] W.H. Zachariasen, J. Am. Chem. Soc. 54 (1932) 3841. [3] B.E. Warren, H. Krutter and O. Momingstar, J. Am. Ceram. Soc. 19 (1936) 202. [4] B.E. Warren and J. Biscoe,J. Am. Ceram. Soc. 21 (1938) 259.
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