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Mixed alkali effect in glass irradiated by 50 keV electron beam
Journal of Non-Crystalline Solids 279 (2001) 14±19
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Mixed alkali eect in glass irradiated by 50 keV electron beam Ondrej Gedeon a,*, Milada Zõmov a a, Karel Jurek b a b
Institute of Chemical Technology, Technick a 5, 166 28 Prague, Czech Republic Institute of Physics AVCR, Cukrovarnick a 10, 162 53 Prague, Czech Republic Received 26 June 2000; received in revised form 14 September 2000
Abstract A series of three sodium±potassium-silicate glasses with dierent alkali contents were prepared. The glasses were exposed to a 50 keV electron bombardment of defocused beams of various current densities. Decay curves (alkali X-ray intensity versus time) have been measured and analysed to obtain incubation periods and maximum transport rates. Obtained data have been compared with those known for binary alkali-silicate glass. The results con®rm the in¯uence of the mixed alkali eect on the transport behaviour of alkali ions under the electron bombardment. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 81.05Kf; 81.40Wx; 66.30-h; 87.50Gi
1. Introduction Glass irradiated by fast electrons undergoes changes in its structure. These changes are observed in the electron probe microanalysis as the decay of alkali X-ray intensities [1] is caused by alkali migration towards the inside of the sample. The same eects are observed in methods using an electron beam with lower primary energy as a probe [2,3]. The glass can also be irradiated by neutral charge probes. It was found that if the glass were irradiated by gamma rays, the electrical conductivity would initially increase [4]. This increase is attributed to defects induced by gamma rays that increase the diusion of mobile ions. The intro-
* Corresponding author. Tel.: +420-2 311 6217; fax: +420-2 2431 3200. E-mail address: [email protected] (O. Gedeon).
duction of point defects in pure silica and in simple alkali-silicate glasses has been observed by irradiating the glasses with neutrons [5]. In general, it appears that irradiation of glass causes signi®cant changes in the glass structure [6]. Primary electrons trapped in a glass create a macroscopic electric ®eld within the exposed volume instantly [7]. If the overall charge distribution is assumed to be homogeneous inside the irradiated volume, the macroscopic electric ®eld is a maximum at the surface and decreases linearly, reaching zero at the electron range [8]. The macroscopic alkali migration in electronirradiated glass can be observed by means of detecting the alkali X-rays coming out from the irradiated volume versus time (decay curve). The X-ray intensity is approximately proportional to the alkali concentration in the irradiated volume [9], so that the change of the intensity indicates the escape of alkali ions from the exposed volume. The measured decay curves generally
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O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
display two distinct parts [10] (also see Fig. 1). Instantaneously after the exposure, the decay curve displays very slow linear decrease. After some time, denoted as the incubation period, the decay curve abruptly changes into an exponentiallike decay. The incubation time can vary in the range from seconds to hours depending on the experimental conditions and the type of the glass, but for the binary sodium-silicate glasses no incubation period has appeared even for the mildest conditions used, i.e., for the current density 1:9 A=m2 (defocused primary beam of 100 lm in diameter was used) and 50 keV of energy [11]. The incubation period is independent of the absorption in the glass [12]. Ions in glass migrate by a hopping mechanism [13]. The activation energy for ion hopping is, in the `classical' model, the sum of an electrostatic binding energy (dissociation energy) and an elastic strain energy (displacement energy), which is needed to open the path from the initial to the ®nal state [14]. In this approach, the activation energy is fully determined by the initial state and the con®guration of its ®rst neighbours. The jump relaxation model [15,16] links the success of an ion hop to relaxation of the Coulomb potential set-up by
15
other mobile cations, while the dynamic structure model [17] links the hopping to the structure of the target site. The last two mentioned models have been combined into uni®ed site relaxation model (USRM) [18]. These theories are based on local relaxations, while the others are based on the relaxation in larger volumes of the order of magnitude of a cooperative region [19]. Although both the sodium and potassium are monovalent, modi®cations of their environments are dierent. The mean distance of the alkali ion for sodium and around oxygen is around 2:3 A 2:6 A for potassium [20]. The larger ion size for potassium also re¯ects in the higher average number of nearest neighbours. The reduction of the diusion coecients accompanied by the decrease of conductivity is observed in glasses containing two or more dierent alkali ions [21,22]. The decrease of conductivity is of the order of about 103 ±104 [23]. This eect is well known as the mixed alkali eect and has been attracting the glass science community for years. In this paper, we present a study of sodium and potassium migrations in mixed sodium±potassium-silicate glasses under the irradiation of 50 keV electron beam and compare the behaviour to that in single alkali glasses. 2. Experimental
Fig. 1. A typical decay curve, in which the incubation period s and the maximum migration rate s are determined. The curve was measured for potassium Ka-line in Na5K10 glass under the 50 keV electron beam set to 50 lm of diameter and of a current 120 nA.
The sodium±potassium-silicate glasses were melted in Pt crucible from pure batch and were held for an hour at 600°C, before cooling down to room temperature. The following glasses were prepared Na5K10 5%Na2 O 10%K2 O 85% SiO2 ; Na7K7 7:5%Na2 O 7:5%K2 O 85%SiO2 and Na10K5 10%Na2 O 5%K2 O 85%SiO2 , all in molar concentrations. The glasses are compared with binary glasses Na15 15%Na2 O 85%SiO2 and K15 15%K2 O 85%SiO2 , the results of which were presented elsewhere [11]. Blocks of glasses were cut into smaller samples and polished under isopropyl alcohol to prevent water corrosion of the glass surface. The samples were then coated by approximately 30 nm carbon layers. Specimens were exposed to a 50 keV electron beam in an electron microprobe analyser; the diameter
16
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
of the beam was measured at the ¯uorescent screen using an optical microscope and set to 50 and/or 100 lm. The widening of the defocused beam caused by electron scattering can be neglected compared with the beam diameter [9]. Decay curves (X-ray intensity of the particular line versus time) were obtained by means of the microanalyser. A typical decay curve together with the determined incubation time and the maximum migration rate u dI=dt is shown in Fig. 1. The order of the time ¯uctuation of X-ray intensity can be also seen from the ®gure. The X-ray continuum background was subtracted from the alkali intensities in all cases. The current densities were chosen so that the temperature increase was below the transformation temperature [24]. Exposed spots were visually monitored by optical microscope to avoid irradiation of spots of evidently bad quality of the surface. In spite of this control, several measurements of decay curves were performed in various places under the same irradiating conditions to ®nd out the possible deviations introduced by glass surface. These deviations in decay curves result in the deviations of the incubation periods, which were found to be below 5%, and appeared to be a dominant source of their total deviations (the instability of microanalyser was below 1%). The in¯uence of the glass surface on the determination of the maximum migration rate was found to be below 1%.
does not exceed the determined incubation point by more than about 5% relative. The dependence of ln is on the reciprocal of the absolute temperature is shown in Fig. 2. Homogeneously distributed energy deposition inside the irradiated volume was assumed. It results in the location of the maximum temperature, which occurs at the surface of the exposed sample. The temperature distribution inside the exposed volume was calculated according to an algorithm published in [24] and for the sake of simplicity the calculated maximum temperatures were set to be inside the whole volume. Slopes of the linear ®ts in Fig. 2 are equal to the `release' activation energies at the incubation points as suggested in [25]. Fits for potassium are depicted in solid and for sodium in dashed lines. The activation energies obtained from the ®ts as well as the corresponding R-squared coecients are presented in Table 1. The signi®cant dierence in activation energy for potassium is seen between Na5K10 glass on one side, and Na7K7 and Na10K5 on the other side. The activation energy
3. Results Decay curves were measured for times long enough to cover the incubation periods as well as to be able to determine the maximum migration rates. Incubation parts of the decay curves were ®tted with straight lines and the incubation periods were determined as points, in which decay curves decline from these straight lines (Fig. 1). The maximum migration rates u dI=dt were also determined for all decay curves and then normalised to the initial rates I0 . In most cases, the point of maximum migration rate can be identi®ed with the incubation point or is slightly higher, but it
Fig. 2. Logarithm of product of current density and incubation period versus 1000/T for sodium±potassium-silicate glasses. The slopes of the ®tted lines correspond to the release activation energies at the incubation points [11]. Temperature T is taken as the maximum temperature in the irradiated volume. The rhombi correspond to data obtained from the sodium decay curves while the triangles correspond to data obtained from the potassium decay curves.
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
17
Table 1 Activation energies E at the incubation period and maximum migration rates s for mixed and binary glassesa
a
Element (glass)
E (eV)
R2
s 10ÿ6 sÿ1
R2
Na (Na15) Na (Na10K5) Na (Na7K7) Na (Na5K10) K (K15) K (Na5K10) K (Na7K7) K (Na10K5)
± ± 0.188 0.137 0.120 0.106 0.311 0.314
± ± 0.96 0.90 0.92 0.86 0.99 0.97
329 9.43 8.25 9.27 43.17 9.24 3.55 2.35
0.997 0.999 0.997 0.994 0.983 0.989 0.996 0.999
R-squared coecients for the corresponding ®ts of experimental data are also presented.
for potassium is nearly the same both for Na7K7 and Na10K5 glasses. In contrast to potassium, smaller dierences are found in the activation energies for sodium (Na7K7 and Na5K10). No incubation period in sodium decay curves was found for Na10K5 glass, however. The normalised maximum migration rates s 1=I0 dI=dt under various experimental conditions are shown in Fig. 3. Linear ®ts are performed again, with solid lines for potassium and dashed lines for sodium, respectively. The results are given in Table 1. The maximum migration rate
Fig. 3. Normalised maximum migration rates s 1=I0 dI=dt versus current density of the primary electron beam for sodium±potassium-silicate glasses. The rhombi and square correspond to data obtained from the sodium decay curves while the triangles correspond to data obtained from the potassium decay curves.
for potassium increases with potassium content, but the dierence in rates between Na5K10 and Na7K7 glasses is signi®cantly higher than the dierence between Na7K7 and Na10K5 glasses. The maximum migration rates for sodium are very close. However, the rate for Na7K7 glass is slightly lower compared with two other glasses.
4. Discussion If the glass is irradiated with fast electrons, an alkali cation can obtain energy and/or momentum from the primary electron, so that it is able to leave its original site, and consequently the cation is driven by the electric ®eld until it recombines with a free or a trapped electron or until its path is blocked by a high-energy barrier of the topological origin. The macroscopic ®eld created by the trapped electrons is, however, not strong enough to release the alkali ions from their sites instantly, as has been indicated by diusion experiments where an alkali-ion-containing glass was subjected to a strong electric ®eld near the electric breakdown. The alkali migration lasted for hours in those experiments [26]. It is the creation of an electric ®eld inside the irradiated volume that causes that changes made by the charged particle beam, in contrast with neutral probes, can be of longer range. If the ion hops out of its original site then the electric ®eld is able to drive the released ion, leaving a new defect behind itself. If the ®eld were not present, the hopping would be restricted to the vicinity of the original site.
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O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
It was assumed that the homogeneously distributed energy deposition and the calculated maximum temperature increase were constant over the entire irradiated volume. However, the change of shape in energy distribution has only a small in¯uence on the maximum temperature increase [24]. On the other hand, it is quite reasonable to assume that the temperature distribution inside the exposed volume is very similar provided the maximum temperature increase is not too high. (The highest calculated temperature has been 337 K in the irradiated glass.) Then the former oversimpli®cations do not signi®cantly in¯uence either the slopes in Fig. 2 or the determination of the activation energy. The diusion process can be divided into two parts. The ®rst one is characterised by the incubation period, while the second one is described by the migration rate. The activation energy characterises both parts: it decreases with irradiation time over the incubation period; its value at the end of the incubation period being one of the most important factors determining the migration rate. During the incubation period, alkali cations are released with the help of the electron elastic scattering [27]: they are then driven by the electric ®eld along the energetically favourable paths, which are type-speci®c [22]. The transport paths are formed by hops from site to site, and according to USRM [18] each site is adapted to the presence of alkali cation, so that new ¯uctuating pathways rise in the glass, contrary to the idea that the pathways become speci®c during the freezing-in of the glass melt [22]. However, we have found earlier by studying the interrupted irradiation, that changes caused by electron irradiation are frozen into the glass [28] below the transformation temperature. If the cross-section of the irradiated volume was etched by 1%HF, some paths could be visualised by SEM [10]. An increasing density of network of paths was observed with time. It was suggested that the incubation period corresponds to the percolation threshold [25], when the individual paths are interconnected into the network. The incubation period seems to be a preparing phase, in which the network of paths of higher conductivity is formed. As soon as the network is inter-
connected, the incubation period ends and fast migration takes place. The activation energies for potassium in glasses K15 and Na5K10 on one side, and in glasses Na7K7 and Na10K5 on the other side, are close to each other, indicating the strong change from the high sodium (low potassium) regime to low sodium (high potassium) regime. No incubation time was found for sodium in the Na10K5 glass, while the incubation periods in Na7K7 and Na5K10 were evidently observable. No incubation period in Na10K5 glass [11] indicates that lower potassium concentration in glass is not able to prevent the immediate sodium migration after exposure to the electron beam. As the potassium concentration increases the sodium transport can be blocked with potassium ions that, presumably, is the cause of the incubation periods in Na7K7 and Na5K10 glasses. The changes in activation energies (incubation periods for sodium) con®rm the transformation from the low potassium regime in sodium-rich glasses to high potassium regime as the sodium cations are replaced with potassium ones. This transformation takes place for the concentration ratio c(K)/c(Na) close to unity. The changes of incubation periods roughly correspond to the changes of activation energies, i.e., the higher the activation energy the higher the incubation period. The alkali cation transport after the incubation period is described by the maximum migration rate. The sodium migration rates (Fig. 3) show no signi®cant dierences. However, these rates are about 40 times lower compared with those in the binary sodium glass Na15. Whereas the increase of sodium migration rate with the sodium concentration decrease had been found for the binary sodium glasses [11], it seems that the presence of potassium ions reduces this dependence in sodium±potassium-silicate glasses. The potassium migration rates in mixed alkali glasses are of the same order as the sodium ones. Comparing with binary potassium glass, the rate is one order lower. The rate increases with the potassium concentration, in contrast to that in the binary potassium glass. The comparison of migration rates versus concentration in mixed alkali glasses with similar data in binary alkali glasses shows a strong in¯uence of the second alkali.
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
Although the topological structure is very similar for all glasses in the ®rst approximation, the strong in¯uence of the second alkali cation in the glass can be clearly seen in all the above-presented results. Though the transport under the electron beam is not identical with the transport under conventional electric ®eld, clear mixed alkali eect is observed. 5. Conclusions The transport behaviour of sodium and potassium ions under the electron bombardment was observed by means of intensity decay curves analysis using an electron probe microanalyser. It was found that sodium and potassium ions strongly in¯uence each other, indicating the presence of a mixed-alkali eect under irradiation conditions. The maximum migration rates are approximately one order lower for potassium and two orders lower for sodium, compared to those in the corresponding binary glasses. It seems that a small addition of a second alkali to the glass does not in¯uence the activation energy of the ®rst alkali. However, the activation energies increase rapidly with increasing addition of the second alkali ion. Acknowledgements This work is ®nancially supported by the Grant Agency of the Czech Republic through the grant No. 104/99/1407. It was also a part of the research project CEZ: MSM 223100002 Chemistry and technology of materials for technical applications, health and environment protection. References [1] A.K. Varshneya, A.R. Cooper, M. Cable, J. Appl. Phys. 37 (5) (1966) 2199.
19
[2] A. Miotelo, J. Phys. C 19 (1986) 445. [3] D.M. Usher, J. Phys. C 14 (1981) 2039. [4] H.A. ElBatal, N.A. Ghoneim, Glastech. Ber. Glass Sci. Technol. C 67 (1994) 215. [5] E. Lell, N.J. Kreidl, J.R. Hensler, in: J. Burke (Ed.), Progress in Ceramic Science, vol. 1, Pergamon, Oxford, 1966, p. 1. [6] W.J. Weber, R.C. Ewing, C.A. Angell, G.W. Arnold, A.N. Cormack, J.M. Delaye, D.L. Griscom, L.W. Hobbs, A. Navrotsky, D.L. Price, A.M. Stoneham, M.C. Weinberg, J. Mater. Res. 12 (8) (1997) 1946. [7] A. Miotelo, Phys. Lett. A 103 (1984) 279. [8] J. Cauzax, J. Appl. Phys. 59 (1986) 1418. [9] L. Reimer, Scanning Electron Microscopy, Springer, Berlin, 1985, p. 365. [10] K. Jurek, O. Gedeon, V. Hulinsky, Mikrochim. Acta 15 (Suppl.) (1998) 269. [11] O. Gedeon, K. Jurek, V. Hulõnsk y, Ceramics 3 (1999) 86. [12] O. Gedeon, K. Jurek, V. Hulõnsk y, Mikrochim. Acta 132 (2000) 505. [13] M.D. Ingram, P. Maass, A. Bunde, Chim. Chronica 23 (1994) 221. [14] O.L. Anderson, D.A. Stuart, J. Am. Ceram. Soc. 37 (1954) 573. [15] K. Funke, Prog. Solid State Chem. 22 (1993) 111. [16] K. Funke, J. Non-Cryst. Solids 172±174 (1994) 1215. [17] A. Bunde, M.D. Ingram, P. Maass, J. Non-Cryst. Solids 172±174 (1994) 1222. [18] A. Bunde, K. Funke, M.D. Ingram, Solid State Ionic 86±88 (1996) 1311. [19] B.M. Schulz, M. Dubiel, M. Schulz, J. Non-Cryst. Solids 241 (1998) 149. [20] G.N. Greaves, S.J. Gurman, C.R.A. Catlow, A.V. Chadwick, S. Houde-Walter, B. Dobson, C.M.B. Henderson, Philos. Mag. A 64 (1991) 1059. [21] D.E. Day, J. Non-Cryst. Solids 21 (1976) 343. [22] G. Tomandl, H.A. Schaeer, J. Non-Cryst. Solids 73 (1985) 179. [23] C.T. Moynihan, N.S. Saad, D.C. Tran, A.V. Lesikar, J. Am. Ceram. Soc. 63 (1980) 485. [24] V. Hulinsky, K. Jurek, O. Gedeon, Mikrochim. Acta 13 (Suppl.) (1996) 325. [25] O. Gedeon, K.V. Jurek, Hulinsky, J. Non-Cryst. Solids 246 (1999) 1. [26] P. Regnier, Y. Serruys, A. Zemsko, Phys. Chem. Glasses 27 (1986) 185. [27] O. Gedeon, M. Liska, in: Proceedings of the First Slovak Glass Conference, Trencin, Slovak Glass Society, 2000, p. 80. [28] O. Gedeon, K. Jurek, in: A. Helebrant, M. Maryska, S. Kasa (Eds.), Glass Science and Technology for the 21th Century, Prague, Czech Glass Society, 1999, p. C2.
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Mixed alkali eect in glass irradiated by 50 keV electron beam Ondrej Gedeon a,*, Milada Zõmov a a, Karel Jurek b a b
Institute of Chemical Technology, Technick a 5, 166 28 Prague, Czech Republic Institute of Physics AVCR, Cukrovarnick a 10, 162 53 Prague, Czech Republic Received 26 June 2000; received in revised form 14 September 2000
Abstract A series of three sodium±potassium-silicate glasses with dierent alkali contents were prepared. The glasses were exposed to a 50 keV electron bombardment of defocused beams of various current densities. Decay curves (alkali X-ray intensity versus time) have been measured and analysed to obtain incubation periods and maximum transport rates. Obtained data have been compared with those known for binary alkali-silicate glass. The results con®rm the in¯uence of the mixed alkali eect on the transport behaviour of alkali ions under the electron bombardment. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 81.05Kf; 81.40Wx; 66.30-h; 87.50Gi
1. Introduction Glass irradiated by fast electrons undergoes changes in its structure. These changes are observed in the electron probe microanalysis as the decay of alkali X-ray intensities [1] is caused by alkali migration towards the inside of the sample. The same eects are observed in methods using an electron beam with lower primary energy as a probe [2,3]. The glass can also be irradiated by neutral charge probes. It was found that if the glass were irradiated by gamma rays, the electrical conductivity would initially increase [4]. This increase is attributed to defects induced by gamma rays that increase the diusion of mobile ions. The intro-
* Corresponding author. Tel.: +420-2 311 6217; fax: +420-2 2431 3200. E-mail address: [email protected] (O. Gedeon).
duction of point defects in pure silica and in simple alkali-silicate glasses has been observed by irradiating the glasses with neutrons [5]. In general, it appears that irradiation of glass causes signi®cant changes in the glass structure [6]. Primary electrons trapped in a glass create a macroscopic electric ®eld within the exposed volume instantly [7]. If the overall charge distribution is assumed to be homogeneous inside the irradiated volume, the macroscopic electric ®eld is a maximum at the surface and decreases linearly, reaching zero at the electron range [8]. The macroscopic alkali migration in electronirradiated glass can be observed by means of detecting the alkali X-rays coming out from the irradiated volume versus time (decay curve). The X-ray intensity is approximately proportional to the alkali concentration in the irradiated volume [9], so that the change of the intensity indicates the escape of alkali ions from the exposed volume. The measured decay curves generally
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 0 ) 0 0 4 0 8 - 7
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
display two distinct parts [10] (also see Fig. 1). Instantaneously after the exposure, the decay curve displays very slow linear decrease. After some time, denoted as the incubation period, the decay curve abruptly changes into an exponentiallike decay. The incubation time can vary in the range from seconds to hours depending on the experimental conditions and the type of the glass, but for the binary sodium-silicate glasses no incubation period has appeared even for the mildest conditions used, i.e., for the current density 1:9 A=m2 (defocused primary beam of 100 lm in diameter was used) and 50 keV of energy [11]. The incubation period is independent of the absorption in the glass [12]. Ions in glass migrate by a hopping mechanism [13]. The activation energy for ion hopping is, in the `classical' model, the sum of an electrostatic binding energy (dissociation energy) and an elastic strain energy (displacement energy), which is needed to open the path from the initial to the ®nal state [14]. In this approach, the activation energy is fully determined by the initial state and the con®guration of its ®rst neighbours. The jump relaxation model [15,16] links the success of an ion hop to relaxation of the Coulomb potential set-up by
15
other mobile cations, while the dynamic structure model [17] links the hopping to the structure of the target site. The last two mentioned models have been combined into uni®ed site relaxation model (USRM) [18]. These theories are based on local relaxations, while the others are based on the relaxation in larger volumes of the order of magnitude of a cooperative region [19]. Although both the sodium and potassium are monovalent, modi®cations of their environments are dierent. The mean distance of the alkali ion for sodium and around oxygen is around 2:3 A 2:6 A for potassium [20]. The larger ion size for potassium also re¯ects in the higher average number of nearest neighbours. The reduction of the diusion coecients accompanied by the decrease of conductivity is observed in glasses containing two or more dierent alkali ions [21,22]. The decrease of conductivity is of the order of about 103 ±104 [23]. This eect is well known as the mixed alkali eect and has been attracting the glass science community for years. In this paper, we present a study of sodium and potassium migrations in mixed sodium±potassium-silicate glasses under the irradiation of 50 keV electron beam and compare the behaviour to that in single alkali glasses. 2. Experimental
Fig. 1. A typical decay curve, in which the incubation period s and the maximum migration rate s are determined. The curve was measured for potassium Ka-line in Na5K10 glass under the 50 keV electron beam set to 50 lm of diameter and of a current 120 nA.
The sodium±potassium-silicate glasses were melted in Pt crucible from pure batch and were held for an hour at 600°C, before cooling down to room temperature. The following glasses were prepared Na5K10 5%Na2 O 10%K2 O 85% SiO2 ; Na7K7 7:5%Na2 O 7:5%K2 O 85%SiO2 and Na10K5 10%Na2 O 5%K2 O 85%SiO2 , all in molar concentrations. The glasses are compared with binary glasses Na15 15%Na2 O 85%SiO2 and K15 15%K2 O 85%SiO2 , the results of which were presented elsewhere [11]. Blocks of glasses were cut into smaller samples and polished under isopropyl alcohol to prevent water corrosion of the glass surface. The samples were then coated by approximately 30 nm carbon layers. Specimens were exposed to a 50 keV electron beam in an electron microprobe analyser; the diameter
16
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
of the beam was measured at the ¯uorescent screen using an optical microscope and set to 50 and/or 100 lm. The widening of the defocused beam caused by electron scattering can be neglected compared with the beam diameter [9]. Decay curves (X-ray intensity of the particular line versus time) were obtained by means of the microanalyser. A typical decay curve together with the determined incubation time and the maximum migration rate u dI=dt is shown in Fig. 1. The order of the time ¯uctuation of X-ray intensity can be also seen from the ®gure. The X-ray continuum background was subtracted from the alkali intensities in all cases. The current densities were chosen so that the temperature increase was below the transformation temperature [24]. Exposed spots were visually monitored by optical microscope to avoid irradiation of spots of evidently bad quality of the surface. In spite of this control, several measurements of decay curves were performed in various places under the same irradiating conditions to ®nd out the possible deviations introduced by glass surface. These deviations in decay curves result in the deviations of the incubation periods, which were found to be below 5%, and appeared to be a dominant source of their total deviations (the instability of microanalyser was below 1%). The in¯uence of the glass surface on the determination of the maximum migration rate was found to be below 1%.
does not exceed the determined incubation point by more than about 5% relative. The dependence of ln is on the reciprocal of the absolute temperature is shown in Fig. 2. Homogeneously distributed energy deposition inside the irradiated volume was assumed. It results in the location of the maximum temperature, which occurs at the surface of the exposed sample. The temperature distribution inside the exposed volume was calculated according to an algorithm published in [24] and for the sake of simplicity the calculated maximum temperatures were set to be inside the whole volume. Slopes of the linear ®ts in Fig. 2 are equal to the `release' activation energies at the incubation points as suggested in [25]. Fits for potassium are depicted in solid and for sodium in dashed lines. The activation energies obtained from the ®ts as well as the corresponding R-squared coecients are presented in Table 1. The signi®cant dierence in activation energy for potassium is seen between Na5K10 glass on one side, and Na7K7 and Na10K5 on the other side. The activation energy
3. Results Decay curves were measured for times long enough to cover the incubation periods as well as to be able to determine the maximum migration rates. Incubation parts of the decay curves were ®tted with straight lines and the incubation periods were determined as points, in which decay curves decline from these straight lines (Fig. 1). The maximum migration rates u dI=dt were also determined for all decay curves and then normalised to the initial rates I0 . In most cases, the point of maximum migration rate can be identi®ed with the incubation point or is slightly higher, but it
Fig. 2. Logarithm of product of current density and incubation period versus 1000/T for sodium±potassium-silicate glasses. The slopes of the ®tted lines correspond to the release activation energies at the incubation points [11]. Temperature T is taken as the maximum temperature in the irradiated volume. The rhombi correspond to data obtained from the sodium decay curves while the triangles correspond to data obtained from the potassium decay curves.
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
17
Table 1 Activation energies E at the incubation period and maximum migration rates s for mixed and binary glassesa
a
Element (glass)
E (eV)
R2
s 10ÿ6 sÿ1
R2
Na (Na15) Na (Na10K5) Na (Na7K7) Na (Na5K10) K (K15) K (Na5K10) K (Na7K7) K (Na10K5)
± ± 0.188 0.137 0.120 0.106 0.311 0.314
± ± 0.96 0.90 0.92 0.86 0.99 0.97
329 9.43 8.25 9.27 43.17 9.24 3.55 2.35
0.997 0.999 0.997 0.994 0.983 0.989 0.996 0.999
R-squared coecients for the corresponding ®ts of experimental data are also presented.
for potassium is nearly the same both for Na7K7 and Na10K5 glasses. In contrast to potassium, smaller dierences are found in the activation energies for sodium (Na7K7 and Na5K10). No incubation period in sodium decay curves was found for Na10K5 glass, however. The normalised maximum migration rates s 1=I0 dI=dt under various experimental conditions are shown in Fig. 3. Linear ®ts are performed again, with solid lines for potassium and dashed lines for sodium, respectively. The results are given in Table 1. The maximum migration rate
Fig. 3. Normalised maximum migration rates s 1=I0 dI=dt versus current density of the primary electron beam for sodium±potassium-silicate glasses. The rhombi and square correspond to data obtained from the sodium decay curves while the triangles correspond to data obtained from the potassium decay curves.
for potassium increases with potassium content, but the dierence in rates between Na5K10 and Na7K7 glasses is signi®cantly higher than the dierence between Na7K7 and Na10K5 glasses. The maximum migration rates for sodium are very close. However, the rate for Na7K7 glass is slightly lower compared with two other glasses.
4. Discussion If the glass is irradiated with fast electrons, an alkali cation can obtain energy and/or momentum from the primary electron, so that it is able to leave its original site, and consequently the cation is driven by the electric ®eld until it recombines with a free or a trapped electron or until its path is blocked by a high-energy barrier of the topological origin. The macroscopic ®eld created by the trapped electrons is, however, not strong enough to release the alkali ions from their sites instantly, as has been indicated by diusion experiments where an alkali-ion-containing glass was subjected to a strong electric ®eld near the electric breakdown. The alkali migration lasted for hours in those experiments [26]. It is the creation of an electric ®eld inside the irradiated volume that causes that changes made by the charged particle beam, in contrast with neutral probes, can be of longer range. If the ion hops out of its original site then the electric ®eld is able to drive the released ion, leaving a new defect behind itself. If the ®eld were not present, the hopping would be restricted to the vicinity of the original site.
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O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
It was assumed that the homogeneously distributed energy deposition and the calculated maximum temperature increase were constant over the entire irradiated volume. However, the change of shape in energy distribution has only a small in¯uence on the maximum temperature increase [24]. On the other hand, it is quite reasonable to assume that the temperature distribution inside the exposed volume is very similar provided the maximum temperature increase is not too high. (The highest calculated temperature has been 337 K in the irradiated glass.) Then the former oversimpli®cations do not signi®cantly in¯uence either the slopes in Fig. 2 or the determination of the activation energy. The diusion process can be divided into two parts. The ®rst one is characterised by the incubation period, while the second one is described by the migration rate. The activation energy characterises both parts: it decreases with irradiation time over the incubation period; its value at the end of the incubation period being one of the most important factors determining the migration rate. During the incubation period, alkali cations are released with the help of the electron elastic scattering [27]: they are then driven by the electric ®eld along the energetically favourable paths, which are type-speci®c [22]. The transport paths are formed by hops from site to site, and according to USRM [18] each site is adapted to the presence of alkali cation, so that new ¯uctuating pathways rise in the glass, contrary to the idea that the pathways become speci®c during the freezing-in of the glass melt [22]. However, we have found earlier by studying the interrupted irradiation, that changes caused by electron irradiation are frozen into the glass [28] below the transformation temperature. If the cross-section of the irradiated volume was etched by 1%HF, some paths could be visualised by SEM [10]. An increasing density of network of paths was observed with time. It was suggested that the incubation period corresponds to the percolation threshold [25], when the individual paths are interconnected into the network. The incubation period seems to be a preparing phase, in which the network of paths of higher conductivity is formed. As soon as the network is inter-
connected, the incubation period ends and fast migration takes place. The activation energies for potassium in glasses K15 and Na5K10 on one side, and in glasses Na7K7 and Na10K5 on the other side, are close to each other, indicating the strong change from the high sodium (low potassium) regime to low sodium (high potassium) regime. No incubation time was found for sodium in the Na10K5 glass, while the incubation periods in Na7K7 and Na5K10 were evidently observable. No incubation period in Na10K5 glass [11] indicates that lower potassium concentration in glass is not able to prevent the immediate sodium migration after exposure to the electron beam. As the potassium concentration increases the sodium transport can be blocked with potassium ions that, presumably, is the cause of the incubation periods in Na7K7 and Na5K10 glasses. The changes in activation energies (incubation periods for sodium) con®rm the transformation from the low potassium regime in sodium-rich glasses to high potassium regime as the sodium cations are replaced with potassium ones. This transformation takes place for the concentration ratio c(K)/c(Na) close to unity. The changes of incubation periods roughly correspond to the changes of activation energies, i.e., the higher the activation energy the higher the incubation period. The alkali cation transport after the incubation period is described by the maximum migration rate. The sodium migration rates (Fig. 3) show no signi®cant dierences. However, these rates are about 40 times lower compared with those in the binary sodium glass Na15. Whereas the increase of sodium migration rate with the sodium concentration decrease had been found for the binary sodium glasses [11], it seems that the presence of potassium ions reduces this dependence in sodium±potassium-silicate glasses. The potassium migration rates in mixed alkali glasses are of the same order as the sodium ones. Comparing with binary potassium glass, the rate is one order lower. The rate increases with the potassium concentration, in contrast to that in the binary potassium glass. The comparison of migration rates versus concentration in mixed alkali glasses with similar data in binary alkali glasses shows a strong in¯uence of the second alkali.
O. Gedeon et al. / Journal of Non-Crystalline Solids 279 (2001) 14±19
Although the topological structure is very similar for all glasses in the ®rst approximation, the strong in¯uence of the second alkali cation in the glass can be clearly seen in all the above-presented results. Though the transport under the electron beam is not identical with the transport under conventional electric ®eld, clear mixed alkali eect is observed. 5. Conclusions The transport behaviour of sodium and potassium ions under the electron bombardment was observed by means of intensity decay curves analysis using an electron probe microanalyser. It was found that sodium and potassium ions strongly in¯uence each other, indicating the presence of a mixed-alkali eect under irradiation conditions. The maximum migration rates are approximately one order lower for potassium and two orders lower for sodium, compared to those in the corresponding binary glasses. It seems that a small addition of a second alkali to the glass does not in¯uence the activation energy of the ®rst alkali. However, the activation energies increase rapidly with increasing addition of the second alkali ion. Acknowledgements This work is ®nancially supported by the Grant Agency of the Czech Republic through the grant No. 104/99/1407. It was also a part of the research project CEZ: MSM 223100002 Chemistry and technology of materials for technical applications, health and environment protection. References [1] A.K. Varshneya, A.R. Cooper, M. Cable, J. Appl. Phys. 37 (5) (1966) 2199.
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