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Trends in homogeneous crystal nucleation in oxide glasses E. D. Zanotto* & M. C. Weinberg Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85712, USA Manuscript received 26 September 1988 Calculations are performed to estimate the temperature of maximum nucleation rate, Tmax for several oxide glasses. H is found that for one class of glasses for which Tmas075. Hence, onc might conclude that the fact that homo- gencous crystal nucleation could not be observed in these systems is due to the suppression of the actual nucleation rate in comparison to the steady state rate. This point is illustrated in Table 2 where the transient times at the temperature of maximum nucle- ation and the ratio of actual to steady state nucleation rates are listed for those systems possessing very long transient times: it may be observed that the nucleation rates are very small fractions of the steady states rates even after prolonged heating. These data seem to support the hypothesis that the absence of homo- geneous nucleation results from transient efiects and in the remainder of this work the plausibility of this argument is analysed in more detail and comparisons are made with experimental findings. Table 2. Predicted values for 3 = 1/2 emas) System Tu es HJº Cat Tomas After 1 hours) B sd 39x 1075 16x 10 1 na 0x 1018 NAS, 04% 97 x 101 96x [0-0 n=310º LP 0595 12x 1010 TEXTO n=3x 108 NS; 0600 72x 10º 76x 1071 n=175 s 0690 DO x 108 1Oxt08 n=65 Ps 0575 8x 108 30x 107! n=50 Physics and Chemistry of Classes Vol, 30 No. 5 October 1989 Analysis of transient effects Governing equations Here, the influence of transient effects upon the po- sition and magnitude of the maximum nucleation rate will be discussed. For times where transient nucleation effects are not negligible, the position of maximum nucleation is shifted to higher temperatures (relative to the temperature of the steady state maximum) and the magnitude of the nucleation rate is reduced. This behaviour is analysed for particular choices of the steady state nucleation rate and the transient time behaviour. If Kt, T) denotes the time dependent nucieation rate and IT) the steady state nucleation rate, then 1=TANHEO (o) where f(t, 1) is a function which describes the transient nucleation and depends upon the transient time, r. The position of the maximum nucleation rate as a function of time can be found by taking the temper- ature derivative of Equation (10) and setting it to zero. One obtains dinf/dT = x(dlnf/dx) (dInt/dT) (11) where x is the time scaled by the transient time. For the transient time behaviour we choose No =1+25 (exporta, (12) which is the expression derived by Kashchiev.(16) If Equation (12) is employed in conjunction with the following form for the logarithm of the relaxation time, Int=2in(T,-ND+2+bMT— T), (3) then the right side of Equation (11) becomes x(dlnf/dx) dinc/dT = [AT DAT = TINg(o) (14) and gog=2x 5 (It nexp(—n?o)/fo). (15) a If the reduced temperature, T;, is introduced and Equation (3) is used for the left side of Equation (11), then use of Equations (14) and (15) leads to b 16n2ºBjh aca tos 272 b =etd EE - ir) as Solutions of Equation (16) for T, for varying x (or t) give the location of the maximum nucleation temper- ature as a function of time. The steady state maximum nucleation temperature is obtained from the solution of Equation (16) with the right side of this equation equal to zero. Tt will be of interest, also, to compare the maximum nucleation ratc at some reduced time, x*, with the 189 E. D. ZANOTTO & M. €. WEINBERG: HOMOGENEOUS NUCLEATION IN OXIDE GLASSES IT - “a - º o lo (NR s + aR i fo. ! -sd | i 7 a 190 E Time (h) Figure 6. Ratio of predicied nucleatiom rate to iss maximum value at 700 K for NS,. Similar ratio for number of crystals formed in time 140 h. For both one step and two step heat treatments crystal growth rates would have been sufficiently large to reveal any internal crystals if they existed but only surface crystallisation was observed. At 700K, the predicted nucieation rate would approach its steady state value after about 100--200 h, even for the worst possible condition (a = 1/2), as is shown by Figure 6, and thus homogencous nucleation should have been detectable by Hishinuma's experiments, At the other two temperatures explored, 770 and 820 K, the transi- ent times are much shorter, but so are the steady state nucleation rates, rendering internal nucleation unobservable. PbO.SiO, (T,=574-695 K) Similar calculations were carried out for PS glasses, again for «= 1/2, and Figure 7 shows the transient times and the ratio between the steady state nucle- ation rate at temperature T and its maximum valve at Thasx: in this case the transient times at Tas (597 K) are very long. H one chooses a higher temperature, say 650 K, where 7 would be greatly reduced, the steady state nuclcation rates would be too much decreased, as is shown by Figure 7. At 612 K, for instance, a heat mo A logtrin seconds) + fatia) SO SO 610 GM 60 640 60 cão Absolute temperaturo Figure 7. Calculated values of transient times and the ratio of the steady state nucleation rate at temperature, T, to the maximum rate, P(Toaxh for PS Physics and Chemistry of Glasses Vol, 30 No. 5 October 1989 treatment of approximately 2000 h would be required to bring the nucleation rates (and crystal number density) to within 2 orders of magnitude of their steady state values. However, for a = 1/3, Tas = 700K and the transient times would be only 5s, as is shown by Table 3, Hishinumal? subjected a PbO.SiO, glass to several heat treatments-—at 670 K for 140 h, from 710 to 730 K for 2200 b, at 760 K for 140 h, and also at higher temperatures (780 to 900 K)—-and onty surface crystallisation was observed. If 1Y Trax) had been suficientiy high, internal nucleation should have been detected by Hishinuma's experiments (for « = 1/3); for a close to 1/2, homogeneous nucleation would not be measurable. B,0s (T,= 5530-564 K) B,O, is an interesting system because it has the longest induction period among the twelve compo- sitions studied, with a Toa OÍ SIOK for «= 1/3 and 463K for x= 1/2. Both temperatures are well below T and the induction periods are extremely long, 46 x 10º and 10!2h, respectively. For a= 1/2 no thermal path can be found which will lead to detectable homogeneous nucleation within a reasonable time period; for the other limiting case, x= 1/3, heat treatments in the vicinity oí 530K for 1000h would be required if nucleation were to be detected. To the authors' knowledge, however, no one has been able to observe crystallisation (internal or surface) in B,O, glass, event when the melt or the external surface has been seeded with B,O, crystals. This indicates that the crystal growth rates are much too low and thus even if internal nucleation occurred, it would not be observed since the nuclei would not grow sufficiently. This is the most difficult case to analyse since 1 is very long, the growth rate is extremely small, and the nucleation rate is unknown. Other systems Albite (NAS,) glass also does not crystaltise, even when seeded, indicating a very low growth rate, For other glasses, such as SiO, and P,Os, the predicted Trax are below T, but the transient times are such that thermal paths can be found, so that they will show homogeneous nucieation. However, SiO, glass, which has been extensively studied due to its commercial importance, has only shown surface nucleation and this is also true for P,Os, although this has been studied much less. Summary The fact that homogencous nucleation cannot be observed in glasses may be related to one or more of the following causes: low nucleation rate, low growth rate, and long induction times. It has been shown that for many oxide glasses which do not exhibit homo- geneous crystal nucieation the predicted Tra will occur well below 7, leading to the reasonahle deduc- 191 E. D. ZANOTTO & M. €. WEINBERG: HOMOGENEOUS NUCLEATION IN OXIDE GLASSES tion that long induction times are responsible for this inability to detect homogeneous nucleation. However, for at least two such systems, NS, and PS, it has been demonstrated that temperature regions exist where the transient times are sufficientiy short and nucle- ation rates sufficiently large to be able to detect homogencous nucleation in a reasonable time period. Furthermore, it has been indicated that such experi- ments have in fact been performed and have failed to reveal any signs of internal nucleation. Hence, for at least several of the glasses which fall into the category described above, their failure to undergo homo- geneous nucleation must be attributabie to their low nucleation rates. SiO, and P,O,, also, probably fall into the fatter class, but systematic evidence has not been compiled for these glass systems. On the other hand, B,O; and albite secm to exhibit extremely long transient times (for all temperatures where Fis not negligible) as well as vanishingly small growth rates. Both of these features appear to be related to the extremely high viscosities of these materials in the regions of their potential crystallisation. Acknowiedgements The authors wish to express their gratitude to the Jet Propulsion Laboratory and the Division of Micro- 192 Physics and Chemistry of Glasses Vol. 30 No, 5 October 1989 gravity Science and Application of NASA and CNPq for the financial support of this work. E. D. Zanotto also acknowledges Capes/Fulbright for the support of a fellowship. References James, P. F. (1985). 4. Non-Cryst. Solids 73, 517, Neilson, G. E & Weinberg, M. C. (1979). 4. Non-Cryst. Solids 34, 137. Rowlands, E. G. & James, P. E. (1979). Physics Chem, Gslasses 20 Et, L. Weinberg, M. C. & Zanotto, E. D. (1989), 4. Nom-Cryst. Solids JOB, 99. Gonzalez-Oliver, €. 1. R. & James, PF. (1980). J. Non-Cryst. Solids a8-39, 699. James, P. F. & Rowlands, E. G. (1979). In Phase transformations. Vol. 2. Institute of Metallurgists, Sec. 3, p. 27. 7. Zanotto, E, D. & James, P. F (1985). J. Non-Cryst. Sotids 74, 373. & James, P. F.(1974), Phpsies Chem. Glasses 15 (4), 95. 9. Weinberg, M. C. Neilson, G. F. & Ublmann, D. R. (1984). 7. Non-Ceysr, Solids 68, 115. 10. Yinnon, E. & Ultlmano, D. R. (1981). 3. Non-Cryst, Solids 44, 37. 1. Zanotto, E. D, & Weinberg, M. C. (1988). J. Non-Cryst. Solids 105, 33. 12. Zanotto, É. D. (1987). 4. Nom-Cryst. Solids 89, 361 13. Guisow, E (1980). Contemp. Phys. 21, 171; ibid, 243. 14. Katinina, A. M Fokin, V. E. & Filipovich, V. N. (1977). Fiziha Kim. Stekta 2, 122. 15, Kelton, K. F, Greer. A. L. & Thompson, C. V. (1983). J. chem. Phys. 79, 6261 16, Kashchiev. D. (1969). Surf. Set. 14, 209. 17. Volterra, V. & Cooper, A. R. (1985). /. Non-Cryst. Sotids 74, 85. 18. Zeldovich, 1. B. (1849), Acta Phys. Chim. USSR 18, 1, 19. Gonzales-Oliver, €. 1. R. (1979). Ph.D, Thesis, University of Sheffield. 20. Hishinuma, A. (1986). M.Sc. Dissertation. Massachusetts Institute of Technology. nappo 
