El Sayed Ali, M.

Sørensen, Ole Toft

The kinetics of the initial sintering stage of CeO2 is evaluated by three different technique:: constant heating rate dilatometry, constant shrinkage rate dilatometry and a new technique recently introduced by the authors called Stepwise Isothermal Dilatometry (SID). Comparative measurements with these techniques showed that too high activation energies were obtained with the two first techniques, both of which can be termed as nonisothermal, whereas activation enegies comparable to those reported for cation diffusion in other fluorite oxides were obtained with the latter technique. Of the three techniques SID is thus considered to be the most accurate for studies of the sintering kinetics. In contrast to the two nonisothermal techniques SID has the further advantage that both the controlling mechanism and its activation energy can be determined in a single experiment. Prom the SID-measurement it was concluded that the initial sintering stage of CeO2 is controlled by grain-boundary diffusion

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Downloaded from orbit.dtu.dk on: Dec 19, 2017Evaluation of dilatometric techniques for studies of sintering kineticsEl Sayed Ali, M.; Sørensen, Ole ToftPublication date:1985Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):El Sayed Ali, M., & Sørensen, O. T. (1985). Evaluation of dilatometric techniques for studies of sintering kinetics.(Denmark. Forskningscenter Risoe. Risoe-R; No. 521).D f c ^ o o o 0 ^ g TD)TJ(^/m.. i ii^ii&m Risø-R-521 s Evaluation of Dilatometric Techniques for Studies of Sintering Kinetics M. El-Sayed Ali and O. Toft Sørensen Risø National Laboratory, DK-4000 Roskilde, Denmark April 1985 RISO-R-521 EVALUATION OF DILATOMETRIC TECHNIQUES FOR STUDIES OF SINTERING KINETICS M. El-Sayed Ali* and O. Toft Sørensen Abstract. The kinetics of the initial sintering stage of Ce02 is evaluated by three different technique:: constant heating rate dilatometry, constant shrinkage rate dilatometry and a new technique recently introduced by the authors called Stepwise Isothermal Dilatometry (SID). Comparative measurements with these techniques showed that too high activation energies were obtained with the two first tech-niques, both of which can be termed as nonisothermal, whereas activation enegies comparable to those reported for cation diffusion in other fluorite oxides were obtained with the latter technique. Of the three techniques SID is thus con-sidered to be the most accurate for studies of the sintering kinetics. In contrast to the two nonisothermal techniques SID has the further advantage that both the controlling mechanism and its activation energy can be determined in a single exper— (continued on next page) April 1985 Risø National Laboratory/ DK-4000 Roskilde, Denmark iment. Prom the SID-measurement it was concluded that the initial sintering stage of Ce02 is controlled by grain-boundary diffusion. INIS descriptors; ACTIVATION ENERGY; CERIUM OXIDES; COMPARATIVE EVALUATIONS; DIFFUSION; DILATOMETRY; ISOTHERMAL PROCESSES; KINETICS; MEASURING METHODS; SHRINKAGE; SINTERING xPresent address: Metallurgy Department, Nuclear Research Cen-tre, Atomic Energy of Egypt, Cairo, Egypt. ISBN 87-550-1102-0 ISSN 0106-2840 Grafisk Service Center , Risø 1985 CONTENTS Page 1. INTRODUCTION 5 2. THEORY 6 3. EXPERIMENTAL 9 4. RESULTS AND DISCUSSION 9 4.1. Stepwise isothermal dilatometry (SID) 9 4.2. Constant heating rate measurements 10 4.3. Constant shrinkage rate measurements 10 5. CONCLUSIONS 11 REFERENCES 12 FIGURES 13 - 5 -1. INTRODUCTION Shrinkage curves determined by ^othermal di latometric measure-ments have p r e v i o u s l y been used by Johnson (1) t o study the k inet i c s of the i n i t i a l s inter ing stage for many materials . For t h e s e measurements i t i s important that the samples be in thermal equilibrium right from the beginning of the s inter ing. As t h i s cannot be obtained in p r a c t i c e Johnson introduced a time and length correct ion technique and, furthermore, recom-mended the use of the d i f f erent ia l form of the s intering equa-t i o n which i s i n s e n s i t i v e to errors in t ime . However, k i n e t i c a n a l y s i s by t h i s method i s rather t ime consuming s i n c e i t requires several measurements, each at a dif ferent temperature. As a simple and quick method for s tudies of s intering k ine t i c s Young and Culler (2) introduced the nonisothermal technique by which the sample i s heated a t a constant ra te (see F i g . l - a ) . The shrinkage curve by t h i s technique i s eva luated under the assumption that a s ing le mechanism i s operating. An e f f e c t i v e act ivat ion energy i s calculated and t h i s i s used to d i s t inguish among the various poss ib le mechanisms. Paral le l mechanisms of s i m i l a r a c t i v a t i o n e n e r g i e s thus cannot be separated by t h i s technique. By repeating the measurements using several heating r a t e s Woolfrey and Bannister (3) however, showed t h a t i t i s a l s o p o s s i b l e t o i d e n t i f y the mechanism and c a l c u l a t e i t s act ivat ion energy by th i s technique. Recent ly , another nonisothermal technique was introduced by Criado (4) . By t h i s t echn ique , which a l s o has been used by Huckabee at al (5) in s inter ing s tudies on oxides powders, the sample i s heated in such a way that the shrinkage rate i s kept constant; t h i s charac ter i s t i ca l l y produces an o s c i l l a t i n g tem-peraturet ime curve as shown in Fig . 1-b. In order to i d e n t i f y the contro l l ing mechanism and to determine i t s act ivat ion ener-gy, t h i s method a l s o requires s evera l measurements wi th d i f -ferent shrinkage rates . - 6 -Finally, a new isothermal technique called "Stepwise Isothermal Dilatometry" (SID) has recently been introduced by the authors (6,7,8). In contrast to the above-mentioned technique, SID has the advantage that both the controlling mechanism and its activation energy can be determined in a single experiment. As shown in Fig. 1-c by this technique the overall heating of the sample is controlled by the shrinkage rate, i.e. by the dl/dt-signal as measured by an electronic derivator. When this sign?I becomes larger than a preset limit, the heating is automati-cally stopped and the sintering now proceeds isothermally until the dl/dt-signal again becomes smaller than the preset limit at which point the heating is resumed. By this technique the sintering thus takes place in isothermal steps from which accurate kinetic data can be evaluated. In the present work dilatometric measurements are described that use the constant heating rate, constant shrinkage rate and the stepwise isothermal techniques. These measurements were performed on the same material, cerium oxide, with the purpose of evaluating the variations among the three techniques. Only initial sintering stage kinetics is considered in this work. 2. THEORY The equations describing the three techniques can be derived from the general shrinkage equation: y = Al / l 0 = (![</!) nexp(-nQ/RTVtn (1) where M = shrinkage 1Q = i n i t i a l sample length K0 = prexponential factor of Arrhenius equation - 7 -Q = activation energy T = absolute temperature R = gas constant t = time n = constant depending on the sintering mechanism. The following equations were used to evaluate kinetic data for the three techniques: 1. Constant heating rate (3) y = (KoTVn0Q)nexp(-nQ/RT) (2) where P is the heating rate (°C/min). On taking the logarithm on both sides of Eq. 2 we have lny * -nln« + nln (K0RT/nQ)-(nQ/R) (1/T) (3) where the two last terms on the right-hand side are constant at constant temperature. Plotting lny versus lnp for constant temperature values should thus produce a straight line front which the n-value can be determined from the slope. When n is known Eq. 3 can also be used to calculate the activation energy Q. 2. Constant shrinkage rate y(l/n-l)y = (nK0/T)exp(-Q/RT)(1 + (Q/RT2)tdT/dt) (4) where y is the shrinkage rate. This equation is obtained on differenting Eq. 1. - 8 -If the second term is neglected, Eq. 4 can be reduced to the form used by Criado (4), which is y (1/n -1)-C = (K0/T)exp(-Q/RT) (5) where C i s the constant shrinkage rate used in these measure-ments. Equation 5 i s thus va l id only i f the measurements are carried out isothermally, i .e dT/dt = 0, which, however, is not the case with this technique as discussed above. 3. Stepwise Isothermal dilatometry. For SID the fol lowing equation has been derived previously (6 ,7 .8) : y = (nK0/T)exp(-Q/RT)y(1-1/n> (6) Eqution 5 can be expressed also as lny = ln(K(T)/N) - (N -1)lny (7) where N = 1/n and K(T) = (KQ/T)exp(-Q/RT) is the Arrhenius con-stant. Plotting lny versus lny, both of which can be determined for any point on the recorded dilatometric curve (Al vs. t), a straight line should thus be obtained for each isothermal step from which both N and thus n as well as the activation energy Q, can be determined. - 9 -3. EXPERIMENTAL The measurements were performed in a horizontal dilatometer (Netzch type 402E) in oxygen in an AI2O3 sample holder. The electronic regulator used for the SID measurements has been described previously (1,2). For the measurements at constant shrinkage rate the Standard Netzsch programme regulator (401) was modified so that the sample was heated or cooled when the shrinkage rate was smaller or larger, respectively, than a preset value. Cylindrical compacts were prepared by pressing CeO? (99,9% purity ) powder at 3t/cm2. This powder had already been milled for 50 h, which is assumed to produce nearly spherical par-ticles of uniform size which make the use of Eq. 1 reasonable. The BET surface area of the milled powder was 4.59 m2/g and the green density of the pressed compacts was 61% TD. 4. RESULTS AND DISCUSSION 4.1 Stepwise Isothermal Dilatometry (SID) The shrinkage curves recorded for each isothermal step were fitted polynomially and the shrinkage rate ,y, was calculated from the expression obtained. Plotting log y versus log y produced a set of nearly parallel straight lines (see Ref. 8) as predicted from Eq. 7. The average n value obtained from the slopes of these lines was 0.33 indicating that the controlling mechanism of the initial sintering stage is grain-boundary diffusion (9). The activation energy for this mechanism was found to be 119.4 kcal/mole (5.2eV). This activation energy corresponds well with the values reported by Natzke (10) for cation diffusion in other fluorite oxides (5.6eV for UO2 for instance). - 10 -4.2 Constant heating rate measurements Three measurements were performed using the heating rates: 0.6, 2.4 and 13.4°C/min. Figure 2 shows the In y vs lnp plots £.t four temperatures which according to Eq. 3 should give a straight line. Some scatter is observed indicating that this equation is not completely fulfilled. Furthermore, drawing the best line through the data points, two set of lines with dif-ferent slopes are apparently obtained at low and high tempera-tures respectively. The n-values calculated fron these lines are 0.36 and 0.31 corresponding to activation energies of 166.7 and 131.2 kcal/mole, respectively. Only the latter n-value agrees reasonably well with the results obtained with the SID technique, whereas the activation energy corresponding to the n-values is too large. It has been suggested that the observed change in slope could be due to surrace diffusion effects (2). In a previous study by one of the authors it was observed that surface diffusion can affect only the very beginning of the initial sintering stage,which is also supported by the studies of Bannister et. al. (11) who concluded that surface diffusion is negligible. The variation in slope together with the scatter observed between data points may thus suggest a lack of equli-briura during the continuous heating of the sample. 4.3. Constant shrinkage rate measurements The variation of temperature, sample length and the dl/dt-signal during a constant shrinkage ra .e measurement is shown schematically in Fig. 3a. In order to keep the shrinkage rate constant the temperature typically oscillates around a mean value, which however, increases with time. Depending on the heating/cooling rate used, this temperature oscillation will inversely affect the shrinkage rate such that this rate gener-ally becomes smaller when the temperature decreases than during a temperature rise. As illustrated in Fig. 3b, which shows sample length and temperature measured experimentally, this effect is very large at high heating rates, but even at l°C/min a true constant shrinkage rate could not be obtained - the rate - 11 -during the heating period was nearly twice that obtained during the cooling period. The assumption for the simplified equation proposed by Criado (4) that dT/dt = 0 is thus generally not valid for these measurements. Assuming that the sample can attain thermal equilibrium with the surroundings instantaneously dT/dt can be zero only at the maximum and minimum points of the oscillating temperature curve. Using the Al values measured at these points and plot-ting these against 1/T the plot shown in Fig. 4 was obtained. Sxcept for the point at the lowest temperature this plot ap-peared to be linear as predicted from Eq. 5, and using the value of n determined by SID (0.33) the activation energy calculated from this line was 151.5 kcal/mole. Compared to the SID technique, constant shrinkage rate measurements thus seem to give too high activation energies, and apparently neither equilibrium nor the condition that dT/dt = 0 is strictly ob-tained by this technique. 5. CONCLUSIONS From the comparative measurements carried out on the same material, Ce02» using Stepwise Isothermal Dilatometry (SID), constant heating rate dilatometry and constant shrinkage rate dilatometry it was shown that deviations from equilibrium in the two latter techniques may considerably affect the results obtained by the kinetic analysis. Only in the case of SID could activation energies comparable to those reported for cation diffusion for similar oxide systems be obtained and this tech-nique thus seems to give the most accurate results. In contrast to the non-isothermal techniques, SID futhermore has the advan-tage that it can give informatin both about the controlling mechanism as well as its activation energy in a single exper-iment. - 12 -REFERENCES JOHNSON, D.L. (1969) J. Appl. Phys. , 4_0_, 192-200. YOUNG, W.S. and CUTLER, I.B., (1970) J. Am. Ceram. Soc, 5.1, 659-663. WOOLFREY, J.L. and BANNISTER, M.J., (1972), iMd, 5.5, 390-394. CRIADO, J.M., (1981) Thermochim. Acta, M , 235-237. HUCKABEE, M.L., HARE, T.M. and PALMOUR III, H., (1978) In: Processing of Crystalline Ceramics. Proceedings of the 14. University Conference on Ceramic Science, Raleigh, N.C., 1977. Ed. by H. Palmour III, R.F. Davis and T.K. Hare (Materials Science Research Ser. vol. 11) (Plenum Press, New York) 205-215. EL SAYED ALI, M., SØRENSEN, O.T. and Hfllldahl, L., (1982) J. Therm. Anal., 25.. 175-180. EL SAYED ALI, M., SØRENSEN, O.T. and Hdlldahl, L., (1982). In: Thermal Analysis. Proceedings of the Seventh Interna-tional Conference on Thermal Analysis, Kingston, August 22-28, 1982. Ed. by B. Miller (Wiley, New York) 344-349. EL SAYED ALI, M. and SØRENSEN, O.T., 1985, Risø R 518. 12 pp. COBLE, R.L., (1958) J. A«n. Ceram. Soc, 41, 55-62. MATZKE, HJ., (1980) In: Nons t ioch iometr i c Oxides. Ed. by O. Toft Sørensen (Academic Press, New York) 155-232. BAINNISTER, M.Z. and BUYKX, W.T., (1977) J. Nucl. Mater., 64x 57-65 - 13 -* (a) Constant Heating Rote Dilatometry • •T ime 4 (b) Constant Shrinkage Rate Dilatometry ••Time h (c) Stepwise Isothermal Dilatometry (SID) Isothermal segment -••Time Fig. 1. Characteristic shrinkage and temperature curves for the three techniques considered. - 14 -- 2 - 1 0 1 2 3 In (3 (heating rate) Fig.2. Shrinkage versus heating ra te curves for s inter ing at various temperatures obtained by constant heating rate measure-ments. - 15 -dl/dt-signal Fig. 3. Variation of temperature, shrinkage and shrinkage rate during constant shrinkage rate measurements. —i 1 1 r- " -i 1 1— 0=151.5kcl/mol -3.0 -CO --5.0 6.5 6.6 6.7 6.8 6.9 7.0 71 7.2 Jf K'1 Fig. 4. Shrinkage versus 1/T plot for constant shrinkage rate measurements. Sales distributors: G.E.C. Gad Strøget Vimmelskaftet 32 DK-1161 Copenhagen K, Denmark Available on exchange from: Risø Library, Risø National Laboratory, ISBN 87-550-1102-0 RO.Box 49, DK-4000 Roskilde, Denmark ISSN 0106-2840 

Evaluation of dilatometric techniques for studies of sintering kinetics

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Evaluation of dilatometric techniques for studies of sintering kinetics

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