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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
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
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
1. INTRODUCTION
Shrinkage curves determined by ^othermal d i l a t o m e t r i c measure-ments have p r e v i o u s l y been used by Johnson (1) t o s t u d y t h e k i n e t i c s of the i n i t i a l s i n t e r i n g s t a g e for many m a t e r i a l s . For t h e s e measurements i t i s important t h a t t h e s a m p l e s be i n thermal equilibrium right from the beginning of the s i n t e r i n g . As t h i s cannot be o b t a i n e d i n p r a c t i c e Johnson i n t r o d u c e d a time and length c o r r e c t i o n technique and, furthermore, recom-mended the use of the d i f f e r e n t i a l form of the s i n t e r i n g equa-t i o n which i s i n s e n s i equa-t i v e equa-t o e r r o r s i n equa-t i m e . However, k i n e equa-t i c a n a l y s i s by t h i s method i s r a t h e r t i m e consuming s i n c e i t
requires several measurements, each a t a d i f f e r e n t temperature. As a simple and quick method for s t u d i e s of s i n t e r i n g k i n e t i c s Young and Culler (2) introduced the nonisothermal technique by which t h e sample i s h e a t e d a t a c o n s t a n t r a t e ( s e e F i g . l - a ) . The s h r i n k a g e c u r v e by t h i s t e c h n i q u e i s e v a l u a t e d under t h e assumption t h a t a s i n g l e mechanism i s operating. An e f f e c t i v e a c t i v a t i o n energy i s c a l c u l a t e d and t h i s i s used t o d i s t i n g u i s h among the various p o s s i b l e mechanisms. P a r a l l e 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 s e p a r a t e d by t h i s technique. By repeating the measurements using several heating r a t e s Woolfrey and B a n n i s t e r (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 t h e mechanism and c a l c u l a t e i t s a c t i v a t i o n energy by t h i s technique.
R e c e n t l y , a n o t h e r n o n i s o t h e r m a l t e c h n i q u e was i n t r o d u c e d by Criado ( 4 ) . By t h i s t e c h n i q u e , which a l s o has been used by Huckabee at a l (5) in s i n t e r i n g s t u d i e s on oxides powders, the sample i s heated in such a way that the shrinkage rate i s kept constant; t h i s c h a r a c t e r i s t i c a l l y produces an o s c i l l a t i n g tem-p e r a t u r e t i m e c u r v e a s shown i n F i g . 1-b. In order t o i d e n t i f y the c o n t r o l l i n g mechanism and t o determine i t s a c t i v a t i o n energ y , t h i s method a l s o r e q u i r e s s e v e r a l measurements w i t h d i f -ferent shrinkage r a t e s .
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 = A l / l0 = (