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On the use of chemical re-equilibration to determine true diffusivity in CoO
J. Phys. Chem. Solids Vol. 54. No. 1. pp. 31-33. 1993 Printed in Great Britain.
0022-3697193 $6.00 + 0.00 0 1992 Pergamon Press Ltd
ON THE USE OF CHEMICAL RE-EQUILIBRATION DETERMINE TRUE DIFFUSIVITY IN Co0 FRANCOIS MORIN~
TO
and R~~DIGER DIECKMANN~
THydro-Quebec Research Institute (IREQ), Varennes, Quebec, Canada J3X IS1 iDepartment of Materials Science and Engineering, Cornell University, Ithaca, NY 14843-1501, U.S.A. (Received 4 May 1992; accepted in revised form 24 July 1992)
Abstract-This paper discusses problems in the use of chemical re-equilibration to precisely determine the true chemical diffusivity in cobaltous oxide, COO. It is concluded that it is not at all trivial to obtain meaningful chemical diffusion data. Results published recently on this subject in this Journal are critically analysed and compared with other literature data. It is concluded that the recently published data do not represent true chemical diffusion data and that further studies of the kinetics of exchange processes at gas/solid interfaces are needed to better understand chemical re-equilibration processes. Keywords: Chemical diffusion, surface reactivity, relaxation, point defects.
INTRODUCTION Binary transition number
metal oxides have attracted
of studies
in the past,
aimed
a slow surface reaction or to measure true diffusivity, will be analysed here. There are the following: (i) the initial conditions within the oxide samples before re-equilibration runs, which rule the mathematical relationship to be used for diffusivity; (ii) the actual reduction of kinetics data; (iii) the scatter of diffusivity measurements and (iv) the comparison with the previous literature.
a large
at a better
understanding of point defect behavior in these compounds and, to a lesser degree, due to their ease of modelhng. Cobaltous oxide is one of these frequently studied compounds. Three additional papers on Co0 have appeared very recently in this Journal [l-3]. In the first of these, Taduy et al. report on chemical diffusion. They make use of the chemical re-equilibration method; the kinetics follow-up is performed electrochemically with some analogies with a previous paper by Holscher and Schmalzried [4]. Although Taduy et al.‘s paper is contributive in regard to the determination of the thermodynamic enhancement factor as a function of the oxygen partial pressure, po2, their analysis of both their own diffusion data and those from the literature on diffusivity in cobaltous oxide suffers several weaknesses which tend to confuse recent issues on COO.
Initial conditions Galvanostatically charging a sample with oxygen implies the build-up of a concentration gradient throughout the sample. In turn, the actual shape of the corresponding concentration curve will be affected by the amplitude and the duration of the applied current. This obviously affects the initial relationship to be used for the reequilibration process, a point which is ignored in [l].
Reduction of kinetics data
THE DETERMINATION OF TRUE CHEMICAL DIFFUSIVITY IN Co0
In re-equilibration experiments with oxidizingreducing mixtures, slow surface reactions are well known to occur [S-11]. In the case of pure oxygen, however, the observation of a slow gas exchange with the oxide has been seldom observed. The claims in [ 1] that this phenomenon is overwhelmingly present in diffusivity measurements and that it is avoided by means of the thereby contained experimental method are largely exaggerated. Several inconsistencies in [ 11, tied up with the basic steps required to either evidence 31
Taduy et al. [l] also resort to a mathematical approximation for reducing their kinetics data. This approach was critically analysed in an earlier paper [12]. To avoid any misinterpretation of diffusivity data, a more accurate method, extending over the whole of the re-equilibration kinetics, must be used. Such a method was suggested in [12]. The approximation for longer times used in [l] is mainly a convenient curve fitting procedure. Its major disadvantage is that, by using only the tail portion of the re-equilibration kinetics, the most sensitive portion of the experiment regarding slow surface kinetics remains concealed although the calculated diffusivities might still be affected. In this case, only apparent
FRANCOIS MORINand R~~DIGER DIECKMANN
32
Comparison with the previous literature
OL -3.0
-2.0
-1.0 0.0 log tpo2 (atmll Fig. 1. Chemical diffusivity results of Taduy et al. (solid triangles) at 1108°C with the correspondingly reported uncertainty band [l]. Results from 1151(inverted triangles) are reported both for 1000°C and extrapolated to 1008°C (see text).
chemical diffusion coefficients are obtained which are smaller than the true values. Unfortunately, no data are reported for the initial IO min of the re-equilibration runs which would allow a new, more appropriate data analysis. Scatter of d@iisivity data Taduy et al.‘s results have been combined in Fig. 1 together with their suggested uncertainty band. One readily observes an unusually large scatter of the data obtained. Such a precision falls short of the aims of either showing the invariance of the chemical diffusion with the oxygen partial pressure or the lack of polarization at the electrode interface.
To validate their own results with diffusivity data from other re-equilibration studies, Taduy et al. have been incorrectly using data from [13] to [15], making an arbitrary use of [13] and [14] while ignoring the most recent data published in this Journal [15]. A more appropriate comparison is made in Fig. 1. There is no indication whatsoever in [1] regarding the procedure used to extrapolate previous results from 1000°C to 1108°C although a satisfactory agreement was found. An activation energy of 136 kJ is used here for the chemical diffusion coefficient, such a value being found in Dieckmann’s regression [16]. Although due care should be given to any extrapolation procedure, this one should be as good as any. Following the discussion in [I 51, only the results from that study and not those from [I 31 and 1141represent true diffusivity. They are, therefore, used for extrapolation purposes. Referring to Fig. 1, it is not all that surprising that the results from [l] are found to fall very significantly below the extrapolated data from [15]. This suggests that the results from Taduy et al. are very likely hampered by some slow interfacial reaction. In Fig. 8 from [15], symbols for the large and thin crystals, respectively, were inadvertently interchanged although the results were correctly reported in the corresponding Table 1. This situation is corrected in Fig. 2. Additional consideration is brought to the data scatter in [15]. Data from a large crystal are fully plotted while, for the sake of clarity, only the extrema are plotted for a thin crystal. Because surface reactivity is a complex function of the oxygen partial
12 r
.:
0 12 c
2o lUo-Otl
’ .O
@
(&cm)-’
I (po2kPt02)~
I
3o
mm)
Fig. 2. Apparent chemical diffusion coefficient of cobaltous oxide at 1000°C from [I 51 either (a) vs the absolute total conductivity change or (b) vs the absolute oxygen partial pressure change. Squares are used for the main results from a large crystal while diamonds are used for a thin crystal. Filled symbols stand for reduction runs and empty symbols for oxidation runs.
Re-equilibration
determination
pressure, two equally significant x-axes have been used to represent these parameters. All data affected by slow surface kinetics appear at the left-end of these axes. The true diffusivity and its constancy for the large sample is confirmed in several ways: one is the constancy of the so-called apparent chemical diffusion coefficient dapp, calculated from the re-equilibration kinetics, for a relatively large portion of the axes used here; this is also confirmed by the entire follow-up of the re-equilibration kinetics up from a fraction of a second; finally, a convincing observation is the disappearance of the slow surface kinetics for the thin crystal and its very close agreement with the large sample for the largest oxygen partial pressure change. The scatter of our data for the true chemical diffusivity in Co0 is also shown in Fig. 2. The scatter of diffusivity data in [15] is thereon established. It is self-explanatory with regard to the results reported in [l] and thus requires no further discussion. FINAL REMARKS
As shown above, precisely measuring true chemical diffusivities by means of re-equilibration experiments is in no case a trivial operation. A complementary field of interest for the re-equilibration method is the determination of the kinetics of exchange processes taking place at the gas/solid interface. As mentioned by Grabke [17], there are not that many studies of this
of Co0 diffusivity
33
kind of interaction. This not only applies for buffering gas mixtures, but is even more true for simple interactions with pure oxygen.
REFERENCES
1. Taduy T., Millot F. and Sol& 53, 323 (1992). 2. Constant K. P., Mason Routbort J. L., J. Phys. 3. Constant K. P., Mason
Dhalenne G., J. Phys. Chem.
T. O., Rothman S. J. and Chem. Solids 53, 405 (1992). T. 0. and Routbort J. L., J. Phys. Chem. Soliak 53, 413 (1992). 4. Ho&her U. and Schmalzried H., Z. Phys. Chem. NF 139, 69 (1984). 5. Stotz S., Ber. Bunsenges. Phys. Chem. 70, 37 (1966). 6. Landler P. F. J. and Komarek K. L., Trans. AIh4E 236, 138 (1966). 7. Bransky I., Tallan N. M., Wimmer J. M. and Gvisbi M., J. Am. Ceram. Sot. 54, 26 (1971). 8. Laub L. W. and Wagner J. B., Oxid. Met. 7, 1 (1973). 9. Franke P. and Dieckmann R., Ber. Bunsenges. Phys. Chem. 91, 49 (1987). 10. Morin F. and Dufour L. C., Solid St. Zonics 32-33, 893 (1989). 11. Carter R. E. and Lay K. W., J. Nucl. Mat. 36,77 (1992). 12. Morin F., J. Compur. Chem. 6, 514 (1985).
13. Morin F., Can. Mer. Quart. 14, 105 (1975). 14. Morin F. and Dieckmann R., Z. Phys. Chem. NF 129, 219 (1982).
15. Morin F. and Dieckmann R., J. Phys. Chem. So/ids 51, 283 (1990).
16. Dieckmann R., Z. Phys. Chem. N.F. 107, 189 (1977). 17. Grabke H. J., Surfaces and Interfaces of Ceramic Materials (Edited by L. C. Dufour, C. Monty and G. Petot-Ervas), NATO ASI Series, Vol. 173, p. 599. Kluwer, Dordrecht (1989).
0022-3697193 $6.00 + 0.00 0 1992 Pergamon Press Ltd
ON THE USE OF CHEMICAL RE-EQUILIBRATION DETERMINE TRUE DIFFUSIVITY IN Co0 FRANCOIS MORIN~
TO
and R~~DIGER DIECKMANN~
THydro-Quebec Research Institute (IREQ), Varennes, Quebec, Canada J3X IS1 iDepartment of Materials Science and Engineering, Cornell University, Ithaca, NY 14843-1501, U.S.A. (Received 4 May 1992; accepted in revised form 24 July 1992)
Abstract-This paper discusses problems in the use of chemical re-equilibration to precisely determine the true chemical diffusivity in cobaltous oxide, COO. It is concluded that it is not at all trivial to obtain meaningful chemical diffusion data. Results published recently on this subject in this Journal are critically analysed and compared with other literature data. It is concluded that the recently published data do not represent true chemical diffusion data and that further studies of the kinetics of exchange processes at gas/solid interfaces are needed to better understand chemical re-equilibration processes. Keywords: Chemical diffusion, surface reactivity, relaxation, point defects.
INTRODUCTION Binary transition number
metal oxides have attracted
of studies
in the past,
aimed
a slow surface reaction or to measure true diffusivity, will be analysed here. There are the following: (i) the initial conditions within the oxide samples before re-equilibration runs, which rule the mathematical relationship to be used for diffusivity; (ii) the actual reduction of kinetics data; (iii) the scatter of diffusivity measurements and (iv) the comparison with the previous literature.
a large
at a better
understanding of point defect behavior in these compounds and, to a lesser degree, due to their ease of modelhng. Cobaltous oxide is one of these frequently studied compounds. Three additional papers on Co0 have appeared very recently in this Journal [l-3]. In the first of these, Taduy et al. report on chemical diffusion. They make use of the chemical re-equilibration method; the kinetics follow-up is performed electrochemically with some analogies with a previous paper by Holscher and Schmalzried [4]. Although Taduy et al.‘s paper is contributive in regard to the determination of the thermodynamic enhancement factor as a function of the oxygen partial pressure, po2, their analysis of both their own diffusion data and those from the literature on diffusivity in cobaltous oxide suffers several weaknesses which tend to confuse recent issues on COO.
Initial conditions Galvanostatically charging a sample with oxygen implies the build-up of a concentration gradient throughout the sample. In turn, the actual shape of the corresponding concentration curve will be affected by the amplitude and the duration of the applied current. This obviously affects the initial relationship to be used for the reequilibration process, a point which is ignored in [l].
Reduction of kinetics data
THE DETERMINATION OF TRUE CHEMICAL DIFFUSIVITY IN Co0
In re-equilibration experiments with oxidizingreducing mixtures, slow surface reactions are well known to occur [S-11]. In the case of pure oxygen, however, the observation of a slow gas exchange with the oxide has been seldom observed. The claims in [ 1] that this phenomenon is overwhelmingly present in diffusivity measurements and that it is avoided by means of the thereby contained experimental method are largely exaggerated. Several inconsistencies in [ 11, tied up with the basic steps required to either evidence 31
Taduy et al. [l] also resort to a mathematical approximation for reducing their kinetics data. This approach was critically analysed in an earlier paper [12]. To avoid any misinterpretation of diffusivity data, a more accurate method, extending over the whole of the re-equilibration kinetics, must be used. Such a method was suggested in [12]. The approximation for longer times used in [l] is mainly a convenient curve fitting procedure. Its major disadvantage is that, by using only the tail portion of the re-equilibration kinetics, the most sensitive portion of the experiment regarding slow surface kinetics remains concealed although the calculated diffusivities might still be affected. In this case, only apparent
FRANCOIS MORINand R~~DIGER DIECKMANN
32
Comparison with the previous literature
OL -3.0
-2.0
-1.0 0.0 log tpo2 (atmll Fig. 1. Chemical diffusivity results of Taduy et al. (solid triangles) at 1108°C with the correspondingly reported uncertainty band [l]. Results from 1151(inverted triangles) are reported both for 1000°C and extrapolated to 1008°C (see text).
chemical diffusion coefficients are obtained which are smaller than the true values. Unfortunately, no data are reported for the initial IO min of the re-equilibration runs which would allow a new, more appropriate data analysis. Scatter of d@iisivity data Taduy et al.‘s results have been combined in Fig. 1 together with their suggested uncertainty band. One readily observes an unusually large scatter of the data obtained. Such a precision falls short of the aims of either showing the invariance of the chemical diffusion with the oxygen partial pressure or the lack of polarization at the electrode interface.
To validate their own results with diffusivity data from other re-equilibration studies, Taduy et al. have been incorrectly using data from [13] to [15], making an arbitrary use of [13] and [14] while ignoring the most recent data published in this Journal [15]. A more appropriate comparison is made in Fig. 1. There is no indication whatsoever in [1] regarding the procedure used to extrapolate previous results from 1000°C to 1108°C although a satisfactory agreement was found. An activation energy of 136 kJ is used here for the chemical diffusion coefficient, such a value being found in Dieckmann’s regression [16]. Although due care should be given to any extrapolation procedure, this one should be as good as any. Following the discussion in [I 51, only the results from that study and not those from [I 31 and 1141represent true diffusivity. They are, therefore, used for extrapolation purposes. Referring to Fig. 1, it is not all that surprising that the results from [l] are found to fall very significantly below the extrapolated data from [15]. This suggests that the results from Taduy et al. are very likely hampered by some slow interfacial reaction. In Fig. 8 from [15], symbols for the large and thin crystals, respectively, were inadvertently interchanged although the results were correctly reported in the corresponding Table 1. This situation is corrected in Fig. 2. Additional consideration is brought to the data scatter in [15]. Data from a large crystal are fully plotted while, for the sake of clarity, only the extrema are plotted for a thin crystal. Because surface reactivity is a complex function of the oxygen partial
12 r
.:
0 12 c
2o lUo-Otl
’ .O
@
(&cm)-’
I (po2kPt02)~
I
3o
mm)
Fig. 2. Apparent chemical diffusion coefficient of cobaltous oxide at 1000°C from [I 51 either (a) vs the absolute total conductivity change or (b) vs the absolute oxygen partial pressure change. Squares are used for the main results from a large crystal while diamonds are used for a thin crystal. Filled symbols stand for reduction runs and empty symbols for oxidation runs.
Re-equilibration
determination
pressure, two equally significant x-axes have been used to represent these parameters. All data affected by slow surface kinetics appear at the left-end of these axes. The true diffusivity and its constancy for the large sample is confirmed in several ways: one is the constancy of the so-called apparent chemical diffusion coefficient dapp, calculated from the re-equilibration kinetics, for a relatively large portion of the axes used here; this is also confirmed by the entire follow-up of the re-equilibration kinetics up from a fraction of a second; finally, a convincing observation is the disappearance of the slow surface kinetics for the thin crystal and its very close agreement with the large sample for the largest oxygen partial pressure change. The scatter of our data for the true chemical diffusivity in Co0 is also shown in Fig. 2. The scatter of diffusivity data in [15] is thereon established. It is self-explanatory with regard to the results reported in [l] and thus requires no further discussion. FINAL REMARKS
As shown above, precisely measuring true chemical diffusivities by means of re-equilibration experiments is in no case a trivial operation. A complementary field of interest for the re-equilibration method is the determination of the kinetics of exchange processes taking place at the gas/solid interface. As mentioned by Grabke [17], there are not that many studies of this
of Co0 diffusivity
33
kind of interaction. This not only applies for buffering gas mixtures, but is even more true for simple interactions with pure oxygen.
REFERENCES
1. Taduy T., Millot F. and Sol& 53, 323 (1992). 2. Constant K. P., Mason Routbort J. L., J. Phys. 3. Constant K. P., Mason
Dhalenne G., J. Phys. Chem.
T. O., Rothman S. J. and Chem. Solids 53, 405 (1992). T. 0. and Routbort J. L., J. Phys. Chem. Soliak 53, 413 (1992). 4. Ho&her U. and Schmalzried H., Z. Phys. Chem. NF 139, 69 (1984). 5. Stotz S., Ber. Bunsenges. Phys. Chem. 70, 37 (1966). 6. Landler P. F. J. and Komarek K. L., Trans. AIh4E 236, 138 (1966). 7. Bransky I., Tallan N. M., Wimmer J. M. and Gvisbi M., J. Am. Ceram. Sot. 54, 26 (1971). 8. Laub L. W. and Wagner J. B., Oxid. Met. 7, 1 (1973). 9. Franke P. and Dieckmann R., Ber. Bunsenges. Phys. Chem. 91, 49 (1987). 10. Morin F. and Dufour L. C., Solid St. Zonics 32-33, 893 (1989). 11. Carter R. E. and Lay K. W., J. Nucl. Mat. 36,77 (1992). 12. Morin F., J. Compur. Chem. 6, 514 (1985).
13. Morin F., Can. Mer. Quart. 14, 105 (1975). 14. Morin F. and Dieckmann R., Z. Phys. Chem. NF 129, 219 (1982).
15. Morin F. and Dieckmann R., J. Phys. Chem. So/ids 51, 283 (1990).
16. Dieckmann R., Z. Phys. Chem. N.F. 107, 189 (1977). 17. Grabke H. J., Surfaces and Interfaces of Ceramic Materials (Edited by L. C. Dufour, C. Monty and G. Petot-Ervas), NATO ASI Series, Vol. 173, p. 599. Kluwer, Dordrecht (1989).