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Chemical diffusion coefficient of CoO
0022-3697/92 S5.00 + 0.00 0 1992 Pergamon Press plc
J. Phys. Chem. Solids Vol. 53, No. 2, pp. 323-327. 1992 Printed in Great Britain.
CHEMICAL DIFFUSION
COEFFICIENT OF Co0
T. TADUY, F. MILLOT and G. DHALENNE Laboratoire des Compods non Stoechiom&triques,URA 446-Universitk Paris-Sud, BBtiment 415-91405-Orsay-C%dex, France (Received 4 June 1990; accepted in revised form
12 June 1991)
Abstract-The chemical diffusion coefficients B and the thermodynamic factors (8 In P,,/d6) of Co,_,0 have been measured with an electrochemical set-up at 1108°Cbetween lo-) and 1 atm oxygen pressures. Our results confirm previous data of b obtained with thermogravimetry. Comparison with available cobalt self-diffusion coefficients D& supports a simple vacancy migration mechanism for cobalt diffusion. Keywords:
Cobalt oxide, non-stoichiometry,
diffusion.
INTRODUCTION High-temperature CO,_~O is a fair example of a moderately non-stoichiometric compound (at 1 atm oxygen pressure and 1000°C it contains approximately 1 per cent cobalt vacancies). It has been extensively studied during the last 30 years because many of its properties are directly dependent on the concentration of cobalt vacancies. Fourteen years ago, Dieckmann [l] compiled and reviewed some of these reproducible properties: S(P,,, T), deviation from stoichiometry; D&(Po,, T), cobalt self-diffusion coefficient; and u,(PoI, T), electronic conductivity. Other reproducible properties, such as thermoelectric power, were consistently reported by various authors [2, 31. Finally, recent direct determinations of the enthalpy of mixing of oxygen, AH(Oz) in Co0 [4] have appeared to be approximately consistent with previous indirect determinations from various isotherms 6 (PC&
Finally, if one discards data obtained from conductivity measurements, disagreement about whether b is P,,dependent or not still persists. Although many arguments have been put forward to account for the discrepancies, the situation is still very confusing. In this context, we have decided to design an experiment which could, at best, eliminate the possible causes of errors and of uncertainties in the determination of B.
EXPERIMENTAL
As was previously mentioned, it has been observed, in some instances, that the solution of Fick’s second law was not obeyed when it was assumed that the kinetics was governed by the migration of cobalt in the sample. When this happens, it is assumed that another kinetic phenomenon slows down the overall redistribution. Slow exchange of oxygen at the interface between the sample and the gas phase is a common one in oxides and thus elimination of gas transfer through interfaces may improve the determination of d. Only a few data have been reported on oxides [5-81 which respected this condition. They In contradiction to this general agreement, chemiconsisted of observing the redistribution of ionic cal diffusion coefficient, a, data are still controversial, migrating species in a concentration gradient prealthough slightly dispersed (typically by a factor of viously built into the volume of the sample. five at a given temperature). Data at 1000°C reported In these experiments, electrochemical cells were on single crystals are collected in Table 1 in such a used to follow the small changes of oxygen chemical way that the sources of disagreement become apparpotential of some part of the sample. This technique ent: some authors reported PO,dependent as (the d of measurement offers the advantage, for instance, in value was approximately doubled between PO2= 10m3 comparison with thermogravimetry, of a high sensiatm and _Pp2 = 1 atm), whereas others observed tivity. Incidentally, the relative variations of concenconstant D m the same pressure range. All these tration during redistribution can almost be identified data were obtained with the assumption that the with the corresponding variations of the chemical kinetics were governed by the isothermal diffusion of potential without introducing causes of uncertainty cobalt in the samples. However, it can be seen from on b (see the equations at the end of this section). Table 1 that disagreement also exists on whether this These advantages make electrochemistry a powerassumption is or is not justified when conductivity ful tool for the investigation of B in comparison with measurements are performed. indirect measurements, for instance from conduc323
T.
324
et al.
TADUY
Table 1. Chemical diffusion coefficient of Co0 single crystal at looo”C reported in the literature Is D dependent on PO,?
Method Conductimetry Manometry Thermogravimetry Conductimetry Conductimetry Conductimetry Thermogravimetry Conductimetry Conductimetry Galvanometry Conductimetry
Is Fick’s 2nd law obeyed? Yes
5-9 4-6.5 8.1 4-10 5-14 9.1-9.2
tivity variations, which can under specified conditions introduce some uncertainties in the data [g-11].
The experimental set-up was designed from the preceding considerations. It is schematically shown in Fig. 1. The sample is a Co0 single crystal grown in an argon atmosphere with an arc image furnace from a 10ppm impurity containing Co,O., powder. It is mechanically machined with diamond tools to have a cylindrical shape (e = 1 mm, @ = 6 mm). The sample is enclosed in a box made of the following assorted materials. The upper flat face is in contact with a 2/100” mm thick platinum sheet and the lower flat face with a ZrO?-9% mol. Y,O, solid electrolyte (from INPGENSEEG Saint Martin d’H&es, France). The annular face is in contact with a ring made of “Vycor” (from Corning Glass) which is itself enclosed in a silica glass cylindrical tube. Glass pieces were mechanically machined with diamonds tools and final adjustments were obtained with chemical attack in 40% HF to better than l/l00 mm.
No Yes Yes No No Yes Yes No
Yes No Yes Yes No
Yes
Year
Ref.
1966 1970 1972-1975 1972-1975 1975-1982 1982 1982 1982 1983 1983, 1984 1990
26 27 16, 17 16, 17 28,29 20 18 18 31 14,15 19
The whole set-up is compressed with a spring outside the furnace and when it is held at 1lOO”C, the viscosity of “Vycor” (q = 10-l’ poises) permits it to deform under the compression of the spring until it occupies all the free volumes (pure SiOz glass is not deformed). Moreover, it reacts with the contact surfaces forming Co, SiO, with Co0 and ZrSiO, with the solid electrolyte. After a two month continuous heating at 1108°C we observed a homogeneous and adhesive 150pm thick layer of CO,SiO, formed on the annular face of COO. This layer constitutes an excellent physical barrier between Co0 and its neighbourhood because diffusion of Co, Si and 0 has been shown to be very small in this compound [12]. ZrSiO, plays the same role between ZrOz and “Vycor”. We also observed after two months of heating that small amounts of cobalt had diffused through the platinum sheet to form small blue spots of Co2 SiO., at the surface of “Vycor” in contact with platinum. Other experimental details (not shown in Fig. 1) consist of a laboratory silica glass tube containing the set-up, a furnace, a PID Eurotherm temperature regulator (+ O.l’C), a Pt/Pt, 10% Rh thermocouple (+2”C) in the neighbourhood of the set-up and Wiisthoff pumps which allow flowing predetermined N2-02 gas mixtures on the set-up. During operation at 1108°C and under well-defined PO,, two kinds of experiments were conducted thus. Equilibrium measurements of the variation of the deviation from stoichiometry 6 with PO2by galvanometry. A definite quantity of oxygen N is transferred through the solid electrolyte from gas phase to Co0 (or conversely) by applying a constant d.c. current I to the cell during time t: N = ZT/2F (F = 96,500 coulombs). This transfer induces a change of the non-stoichiometry 6 of the sample: A6 = NVm/V, where Vm is the molar volume of Co0 and V is the volume of the sample. The e.m.f. of cell
Fig. 1. Experimental set-up: (1) alumina; (2) silica glass; (3) “Vycor” glass; (4) Co0 sample; (5) ZrO,/Y,O, solid electrolyte; (6) Pt grid and Pt and (7) Pt sheet a, b, a’, b’ Pt electrical connections.
DT
DC-=‘)
Chemical diffusion coefficient of Co0
is measured before I is applied (E,) and after the current has been cut off and the sample has returned to equilibrium (Ez). We then have AInPr’=
325
We also have that:
4P (E, RT- E,) ,
and finally the quantity q
If small variations of C are considered, the quantities (a In PO,/8 In a), and V,,, are almost invariant with PO, so that.
(PO,,n,
is deduced from small changes of the deviation from stoichiometry with PO*. In practice, the currents (typically 50-100 PA) were applied for between 10-30 mins resulting in (E, - E,) values between 1 and 40 mV (a 10% change of PO, at 1108°C corresponds to E2 - E, = 6.85 mV). The composition of the N&r mixture flowing along the laboratory tube was chosen to minimize the drifts of E signals corresponding to equilibrium. Corrections were done of the actual volume V of sample to take into account the formation of the annular Co,SiO, layer (a parabolic law was presumed). Chemical diffusion coefficient measurements. These experiments were conducted at the same time as equilibrium measurements. As a matter of fact, the transfer of oxygen through the solid electrolyte induces a concentration gradient of cobalt in the sample. Once the current is cut off, no more matter can enter or leave the sample and the cobalt concentration gradient relaxes to return to chemical equilibrium. These changes were observed by measuring the e.m.f. E between a and b of the platinium wire (see Fig. 1) with a high impedance voltmeter (7066 datastore from Schlumberger). In practice, however, we have found that a 10 min delay was necessary after stopping the current to obtain E values obeying the Nernst-Einstein law. (This effect probably results from polarization and thermal effects at the (ZrO,Y,O,)/CoO interface when the current is applied.) The chemical diffusion coefficient b was deduced from the variation of In (Eab(t) - Eab(t = a)) with time t. In effect, the solution of Fick’s second law corresponding to the boundary conditions of our experimental set-up is [13]: ln(C(t) - C(t = CO))= - Iz l-12Dt + constant if -> 12
1.5,
where 1 is the thickness of the sample and C(t) is the concentration of cobalt atoms in unit volume at time t (lIZDt/12 = 1.5 at t N 15 min). The origin of the time, t, is when current is no longer applied and, consequently, no more oxygen is transferred through the CoO/(ZrO,/Y,O~) interface. PCS 53:2-H
ln(E,,(t)
l-FL% - Eab(t = co)) = -12 + constant.
RESULTS AND COMPARISON WITH THE LITERATURE In order to determine the amounts of foreign ions which could have diffused in Co0 after two months of heating, chemical analysis of the sample was performed (by SCA-CNRS Vemaison, France). One hundred parts per million K, 30 ppm B, 90 ppm Zr, 15 ppm Y and 0.4% Si were detected. The high quantity of silicon could be correlated with small Co2Si04 grains at the annular surface of Co0 by optical microscopy. However, in order to determine the actual Si content in the volume of Co0 an independent experiment was carried out: a diffusion couple of Co0 with C02Si0, was prepared as follows: a Co0 single crystal having a cylindrical shape (e = 1 mm, 0 = 6 mm) was optically polished on one of its two flat faces. A dense COrSiO, sinter was obtained with an arc image furnace and machined to have the same shape as the COO. One of its flat faces was optically polished. The two polished faces of Co0 and CO, SiO, were then put in compressive contact and held in Or gas at 1100°C for 15 days. After cooling, the two oxides could be separated. However, we have observed that an approximately 100 microns thick layer of C02Si04 was strongly attached to the surface of COO. This layer was removed by mechanical abrasion and an analysis for silicon was achieved approximately 20 microns inside Co0 with an electronic microprobe. The results showed no difference between this sample and a reference Co0 crystal indicating a Si content lower than 150 ppm (the resolution of the microprobe). The (a In Po,/aS), results obtained at 1108°C between 10m3and 1 atm oxygen pressures are shown on Fig. 2. These data were compared with two other sets of data: Dieckmann’s regression [1] based on a large set of published data; and Hiischler and Schmalzried’s data obtained by galvanometry [14, 151 and extrapolated from 1100°C. The three curves in Fig. 2 show very similar behaviour. Dispersion is 18% at 1 atm O2 (between Dieckmann’s and Hlischler’s data) and 10% at
326
T.
TADIJYet al.
flowing in the chamber leads to a 60 FV variation of AEab (the variation is only 60 nV at 1 atm oxygen pressure). Comparison of our data with previous data merits the following comments. Our observation is that B is independent of or slightly decreasing with PO,. This result is in a qualitative agreement with previous predictions of PO2 independent b results [ 16-191 but disagrees with
the other results (see Table 1). Among PO, dependent fi results in the literature our data are in relatively good agreement with those obtained by thermogravimetry: Wimmer et al. [16, 171 give b (llOS”C)= 1.3 x 10m6cm2 s-r and Chowdhry and Coble [18] propose b (1108°C) = 1.7 x 1O-6 cm2 s-r.
DISCUSSION
0
-2
-4
-6
Ln(Q.tm
Fig. 2. Thermodynamic factor (a In P,,/%I), vs oxygen pressure of Co0 at 1108°C: black points, our data; dotted line, Hdschler and Schmalzried’s data [14, 151; continuous line, Dieckmann’s regression [l].
lo--‘atm O2 (between Dieckmann’s and our results). Our data appear to be about 10% lower than Dieckmann’s regression in the studied range of Po,s. Chemical diffusion coefficients of Co0 obtained at 1108°C between 10m3and 1 atm oxygen pressures are shown in Fig. 3. Dispersion of experimental points clearly increases as PO2 decreases. This tendency is to be put in conjunction with the decrease of the reproducibility of the AEab signal at low PO,. In fact at 10m3atm a 1 ppm O2 variation in the gas mixture to’bkmh
I
The main interest in the precise determination of the chemical diffusion coefficient B in such a material as Co0 is that it may be compared with other diffusion data which are explicitly dependent on the diffusion mechanism, for instance the self-diffusion coefficient D& of cobalt. It has been shown by Sato and Kikuchi [20] and later by Murch [21] that in some simple cases it is possible to know the value of the Haven ratio
from
0
1
0
28
*
29
*
30
ref.
to‘b(cm~
t
‘I
2.5
1
-2.5
.
.
-2
. .
.
.
. . . . *.*.
l
.
.
.
. .
.
.
.
.ls
.
Itm I -3
-2
-t
O
‘~‘%!tm.
Fig. 3. Chemical diffusion coefficient a of Co0 vs PO, at 1108°C.
Fig. 4. Calculated chemical diffusion coefficients from various D& data in the literature and assuming a simple
vacancy migration mechanism. The hatched domain contains 90% of our a data.
Chemical diffusion coefficient of Co0
In particular, if one considers a simple vacancy migration mechanism in a c.f.c. solid containing not too many vacancies one has: HR =fd = 0.7815,
327
5. Ait Younes N., Millot F. and Gerdanian P., Solid Stare Ionics 12, 437 (1984). 6. Millot F., J. Nucl. Mater. 125, 64 (1984). 7. Millot F. and De Mierry P., J. Phys. Chem. Solid 46, 797 (1985). 8. Millot F. and Berthon J., J. Phys. Chem. Solids 47, 1
(1986).
wheref, is the geometrical correlation factor. Such a simple model looks attractive, or at least plausible for describing cobalt migration in COO. As a matter of fact, oxygen moves much more slowly than Co (D&,/D,* N 5 x lo4 at 1200°C) and Co0 is a metal deficient non-stoichiometric oxide. We have compared our data of B with the calculated ones using available DE, from the literature and our (a In Po,/aS), data (HR is assumed to be equal to 0.7815). This comparison appears on Fig. 4. Dieckmann’s data [1] come from the original 1108°C DE, isotherm. Other data [22-241 were obtained by interpolating between data at other temperatures. The results of Crow [25] have been excluded for clarity since they are significantly higher than all the other results at 1100°C. Examination of Fig. 4 shows that within the dispersion of data, close agreement is obtained between these calculated chemical diffusion coefficients and our data. This comparison is then a support for a simple vacancy migration mechanism of cobalt in cobaltous oxide.
REFERENCES 1. Dieckmann (1977). 2.
R.,
Z.
Whys. Chem.
N.F.
107, 189
Fisher B. and Tannhauser D. S., J. Chem. Phys. 44,
1663 (1966). 3. Chen H. C. and Mason T. O., J. Am. Ceram. Sot. 64, Cl30 (1981). 4. Picard C. and Gerdanian P., J. Phys. Chem. Solids 50, 383 (1989).
9. Morin F., React. Solids 7, 307 (1989). 10. Morin F., Can. Met. Quart. 14,.97 (1975). 11. Morin F.. J. Elecrrochem. Sot. 128. 2439 (1981).
12. Windhager H. J. and Borchardt G., Ber. B&enges Phys. Chem. 79, 1115 (1975). 13. Mathematics of Diffusion (Edited by J. Crank). Clarendon Press, Oxford-(1956)’ _ 14. Ho&her U.. Dr. Ine. Dissertation. Technical University Clausthal (1983; 15. Hiilscher V. and Schmalzried H., Z. Phys. Chem. N.F. 139, 69 (1984). 16. Wimmer J. M., Ph.D. Thesis, Marquette University (1972). 17. Wimmer J. M., Blumenthal R. N. and Bransky I., J. Phys. Chem. Soliak 36, 269 (1975). 18. Chowdhry V. and Coble R. L., J. Am. Ceram. Sot. 65, 336 (1982). 19. Morin F. and Dieckmann R., J. Phys. Chem. Solids 51, 283 (1990). 20. Sato H. and Kikuchi R., J. Chem. Phys. 55,677 and 702 (1971). 21. Murch G. E., Diff. and Defects Monographs Series No. 6. Trans. Tech. Publ., Aedermannsdorf (1980). 22. Carter R. E. and Richardson F. D., Trans. AIME 200, 1244 (1954). 23. Rahman S. R. and Berard M. F., J. Am. Ceram. Sot. 60, 67 (1977). 24. Chen W. K., Peterson N. L. and Reeves W. T., Phys. Rev. 186, 887 (1969). 25. Crow W. B.. Ph.D. Thesis. Ohio State Univ. (1969). 26. Price J. B. and Wagner J. B., Z. Phys. Chem. N:F. 44, 257 (1966). 27. Meurer H., Dr. Ing. Dissertation, Technical University Clausthal (1970). 28. Morin F., Can. Met. Quart. 14, 105 (1975). 29. Morin F. and Dieckmann R., Z. Phys. Chem. N.F. 129, 219 (1982). 30. Sossa B. C., Thesis, Paris XIII University (1982). 31. Petot-Ervas G., Radji O., Ochin P. and Sossa B., Radiation Ejects 69, 301 (1983).
J. Phys. Chem. Solids Vol. 53, No. 2, pp. 323-327. 1992 Printed in Great Britain.
CHEMICAL DIFFUSION
COEFFICIENT OF Co0
T. TADUY, F. MILLOT and G. DHALENNE Laboratoire des Compods non Stoechiom&triques,URA 446-Universitk Paris-Sud, BBtiment 415-91405-Orsay-C%dex, France (Received 4 June 1990; accepted in revised form
12 June 1991)
Abstract-The chemical diffusion coefficients B and the thermodynamic factors (8 In P,,/d6) of Co,_,0 have been measured with an electrochemical set-up at 1108°Cbetween lo-) and 1 atm oxygen pressures. Our results confirm previous data of b obtained with thermogravimetry. Comparison with available cobalt self-diffusion coefficients D& supports a simple vacancy migration mechanism for cobalt diffusion. Keywords:
Cobalt oxide, non-stoichiometry,
diffusion.
INTRODUCTION High-temperature CO,_~O is a fair example of a moderately non-stoichiometric compound (at 1 atm oxygen pressure and 1000°C it contains approximately 1 per cent cobalt vacancies). It has been extensively studied during the last 30 years because many of its properties are directly dependent on the concentration of cobalt vacancies. Fourteen years ago, Dieckmann [l] compiled and reviewed some of these reproducible properties: S(P,,, T), deviation from stoichiometry; D&(Po,, T), cobalt self-diffusion coefficient; and u,(PoI, T), electronic conductivity. Other reproducible properties, such as thermoelectric power, were consistently reported by various authors [2, 31. Finally, recent direct determinations of the enthalpy of mixing of oxygen, AH(Oz) in Co0 [4] have appeared to be approximately consistent with previous indirect determinations from various isotherms 6 (PC&
Finally, if one discards data obtained from conductivity measurements, disagreement about whether b is P,,dependent or not still persists. Although many arguments have been put forward to account for the discrepancies, the situation is still very confusing. In this context, we have decided to design an experiment which could, at best, eliminate the possible causes of errors and of uncertainties in the determination of B.
EXPERIMENTAL
As was previously mentioned, it has been observed, in some instances, that the solution of Fick’s second law was not obeyed when it was assumed that the kinetics was governed by the migration of cobalt in the sample. When this happens, it is assumed that another kinetic phenomenon slows down the overall redistribution. Slow exchange of oxygen at the interface between the sample and the gas phase is a common one in oxides and thus elimination of gas transfer through interfaces may improve the determination of d. Only a few data have been reported on oxides [5-81 which respected this condition. They In contradiction to this general agreement, chemiconsisted of observing the redistribution of ionic cal diffusion coefficient, a, data are still controversial, migrating species in a concentration gradient prealthough slightly dispersed (typically by a factor of viously built into the volume of the sample. five at a given temperature). Data at 1000°C reported In these experiments, electrochemical cells were on single crystals are collected in Table 1 in such a used to follow the small changes of oxygen chemical way that the sources of disagreement become apparpotential of some part of the sample. This technique ent: some authors reported PO,dependent as (the d of measurement offers the advantage, for instance, in value was approximately doubled between PO2= 10m3 comparison with thermogravimetry, of a high sensiatm and _Pp2 = 1 atm), whereas others observed tivity. Incidentally, the relative variations of concenconstant D m the same pressure range. All these tration during redistribution can almost be identified data were obtained with the assumption that the with the corresponding variations of the chemical kinetics were governed by the isothermal diffusion of potential without introducing causes of uncertainty cobalt in the samples. However, it can be seen from on b (see the equations at the end of this section). Table 1 that disagreement also exists on whether this These advantages make electrochemistry a powerassumption is or is not justified when conductivity ful tool for the investigation of B in comparison with measurements are performed. indirect measurements, for instance from conduc323
T.
324
et al.
TADUY
Table 1. Chemical diffusion coefficient of Co0 single crystal at looo”C reported in the literature Is D dependent on PO,?
Method Conductimetry Manometry Thermogravimetry Conductimetry Conductimetry Conductimetry Thermogravimetry Conductimetry Conductimetry Galvanometry Conductimetry
Is Fick’s 2nd law obeyed? Yes
5-9 4-6.5 8.1 4-10 5-14 9.1-9.2
tivity variations, which can under specified conditions introduce some uncertainties in the data [g-11].
The experimental set-up was designed from the preceding considerations. It is schematically shown in Fig. 1. The sample is a Co0 single crystal grown in an argon atmosphere with an arc image furnace from a 10ppm impurity containing Co,O., powder. It is mechanically machined with diamond tools to have a cylindrical shape (e = 1 mm, @ = 6 mm). The sample is enclosed in a box made of the following assorted materials. The upper flat face is in contact with a 2/100” mm thick platinum sheet and the lower flat face with a ZrO?-9% mol. Y,O, solid electrolyte (from INPGENSEEG Saint Martin d’H&es, France). The annular face is in contact with a ring made of “Vycor” (from Corning Glass) which is itself enclosed in a silica glass cylindrical tube. Glass pieces were mechanically machined with diamonds tools and final adjustments were obtained with chemical attack in 40% HF to better than l/l00 mm.
No Yes Yes No No Yes Yes No
Yes No Yes Yes No
Yes
Year
Ref.
1966 1970 1972-1975 1972-1975 1975-1982 1982 1982 1982 1983 1983, 1984 1990
26 27 16, 17 16, 17 28,29 20 18 18 31 14,15 19
The whole set-up is compressed with a spring outside the furnace and when it is held at 1lOO”C, the viscosity of “Vycor” (q = 10-l’ poises) permits it to deform under the compression of the spring until it occupies all the free volumes (pure SiOz glass is not deformed). Moreover, it reacts with the contact surfaces forming Co, SiO, with Co0 and ZrSiO, with the solid electrolyte. After a two month continuous heating at 1108°C we observed a homogeneous and adhesive 150pm thick layer of CO,SiO, formed on the annular face of COO. This layer constitutes an excellent physical barrier between Co0 and its neighbourhood because diffusion of Co, Si and 0 has been shown to be very small in this compound [12]. ZrSiO, plays the same role between ZrOz and “Vycor”. We also observed after two months of heating that small amounts of cobalt had diffused through the platinum sheet to form small blue spots of Co2 SiO., at the surface of “Vycor” in contact with platinum. Other experimental details (not shown in Fig. 1) consist of a laboratory silica glass tube containing the set-up, a furnace, a PID Eurotherm temperature regulator (+ O.l’C), a Pt/Pt, 10% Rh thermocouple (+2”C) in the neighbourhood of the set-up and Wiisthoff pumps which allow flowing predetermined N2-02 gas mixtures on the set-up. During operation at 1108°C and under well-defined PO,, two kinds of experiments were conducted thus. Equilibrium measurements of the variation of the deviation from stoichiometry 6 with PO2by galvanometry. A definite quantity of oxygen N is transferred through the solid electrolyte from gas phase to Co0 (or conversely) by applying a constant d.c. current I to the cell during time t: N = ZT/2F (F = 96,500 coulombs). This transfer induces a change of the non-stoichiometry 6 of the sample: A6 = NVm/V, where Vm is the molar volume of Co0 and V is the volume of the sample. The e.m.f. of cell
Fig. 1. Experimental set-up: (1) alumina; (2) silica glass; (3) “Vycor” glass; (4) Co0 sample; (5) ZrO,/Y,O, solid electrolyte; (6) Pt grid and Pt and (7) Pt sheet a, b, a’, b’ Pt electrical connections.
DT
DC-=‘)
Chemical diffusion coefficient of Co0
is measured before I is applied (E,) and after the current has been cut off and the sample has returned to equilibrium (Ez). We then have AInPr’=
325
We also have that:
4P (E, RT- E,) ,
and finally the quantity q
If small variations of C are considered, the quantities (a In PO,/8 In a), and V,,, are almost invariant with PO, so that.
(PO,,n,
is deduced from small changes of the deviation from stoichiometry with PO*. In practice, the currents (typically 50-100 PA) were applied for between 10-30 mins resulting in (E, - E,) values between 1 and 40 mV (a 10% change of PO, at 1108°C corresponds to E2 - E, = 6.85 mV). The composition of the N&r mixture flowing along the laboratory tube was chosen to minimize the drifts of E signals corresponding to equilibrium. Corrections were done of the actual volume V of sample to take into account the formation of the annular Co,SiO, layer (a parabolic law was presumed). Chemical diffusion coefficient measurements. These experiments were conducted at the same time as equilibrium measurements. As a matter of fact, the transfer of oxygen through the solid electrolyte induces a concentration gradient of cobalt in the sample. Once the current is cut off, no more matter can enter or leave the sample and the cobalt concentration gradient relaxes to return to chemical equilibrium. These changes were observed by measuring the e.m.f. E between a and b of the platinium wire (see Fig. 1) with a high impedance voltmeter (7066 datastore from Schlumberger). In practice, however, we have found that a 10 min delay was necessary after stopping the current to obtain E values obeying the Nernst-Einstein law. (This effect probably results from polarization and thermal effects at the (ZrO,Y,O,)/CoO interface when the current is applied.) The chemical diffusion coefficient b was deduced from the variation of In (Eab(t) - Eab(t = a)) with time t. In effect, the solution of Fick’s second law corresponding to the boundary conditions of our experimental set-up is [13]: ln(C(t) - C(t = CO))= - Iz l-12Dt + constant if -> 12
1.5,
where 1 is the thickness of the sample and C(t) is the concentration of cobalt atoms in unit volume at time t (lIZDt/12 = 1.5 at t N 15 min). The origin of the time, t, is when current is no longer applied and, consequently, no more oxygen is transferred through the CoO/(ZrO,/Y,O~) interface. PCS 53:2-H
ln(E,,(t)
l-FL% - Eab(t = co)) = -12 + constant.
RESULTS AND COMPARISON WITH THE LITERATURE In order to determine the amounts of foreign ions which could have diffused in Co0 after two months of heating, chemical analysis of the sample was performed (by SCA-CNRS Vemaison, France). One hundred parts per million K, 30 ppm B, 90 ppm Zr, 15 ppm Y and 0.4% Si were detected. The high quantity of silicon could be correlated with small Co2Si04 grains at the annular surface of Co0 by optical microscopy. However, in order to determine the actual Si content in the volume of Co0 an independent experiment was carried out: a diffusion couple of Co0 with C02Si0, was prepared as follows: a Co0 single crystal having a cylindrical shape (e = 1 mm, 0 = 6 mm) was optically polished on one of its two flat faces. A dense COrSiO, sinter was obtained with an arc image furnace and machined to have the same shape as the COO. One of its flat faces was optically polished. The two polished faces of Co0 and CO, SiO, were then put in compressive contact and held in Or gas at 1100°C for 15 days. After cooling, the two oxides could be separated. However, we have observed that an approximately 100 microns thick layer of C02Si04 was strongly attached to the surface of COO. This layer was removed by mechanical abrasion and an analysis for silicon was achieved approximately 20 microns inside Co0 with an electronic microprobe. The results showed no difference between this sample and a reference Co0 crystal indicating a Si content lower than 150 ppm (the resolution of the microprobe). The (a In Po,/aS), results obtained at 1108°C between 10m3and 1 atm oxygen pressures are shown on Fig. 2. These data were compared with two other sets of data: Dieckmann’s regression [1] based on a large set of published data; and Hiischler and Schmalzried’s data obtained by galvanometry [14, 151 and extrapolated from 1100°C. The three curves in Fig. 2 show very similar behaviour. Dispersion is 18% at 1 atm O2 (between Dieckmann’s and Hlischler’s data) and 10% at
326
T.
TADIJYet al.
flowing in the chamber leads to a 60 FV variation of AEab (the variation is only 60 nV at 1 atm oxygen pressure). Comparison of our data with previous data merits the following comments. Our observation is that B is independent of or slightly decreasing with PO,. This result is in a qualitative agreement with previous predictions of PO2 independent b results [ 16-191 but disagrees with
the other results (see Table 1). Among PO, dependent fi results in the literature our data are in relatively good agreement with those obtained by thermogravimetry: Wimmer et al. [16, 171 give b (llOS”C)= 1.3 x 10m6cm2 s-r and Chowdhry and Coble [18] propose b (1108°C) = 1.7 x 1O-6 cm2 s-r.
DISCUSSION
0
-2
-4
-6
Ln(Q.tm
Fig. 2. Thermodynamic factor (a In P,,/%I), vs oxygen pressure of Co0 at 1108°C: black points, our data; dotted line, Hdschler and Schmalzried’s data [14, 151; continuous line, Dieckmann’s regression [l].
lo--‘atm O2 (between Dieckmann’s and our results). Our data appear to be about 10% lower than Dieckmann’s regression in the studied range of Po,s. Chemical diffusion coefficients of Co0 obtained at 1108°C between 10m3and 1 atm oxygen pressures are shown in Fig. 3. Dispersion of experimental points clearly increases as PO2 decreases. This tendency is to be put in conjunction with the decrease of the reproducibility of the AEab signal at low PO,. In fact at 10m3atm a 1 ppm O2 variation in the gas mixture to’bkmh
I
The main interest in the precise determination of the chemical diffusion coefficient B in such a material as Co0 is that it may be compared with other diffusion data which are explicitly dependent on the diffusion mechanism, for instance the self-diffusion coefficient D& of cobalt. It has been shown by Sato and Kikuchi [20] and later by Murch [21] that in some simple cases it is possible to know the value of the Haven ratio
from
0
1
0
28
*
29
*
30
ref.
to‘b(cm~
t
‘I
2.5
1
-2.5
.
.
-2
. .
.
.
. . . . *.*.
l
.
.
.
. .
.
.
.
.ls
.
Itm I -3
-2
-t
O
‘~‘%!tm.
Fig. 3. Chemical diffusion coefficient a of Co0 vs PO, at 1108°C.
Fig. 4. Calculated chemical diffusion coefficients from various D& data in the literature and assuming a simple
vacancy migration mechanism. The hatched domain contains 90% of our a data.
Chemical diffusion coefficient of Co0
In particular, if one considers a simple vacancy migration mechanism in a c.f.c. solid containing not too many vacancies one has: HR =fd = 0.7815,
327
5. Ait Younes N., Millot F. and Gerdanian P., Solid Stare Ionics 12, 437 (1984). 6. Millot F., J. Nucl. Mater. 125, 64 (1984). 7. Millot F. and De Mierry P., J. Phys. Chem. Solid 46, 797 (1985). 8. Millot F. and Berthon J., J. Phys. Chem. Solids 47, 1
(1986).
wheref, is the geometrical correlation factor. Such a simple model looks attractive, or at least plausible for describing cobalt migration in COO. As a matter of fact, oxygen moves much more slowly than Co (D&,/D,* N 5 x lo4 at 1200°C) and Co0 is a metal deficient non-stoichiometric oxide. We have compared our data of B with the calculated ones using available DE, from the literature and our (a In Po,/aS), data (HR is assumed to be equal to 0.7815). This comparison appears on Fig. 4. Dieckmann’s data [1] come from the original 1108°C DE, isotherm. Other data [22-241 were obtained by interpolating between data at other temperatures. The results of Crow [25] have been excluded for clarity since they are significantly higher than all the other results at 1100°C. Examination of Fig. 4 shows that within the dispersion of data, close agreement is obtained between these calculated chemical diffusion coefficients and our data. This comparison is then a support for a simple vacancy migration mechanism of cobalt in cobaltous oxide.
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R.,
Z.
Whys. Chem.
N.F.
107, 189
Fisher B. and Tannhauser D. S., J. Chem. Phys. 44,
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