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Up-quenching and diffusional transitory creep of non-stoichiometric NiO
J. Phys. Chem. SolidsVol. Printed in Great Britain.
0022-3697/91 %3.00 + 0.00 0 1991 Pergamon Press plc
S2, No. 3. pp. 517-521, 1991
UP-QUENCHING AND DIFFUSIONAL TRANSITORY CREEP OF NON-STOICHIOMETRIC NiO M. JIMBNEZ-MELENDO,~ A. DotiNGmz-RoDRfGuEzt
and J. CASTAING$
TDepartmento de Fisica de la Materia Condensada, Aptdo. 1065. 41080 Sevilla, Spain SLaboratoire de Physique des Materiaux, C.N.R.S. Bellevue, 92195 Meudon Cedex, France (Received
23 April 1990; accepted in revised form
19 September
1990)
Abstract-A
sudden increase of temperature during the creep of non-stoichiometric NiO permitted the determintion of two parameters: first, the migration energy of the rate controlling diffusing species. viz. oxygen; second, the chemical diffusion coefficient associated with the process leading to thermodynamic equilibrium. Keywords:
NiO, creep, diffusion, up-quenching.
1. INTRODUCTION Many properties of binary oxides depend on the concentration of various point defects that they contain. Transport is particularly sensitive to changes in these concentrations. Electrical conductivity and cation diffusion are related to departure from stoichiometry in transition metal oxides [l-3]; they depend only on the amount of cation vacancies in Cu,O, NiO and COO. The thermodynamic equilibrium is determined by two parameters, temperature T and oxygen activity (partial pressure of oxygen PO, in the surrounding atmosphere) being the most easy to control. A change in T or PO, is followed by a transient; the kinetics to reach the new equilibrium can be described by a chemical diffusion coefficient, which corresponds to the motion of cation vacancies to/from the surface where they are annihilated/created. At this point, we have considered only those properties related to dominant point defects, which permit fast atomic transport. It is clear that some phenomena do not depend on them, for instance the transport of matter (sintering, plastic deformation, . . . ) which requires the motion of fast as well as slow diffusing species. For the abovementioned oxides, these slow species are oxygen; they have been shown to control the rate of their high temperature deformation [2,3]. Oxygen diffusion takes place via defects in the oxygen sub-lattice; their concentration is determined by T and PO>. Using creep experiments, it has been shown that the transients to reach equilibrium in the oxygen sublattice of Cu,O and Co0 are controlled by the diffusion of dominant cationic point defects (chemical diffusion )[4, 51. These experiments were performed using PO,-induced variations in the creep rate i. Such an approach was not possible for NiO because its creep rate is almost independent of PO, for
single crystals [6] and polycrystals [7]. For that compound, we have, therefore, performed tests to study transitory creep following step-like temperature increases. This up-quenching at first does not change the point defect concentrations; however, the creep rate i is increased because of their acceleration migration. This allowed us to reach values for the energy of migration of the point defects responsible for oxygen diffusion. The sudden increases of i are followed by transients, analogous to the ones already observed for Cu,O and Co0 [4, 51, that we analyze in similar ways. 2. EXPERIMENTAL TECHNIQUES 2.1. Specimen preparation We have used two types of materials: (i) NiO single crystals grown in an arc-image furnace that we have used in previous works [6,8] and (ii) NiO polycrystals which were also studied in detail [7]. Mechanical tests were performed in compression on speciments of 5.0 x 3.0 x 3.0 mm in size. The single crystals had {IOO}faces. The stress was parallel to the length of the parallelepipeds. 2.2. Creep tests Deformation was achieved in air (PO, = 0.21 atm) under constant load compression in the creep machine [9] used in previous works [4-81. The deformation jig is made of alumina; it is surrounded by a high temperature furnace which has a large thermal inertia. To achieve the temperature steps, we placed a micro-furnace (diameter 11 mm, height 10 mm) surrounding the specimen. The micro-furnace was made of alumina, with platinum-rhodium (Pt-Rh 30%) wiring as heating elements. The wires were embedded in an alumina-based ceramic paste. Two 517
M. JIM~NEZ-MELENDO et al.
518
thermocouples were placed; one in contact to the specimen and the other just outside the microfurnace. The starting thermal conditions were established by the high temperature furnace, which is controlled by a thermocouple located within its heating elements. Temperature steps (AT g 5OC) were obtained by applying a voltage of about 25 V to the micro-furnace wires. We recorded the rate of temperature increase on the specimen thermocouple [Fig. l(a)] which always took less than 5 min. Thermal expansion in the system was induced by AT; it was recorded with specimen creep condition giving i = 0 [curve M, Fig. l(b)]. By using the standard chart, this can be described as an expansion of the specimen, or a contraction of the deformation rod; typical values of 15 pm were obtained. In order to have the actual shortening due to the specimen deformation, we subtracted the dilatation from the recorded curve [curve T, Fig. l(b)]. By this process, the error on the specimen length-time curve [curve S, Fig. l(b)] is negligible, corresponding to errors on strains t much smaller than 0.3%. This does not induce any scatter to the data points, compared with that obtained in conventional creep tests [lo].
2.3. Creep curves For significant experiments, we first have to meet the conditions for steady state creep [lo], where diffusion controls i. It has been shown that for NiO single crystals, t rr 20% had to be reached [6]; at that stage, a polygonized structure is established and t’ is related to the climb of dislocations [lo]. For NiO polycrystals, we chose conditions corresponding to the same creep mechanism as for single crystals, i.e. large enough stresses had to be applied to avoid viscous flow [7]. Steady-state was reached for t = 5%. Typical creep curves plotted as log i-e, are shown in Fig. 2 displaying various changes of stress and one temperature step. The steady-state corresponds to a straight line in the log i-t plot (Fig. 2) with a negative slope because of the constant load [lo].
-1: ;! =
1000
500
_.’
I
1100
1150
TEHrEnATunEPC)
-10
0
umman
~~~~
lo-'5
!
10
I
10
I
I
20
(pm)
Fig. 1. Records of variation with time of: (a) temperature at the specimen; (b) extensometer giving apparent specimen length changes for creep rate equal to zero (curve M), for creep transient (curve T) and the deduced actual result (curve S).
I
15
I
LO LTRAIW (X)
I
I
25
30
Fig. 2. Creep curve of NiO single crystal in log i-scale. The test shows various c changes and one temperature step. The time after the temperature change is also displayed.
3. CREEP DATA ANALYSIS We use the same formalism as the one established in previous works [2, 3, lo]. The steady-state creep rate i can be described by the equation:
(1) where A is a parameter which contains microstructural aspects, u is the stress and D the diffusion coefficient of oxygen. D can be written as D = B . [X] exp( - AH,/kT),
(2)
where B is a constant, [X] is the concentration of defects responsible for diffusion and AH,,, is the energy of migration of the defects. Using conventional point defect chemistry [2, 111, the calculation of [X] relies on an equation of the form: [A’] = E . P;;, exp( - AHJkT),
(3)
where E is a constant and AH, is the apparent energy of formation of the defects. The creep rate i is now written [eqns (l), (2) and
(311: A .B.E i = ___ T
a)
Y,
10-S
.6”. PE,. exp( - AHlkT),
(4)
where AH = AH,,, + AH/ is the self-diffusion activation energy. This equation is normally used to analyze creep data and to determine the rate controlling mechanism [6-81. For a temperature change AT = T2 - T, , the new thermodynamic equilibrium is reached after a long to the establishment of the time t,, corresponding new point defect concentrations via their creation or annihilation at the surface and diffusion in the bulk [l, 2, 61. Let [X,] and [X,] be the equilibrium point defect concentrations at the temperatures T, and T2, respectively. At first, after the temperature change, [X,] in eqn (2) is not changed, but the creep
Creep of non-stoichiometric
NiO
519
-10-5 7 Z!
5
:
5
: -4 z II z
* EXPERlNENtll 0 Allm=3.6eV
2
lo-' 0
flit
20
15
10
5
(x15's]
Fig. 3. Analysis of the creep transient of Fig. 2; plot of log i vs time t. (u = 80 MPa, T, = 1106”C, T2 = 1152°C AT = 46°C). Comparison of experiments with the calculated points for various AH, values. is increased to iy rate i, by a factor (r, /T2) . exp(AH, AT/k T, . T2) [eqns (1) and (2)]; the corresponding activation energy is AH,,,. After a time leg, the new concentration [X,] is reached and the activation energy for creep AH can be measured. During the transitent stage, the point defect concentration is not uniform in the specimen, being between [X,] and [X,]. The specimen is like a composite submitted to a uniform strain rate i, inducing a stress distribution [5]. This allowed us to analyze the creep transients with the same method as used for the PO, changes [5]; in the present case, we had to adjust two parameters: 6, the chemical diffusion coefficient, as in Ref. 4 and (7, the creep rate just after the temperature step (Fig. 2) that is for t = 0. The sensitivity of the determination of iy (or AH,) is shown in Fig. 3, which displays the creep transient of Fig. 2, plotted as log i vs time t. The three upper curves are clearly separated; they correspond to AH, values 0.4 eV apart, which is only slightly larger than the expected scatter for AH from creep eperiments [IO]. The accuracy for AH,,, is therefore similar to the one for AH.
A factor of 2 on d gives definitely different curves (Fig. 4), corresponding to an excellent accuracy in the determination of B values, as already mentioned in Ref. 5. In all our analysis, we have used a stress exponent n = 7, close to experimental values [6, 71; the value of n is not critical for the determination of the creep transient [5].
4. RESULTS AND DISCUSSION Experimental conditions to perform this type of creep transient are not easy to meet. One needs reasonable i values so that the specimen is not submitted to excessive deformation during the transient creep. The rate controlling mechanism of the deformation must be related to point defects in the materials, control by diffusion being the easiest to achieve. Finally, the chemical diffusion must be such that observations are possible. Similar kinds of experiments have been performed by ourselves on Cu,O and Co0 [4,5] and by Poumellec and Jaoul on olivine [12] using PO2 steps.
2
z ; I
4 2
10-s 0
* EXPERllEIlIL ~i=t.o~io-~ cm2t-t qi=z.ori0* cmzs-1 li=u ~10~~ cmzs-1 5
15
10 TIME
20
Ix103sl
Fig. 4. Creep transient for NiO single crystal plotted as log 6 vs time t. (a = 72 MPa, T, = llSO”C, T, = 1213°C. AT = 63°C). Comparison of experiments with the calculated points for various b values.
520
M. JI&NEZ-MELENDO et al. Table 1. Values of the migration energy AH,,, and the chemical diffusion coefficient L?i,deduced from the comparison of theoretical and experimental transient creep after temperature steps
T(“C)
Materialt
1152 1167 1178 1213 1283 1344 t D, is the chemical ]151. 1 S = Single crystal, Table
coo NiO
diffusion
@cm* s-i)
AH,., (eV)
s P P S S S
3.6 3.6 3.5 3.8 3.5 3.3 coefficient
6 x 1+ 1x 1x 2 x 4 x
from electrical
D,(cm* s-i)?
lo-’ 1o-6 lo-6 IO-6 1o-6 10-G
conductivity
5.1 6.6 7.2 9.7 1.7 2.6
x x x x x x
10-7 IO-’ IO-’ IO-’ 10-e lO-6
data at PO, = 0.21 atm
P = polycrystal.
2. Calculated energy for the migration AH, and formation doubly-charged oxygen vacancies Vo in Co0 and NiO [13,14]
AH,
AH, (eV)
AHdeW
AfMW
Ref.
1.85 2.1
9.9 7.05
8.05 4.95
13 12
t AH, is the corresponding
of
activation energy for oxygen diffusion.
Some results of our experiments on NiO, using sudden increases of temperature, are shown in Fig. 2 for a standard plot [lo] and in Figs 3 and 4 for log t’ vs time t plots. In Fig. 2, one can see the jump in i due to the enhancement of the migration of the creep rate controlling point defects; the jump is followed by a transient before reaching the straight line which corresponds to steady-state creep. In Figs 3 and 4, the experimental points are compared with those calculated according to the model; fairly good fits are achieved. The results that we obtained are displayed in Table 1. We found for the activation energy for the migration of point defects controlling creep: AH,, = 3.6 k 0.2 eV. For the creep of NiO, the activation energy is AH = 6.2 + 0.4 eV [7, 81, oxygen diffusion taking place via double-charged vacancies Vb; [6,7]. We can deduce the data for the apparent formation energy of oxygen vacancies in NiO, AH, N 2.6 eV; it is smaller than the migration energy. Calculations have been performed for NiO [I 31 following the same procedure used for Co0 [ 141. The results of the calculations are shown in Table 2 for the V,. There are uncertainties in the calculations due to inaccuracies in physical parameters such as electron affinity and electron localization. Previous works gave lower values by 223 eV, as reviewed in [2] and [3]. The discrepancy for NiO between activation energies for creep (6.2 eV), for tracer diffusion (5.6 eV) and for calculation (7.05 eV) may shed some doubt on the latter. The calculations indicate that AH,,, < AH, which is opposite from what we found experimentally. There is no simple way either to waive, or to explain this discrepancy. There is clearly a need for more experimental and theoretical investigations on oxygen diffusion in NiO. Table I also displays the values of the chemical diffusion coefficients deduced from our creep experiments; they are very close to those of others [1.5]
obtained by electrical conductivity, a technique sensitive to cation vacancy population. This indicates that the change of oxygen vacancy concentration is directly linked to the diffusion of nickel vacancies to/from the surface, a result similar to the one found for Cur0 and Co0 [4,5]. A similar conclusion was drawn from olivine where magnesium vacancy diffusion was found to control the creep transients [12]. Sudden temperature changes are therefore useful tools to give interesting data on point defects in compounds. Acknowledgements-The support of CICYT No. MAT/880181-CO2-01 (Ministerio de Education y Ciencia, Spain) and Action Integrada No. 45 is acknowledged.
REFERENCES 1. Kofstad P., Non-stoichiometric, Dt’ision and Electrical Conductivity in Binary Oxides. Wiley Interscience, New York (1972). 2. Castaing J., Dominguez-Rodriguez A. and Monty C., Deformation of Ceramic Materials II (Edited by R. E. Tressler and R. C. Bradt), Vol. 18. p. 141. Plenum Press, New York (1984). 3. Castaing J., Monty C. and Dominguez-Rodriguez A., Def Dtjiision Forum 64/65, 139 (1989). 4. Dominguez-Rodriguez A., Monty C. and Philibert J., Phil. Mug. A46, 869 (1982). 5. Clauss C., Dominguez-Rodriguez A. and Castaing J., Rev. Phys. Appl. 21, 343 (1986). 6. Cabrera-Cano J., Dominguez-Rodriguez A., Marquez R., Castaing J. and Philibert J., Phil. Mug. A46, 397 (1982). 7. Jimenez-Melendo M., Dominguez-Rodriguez A., Marquez R. and Castaing J., Phil. Mug. A56, 767 (1987). 8. Jimenez-Melendo M., Guiberteau F., Dominguez-Rodriguez A., Marquez R. and Castaing J., Crysr. Latt. Def amorph. Mater. 16, 99 (1987). 9. Gervais H., Pellissier B. and Castaing J., Rev. Znt. htes temp. Refract. 15, 43 (1978). 10. Bretheau T., Castaing J., Rabier J. and Veyssiere P., Adv. Phys. 28, 835 (1979).
Creep of non-stoichiometric
11. Monty C., DPfauts Ponctuels dans les Solides, p. 345, Les Editions de Physique, Orsay (1977). 12. Poumellec B. and Jaoul O., Deformation of Ceramics II (Edited by R. E. Tressler and R. C. Bradt), Vol. 18, p. 281. Plenum Press, New York (1984).
NiO
521
13. Tarento R. J., unpublished results. 14. Tarento R. J., Rev. Phys. Appl. 24, 643 (1989). 15. Fahri R. and Petot-Ervas G., J. Phys. Chem. Solids 39,
1175 (1978).
0022-3697/91 %3.00 + 0.00 0 1991 Pergamon Press plc
S2, No. 3. pp. 517-521, 1991
UP-QUENCHING AND DIFFUSIONAL TRANSITORY CREEP OF NON-STOICHIOMETRIC NiO M. JIMBNEZ-MELENDO,~ A. DotiNGmz-RoDRfGuEzt
and J. CASTAING$
TDepartmento de Fisica de la Materia Condensada, Aptdo. 1065. 41080 Sevilla, Spain SLaboratoire de Physique des Materiaux, C.N.R.S. Bellevue, 92195 Meudon Cedex, France (Received
23 April 1990; accepted in revised form
19 September
1990)
Abstract-A
sudden increase of temperature during the creep of non-stoichiometric NiO permitted the determintion of two parameters: first, the migration energy of the rate controlling diffusing species. viz. oxygen; second, the chemical diffusion coefficient associated with the process leading to thermodynamic equilibrium. Keywords:
NiO, creep, diffusion, up-quenching.
1. INTRODUCTION Many properties of binary oxides depend on the concentration of various point defects that they contain. Transport is particularly sensitive to changes in these concentrations. Electrical conductivity and cation diffusion are related to departure from stoichiometry in transition metal oxides [l-3]; they depend only on the amount of cation vacancies in Cu,O, NiO and COO. The thermodynamic equilibrium is determined by two parameters, temperature T and oxygen activity (partial pressure of oxygen PO, in the surrounding atmosphere) being the most easy to control. A change in T or PO, is followed by a transient; the kinetics to reach the new equilibrium can be described by a chemical diffusion coefficient, which corresponds to the motion of cation vacancies to/from the surface where they are annihilated/created. At this point, we have considered only those properties related to dominant point defects, which permit fast atomic transport. It is clear that some phenomena do not depend on them, for instance the transport of matter (sintering, plastic deformation, . . . ) which requires the motion of fast as well as slow diffusing species. For the abovementioned oxides, these slow species are oxygen; they have been shown to control the rate of their high temperature deformation [2,3]. Oxygen diffusion takes place via defects in the oxygen sub-lattice; their concentration is determined by T and PO>. Using creep experiments, it has been shown that the transients to reach equilibrium in the oxygen sublattice of Cu,O and Co0 are controlled by the diffusion of dominant cationic point defects (chemical diffusion )[4, 51. These experiments were performed using PO,-induced variations in the creep rate i. Such an approach was not possible for NiO because its creep rate is almost independent of PO, for
single crystals [6] and polycrystals [7]. For that compound, we have, therefore, performed tests to study transitory creep following step-like temperature increases. This up-quenching at first does not change the point defect concentrations; however, the creep rate i is increased because of their acceleration migration. This allowed us to reach values for the energy of migration of the point defects responsible for oxygen diffusion. The sudden increases of i are followed by transients, analogous to the ones already observed for Cu,O and Co0 [4, 51, that we analyze in similar ways. 2. EXPERIMENTAL TECHNIQUES 2.1. Specimen preparation We have used two types of materials: (i) NiO single crystals grown in an arc-image furnace that we have used in previous works [6,8] and (ii) NiO polycrystals which were also studied in detail [7]. Mechanical tests were performed in compression on speciments of 5.0 x 3.0 x 3.0 mm in size. The single crystals had {IOO}faces. The stress was parallel to the length of the parallelepipeds. 2.2. Creep tests Deformation was achieved in air (PO, = 0.21 atm) under constant load compression in the creep machine [9] used in previous works [4-81. The deformation jig is made of alumina; it is surrounded by a high temperature furnace which has a large thermal inertia. To achieve the temperature steps, we placed a micro-furnace (diameter 11 mm, height 10 mm) surrounding the specimen. The micro-furnace was made of alumina, with platinum-rhodium (Pt-Rh 30%) wiring as heating elements. The wires were embedded in an alumina-based ceramic paste. Two 517
M. JIM~NEZ-MELENDO et al.
518
thermocouples were placed; one in contact to the specimen and the other just outside the microfurnace. The starting thermal conditions were established by the high temperature furnace, which is controlled by a thermocouple located within its heating elements. Temperature steps (AT g 5OC) were obtained by applying a voltage of about 25 V to the micro-furnace wires. We recorded the rate of temperature increase on the specimen thermocouple [Fig. l(a)] which always took less than 5 min. Thermal expansion in the system was induced by AT; it was recorded with specimen creep condition giving i = 0 [curve M, Fig. l(b)]. By using the standard chart, this can be described as an expansion of the specimen, or a contraction of the deformation rod; typical values of 15 pm were obtained. In order to have the actual shortening due to the specimen deformation, we subtracted the dilatation from the recorded curve [curve T, Fig. l(b)]. By this process, the error on the specimen length-time curve [curve S, Fig. l(b)] is negligible, corresponding to errors on strains t much smaller than 0.3%. This does not induce any scatter to the data points, compared with that obtained in conventional creep tests [lo].
2.3. Creep curves For significant experiments, we first have to meet the conditions for steady state creep [lo], where diffusion controls i. It has been shown that for NiO single crystals, t rr 20% had to be reached [6]; at that stage, a polygonized structure is established and t’ is related to the climb of dislocations [lo]. For NiO polycrystals, we chose conditions corresponding to the same creep mechanism as for single crystals, i.e. large enough stresses had to be applied to avoid viscous flow [7]. Steady-state was reached for t = 5%. Typical creep curves plotted as log i-e, are shown in Fig. 2 displaying various changes of stress and one temperature step. The steady-state corresponds to a straight line in the log i-t plot (Fig. 2) with a negative slope because of the constant load [lo].
-1: ;! =
1000
500
_.’
I
1100
1150
TEHrEnATunEPC)
-10
0
umman
~~~~
lo-'5
!
10
I
10
I
I
20
(pm)
Fig. 1. Records of variation with time of: (a) temperature at the specimen; (b) extensometer giving apparent specimen length changes for creep rate equal to zero (curve M), for creep transient (curve T) and the deduced actual result (curve S).
I
15
I
LO LTRAIW (X)
I
I
25
30
Fig. 2. Creep curve of NiO single crystal in log i-scale. The test shows various c changes and one temperature step. The time after the temperature change is also displayed.
3. CREEP DATA ANALYSIS We use the same formalism as the one established in previous works [2, 3, lo]. The steady-state creep rate i can be described by the equation:
(1) where A is a parameter which contains microstructural aspects, u is the stress and D the diffusion coefficient of oxygen. D can be written as D = B . [X] exp( - AH,/kT),
(2)
where B is a constant, [X] is the concentration of defects responsible for diffusion and AH,,, is the energy of migration of the defects. Using conventional point defect chemistry [2, 111, the calculation of [X] relies on an equation of the form: [A’] = E . P;;, exp( - AHJkT),
(3)
where E is a constant and AH, is the apparent energy of formation of the defects. The creep rate i is now written [eqns (l), (2) and
(311: A .B.E i = ___ T
a)
Y,
10-S
.6”. PE,. exp( - AHlkT),
(4)
where AH = AH,,, + AH/ is the self-diffusion activation energy. This equation is normally used to analyze creep data and to determine the rate controlling mechanism [6-81. For a temperature change AT = T2 - T, , the new thermodynamic equilibrium is reached after a long to the establishment of the time t,, corresponding new point defect concentrations via their creation or annihilation at the surface and diffusion in the bulk [l, 2, 61. Let [X,] and [X,] be the equilibrium point defect concentrations at the temperatures T, and T2, respectively. At first, after the temperature change, [X,] in eqn (2) is not changed, but the creep
Creep of non-stoichiometric
NiO
519
-10-5 7 Z!
5
:
5
: -4 z II z
* EXPERlNENtll 0 Allm=3.6eV
2
lo-' 0
flit
20
15
10
5
(x15's]
Fig. 3. Analysis of the creep transient of Fig. 2; plot of log i vs time t. (u = 80 MPa, T, = 1106”C, T2 = 1152°C AT = 46°C). Comparison of experiments with the calculated points for various AH, values. is increased to iy rate i, by a factor (r, /T2) . exp(AH, AT/k T, . T2) [eqns (1) and (2)]; the corresponding activation energy is AH,,,. After a time leg, the new concentration [X,] is reached and the activation energy for creep AH can be measured. During the transitent stage, the point defect concentration is not uniform in the specimen, being between [X,] and [X,]. The specimen is like a composite submitted to a uniform strain rate i, inducing a stress distribution [5]. This allowed us to analyze the creep transients with the same method as used for the PO, changes [5]; in the present case, we had to adjust two parameters: 6, the chemical diffusion coefficient, as in Ref. 4 and (7, the creep rate just after the temperature step (Fig. 2) that is for t = 0. The sensitivity of the determination of iy (or AH,) is shown in Fig. 3, which displays the creep transient of Fig. 2, plotted as log i vs time t. The three upper curves are clearly separated; they correspond to AH, values 0.4 eV apart, which is only slightly larger than the expected scatter for AH from creep eperiments [IO]. The accuracy for AH,,, is therefore similar to the one for AH.
A factor of 2 on d gives definitely different curves (Fig. 4), corresponding to an excellent accuracy in the determination of B values, as already mentioned in Ref. 5. In all our analysis, we have used a stress exponent n = 7, close to experimental values [6, 71; the value of n is not critical for the determination of the creep transient [5].
4. RESULTS AND DISCUSSION Experimental conditions to perform this type of creep transient are not easy to meet. One needs reasonable i values so that the specimen is not submitted to excessive deformation during the transient creep. The rate controlling mechanism of the deformation must be related to point defects in the materials, control by diffusion being the easiest to achieve. Finally, the chemical diffusion must be such that observations are possible. Similar kinds of experiments have been performed by ourselves on Cu,O and Co0 [4,5] and by Poumellec and Jaoul on olivine [12] using PO2 steps.
2
z ; I
4 2
10-s 0
* EXPERllEIlIL ~i=t.o~io-~ cm2t-t qi=z.ori0* cmzs-1 li=u ~10~~ cmzs-1 5
15
10 TIME
20
Ix103sl
Fig. 4. Creep transient for NiO single crystal plotted as log 6 vs time t. (a = 72 MPa, T, = llSO”C, T, = 1213°C. AT = 63°C). Comparison of experiments with the calculated points for various b values.
520
M. JI&NEZ-MELENDO et al. Table 1. Values of the migration energy AH,,, and the chemical diffusion coefficient L?i,deduced from the comparison of theoretical and experimental transient creep after temperature steps
T(“C)
Materialt
1152 1167 1178 1213 1283 1344 t D, is the chemical ]151. 1 S = Single crystal, Table
coo NiO
diffusion
@cm* s-i)
AH,., (eV)
s P P S S S
3.6 3.6 3.5 3.8 3.5 3.3 coefficient
6 x 1+ 1x 1x 2 x 4 x
from electrical
D,(cm* s-i)?
lo-’ 1o-6 lo-6 IO-6 1o-6 10-G
conductivity
5.1 6.6 7.2 9.7 1.7 2.6
x x x x x x
10-7 IO-’ IO-’ IO-’ 10-e lO-6
data at PO, = 0.21 atm
P = polycrystal.
2. Calculated energy for the migration AH, and formation doubly-charged oxygen vacancies Vo in Co0 and NiO [13,14]
AH,
AH, (eV)
AHdeW
AfMW
Ref.
1.85 2.1
9.9 7.05
8.05 4.95
13 12
t AH, is the corresponding
of
activation energy for oxygen diffusion.
Some results of our experiments on NiO, using sudden increases of temperature, are shown in Fig. 2 for a standard plot [lo] and in Figs 3 and 4 for log t’ vs time t plots. In Fig. 2, one can see the jump in i due to the enhancement of the migration of the creep rate controlling point defects; the jump is followed by a transient before reaching the straight line which corresponds to steady-state creep. In Figs 3 and 4, the experimental points are compared with those calculated according to the model; fairly good fits are achieved. The results that we obtained are displayed in Table 1. We found for the activation energy for the migration of point defects controlling creep: AH,, = 3.6 k 0.2 eV. For the creep of NiO, the activation energy is AH = 6.2 + 0.4 eV [7, 81, oxygen diffusion taking place via double-charged vacancies Vb; [6,7]. We can deduce the data for the apparent formation energy of oxygen vacancies in NiO, AH, N 2.6 eV; it is smaller than the migration energy. Calculations have been performed for NiO [I 31 following the same procedure used for Co0 [ 141. The results of the calculations are shown in Table 2 for the V,. There are uncertainties in the calculations due to inaccuracies in physical parameters such as electron affinity and electron localization. Previous works gave lower values by 223 eV, as reviewed in [2] and [3]. The discrepancy for NiO between activation energies for creep (6.2 eV), for tracer diffusion (5.6 eV) and for calculation (7.05 eV) may shed some doubt on the latter. The calculations indicate that AH,,, < AH, which is opposite from what we found experimentally. There is no simple way either to waive, or to explain this discrepancy. There is clearly a need for more experimental and theoretical investigations on oxygen diffusion in NiO. Table I also displays the values of the chemical diffusion coefficients deduced from our creep experiments; they are very close to those of others [1.5]
obtained by electrical conductivity, a technique sensitive to cation vacancy population. This indicates that the change of oxygen vacancy concentration is directly linked to the diffusion of nickel vacancies to/from the surface, a result similar to the one found for Cur0 and Co0 [4,5]. A similar conclusion was drawn from olivine where magnesium vacancy diffusion was found to control the creep transients [12]. Sudden temperature changes are therefore useful tools to give interesting data on point defects in compounds. Acknowledgements-The support of CICYT No. MAT/880181-CO2-01 (Ministerio de Education y Ciencia, Spain) and Action Integrada No. 45 is acknowledged.
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NiO
521
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