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Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3
Physics of the Earth and Planetary Interiors, 34 (1984) 271—274 Elsevier Science Publishers B.V., Amsterdam — Printed in The Netherlands
271
Comment
“Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3” S. Karato Research School ofEarth Sciences, The A ustralian National University, Canberra 2601, A. C. T. (Australia) (Received October 4, 1983; revision accepted March 5, 1984)
Karato, S., 1984. “Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3”—comment. Phys. Earth Planet. Inter., 34: 271 —274.
In a recent paper, Poirier et al. (1983) tried to shed some light on the rheology of the lower mantle by the experimental study of creep (and electrical conductivity) of perovskite KZnF3 as an analogue of MgSiO3 perovskite. This pioneering work contained a number of interesting observations, including the discovery of anomalous creep behaviour associated with solid electrolyte type behaviour near the melting point. Unfortunately, however, some of their interpretations on anomabus behaviour appear unreasonable and are worth re-examination in the essential aspects. In the following, I first examine their experimental results on creep, then discuss their model on the mechanisms of anomalous creep behaviour, and finally some comments will be given on their speculations on the rheology of the lower mantle.
1. Re-examination of experimental results on creep Poirier et al. (1983) made interesting observations concerning the rheology of KZnF3, which include, (1) anomalous temperature dependence: above T/T 0.88, the creep rate first decreases with increase of temperature, but at T/T > 0.95 the m creep rate increases more than exponentially. (2) anomalously low stress component. —
0031-9201/84/$03.OO
© 1984 Elsevier Science Publishers By.
These two observations have important geophysical implications and are worth careful re-examination. I discuss first the stress dependence of strain rate. Figure 1 reproduces their fig. 8, but this time the origin is also included. Solid lines indicate their best fit lines, which they considered to show the linear dependence of strain rate on
-7
.
E-.
842 °C
S
3~ 726 20
10
—
,‘ ‘‘
~ I
I
I
‘~
MPa
Fig. 1. Linear plot of the creep rate versus applied stress including the origin. Data and solid lines are the same as fig. 8 .
.
.
of Poirier Ct al. (1983). Note that the solid lines do not pass the origin, indicating non-Newtonian (existence of threshold stress or non-linear rheology) behaviour.
272
stress a, i.e., Newtonian rheology. Figure 1 shows that these lines do not pass the origin. This means that either there are threshold stresses (i.e., Bingham body) or that the stress exponent n is > I (i.e., non-linear rheology). In either case, the rheology is non-Newtonian. (Note that the magnitude of the threshold stress is significantly larger than that associated with post-glacial rebound.) Their data are repbotted on a log a log diagram in Fig. 2. This shows that, when the data are compared with a relation a’1, the stress exponent n is > 1 and that the stress exponent at lower temperatures is significantly larger than those at higher temperatures. A similar trend is also shown in Fig. 1, i.e., the threshold stress increases with a decrease of temperature. From these trends it is suggested that the rheology is highly non-Newtonian at a lower temperature r:gime (T/Tm <0 85)
where anomalous temperature dependence of creep rate was not seen, although departure from Newtonian rheology is smaller in a high temperature regime. Such a temperature dependence of stress sensitivity suggests that several deformation mechanisms are simultaneously operating in this ternperature (and stress) regime. It is, therefore, dubi-
r~ r
—
0.9
—
1
0
\
•726
.~
0. 8 I
0779
4
m
10~
nzi.3
.
5-
\\
\\
1.1
.~
/
1031T
I
I
fQ I
~ MPa Fig. 2. Log— log plot of the creep rate versus applied stress. Data from fig. 8 of Poirier Ct al. [1983].
Fig. 3. Arrhenius plot of creep rate (In versus 1/T) and conductivity (in p versus 1/T). Data from figs. 10 and 11 of Poirier et al. [19831.Note the close relation between conductivity and creep rate. A broken line indicates creep rates extrapolated from a low temperature region where normal exponential temperature dependence of creep rate is assumed (t — exp( — E*/RT)). Note that creep rates in the anomalous regime (T/Tm> 0.88) are always smaller than these extrapolated values.
273
ous if the stress exponent, thus determined, has clear physical meaning or not. Clearly more data are needed to understand the stress sensitivity at this interesting but complex regime (T/Tm> 0.85). Next, I examine the temperature dependence of creep rate. Figure 3 reproduces their fig. 10. In Fig. 3, I also drew a broken line which indicates strain rates extrapolated from a lower temperature regime (T/Tm < 0.87) where I assumed a normal exponential temperature dependence of strain rate exp( E */RT)). Figure 3 shows that the creep rate in the high temperature regime (T/Tm > 0.88) is always smaller than would be expected from the extrapolation of data in the lower ternperature regime. In other words, what was found in the anomalous region is essentially hardening and not softening. Although rapid increase in strain rate is found at the highest temperature region (T/Tm> 0.95), strain rate does not exceed the value that would be expected from the normal region. Also plotted in Fig. 3 are the results of conductivity measurements. It is noted that anomalous creep behaviour occurs almost exactly at temperatures where anomalous electrical conduction is seen. It is concluded, therefore, that anomalous hardening occurs associated with solid electrolyte type behaviour. Poirier et al. (1983), on the other hand, emphasised the softening in their discussion of mechanisms and also of geophysical implications. —
—
2. On the mechanisms of anomalous rheology When the present interpretation, i.e., hardening associated with solid electrolyte type behaviour, is accepted, models for this anomalous behaviour have to be re-examined. In Poirier et al.’s (1983) model, hardening is attributed to thermally activated splitting of dislocations, which has no direct relation with solid electrolyte type behaviour, while softening is attributed to solid electrolyte type behaviour, However, as emphasised in section 1 (see Fig. 3), what was found experimentally is essentially hardening at temperatures where conductivity increases abnormally. Almost exact agreement of temperatures of the beginning of hardening and of
the abnormal increase in conductivity should be noted. I think that it is this feature that should be explained by any model of the anomalous temperature dependence of creep rate. Poirier et al.’s (1983) model is inconsistent with this essential point and, therefore, appears to be unreasonable. Inspection of Fig. 3 shows firstly that the creep rate is smaller than “normal” values (broken line) where abnormal increase in conductivity (solid electrolyte type behaviour) is seen, and secondly (more precisely) that the creep rate decreases significantly when conductivity increases rapidly but that creep rate begins to increase when conductivity becomes independent of temperature. The observed change in conductivity is considered to be owing to the change in point defect concentration (Oberschmidt and Lazarus, 1979), namely, concentration of point defects responsible for electrical conduction increases rapidly in region II of Fig. 3, but their concentration decreases (as a result of mutual interaction) in region I. If one accepts this model for electrical conduction it is tempting to suggest that dislocation-point defect interaction is responsible for the observed anomabus creep behaviour.
3. On the geophysical implications Based on their experimental result, Poirier et al. (1983) discussed geophysical implications: “(1) the lower mantle would flow by dislocation creep with Newtonian viscosity” and “(2) the viscosity of the lower mantle would not increase with depth and could even decrease: the existence of an asthenosphere at the bottom of the mantle is a distinct possibility”. These arguments depend, among others, on the assumption that solid electrolyte type behaviour occurs at the lower mantle. A recent estimate of the melting temperature of perovskite MgSiO3 (Ohtani, 1983) showed that T/Tm 0.5 in most of the lower mantle. Solid electrolyte type behaviour in fluoperovskites is observed at T/Tm > 0.9 (O’Keefe and Bovin, 1979; Poirier et al., 1983). Although the estimation of homologous temperature (T/ Tm) in the lower mantle may have some uncertainties, such a high homologous temperature appears unlikely, because —
274
such a high homologous temperature of one phase would significantly exceed the solidus of a real multi-component system in the Earth and mantle rock would be extensively molten at such a high temperature. Therefore, to have solid electrolyte type behaviour in the lower mantle, it would be necessary that solid electrolyte behaviour occurs at significantly lower homologous temperatures in the lower mantle than found in these experiments. Although it may not be impossible to have such a situation, possibly owing to the decrease in transition homologous temperature of solid electrolyte behaviour with pressure (and also with the incorporation of aliovalent impurity ions), no experimental data are available for perovskites to test the above suggestions. It is clearly necessary to do some high pressure experiments before any extrapolation to the Earth can be made. It should be noted that, even if one assumes that solid electrolyte behaviour occurs in the lower mantle, the geophysical implications that one would get can be quite different from Poirier et al.’s (1983). I show that what was observed by their experiments is hardening associated with solid electrolyte behaviour. Therefore, if one accepts the occurrence of solid electrolyte behaviour in the lower mantle, a reasonable conclusion would be the existence of lithosphere (high viscosity) rather than asthenosphere in the lower mantle, In summary, although Poirier et al.’s (1983) experiments have revealed interesting rheological behaviour of KZnF3, some of their interpretations of anomalous behaviour may not be justified. In particular, their interpretation that KZnF3 shows anomalous weakening associated with solid elec-
trolyte behaviour appears misleading. If so, there would be no experimental basis to support their model of anomalous creep behaviour, and their argument that the lower mantle may have low (Newtonian) viscosity would not be justified by their experimental results.
References Oberschimdt, J.M. and Lazarus, D., 1979. Activation volumes
of some superionic conductors with the fluorite structure. In: Vashista, Mundy, Shenoy (Editors), Fast Ion Transport in Solids. Elsevier, North Holland, pp. 691—694. Ohtani, E., 1983. Melting temperature distribution in the lower mantle. Phys. Earth Planet. Inter., 33: 12—25. O’Keefe, M. and Bovin, JO., 1979. Solid electrolyte behavior of
NaMgF
3.
Geophysical
implications.
Science,
206:
599—600. Poirier, J.P., Peyronneau, J., Gesland, J.Y. and Brebec, G., 1983. Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3. Phys. Earth Planet. Inter., 32: 273—287.
Note added in proof I thank Dr. Karato for sparing me the trouble of correcting a slight mistake: n is indeed equal to 1.3, not to 1. This correction has no serious consequences. As to Dr. Karato’s reinterpretation of our experiments, we believe such interpretation has no objective basis, and therefore feel that we are under no obligation to rebut what we consider to be mere opinion. J.P. Poirier (Paris, France)
271
Comment
“Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3” S. Karato Research School ofEarth Sciences, The A ustralian National University, Canberra 2601, A. C. T. (Australia) (Received October 4, 1983; revision accepted March 5, 1984)
Karato, S., 1984. “Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3”—comment. Phys. Earth Planet. Inter., 34: 271 —274.
In a recent paper, Poirier et al. (1983) tried to shed some light on the rheology of the lower mantle by the experimental study of creep (and electrical conductivity) of perovskite KZnF3 as an analogue of MgSiO3 perovskite. This pioneering work contained a number of interesting observations, including the discovery of anomalous creep behaviour associated with solid electrolyte type behaviour near the melting point. Unfortunately, however, some of their interpretations on anomabus behaviour appear unreasonable and are worth re-examination in the essential aspects. In the following, I first examine their experimental results on creep, then discuss their model on the mechanisms of anomalous creep behaviour, and finally some comments will be given on their speculations on the rheology of the lower mantle.
1. Re-examination of experimental results on creep Poirier et al. (1983) made interesting observations concerning the rheology of KZnF3, which include, (1) anomalous temperature dependence: above T/T 0.88, the creep rate first decreases with increase of temperature, but at T/T > 0.95 the m creep rate increases more than exponentially. (2) anomalously low stress component. —
0031-9201/84/$03.OO
© 1984 Elsevier Science Publishers By.
These two observations have important geophysical implications and are worth careful re-examination. I discuss first the stress dependence of strain rate. Figure 1 reproduces their fig. 8, but this time the origin is also included. Solid lines indicate their best fit lines, which they considered to show the linear dependence of strain rate on
-7
.
E-.
842 °C
S
3~ 726 20
10
—
,‘ ‘‘
~ I
I
I
‘~
MPa
Fig. 1. Linear plot of the creep rate versus applied stress including the origin. Data and solid lines are the same as fig. 8 .
.
.
of Poirier Ct al. (1983). Note that the solid lines do not pass the origin, indicating non-Newtonian (existence of threshold stress or non-linear rheology) behaviour.
272
stress a, i.e., Newtonian rheology. Figure 1 shows that these lines do not pass the origin. This means that either there are threshold stresses (i.e., Bingham body) or that the stress exponent n is > I (i.e., non-linear rheology). In either case, the rheology is non-Newtonian. (Note that the magnitude of the threshold stress is significantly larger than that associated with post-glacial rebound.) Their data are repbotted on a log a log diagram in Fig. 2. This shows that, when the data are compared with a relation a’1, the stress exponent n is > 1 and that the stress exponent at lower temperatures is significantly larger than those at higher temperatures. A similar trend is also shown in Fig. 1, i.e., the threshold stress increases with a decrease of temperature. From these trends it is suggested that the rheology is highly non-Newtonian at a lower temperature r:gime (T/Tm <0 85)
where anomalous temperature dependence of creep rate was not seen, although departure from Newtonian rheology is smaller in a high temperature regime. Such a temperature dependence of stress sensitivity suggests that several deformation mechanisms are simultaneously operating in this ternperature (and stress) regime. It is, therefore, dubi-
r~ r
—
0.9
—
1
0
\
•726
.~
0. 8 I
0779
4
m
10~
nzi.3
.
5-
\\
\\
1.1
.~
/
1031T
I
I
fQ I
~ MPa Fig. 2. Log— log plot of the creep rate versus applied stress. Data from fig. 8 of Poirier Ct al. [1983].
Fig. 3. Arrhenius plot of creep rate (In versus 1/T) and conductivity (in p versus 1/T). Data from figs. 10 and 11 of Poirier et al. [19831.Note the close relation between conductivity and creep rate. A broken line indicates creep rates extrapolated from a low temperature region where normal exponential temperature dependence of creep rate is assumed (t — exp( — E*/RT)). Note that creep rates in the anomalous regime (T/Tm> 0.88) are always smaller than these extrapolated values.
273
ous if the stress exponent, thus determined, has clear physical meaning or not. Clearly more data are needed to understand the stress sensitivity at this interesting but complex regime (T/Tm> 0.85). Next, I examine the temperature dependence of creep rate. Figure 3 reproduces their fig. 10. In Fig. 3, I also drew a broken line which indicates strain rates extrapolated from a lower temperature regime (T/Tm < 0.87) where I assumed a normal exponential temperature dependence of strain rate exp( E */RT)). Figure 3 shows that the creep rate in the high temperature regime (T/Tm > 0.88) is always smaller than would be expected from the extrapolation of data in the lower ternperature regime. In other words, what was found in the anomalous region is essentially hardening and not softening. Although rapid increase in strain rate is found at the highest temperature region (T/Tm> 0.95), strain rate does not exceed the value that would be expected from the normal region. Also plotted in Fig. 3 are the results of conductivity measurements. It is noted that anomalous creep behaviour occurs almost exactly at temperatures where anomalous electrical conduction is seen. It is concluded, therefore, that anomalous hardening occurs associated with solid electrolyte type behaviour. Poirier et al. (1983), on the other hand, emphasised the softening in their discussion of mechanisms and also of geophysical implications. —
—
2. On the mechanisms of anomalous rheology When the present interpretation, i.e., hardening associated with solid electrolyte type behaviour, is accepted, models for this anomalous behaviour have to be re-examined. In Poirier et al.’s (1983) model, hardening is attributed to thermally activated splitting of dislocations, which has no direct relation with solid electrolyte type behaviour, while softening is attributed to solid electrolyte type behaviour, However, as emphasised in section 1 (see Fig. 3), what was found experimentally is essentially hardening at temperatures where conductivity increases abnormally. Almost exact agreement of temperatures of the beginning of hardening and of
the abnormal increase in conductivity should be noted. I think that it is this feature that should be explained by any model of the anomalous temperature dependence of creep rate. Poirier et al.’s (1983) model is inconsistent with this essential point and, therefore, appears to be unreasonable. Inspection of Fig. 3 shows firstly that the creep rate is smaller than “normal” values (broken line) where abnormal increase in conductivity (solid electrolyte type behaviour) is seen, and secondly (more precisely) that the creep rate decreases significantly when conductivity increases rapidly but that creep rate begins to increase when conductivity becomes independent of temperature. The observed change in conductivity is considered to be owing to the change in point defect concentration (Oberschmidt and Lazarus, 1979), namely, concentration of point defects responsible for electrical conduction increases rapidly in region II of Fig. 3, but their concentration decreases (as a result of mutual interaction) in region I. If one accepts this model for electrical conduction it is tempting to suggest that dislocation-point defect interaction is responsible for the observed anomabus creep behaviour.
3. On the geophysical implications Based on their experimental result, Poirier et al. (1983) discussed geophysical implications: “(1) the lower mantle would flow by dislocation creep with Newtonian viscosity” and “(2) the viscosity of the lower mantle would not increase with depth and could even decrease: the existence of an asthenosphere at the bottom of the mantle is a distinct possibility”. These arguments depend, among others, on the assumption that solid electrolyte type behaviour occurs at the lower mantle. A recent estimate of the melting temperature of perovskite MgSiO3 (Ohtani, 1983) showed that T/Tm 0.5 in most of the lower mantle. Solid electrolyte type behaviour in fluoperovskites is observed at T/Tm > 0.9 (O’Keefe and Bovin, 1979; Poirier et al., 1983). Although the estimation of homologous temperature (T/ Tm) in the lower mantle may have some uncertainties, such a high homologous temperature appears unlikely, because —
274
such a high homologous temperature of one phase would significantly exceed the solidus of a real multi-component system in the Earth and mantle rock would be extensively molten at such a high temperature. Therefore, to have solid electrolyte type behaviour in the lower mantle, it would be necessary that solid electrolyte behaviour occurs at significantly lower homologous temperatures in the lower mantle than found in these experiments. Although it may not be impossible to have such a situation, possibly owing to the decrease in transition homologous temperature of solid electrolyte behaviour with pressure (and also with the incorporation of aliovalent impurity ions), no experimental data are available for perovskites to test the above suggestions. It is clearly necessary to do some high pressure experiments before any extrapolation to the Earth can be made. It should be noted that, even if one assumes that solid electrolyte behaviour occurs in the lower mantle, the geophysical implications that one would get can be quite different from Poirier et al.’s (1983). I show that what was observed by their experiments is hardening associated with solid electrolyte behaviour. Therefore, if one accepts the occurrence of solid electrolyte behaviour in the lower mantle, a reasonable conclusion would be the existence of lithosphere (high viscosity) rather than asthenosphere in the lower mantle, In summary, although Poirier et al.’s (1983) experiments have revealed interesting rheological behaviour of KZnF3, some of their interpretations of anomalous behaviour may not be justified. In particular, their interpretation that KZnF3 shows anomalous weakening associated with solid elec-
trolyte behaviour appears misleading. If so, there would be no experimental basis to support their model of anomalous creep behaviour, and their argument that the lower mantle may have low (Newtonian) viscosity would not be justified by their experimental results.
References Oberschimdt, J.M. and Lazarus, D., 1979. Activation volumes
of some superionic conductors with the fluorite structure. In: Vashista, Mundy, Shenoy (Editors), Fast Ion Transport in Solids. Elsevier, North Holland, pp. 691—694. Ohtani, E., 1983. Melting temperature distribution in the lower mantle. Phys. Earth Planet. Inter., 33: 12—25. O’Keefe, M. and Bovin, JO., 1979. Solid electrolyte behavior of
NaMgF
3.
Geophysical
implications.
Science,
206:
599—600. Poirier, J.P., Peyronneau, J., Gesland, J.Y. and Brebec, G., 1983. Viscosity and conductivity of the lower mantle; an experimental study on a MgSiO3 perovskite analogue: KZnF3. Phys. Earth Planet. Inter., 32: 273—287.
Note added in proof I thank Dr. Karato for sparing me the trouble of correcting a slight mistake: n is indeed equal to 1.3, not to 1. This correction has no serious consequences. As to Dr. Karato’s reinterpretation of our experiments, we believe such interpretation has no objective basis, and therefore feel that we are under no obligation to rebut what we consider to be mere opinion. J.P. Poirier (Paris, France)