- Email: [email protected]
Reply to the comments by tanabe on “the compensation effect on the diffusion constants of hydrogen in metals”
Journal of Nuclear Materials182 (1991) 274-2’76
214
Nor~-~o~l~Rd
Letter to the Editors
Reply to the comments by Tanabe on “The compensation on the diffusion constants of hydrogen in metals” Kuniaki
Watanabe,
Kan Ashida
and Masao
effect
Matsuyama
Hydrogen Isotope Research Center, royama University, Gofuku 3190, Tuyama 930, Japan Received22 October 1990; accepted 29 October 1990
The essential points of Tanabe’s comments on our previous paper [l] are: (1) A set of unique D,, and Ed should exist for the diffusion constants of hydrogen in a given material and/or substanee. Consequently, the compensation effect on the diffusion constants of hydrogen in a given metal is very likely spurious. (2) On the contrary, the compensation effect should appear among different materials, although the mechanisms are an open question. In this letter, we will briefly discuss these two points. With respect to the first point, it is quite natural to expect an “intrinsic diffusion constant” (a set of De and Ed) for a given diffusion mechanism in an ideal matrix for a given material. Unfortunately, the diffusion constants of hydrogen were determined using samples which were very often prepared and/or treated in different conditions. One then has the problem that the experimental data tend to differ considerably from each other. In some cases, however, one observes a relation between the logarithms of the pre-exponential factors and the activation energies for the different diffusion constants. Everett has already pointed out that spurious compensation effects would appear owing to erroneous measurements and/or the errors which Tanabe described as statistical [2]. Nevertheless, the presence of the compensation effect is widely accepted for many chemical reactions as a result of the linear Gibbs energy reIatio~~ps and/or other reasons [3,4]. Examples are seen for many heterogeneous catalytic reactions over a series of related catalysts [4]: The catalysts may be a series of different metals, or a given metal or metal oxide treated in various ways, or a series of catalysts of increasing promoter content [4,5]. On analogy with this fact, we can expect the appearance of compensation effects on the diffusion constants of hydrogen for rele-
vant materials and have observed these effects for many metals [l], alloys [6,7] and oxides [8]. It appears that there is no plausible reason to refute the compensation effect on the diffusion constants of hydrogen in a given metal. In fact, we observed the compensation effects on the hydrogen diffusion constants for o-Fe, Al and C as well as for Ni, Pd and Cu [l], although for the latter three Tanabe denies the presence of compensation effects. Namely, with respect to Ni, Pd, and Cu, Tanabe asserts that the scatters of the data are considerably small in extent. In addition, it is also pointed out that no clear correlation is observed between log{ Da) and Ed for Ni, if reference No.15 in the previous paper [l] is lacking. To look at this point, we show, as an example, the Arrhenius plots of the diffusion constants of hydrogen for Ni in fig. 1, where for simplicity only several reference data cited in the previous paper [l] have been shown. The more complete sets of data can be seen in the literature [9]. The bold dotted lines in the figure are the so-called best values for Ni, evaluated by Valkl and Alefeid 191. One can see that most of the data lie very close to the bold dotted lines, suggesting it would seem that the deviations from them are due to errors. Looking at the indi~dual data, however, one can very often see considerably good linearity of the Arrhenius plots of the diffusion constants in each paper. As an example, we show the comparison between the best value and the observations by Hill and Johnson [lo] in fig. 2. The differences between the observations and the best value appear relatively large in decreasing temperature. Suppose that the desorption of hydrogen had been measured and found to obey a semi-infinite diffusion model, the (imaginary) desorption curve from which investigators determined the diffusion constant at 653 K, which was the lowest experimental temperature, would clearly
002%3115/91/$03.50 0 1991 - Ekevier Science PublishersB.V. (North-Holland)
275
K. Watanabe et al. J Reply to comments by T. Tanabe 2000 -4.0
I
300
500
1000
I”’ ’ I’ ’ ’ ’ ‘\_
I
/K
I
I
1.0
.
l* \* ’ - \ “,
\ \.
I
I
I
I
semi-infinite diffusion model
= -6.0 ln
. N
i? E -8.0
diffusion constants of hydrogen isotopes in Ni
f -10.0
-
I 0
I
I
I
1.0
I
I
2.0
I
I
I 4.0
3.0
1000/T Fig.1. Arrhenius plots of the diffusion constants of hydrogen isotopes for Ni. The so-called best values are shown by the bold dotted lines.
differ from the desorption curve which gave the best value at 653 K. The clear difference between them can be seen in fig. 3. It should also be mentioned here that only the reference No. 15 among 18 references for Ni
cited in our previous paper [l] used electrochemical techniques to determine the diffusion constants [lo],
1200 1000
800
/K
Hill and Johnson
1.0
1.5
1000/T Fig. 2. Comparison of the Arrhenius plots of the diffusion constants of hydrogen between the best value and the observations by Hill and Johnson [lo].
0’
I
I
I
I
I
I
Timejarbit. Fig. 3. Comparison between the imaginary desorption curves at 653 K which give the so-called best value and the value reported by Hill and Johnson [lo]: It was assumed that the desorption obeyed a semi-infinite diffusion model.
suggesting that the hydrogen concentrations and/or surface states differ considerably from the others. Aren’t those facts mentioned above suggesting that the individual data have their own importance? In other words, could their differences be attributed to the differences in individual sample characteristics? It is plausible to assume that the hydrogen diffusion constants depend on the sample characteristics, which might be due to the differences in preparation techniques and/or conditions, such as the defect and/or boundary structures, the presence of impurities, hydrogen wncentrations as well as the crystallographic and/or electronic structures of a given metal. The effect of the surface process should also be taken into account. Similar arguments would also be valid for Pd and Cu. From another viewpoint, it is interesting to note here that two different best values are evaluated for Ni above and below the Curie temperature (626 K), respectively. We wuld consider this fact too as an aspect of the compensation effect. As for Cu, one can find two sets of data which differ considerably from the socalled best value [ll]. Consequently, the case of Cu meets the similar situation as that of Ni mentioned above. Contrary to the above, the compensation effects for the former three materials, a-Fe, Al, and C, are evident: they can not be attributed to statistical errors. This is because the scatters of the experimental data are so clear in the Arrhenius plots ‘diagrams [9,12-151. Such
216
K. Watanabe et al. / Reply to comments by T. Tanabe
-6.0
0 0 I 0
I 20
I
I
40 Ed
I
I 60
I
I 80
lk;i/moll
Fig. 4. Plots of log(Q) versus Ed for various metals cited in our previouspaper [l]. that one cannot easily refute the presence of the compensation effects in a given metal. With respect to the second point in Tanabe’s comments, fig. 4 shows the sets of D,, and Ed plotted for various metals cited in the previous paper [l], although the data for carbon (graphite) and some data for the metals were excluded because they went beyond the scale of this figure. It is apparent that there is no clear relation between log( Do) and E,, for those materials. In addition, we should also take account of the diffusion constants for a variety of alloys and ceramic materials, which add more widely scattered points to this diagram. The different feature of this figure from fig. 3 in Tanabe’s comments lies in the fact that he principally accounts for Fe and ferric alloys, whereas we take a wider variety of metals into consideration. It is not surprising therefore, that no clear correlation is observed for a wide variety of different materials, as shown in fig. 4. A compensation effect in chemical reactions has been observed for a series of related reactions. Namely, for the compensation effect to arise, some basic properties should be held in common over a series of reactions. This is also expected to be true for the appearance of the compensation effect on the diffusion constants of hydrogen in materials. Namely, it could appear for a series of related metals, or a given metal treated and/or prepared in various ways, or a series of alloys. The significance of the compensation effect is merely that the Arrhenius plots of the rate constants for some reactions intersect each other at a point in the diagram
for relevant reaction systems. With respect to the diffusion constants of hydrogen for relevant materials, sets of log( D,,) and E,, are not usually found on a straight line but scatter appreciably about this line. It indicates that the Arrhenius plots of the diffusion constants intersect each other in a narrow zone, not a point, in the diagram. It is considered, however, to be a kind of compensation effect, although the tightness of the compensation seems rather loose in comparison with those for many chemical reactions. Nevertheless, one cannot refute the presence of the compensation effect on the diffusion constants of hydrogen for relevant materials and hence we cannot help being urged to explain and/or understand its mechanism(s). For this purpose, one has to examine further the compensation effects on hydrogen diffusion, in a wide variety of systems which, of course, should be carefully judged from experimental data. The appearance of the compensation effects implies a number of theoretical considerations, including the potential field in crystal lattice, the presence of defects and/or impurities acting as trapping sites as well as the presence of different diffusion channels, the effects of surface processes and so on.
References PI K. Watanabe, K. Ashida and M. Sonobe, J. Nucl. Mater. 173 (1990) 294. PI D.H. Everett, Trans. Farad. Sot. 46 (1950) 957. [31 K.J. Laidler, Chemical Kinetics, 3rd Edition (Harper and Row, New York, 1987) p. 209.
[41 G.C. Bond, Catalysis by Metals (Academic Press, New York, London, 1962) p. 140. of Adsorption and Catalysis (Academic Press, New York, London, 1970) p. 260. [61 Y. Yamanishi, T. Tanabe and S. Imoto, Trans. JIM 24 (1983) 49. 171 T. Tanabe, Y. Yamanishi and S. imoto, J. Nucl. Mater. 123 & 124 (1984) 1568. PI K. Watanabe, K. Ashida, M. Matsuyama and H. Miyake, submitted to J. Nucl. Mater. 191 J. Viilkl and G. Alefeld, Hydrogen in Metals, Fds. G. Alefeld and J. Valkl (Springer-Verlag, Berlin, Heidelberg, New York, 1978) p. 321. [lo] M.L. Hill and E.W. Johnson, Acta Metall. 3 (1955) 566. [ll] Y. Furuyama, T. Tanabe and S. Imoto, J. Japan. Inst. Metals 50 (1986) 688. [12] T. Tanabe, Y. Yamanishi and S. Imoto, Trans. JIM 25 (1984) 1. [13] M. Sonobe, S. Tada, S. Ikeno, K. Ashida and K. Watanabe, J. Nucl. Mater., in press. [14] T. Tanabe and Y. Watanabe, J. Nucl. Mater., in press. [15] K. Ashida and K. Watanabe, submitted to J. Nucl. Mater.
[51 A. Clark, The Theory
214
Nor~-~o~l~Rd
Letter to the Editors
Reply to the comments by Tanabe on “The compensation on the diffusion constants of hydrogen in metals” Kuniaki
Watanabe,
Kan Ashida
and Masao
effect
Matsuyama
Hydrogen Isotope Research Center, royama University, Gofuku 3190, Tuyama 930, Japan Received22 October 1990; accepted 29 October 1990
The essential points of Tanabe’s comments on our previous paper [l] are: (1) A set of unique D,, and Ed should exist for the diffusion constants of hydrogen in a given material and/or substanee. Consequently, the compensation effect on the diffusion constants of hydrogen in a given metal is very likely spurious. (2) On the contrary, the compensation effect should appear among different materials, although the mechanisms are an open question. In this letter, we will briefly discuss these two points. With respect to the first point, it is quite natural to expect an “intrinsic diffusion constant” (a set of De and Ed) for a given diffusion mechanism in an ideal matrix for a given material. Unfortunately, the diffusion constants of hydrogen were determined using samples which were very often prepared and/or treated in different conditions. One then has the problem that the experimental data tend to differ considerably from each other. In some cases, however, one observes a relation between the logarithms of the pre-exponential factors and the activation energies for the different diffusion constants. Everett has already pointed out that spurious compensation effects would appear owing to erroneous measurements and/or the errors which Tanabe described as statistical [2]. Nevertheless, the presence of the compensation effect is widely accepted for many chemical reactions as a result of the linear Gibbs energy reIatio~~ps and/or other reasons [3,4]. Examples are seen for many heterogeneous catalytic reactions over a series of related catalysts [4]: The catalysts may be a series of different metals, or a given metal or metal oxide treated in various ways, or a series of catalysts of increasing promoter content [4,5]. On analogy with this fact, we can expect the appearance of compensation effects on the diffusion constants of hydrogen for rele-
vant materials and have observed these effects for many metals [l], alloys [6,7] and oxides [8]. It appears that there is no plausible reason to refute the compensation effect on the diffusion constants of hydrogen in a given metal. In fact, we observed the compensation effects on the hydrogen diffusion constants for o-Fe, Al and C as well as for Ni, Pd and Cu [l], although for the latter three Tanabe denies the presence of compensation effects. Namely, with respect to Ni, Pd, and Cu, Tanabe asserts that the scatters of the data are considerably small in extent. In addition, it is also pointed out that no clear correlation is observed between log{ Da) and Ed for Ni, if reference No.15 in the previous paper [l] is lacking. To look at this point, we show, as an example, the Arrhenius plots of the diffusion constants of hydrogen for Ni in fig. 1, where for simplicity only several reference data cited in the previous paper [l] have been shown. The more complete sets of data can be seen in the literature [9]. The bold dotted lines in the figure are the so-called best values for Ni, evaluated by Valkl and Alefeid 191. One can see that most of the data lie very close to the bold dotted lines, suggesting it would seem that the deviations from them are due to errors. Looking at the indi~dual data, however, one can very often see considerably good linearity of the Arrhenius plots of the diffusion constants in each paper. As an example, we show the comparison between the best value and the observations by Hill and Johnson [lo] in fig. 2. The differences between the observations and the best value appear relatively large in decreasing temperature. Suppose that the desorption of hydrogen had been measured and found to obey a semi-infinite diffusion model, the (imaginary) desorption curve from which investigators determined the diffusion constant at 653 K, which was the lowest experimental temperature, would clearly
002%3115/91/$03.50 0 1991 - Ekevier Science PublishersB.V. (North-Holland)
275
K. Watanabe et al. J Reply to comments by T. Tanabe 2000 -4.0
I
300
500
1000
I”’ ’ I’ ’ ’ ’ ‘\_
I
/K
I
I
1.0
.
l* \* ’ - \ “,
\ \.
I
I
I
I
semi-infinite diffusion model
= -6.0 ln
. N
i? E -8.0
diffusion constants of hydrogen isotopes in Ni
f -10.0
-
I 0
I
I
I
1.0
I
I
2.0
I
I
I 4.0
3.0
1000/T Fig.1. Arrhenius plots of the diffusion constants of hydrogen isotopes for Ni. The so-called best values are shown by the bold dotted lines.
differ from the desorption curve which gave the best value at 653 K. The clear difference between them can be seen in fig. 3. It should also be mentioned here that only the reference No. 15 among 18 references for Ni
cited in our previous paper [l] used electrochemical techniques to determine the diffusion constants [lo],
1200 1000
800
/K
Hill and Johnson
1.0
1.5
1000/T Fig. 2. Comparison of the Arrhenius plots of the diffusion constants of hydrogen between the best value and the observations by Hill and Johnson [lo].
0’
I
I
I
I
I
I
Timejarbit. Fig. 3. Comparison between the imaginary desorption curves at 653 K which give the so-called best value and the value reported by Hill and Johnson [lo]: It was assumed that the desorption obeyed a semi-infinite diffusion model.
suggesting that the hydrogen concentrations and/or surface states differ considerably from the others. Aren’t those facts mentioned above suggesting that the individual data have their own importance? In other words, could their differences be attributed to the differences in individual sample characteristics? It is plausible to assume that the hydrogen diffusion constants depend on the sample characteristics, which might be due to the differences in preparation techniques and/or conditions, such as the defect and/or boundary structures, the presence of impurities, hydrogen wncentrations as well as the crystallographic and/or electronic structures of a given metal. The effect of the surface process should also be taken into account. Similar arguments would also be valid for Pd and Cu. From another viewpoint, it is interesting to note here that two different best values are evaluated for Ni above and below the Curie temperature (626 K), respectively. We wuld consider this fact too as an aspect of the compensation effect. As for Cu, one can find two sets of data which differ considerably from the socalled best value [ll]. Consequently, the case of Cu meets the similar situation as that of Ni mentioned above. Contrary to the above, the compensation effects for the former three materials, a-Fe, Al, and C, are evident: they can not be attributed to statistical errors. This is because the scatters of the experimental data are so clear in the Arrhenius plots ‘diagrams [9,12-151. Such
216
K. Watanabe et al. / Reply to comments by T. Tanabe
-6.0
0 0 I 0
I 20
I
I
40 Ed
I
I 60
I
I 80
lk;i/moll
Fig. 4. Plots of log(Q) versus Ed for various metals cited in our previouspaper [l]. that one cannot easily refute the presence of the compensation effects in a given metal. With respect to the second point in Tanabe’s comments, fig. 4 shows the sets of D,, and Ed plotted for various metals cited in the previous paper [l], although the data for carbon (graphite) and some data for the metals were excluded because they went beyond the scale of this figure. It is apparent that there is no clear relation between log( Do) and E,, for those materials. In addition, we should also take account of the diffusion constants for a variety of alloys and ceramic materials, which add more widely scattered points to this diagram. The different feature of this figure from fig. 3 in Tanabe’s comments lies in the fact that he principally accounts for Fe and ferric alloys, whereas we take a wider variety of metals into consideration. It is not surprising therefore, that no clear correlation is observed for a wide variety of different materials, as shown in fig. 4. A compensation effect in chemical reactions has been observed for a series of related reactions. Namely, for the compensation effect to arise, some basic properties should be held in common over a series of reactions. This is also expected to be true for the appearance of the compensation effect on the diffusion constants of hydrogen in materials. Namely, it could appear for a series of related metals, or a given metal treated and/or prepared in various ways, or a series of alloys. The significance of the compensation effect is merely that the Arrhenius plots of the rate constants for some reactions intersect each other at a point in the diagram
for relevant reaction systems. With respect to the diffusion constants of hydrogen for relevant materials, sets of log( D,,) and E,, are not usually found on a straight line but scatter appreciably about this line. It indicates that the Arrhenius plots of the diffusion constants intersect each other in a narrow zone, not a point, in the diagram. It is considered, however, to be a kind of compensation effect, although the tightness of the compensation seems rather loose in comparison with those for many chemical reactions. Nevertheless, one cannot refute the presence of the compensation effect on the diffusion constants of hydrogen for relevant materials and hence we cannot help being urged to explain and/or understand its mechanism(s). For this purpose, one has to examine further the compensation effects on hydrogen diffusion, in a wide variety of systems which, of course, should be carefully judged from experimental data. The appearance of the compensation effects implies a number of theoretical considerations, including the potential field in crystal lattice, the presence of defects and/or impurities acting as trapping sites as well as the presence of different diffusion channels, the effects of surface processes and so on.
References PI K. Watanabe, K. Ashida and M. Sonobe, J. Nucl. Mater. 173 (1990) 294. PI D.H. Everett, Trans. Farad. Sot. 46 (1950) 957. [31 K.J. Laidler, Chemical Kinetics, 3rd Edition (Harper and Row, New York, 1987) p. 209.
[41 G.C. Bond, Catalysis by Metals (Academic Press, New York, London, 1962) p. 140. of Adsorption and Catalysis (Academic Press, New York, London, 1970) p. 260. [61 Y. Yamanishi, T. Tanabe and S. Imoto, Trans. JIM 24 (1983) 49. 171 T. Tanabe, Y. Yamanishi and S. imoto, J. Nucl. Mater. 123 & 124 (1984) 1568. PI K. Watanabe, K. Ashida, M. Matsuyama and H. Miyake, submitted to J. Nucl. Mater. 191 J. Viilkl and G. Alefeld, Hydrogen in Metals, Fds. G. Alefeld and J. Valkl (Springer-Verlag, Berlin, Heidelberg, New York, 1978) p. 321. [lo] M.L. Hill and E.W. Johnson, Acta Metall. 3 (1955) 566. [ll] Y. Furuyama, T. Tanabe and S. Imoto, J. Japan. Inst. Metals 50 (1986) 688. [12] T. Tanabe, Y. Yamanishi and S. Imoto, Trans. JIM 25 (1984) 1. [13] M. Sonobe, S. Tada, S. Ikeno, K. Ashida and K. Watanabe, J. Nucl. Mater., in press. [14] T. Tanabe and Y. Watanabe, J. Nucl. Mater., in press. [15] K. Ashida and K. Watanabe, submitted to J. Nucl. Mater.
[51 A. Clark, The Theory