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Comment on a possible correlation between Tc and the number of stable isotopes of superconducting elements
Solid State Communications,VoL 17, pp. 137—138, 1975.
Pergarnon Press.
Printed in Great Britain
COMMENT ON A POSSIBLE CORRELATION BETWEEN T~,AND THE NUMBER OF STABLE ISOTOPES OF SUPERCONDUCTING ELEMENTS T. Ottinsen and H. Parr Institute of Physics, University of Oslo, Blindern, Oslo 3, Norway
(Received 5 March 1975 by 0. V. Lounasmaa)
Recently a correlation between T~and the number of naturally occurring isotopes N of the superconducting elements has been claimed. We propose that this merely reflects the connection between 7, and the valence: odd valence means odd Z and few stable isotopes. I
IN A RECENT communication,’ a weak empirical correlation between the superconducting transition ternperature T~ and the number of naturally occurring isotopes N has been obtained. In a plot of T~vs N, the elements seem to divide into two branches in which T~ decreases with increasing N. There are two possible reasons for this correlation:
I
i
-r
• Transition metals II
0
8
Nontronsition metals
°
7.
0
0
S
6
•
(I) It could be an impurity effect, whereby a mixture of many isotopes would have a lower 7~.. (2) There might be a correlation between N and the valence. This could lead to a correlation between
0
0
•
‘-s’ ~
0
8
0
0 0
:
0
2
.
7,andN.
•
S
$
0
The impurity effect hypothesis is an unlikely one. Even at 99.5 per cent isotopic purity, the isotope effect experiments have never yielded a dependence of T~ upon the mass distribution, only upon the mean isotopic mass.24
o
1
2
I
I
3
5
N
$0
6
I
I
I
7
8
9
10
—~
FIG. 1. 7 for superconducting elements vs N, number of naturally occurring isotopes. High-pressure and metastable phases are included. The elements are grouped as transition or non-transition metals. Be, Cs, and Ba, not typical of any of the groups have been omitted. Two reported high-pressure phases of Pb and Sn not included in reference 1, have been added.
Turning to the second hypothesis, we observe that even-Z nuclei tend to have many stable isotopes, while odd-Z nuclei usually have one or two. For the superconducting elements, the average number of stable isotopes and the RMS deviation are N = 5.8 ±2.0 for Z even and N = 1.5 ±0.5 for Z odd. it is an experimental fact that most odd-valence transition metals have a relatively high T~,5while even-valence trans. ition metals have a low T~.On the other hand, most of the even-valence non-transition metals have a hIgh
T~, while the odd-valence non-transition elements show aodd large in valence 7~,.Sincetoodd Z, spread and even evenvalence Z, thiscorresponds should lead to to a correlation between T~and N. In Fig 1, we have reproduced the plot of T~vs N, distinguishing between transition and non-transition metals. For the transition metals, T~clearly decreases with N. The “upper branch” 137
138
CORRELATION BETWEEN T0 AND THE NUMBER OF STABLE ISOTOPES
(for N ~ 3) in the figure in reference 1 consists exclusively of even-valence non-transition elements. Thus the two branches in this figure merely reflect the connection explained above between 7~and valence. The apparent downward slope in the “upper branch” is probably accidental. Of course, the question of why certain groups of elements have high transition temperatures, still remains. It seems that the electronic properties and the
Vol. 17, No.2
crystal structure are the important factors. From a theoretical point of view, it is hard to imagine how the transition temperature could be related to the number of isotopes in any fundamental way. We conclude that there is at present no data pointing to any fundamental relation between T~and the number of isotopes of superconducting elements. The weak correlation that exists in all probability just reflects the strong connection between 7’~,and the valence.
REFERENCES 1.
WANG F.E. and MITCHELL MA., Solid State Commun. 15,867(1974).
2. 3.
SHAW R.W., MAPOTHER D.E. and HOPKINS D.C.,Phys. Rev. 121,86(1961). FASSNACHT R.E. and DILLINGER J.R.,Phys. Lett. 28A, 741 (1969).
4. 5.
PARRH.,Phys. Rev. B1O,4572 (1974). See for instance Cli. 13 in Superconductivity (Edited by PARKS R.D.) Marcel Dekker, New York (1969).
Pergarnon Press.
Printed in Great Britain
COMMENT ON A POSSIBLE CORRELATION BETWEEN T~,AND THE NUMBER OF STABLE ISOTOPES OF SUPERCONDUCTING ELEMENTS T. Ottinsen and H. Parr Institute of Physics, University of Oslo, Blindern, Oslo 3, Norway
(Received 5 March 1975 by 0. V. Lounasmaa)
Recently a correlation between T~and the number of naturally occurring isotopes N of the superconducting elements has been claimed. We propose that this merely reflects the connection between 7, and the valence: odd valence means odd Z and few stable isotopes. I
IN A RECENT communication,’ a weak empirical correlation between the superconducting transition ternperature T~ and the number of naturally occurring isotopes N has been obtained. In a plot of T~vs N, the elements seem to divide into two branches in which T~ decreases with increasing N. There are two possible reasons for this correlation:
I
i
-r
• Transition metals II
0
8
Nontronsition metals
°
7.
0
0
S
6
•
(I) It could be an impurity effect, whereby a mixture of many isotopes would have a lower 7~.. (2) There might be a correlation between N and the valence. This could lead to a correlation between
0
0
•
‘-s’ ~
0
8
0
0 0
:
0
2
.
7,andN.
•
S
$
0
The impurity effect hypothesis is an unlikely one. Even at 99.5 per cent isotopic purity, the isotope effect experiments have never yielded a dependence of T~ upon the mass distribution, only upon the mean isotopic mass.24
o
1
2
I
I
3
5
N
$0
6
I
I
I
7
8
9
10
—~
FIG. 1. 7 for superconducting elements vs N, number of naturally occurring isotopes. High-pressure and metastable phases are included. The elements are grouped as transition or non-transition metals. Be, Cs, and Ba, not typical of any of the groups have been omitted. Two reported high-pressure phases of Pb and Sn not included in reference 1, have been added.
Turning to the second hypothesis, we observe that even-Z nuclei tend to have many stable isotopes, while odd-Z nuclei usually have one or two. For the superconducting elements, the average number of stable isotopes and the RMS deviation are N = 5.8 ±2.0 for Z even and N = 1.5 ±0.5 for Z odd. it is an experimental fact that most odd-valence transition metals have a relatively high T~,5while even-valence trans. ition metals have a low T~.On the other hand, most of the even-valence non-transition metals have a hIgh
T~, while the odd-valence non-transition elements show aodd large in valence 7~,.Sincetoodd Z, spread and even evenvalence Z, thiscorresponds should lead to to a correlation between T~and N. In Fig 1, we have reproduced the plot of T~vs N, distinguishing between transition and non-transition metals. For the transition metals, T~clearly decreases with N. The “upper branch” 137
138
CORRELATION BETWEEN T0 AND THE NUMBER OF STABLE ISOTOPES
(for N ~ 3) in the figure in reference 1 consists exclusively of even-valence non-transition elements. Thus the two branches in this figure merely reflect the connection explained above between 7~and valence. The apparent downward slope in the “upper branch” is probably accidental. Of course, the question of why certain groups of elements have high transition temperatures, still remains. It seems that the electronic properties and the
Vol. 17, No.2
crystal structure are the important factors. From a theoretical point of view, it is hard to imagine how the transition temperature could be related to the number of isotopes in any fundamental way. We conclude that there is at present no data pointing to any fundamental relation between T~and the number of isotopes of superconducting elements. The weak correlation that exists in all probability just reflects the strong connection between 7’~,and the valence.
REFERENCES 1.
WANG F.E. and MITCHELL MA., Solid State Commun. 15,867(1974).
2. 3.
SHAW R.W., MAPOTHER D.E. and HOPKINS D.C.,Phys. Rev. 121,86(1961). FASSNACHT R.E. and DILLINGER J.R.,Phys. Lett. 28A, 741 (1969).
4. 5.
PARRH.,Phys. Rev. B1O,4572 (1974). See for instance Cli. 13 in Superconductivity (Edited by PARKS R.D.) Marcel Dekker, New York (1969).