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Possible isotope effect on Frenkel defect production in ionic crystals
Volume 46A, number 6
PHYSICS LETTERS
28 January 1974
POSSIBLE ISOTOPE EFFECT ON FRENKEL DEFECT PROD UCTION IN IONIC CRYSTALS F.J. KELLER Clemson University, Clemson, South Carolina 29631, USA Received 23 November 1973 An argument is given for the possibility that differing isotope masses for anions in ionic crystals cause a sizeable effect in defect production.
One of the principal requirements for creating a Frenkel pair at low temperatures in ionic crystals according to the model that is presently accepted [l—5] is that the distribution of kinetic energy between the two anions upon electron-VK center recombination be asymmetric. One way for this asymmetry to come about is for the ions to have different masses. The possibility exists that mass differences between the anions due to the natural abundance of isotopes may be an important feature of defect production. This possibility has so far been neglected in almost all experimental and theoretical investigations, A cursory look at the distribution of kinetic energy due to mass differences in isotopes leads one to believe this neglection to be valid. The largest effect would be expected in KC1 where the masses if the anion isotopes are 35 and 37. In a two-body explosion with this mass ratio the body with the lighter mass receives 51.4% of the kinetic energy; a number that is not impressively different from 50%. However, if the VK center involved in the recombination were CIBr rather than Cli, then the lighter anion receives 69% of the energy. An experiment performed by Keller and Patten [6J reveals data relating to this question. They found the electron-ClBr recombination to be a factor of 21 more efficient at creating the H centers that electronCl~recombination. The reason the electron-C1Br recombination is so much more efficient may be partly due to effects other than the mass difference. Two effects immediately come to mind: 1) the energy available in the C1Br2 excited state is different from the excited state, and 2) the lattice interaction of the ClBr2 will be different from that of the C1~due to the bromine being squeezed in the KCI lattice. -
Since the electron-C1Br recombination is over a factor of 20 more efficient, let us, as a first approximation, neglect these effects and concentrate on mass differences only. Consider the relationship between the efficiency for defect production and the fraction of kinetic energy given the lighter ion upon electron-VK center recombination. To find such a relationship would involve a sophisticated calculation so, instead, let us simplify the situation by neglecting the rest of the lattice and consider the relationship between the efficiency for defect production and the fraction of kinetic energy given the lighter ion upon explosion of the two ions in empty space. This relationship is surely a monotonically increasing function. Two data points are available from the experiment discussed above: one for C1Br2 and one for Cl~.The latter constitutes a mixture of~-(37Cl 37C1)2, (~5Cl 35C1)2, and ~ (35 Cl 37Cl)2. If one assumes a linear relationship between the efficiency for defect production and the fraction of the energy given the light ion in the twobody explosion, then the efficiency for mixed isotopes, [(35C1 37C1)2—] is a factor of three greater than that for identical isotopes, [(37Cl 37C1)2 and (35Cl ~5Cl)~J. There is no justification for making a linear assumption for this function other than knowing it is monotonically increasing and only two data points are available. However, the point of this paper is that the possibiity exists that this isotope effect may be much larger than a cursory calculation indicates. Indeed, it may be even larger than the simple argument above indicates. If this effect is sizeable, then isotopically pure ionic crystals will be found to be more resistant to radiation damage at low temperatures than those with natural isotopic abundance. 393 -
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Volume 46A, number 6
PHYSICS LETTERS
The author is indebted to R.B. Murray and R.F. Wood for helpful discussions.
References [1] D. Pooley, Solid State Commun. 3(1965)241; Proc. Phys. Soc. Lond. 87 (1966) 245, 257.
394
28 January 1974
[21 H.N. Hersh, Phys. Rev. 148 (1966) 928. [3j I. McC. Torrens and L.T. Chadderton, Phys. Rev. 159 (1967) 671. [4] J.1-1. Crawford, Jr.. Adv. Phys. 17 (1968) 93. [51 R. Smoluchowski, OW. Lazareth, R.D. Hatcher and G.J. Dienes.Phys. Rev. Lett. 27(1971)1288. [6] F.J. Keller and F.W. Patten, Solid State Comniun. 7 (1969) 1603.
PHYSICS LETTERS
28 January 1974
POSSIBLE ISOTOPE EFFECT ON FRENKEL DEFECT PROD UCTION IN IONIC CRYSTALS F.J. KELLER Clemson University, Clemson, South Carolina 29631, USA Received 23 November 1973 An argument is given for the possibility that differing isotope masses for anions in ionic crystals cause a sizeable effect in defect production.
One of the principal requirements for creating a Frenkel pair at low temperatures in ionic crystals according to the model that is presently accepted [l—5] is that the distribution of kinetic energy between the two anions upon electron-VK center recombination be asymmetric. One way for this asymmetry to come about is for the ions to have different masses. The possibility exists that mass differences between the anions due to the natural abundance of isotopes may be an important feature of defect production. This possibility has so far been neglected in almost all experimental and theoretical investigations, A cursory look at the distribution of kinetic energy due to mass differences in isotopes leads one to believe this neglection to be valid. The largest effect would be expected in KC1 where the masses if the anion isotopes are 35 and 37. In a two-body explosion with this mass ratio the body with the lighter mass receives 51.4% of the kinetic energy; a number that is not impressively different from 50%. However, if the VK center involved in the recombination were CIBr rather than Cli, then the lighter anion receives 69% of the energy. An experiment performed by Keller and Patten [6J reveals data relating to this question. They found the electron-ClBr recombination to be a factor of 21 more efficient at creating the H centers that electronCl~recombination. The reason the electron-C1Br recombination is so much more efficient may be partly due to effects other than the mass difference. Two effects immediately come to mind: 1) the energy available in the C1Br2 excited state is different from the excited state, and 2) the lattice interaction of the ClBr2 will be different from that of the C1~due to the bromine being squeezed in the KCI lattice. -
Since the electron-C1Br recombination is over a factor of 20 more efficient, let us, as a first approximation, neglect these effects and concentrate on mass differences only. Consider the relationship between the efficiency for defect production and the fraction of kinetic energy given the lighter ion upon electron-VK center recombination. To find such a relationship would involve a sophisticated calculation so, instead, let us simplify the situation by neglecting the rest of the lattice and consider the relationship between the efficiency for defect production and the fraction of kinetic energy given the lighter ion upon explosion of the two ions in empty space. This relationship is surely a monotonically increasing function. Two data points are available from the experiment discussed above: one for C1Br2 and one for Cl~.The latter constitutes a mixture of~-(37Cl 37C1)2, (~5Cl 35C1)2, and ~ (35 Cl 37Cl)2. If one assumes a linear relationship between the efficiency for defect production and the fraction of the energy given the light ion in the twobody explosion, then the efficiency for mixed isotopes, [(35C1 37C1)2—] is a factor of three greater than that for identical isotopes, [(37Cl 37C1)2 and (35Cl ~5Cl)~J. There is no justification for making a linear assumption for this function other than knowing it is monotonically increasing and only two data points are available. However, the point of this paper is that the possibiity exists that this isotope effect may be much larger than a cursory calculation indicates. Indeed, it may be even larger than the simple argument above indicates. If this effect is sizeable, then isotopically pure ionic crystals will be found to be more resistant to radiation damage at low temperatures than those with natural isotopic abundance. 393 -
~-
—
—
,
—
-.-
Volume 46A, number 6
PHYSICS LETTERS
The author is indebted to R.B. Murray and R.F. Wood for helpful discussions.
References [1] D. Pooley, Solid State Commun. 3(1965)241; Proc. Phys. Soc. Lond. 87 (1966) 245, 257.
394
28 January 1974
[21 H.N. Hersh, Phys. Rev. 148 (1966) 928. [3j I. McC. Torrens and L.T. Chadderton, Phys. Rev. 159 (1967) 671. [4] J.1-1. Crawford, Jr.. Adv. Phys. 17 (1968) 93. [51 R. Smoluchowski, OW. Lazareth, R.D. Hatcher and G.J. Dienes.Phys. Rev. Lett. 27(1971)1288. [6] F.J. Keller and F.W. Patten, Solid State Comniun. 7 (1969) 1603.