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Electron shake-off mechanism of the extended fine structure of X-ray absorption edges
Volume 41A, number 1
PHYSICS LETTERS
28 August 1972
ELECTRON SHAKE-OFF MECHANISM OF THE EXTENDED FINE STRUCTURE OF X-RAY ABSORPTION EDGES T. UNGAR Institute for General Physics, Eötvös University, Budapest, Hungary Received 19 April 1972 A new mechanism for the extended fine structure of X-ray absorption edges is suggested. Electron shake-off following photo-ionization produces a positive ion and the ejected electron makes a transition into an eigenstate of the potential corresponding to this ion.
The extended fine structure (EFS) appearing on the high energy side of an X-ray absorption edge has
the potential and a is its width. The range of extension of the eigenstates is somewhat smaller than V0
been studied for almost fourty years. There were two basically different mechanisms suggested to explain the EFS. The long-range-order theory, first introduced by Kronig [1] then further developed by Hayasi [2] and the short-range-order theory first proposed by Hartree et al. [31and further developed by Kostarev [4] Sawada [5] and Kozlenkov [6] Recently Perel and Deslattes [7] have made a systematic evaluation of the EFS found in four different perovskites. They have concluded that neither of the two approximations can explain even the “gross” features of the EFS in these crystals. Nordstrand [8] in his review article arrived at the same conclusion. According to him no satisfactory explanation exists for the large variety of EFS in different crystals. Lytle [9] has proposed a third, different model to explain the EFS. According to this model the ejected photo-electron makes a transition from an innner shell state to one of the eigenstates of an infinite potential barrier surrounding the absorbing atom. A relatively good agreement has been found between the positions of the absorption maxima and the eigenstates of the potential barrier in the case of several crystals. The physical existence, however of an infinite potential barrier in a crystal can hardly be understood. We have tried to fit the absorption maxima of the EFS’s of several crystals to the eigenstates of a finite spherically symmetric model potential. The potential has been taken in the following form: V(r) = V0 at r a and V = 0 at r > a, where r is the distance from the centre of the absorbing atom, V0 is the depth of
and the number of them depends on a. This means that V0 has to be chosen approximately equal or somewhat larger than the last absorption maximum in the EFS and the width of the potential is determined by the number of the maxima. In all cases, we have examined, the agreement between the experimental and calculated values of the absorption maxima of the EFS’s was fairly satisfactory. The details of this cornparison will be published elsewhere. In the following we give the physical interpretation of the finite potential valley described above. Let us take into account that a 50 eV electron of normal effective mass travels with a speed of about 4 X 108 cm/s which is commensurable with the orbital speed of an average atomic electron. This implies that the “sudden approximation” [10] should be the appropriate description for the quantum state of the absorbing atom. In that case the photo-ionization taking place in the absorbing atom will cause an electron shake-off in the outer shells of the atom. As a result of this process a large positive ion is being formed in the material. We identify our model potential with the potential energy of this ion. There is direct evidence that electron shake-off or Auger cascading, following photo-ionization of a core electron, in gases causes large positive ions [11] Though there is no direct evidence as yet for extensive electron shake-off in a crystalline material the assumption of its existence seems quite obvious. This assumption can be further supported by the well known low fluorescence yield of materials. Krause et al. [121 have shown that in neon purely radiative
,
,
,
-
—
47
Volume 41A, number I
PHYSICS LETTERS
transitions as a consequence of a vacancy in the dcctron core will occur in 0.7% of the cases. The readjustment of the neon atom after photo-ionization takes place mainly by electron shake-off or Auger cascading. The effect of the absorbing atom itself has so far not been taken into account in any of the existing theories. In his review article Parratt [13] describes the importance of the hole left behind by the ejected electron, but no further connections between the EFS and this hole have been pointed out. In fact in all the existing theories of the EFS it is a basic assumption that the inner shell vacancy left behind by the ejected electron does not alter the normal bands or the electron shells of the absorbing atom [13] . This is in contradiction with the “sudden approximation” which is the proper description in this case. Let us summarise the mechanism suggested here, The photo-ionisation causes a sudden change in a hamiltonian of the absorbing atom. This results in a large positive ion by electron shake-off or Auger cascading, and the ejected electron makes a transition from an internal atomic state (K, L or etc.) to an eigenstate due to the potential corresponding to the positive ion. The basic difference between the EFS of an isolated atom and that of a crystalline material can be explained by this mechanism as follows. If the ejected electron is coming from an isolated atom it can escape froni it easily and the positive ion left behind will not have much effect on it. In a crystalline material, however the ejected electron remains in the vicinity of the absorbing atom and it makes a transition into one of the eigenstates of the potential of the positive ion. It can be said simply that the surrounding atoms do not . . permit the ejected electron to move very far from the absorbing atom and the positive ion produces extra bound states for the electron. The stopping effect of the surrounding atoms can also be supprted by Pauli’s principle. It is quite evident that the electron shake-off probability will be strongly influenced by the nature of chemical bond for those shells which are involved in chemical binding. On the basis of this the strong influence of chemical binding on the EFS of crystalline materials can be understood,since electron shake-off
48
28 August 1972
probability, as calculated by Carlson et a!. 1151 is increasing towards the outer shells of an atom, the whole shake-off process and, therefore, the EFS of different materials will be very sensitive to chemical binding. The positive ion produced by electron shake-off will probably have a relatively short life time. The surrounding atoms will make it relax very rapidly. The width of an absorption maximum in an average EFS is of the order of 10 eV. This gives for the life time of the positive ion about l0~15s which is of a good order of magnitude compared to times involved in X-ray transitions. On the basis of the mechanism suggested here the relaxation process of the core of an atom in a solid material could be studied by means of its EFS. Moreover the mutual influence of the chemical binding and electron shake-off could be investigated. The author is grateful to N.M. Luat for his assistance in carrying out numerical calculations, to A. Nagy for helpful discussions and to Dr. I. Kovacs for reading the manuscript prior to publication. References [11 R. de L. Kronig, Z. Physik 70(1931)317. 121 T. Hayasi, Sc!. Repts Tohoku Univ. 33(1949)123. [3] DR. Hartree, R. de L. Kronig and H. Petersen, Physica 1(1934) 895. [41 Al. Kostarev, Zh. Experim. i. Teor. liz. 11(1941)60. 151 T. Shiraiwa, T. Ishimura and M. Sawada, J. Phys. Soc. Japan 13(1958) 847. [6J Al. Kozlenkov, Jzv. Akad. Nauk SSSR 25 (1961) 957. [71 J. Perel and RD. Deslattes, Phys. Rev. 2B (1970) 1317. [81 R.A. Van Nordstrai3d, Flangbook of X-Rays, ed. EL. Kaclble (McGraw-Hill, New York, 1968) p. 43-1.
191 F.W. Lytle, Advances in X-Ray Analysis Vol. 9, eds.
1101 [111 1121 1131 [14)
G.R. Mallett et al. (Plenum Press, New York, 1965) p. 398. U. Fano and J.W. Cooper, Rev. Mod. Phys. 40 (1968) TA. Carlson and R.M. ~iite. J. Chem. Phys. 48 (1968) 5191. MO. Krause etal., Phys. Rev. 133A (1964) 385. L.G. Parratt, Rev. Mod. Phys. 31(1959)616. T.A. Carlson et al., Phys. Rev. 169 (1968) 27.
PHYSICS LETTERS
28 August 1972
ELECTRON SHAKE-OFF MECHANISM OF THE EXTENDED FINE STRUCTURE OF X-RAY ABSORPTION EDGES T. UNGAR Institute for General Physics, Eötvös University, Budapest, Hungary Received 19 April 1972 A new mechanism for the extended fine structure of X-ray absorption edges is suggested. Electron shake-off following photo-ionization produces a positive ion and the ejected electron makes a transition into an eigenstate of the potential corresponding to this ion.
The extended fine structure (EFS) appearing on the high energy side of an X-ray absorption edge has
the potential and a is its width. The range of extension of the eigenstates is somewhat smaller than V0
been studied for almost fourty years. There were two basically different mechanisms suggested to explain the EFS. The long-range-order theory, first introduced by Kronig [1] then further developed by Hayasi [2] and the short-range-order theory first proposed by Hartree et al. [31and further developed by Kostarev [4] Sawada [5] and Kozlenkov [6] Recently Perel and Deslattes [7] have made a systematic evaluation of the EFS found in four different perovskites. They have concluded that neither of the two approximations can explain even the “gross” features of the EFS in these crystals. Nordstrand [8] in his review article arrived at the same conclusion. According to him no satisfactory explanation exists for the large variety of EFS in different crystals. Lytle [9] has proposed a third, different model to explain the EFS. According to this model the ejected photo-electron makes a transition from an innner shell state to one of the eigenstates of an infinite potential barrier surrounding the absorbing atom. A relatively good agreement has been found between the positions of the absorption maxima and the eigenstates of the potential barrier in the case of several crystals. The physical existence, however of an infinite potential barrier in a crystal can hardly be understood. We have tried to fit the absorption maxima of the EFS’s of several crystals to the eigenstates of a finite spherically symmetric model potential. The potential has been taken in the following form: V(r) = V0 at r a and V = 0 at r > a, where r is the distance from the centre of the absorbing atom, V0 is the depth of
and the number of them depends on a. This means that V0 has to be chosen approximately equal or somewhat larger than the last absorption maximum in the EFS and the width of the potential is determined by the number of the maxima. In all cases, we have examined, the agreement between the experimental and calculated values of the absorption maxima of the EFS’s was fairly satisfactory. The details of this cornparison will be published elsewhere. In the following we give the physical interpretation of the finite potential valley described above. Let us take into account that a 50 eV electron of normal effective mass travels with a speed of about 4 X 108 cm/s which is commensurable with the orbital speed of an average atomic electron. This implies that the “sudden approximation” [10] should be the appropriate description for the quantum state of the absorbing atom. In that case the photo-ionization taking place in the absorbing atom will cause an electron shake-off in the outer shells of the atom. As a result of this process a large positive ion is being formed in the material. We identify our model potential with the potential energy of this ion. There is direct evidence that electron shake-off or Auger cascading, following photo-ionization of a core electron, in gases causes large positive ions [11] Though there is no direct evidence as yet for extensive electron shake-off in a crystalline material the assumption of its existence seems quite obvious. This assumption can be further supported by the well known low fluorescence yield of materials. Krause et al. [121 have shown that in neon purely radiative
,
,
,
-
—
47
Volume 41A, number I
PHYSICS LETTERS
transitions as a consequence of a vacancy in the dcctron core will occur in 0.7% of the cases. The readjustment of the neon atom after photo-ionization takes place mainly by electron shake-off or Auger cascading. The effect of the absorbing atom itself has so far not been taken into account in any of the existing theories. In his review article Parratt [13] describes the importance of the hole left behind by the ejected electron, but no further connections between the EFS and this hole have been pointed out. In fact in all the existing theories of the EFS it is a basic assumption that the inner shell vacancy left behind by the ejected electron does not alter the normal bands or the electron shells of the absorbing atom [13] . This is in contradiction with the “sudden approximation” which is the proper description in this case. Let us summarise the mechanism suggested here, The photo-ionisation causes a sudden change in a hamiltonian of the absorbing atom. This results in a large positive ion by electron shake-off or Auger cascading, and the ejected electron makes a transition from an internal atomic state (K, L or etc.) to an eigenstate due to the potential corresponding to the positive ion. The basic difference between the EFS of an isolated atom and that of a crystalline material can be explained by this mechanism as follows. If the ejected electron is coming from an isolated atom it can escape froni it easily and the positive ion left behind will not have much effect on it. In a crystalline material, however the ejected electron remains in the vicinity of the absorbing atom and it makes a transition into one of the eigenstates of the potential of the positive ion. It can be said simply that the surrounding atoms do not . . permit the ejected electron to move very far from the absorbing atom and the positive ion produces extra bound states for the electron. The stopping effect of the surrounding atoms can also be supprted by Pauli’s principle. It is quite evident that the electron shake-off probability will be strongly influenced by the nature of chemical bond for those shells which are involved in chemical binding. On the basis of this the strong influence of chemical binding on the EFS of crystalline materials can be understood,since electron shake-off
48
28 August 1972
probability, as calculated by Carlson et a!. 1151 is increasing towards the outer shells of an atom, the whole shake-off process and, therefore, the EFS of different materials will be very sensitive to chemical binding. The positive ion produced by electron shake-off will probably have a relatively short life time. The surrounding atoms will make it relax very rapidly. The width of an absorption maximum in an average EFS is of the order of 10 eV. This gives for the life time of the positive ion about l0~15s which is of a good order of magnitude compared to times involved in X-ray transitions. On the basis of the mechanism suggested here the relaxation process of the core of an atom in a solid material could be studied by means of its EFS. Moreover the mutual influence of the chemical binding and electron shake-off could be investigated. The author is grateful to N.M. Luat for his assistance in carrying out numerical calculations, to A. Nagy for helpful discussions and to Dr. I. Kovacs for reading the manuscript prior to publication. References [11 R. de L. Kronig, Z. Physik 70(1931)317. 121 T. Hayasi, Sc!. Repts Tohoku Univ. 33(1949)123. [3] DR. Hartree, R. de L. Kronig and H. Petersen, Physica 1(1934) 895. [41 Al. Kostarev, Zh. Experim. i. Teor. liz. 11(1941)60. 151 T. Shiraiwa, T. Ishimura and M. Sawada, J. Phys. Soc. Japan 13(1958) 847. [6J Al. Kozlenkov, Jzv. Akad. Nauk SSSR 25 (1961) 957. [71 J. Perel and RD. Deslattes, Phys. Rev. 2B (1970) 1317. [81 R.A. Van Nordstrai3d, Flangbook of X-Rays, ed. EL. Kaclble (McGraw-Hill, New York, 1968) p. 43-1.
191 F.W. Lytle, Advances in X-Ray Analysis Vol. 9, eds.
1101 [111 1121 1131 [14)
G.R. Mallett et al. (Plenum Press, New York, 1965) p. 398. U. Fano and J.W. Cooper, Rev. Mod. Phys. 40 (1968) TA. Carlson and R.M. ~iite. J. Chem. Phys. 48 (1968) 5191. MO. Krause etal., Phys. Rev. 133A (1964) 385. L.G. Parratt, Rev. Mod. Phys. 31(1959)616. T.A. Carlson et al., Phys. Rev. 169 (1968) 27.