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Core level shift in random CuPd and AgPd alloys by the complete screening picture
Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69 www.elsevier.com / locate / elspec
Core level shift in random CuPd and AgPd alloys by the complete screening picture a, a a ,b W. Olovsson *, I.A. Abrikosov , B. Johansson a
b
Condensed Matter Theory Group, Department of Physics, Uppsala University, SE-751 21 Uppsala, Sweden Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Abstract A first-principles investigation of the core-level binding energy shifts (CLS) for the 3d 5 / 2 core-electrons of Ag, Pd and 2p 3 / 2 of Cu was carried out for the f.c.c. Ag–Pd and Cu–Pd random alloys within the model of complete screening, which includes both the initial and final state effects, and compared to initial state calculations. It is shown that the model of complete screening in general gives good agreement with experiment and is in substantially better agreement with experiment in the case of Pd when compared to the initial state calculations. 2002 Elsevier Science B.V. All rights reserved. Keywords: Core level shift; Complete screening; Alloys
1. Introduction A deeper understanding of the underlying properties of bonding and electronic structure in a solid may be obtained by studying the binding energy shifts of core-electrons between the pure metal and alloy, as the shifts depend on the chemical environment of the atom. Among the properties that have been related to the core level energy binding shift (CLS) are, for example, the cohesive energy [1] and the segregation energy [2] for certain materials. Also, chemical shifts of two core-holes, which are part of the Auger electron energies, have been related to similar properties. An introduction to this, covering a large part of the Periodic Table, can be found in Ref. [3]. Experimentally it is relatively easy to measure *Corresponding author. E-mail address: [email protected] (W. Olovsson).
CLS with X-ray photoelectron spectroscopy. The sign of the shift is defined from an experimental point of view, by considering the difference in the core-electron binding energy, EB . 0, for an atom in the alloy compared to the atom in the pure metal. In metallic alloys, CLS values are typically small, about 1 eV, compared to molecular systems where it may be as large as 5 eV. Therefore, a theoretical approach for calculating CLS in alloys needs a high degree of accuracy. There are many factors that determine the core level shift in an alloy. Weinert and Watson [4] listed four factors, namely, core-hole screening, changes in the Fermi level, intra-atomic charge transfer, and redistribution of charge due to bonding and hybridization. The contribution from core-hole screening is usually associated with the so-called final state effect, and comes from the relaxation of the remaining electrons due to the core-hole created by the leaving electron. The initial state CLS corresponds to
0368-2048 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 02 )00173-1
66
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
the difference between theoretically calculated corelevel eigenenergies for an atom in a pure metal and in an alloy. The present work was inspired by an ongoing discussion in the literature concerning different models for estimating CLS. In the work of Cole et al. [5], a potential model based on the inter-atomic charge transfer was used for the f.c.c. CuPd alloys. The application of such a model was later questioned by Faulkner et al. [6], and lead to a discussion between these authors [7,8]. Faulkner et al. used an initial state approach based on density functional theory (DFT) [8,9] and investigated CuPd, AgPd and CuZn for some concentrations. Here, we use the complete screening picture, which includes both initial and final state effects in the same scheme, and which has been successfully applied for surface CLS [10]. In this work, the whole concentration interval of the f.c.c. random alloys CuPd and AgPd is examined by using the complete screening calculations of the CLS. We also used an initial state model to make comparison with the complete screening picture and determine the effect of including the final state contribution. As will be seen, our results clearly show that all the mentioned effects need to be included in order to have an accurate theoretical scheme to calculate core level shifts. Then both initial and final state properties must be fully included before theory is compared to experiment. This is exactly what was claimed already in Ref. [1].
2. Method The initial state calculations are associated with the shift of the theoretically calculated eigenvalues of the core-electron: A AB E ACLS 5sE core 2 E FAd 2sE core 2 E FABd
calculate the core level shift between a free atom and an atom in a metal, and it has also been successfully applied to studies of surface CLS [10]. The most important property in the model is the generalized thermodynamic chemical potential, which is given by: ≠Etot m 5 ]]u c→0 ≠c
(2)
where we consider a completely random alloy, A 12x B x , in which Etot represents the total energy of the system where a specific core-electron of atom A (or B) has been ionized, with a concentration of c ionized atoms in the alloy. The chemical potential is then determined by an extrapolation to zero concentration c. Note that x denote atomic concentration of B atoms in the alloy. The core level shift will in its turn be given by the difference between these chemical potentials in the pure metal and in the alloy: ECLS 5 mpure 2 malloy
(3)
Observe that the model of complete screening does not depend on the particular computational method that is used for the actual total energy calculations. Of course, compared to the initial state model (also used here), the complete screening calculations take longer time as they must be done for a number of different ionizations c. To calculate the core-electron energy eigenvalues and the total energies, the coherent potential approximation (CPA) [11,12], within the local density approximation [13], was used with a basis set consisting of s, p and d linear muffin-tin orbitals (LMTO) [14] and within the atomic sphere approximation (ASA). The lattice constants for the pure metals, the alloys with different concentrations and ionizations were fully relaxed.
(1) 3. Result and discussion
Here E ACLS is the core-electron energy shift on atom A A AB AB A, E core and E F and E core and E F are the energyeigenvalues for atom A and Fermi energies in the pure metal and in the alloy, respectively. This data was readily obtained as a by-product when making the necessary complete screening calculations. The complete screening picture was first used to
The result of our studies of core level shifts over the whole concentration interval of the f.c.c. CuPd and AgPd random alloys are as follows. Beginning with the shift of the Cu 2p 3 / 2 coreelectrons in Cu 12x Pd x (Fig. 1), one observes that the complete screening approach and the initial state
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
Fig. 1. CLS for Cu 2p 3 / 2 in Cu 12x Pd x . The result of the complete screening picture (filled boxes, dashed line) and the initial state approach (empty boxes, dot-dashed line) is compared to two experimental sets (filled and empty circles).
model follow each other very closely. Therefore, they both differ only slightly from the experimental result. The CLS is here negative, which means that the binding energy of the core electrons in the alloy is smaller than in the metal. Also notice that there exist some disagreement between the two sets of experimentally obtained CLS [15,5]. Turning to the Pd 3d 5 / 2 CLS in the Cu 12x Pd x alloy (Fig. 2), we now find a large difference between the calculated shifts, depending on the model we use. While the complete screening results closely follow the experimental values the initial state CLS do not. One observes that within the complete screening treatment the agreement with the experiment for Pd 3d 5 / 2 is even better than in the case of Cu 2p 3 / 2 . In the calculations concerning the second random alloy in our study, Ag 12x Pd x , we first investigate the
67
Fig. 2. CLS for Pd 3d 5 / 2 in Cu 12x Pd x . The notation is the same as in Fig. 1.
result of the Ag 3d 5 / 2 shift (Fig. 3). Here one finds that, as in the case of Cu above (Fig. 1), the two models give very similar results. Also the calculated CLS is close to experiment. Notice, however, that the trend obtained within the initial state approach is becoming worse for higher Pd concentration. In Fig. 4 we show the Pd 3d 5 / 2 CLS in Ag 12x Pdx . As in the case of Pd CLS in CuPd (Fig. 2), there is a big difference between the two models, totally in favor of the complete screening treatment. Regarding the influence of local lattice relaxations on the result, it is expected to be small in AgPd, while it could probably influence the result in CuPd, judging from the size difference of the atoms which constitute these alloys. At the same time, there is no big difference in the accuracy of our calculations in these two systems. This indicates that the influence of local lattice relaxations on the calculated CLS is not expected to be large in general.
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W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
Fig. 3. CLS for Ag 3d 5 / 2 in Ag 12x Pd x . The complete screening picture (filled boxes, dashed line) and the initial state approach (empty boxes, dot-dashed line) is compared to experimental values ¨ from the work of Steiner and Hufner [14] (empty circles).
Fig. 4. CLS for Pd 3d 5 / 2 in Ag 12x Pd x . The notation is the same as in Fig. 3.
4. Summary A way to interpret the influence of the final state effects on the calculated CLS within the complete screening approach is as follows: the orbital character of the screening charge plays an important role on the magnitude of the final state effect [1]. One would then expect that different orbital characters of the screening electrons in the pure metal and in the alloy would lead to a bigger effect than if they were of a similar character. In our situation this means that electrons at the Fermi level, EF , in pure Pd have more of a d-character, while the corresponding electrons in an alloy of Pd with Ag or Cu, have more of an sp-character. The density of states calculations for these alloys very much support this picture. Notice also that the final state effect is larger in the concentration interval 0–50% Pd in Figs. 2 and 4 and almost constant, while above 50% it decreases with higher concentration, if compared with the initial state approach.
We have carried out a calculation of the core level binding energy shifts in the random f.c.c. alloys CuPd and AgPd, and have shown that the model of complete screening gives good results compared to experiment. In this model, initial and final state effects are incorporated into one scheme, and the result for the Pd CLS in both alloys clearly shows that an initial state approach is not at all appropriate for describing the core level shift. The final state effects can not be excluded or approximated to be the same in the pure metal and in the alloy, particularly when considering Pd in the f.c.c. CuPd and AgPd random alloys.
Acknowledgements This work was supported by the Swedish Foundation for Strategic Research. IAA and BJ are grateful
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
to the Swedish Research Council, Natural and Engineering Sciences for financial support.
References ˚ [1] B. Johansson, N. Martensson, Phys. Rev. B 21 (1980) 4427. [2] A. Rosengren, B. Johansson, Phys. Rev. B 23 (1981) 3852. ˚ ˚ [3] N. Martensson, P. Hedegard, B. Johansson, Phys. Scripta 29 (1984) 154. [4] M. Weinert, R.E. Watson, Phys. Rev. B 51 (1995) 17168. [5] R.J. Cole, N.J. Brooks, P. Weightman, Phys. Rev. Lett. 78 (1997) 3777; R.J. Cole, N.J. Brooks, P. Weightman, Phys. Rev. B 56 (1997) 12178. [6] J.S. Faulkner, Y. Wang, G.M. Stocks, Phys. Rev. Lett. 81 (1998) 1905. [7] J.S. Faulkner, Y. Wang, G.M. Stocks, Phys. Rev. Lett. 83 (1999) 3572.
69
[8] P. Weightman, R.J. Cole, Phys. Rev. Lett. 83 (1999) 3571. [9] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864; W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. ´ H.L. Skriver, B. Johansson, Phys. Rev. Lett. 71 [10] M. Alden, (1993) 2449; ´ I.A. Abrikosov, B. Johansson, N.M. Rosengaard, M. Alden, H.L. Skriver, Phys. Rev. B 50 (1994) 5131. [11] I.A. Abrikosov, H.L. Skriver, Phys. Rev. B 47 (1993) 16532. [12] I.A. Abrikosov, W. Olovsson, B. Johansson, Phys. Rev. Lett. 87 (2001) 176403. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] O.K. Andersen, Phys. Rev. B 12 (1975) 3060; O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) 2571. ˚ ´ [15] N. Martensson, R. Nyholm, H. Calen, J. Hedman, B. Johansson, Phys. Rev. B 24 (1981) 1725. ¨ [16] P. Steiner, S. Hufner, Acta Metal. 29 (1981) 1885.
Core level shift in random CuPd and AgPd alloys by the complete screening picture a, a a ,b W. Olovsson *, I.A. Abrikosov , B. Johansson a
b
Condensed Matter Theory Group, Department of Physics, Uppsala University, SE-751 21 Uppsala, Sweden Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Abstract A first-principles investigation of the core-level binding energy shifts (CLS) for the 3d 5 / 2 core-electrons of Ag, Pd and 2p 3 / 2 of Cu was carried out for the f.c.c. Ag–Pd and Cu–Pd random alloys within the model of complete screening, which includes both the initial and final state effects, and compared to initial state calculations. It is shown that the model of complete screening in general gives good agreement with experiment and is in substantially better agreement with experiment in the case of Pd when compared to the initial state calculations. 2002 Elsevier Science B.V. All rights reserved. Keywords: Core level shift; Complete screening; Alloys
1. Introduction A deeper understanding of the underlying properties of bonding and electronic structure in a solid may be obtained by studying the binding energy shifts of core-electrons between the pure metal and alloy, as the shifts depend on the chemical environment of the atom. Among the properties that have been related to the core level energy binding shift (CLS) are, for example, the cohesive energy [1] and the segregation energy [2] for certain materials. Also, chemical shifts of two core-holes, which are part of the Auger electron energies, have been related to similar properties. An introduction to this, covering a large part of the Periodic Table, can be found in Ref. [3]. Experimentally it is relatively easy to measure *Corresponding author. E-mail address: [email protected] (W. Olovsson).
CLS with X-ray photoelectron spectroscopy. The sign of the shift is defined from an experimental point of view, by considering the difference in the core-electron binding energy, EB . 0, for an atom in the alloy compared to the atom in the pure metal. In metallic alloys, CLS values are typically small, about 1 eV, compared to molecular systems where it may be as large as 5 eV. Therefore, a theoretical approach for calculating CLS in alloys needs a high degree of accuracy. There are many factors that determine the core level shift in an alloy. Weinert and Watson [4] listed four factors, namely, core-hole screening, changes in the Fermi level, intra-atomic charge transfer, and redistribution of charge due to bonding and hybridization. The contribution from core-hole screening is usually associated with the so-called final state effect, and comes from the relaxation of the remaining electrons due to the core-hole created by the leaving electron. The initial state CLS corresponds to
0368-2048 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0368-2048( 02 )00173-1
66
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
the difference between theoretically calculated corelevel eigenenergies for an atom in a pure metal and in an alloy. The present work was inspired by an ongoing discussion in the literature concerning different models for estimating CLS. In the work of Cole et al. [5], a potential model based on the inter-atomic charge transfer was used for the f.c.c. CuPd alloys. The application of such a model was later questioned by Faulkner et al. [6], and lead to a discussion between these authors [7,8]. Faulkner et al. used an initial state approach based on density functional theory (DFT) [8,9] and investigated CuPd, AgPd and CuZn for some concentrations. Here, we use the complete screening picture, which includes both initial and final state effects in the same scheme, and which has been successfully applied for surface CLS [10]. In this work, the whole concentration interval of the f.c.c. random alloys CuPd and AgPd is examined by using the complete screening calculations of the CLS. We also used an initial state model to make comparison with the complete screening picture and determine the effect of including the final state contribution. As will be seen, our results clearly show that all the mentioned effects need to be included in order to have an accurate theoretical scheme to calculate core level shifts. Then both initial and final state properties must be fully included before theory is compared to experiment. This is exactly what was claimed already in Ref. [1].
2. Method The initial state calculations are associated with the shift of the theoretically calculated eigenvalues of the core-electron: A AB E ACLS 5sE core 2 E FAd 2sE core 2 E FABd
calculate the core level shift between a free atom and an atom in a metal, and it has also been successfully applied to studies of surface CLS [10]. The most important property in the model is the generalized thermodynamic chemical potential, which is given by: ≠Etot m 5 ]]u c→0 ≠c
(2)
where we consider a completely random alloy, A 12x B x , in which Etot represents the total energy of the system where a specific core-electron of atom A (or B) has been ionized, with a concentration of c ionized atoms in the alloy. The chemical potential is then determined by an extrapolation to zero concentration c. Note that x denote atomic concentration of B atoms in the alloy. The core level shift will in its turn be given by the difference between these chemical potentials in the pure metal and in the alloy: ECLS 5 mpure 2 malloy
(3)
Observe that the model of complete screening does not depend on the particular computational method that is used for the actual total energy calculations. Of course, compared to the initial state model (also used here), the complete screening calculations take longer time as they must be done for a number of different ionizations c. To calculate the core-electron energy eigenvalues and the total energies, the coherent potential approximation (CPA) [11,12], within the local density approximation [13], was used with a basis set consisting of s, p and d linear muffin-tin orbitals (LMTO) [14] and within the atomic sphere approximation (ASA). The lattice constants for the pure metals, the alloys with different concentrations and ionizations were fully relaxed.
(1) 3. Result and discussion
Here E ACLS is the core-electron energy shift on atom A A AB AB A, E core and E F and E core and E F are the energyeigenvalues for atom A and Fermi energies in the pure metal and in the alloy, respectively. This data was readily obtained as a by-product when making the necessary complete screening calculations. The complete screening picture was first used to
The result of our studies of core level shifts over the whole concentration interval of the f.c.c. CuPd and AgPd random alloys are as follows. Beginning with the shift of the Cu 2p 3 / 2 coreelectrons in Cu 12x Pd x (Fig. 1), one observes that the complete screening approach and the initial state
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
Fig. 1. CLS for Cu 2p 3 / 2 in Cu 12x Pd x . The result of the complete screening picture (filled boxes, dashed line) and the initial state approach (empty boxes, dot-dashed line) is compared to two experimental sets (filled and empty circles).
model follow each other very closely. Therefore, they both differ only slightly from the experimental result. The CLS is here negative, which means that the binding energy of the core electrons in the alloy is smaller than in the metal. Also notice that there exist some disagreement between the two sets of experimentally obtained CLS [15,5]. Turning to the Pd 3d 5 / 2 CLS in the Cu 12x Pd x alloy (Fig. 2), we now find a large difference between the calculated shifts, depending on the model we use. While the complete screening results closely follow the experimental values the initial state CLS do not. One observes that within the complete screening treatment the agreement with the experiment for Pd 3d 5 / 2 is even better than in the case of Cu 2p 3 / 2 . In the calculations concerning the second random alloy in our study, Ag 12x Pd x , we first investigate the
67
Fig. 2. CLS for Pd 3d 5 / 2 in Cu 12x Pd x . The notation is the same as in Fig. 1.
result of the Ag 3d 5 / 2 shift (Fig. 3). Here one finds that, as in the case of Cu above (Fig. 1), the two models give very similar results. Also the calculated CLS is close to experiment. Notice, however, that the trend obtained within the initial state approach is becoming worse for higher Pd concentration. In Fig. 4 we show the Pd 3d 5 / 2 CLS in Ag 12x Pdx . As in the case of Pd CLS in CuPd (Fig. 2), there is a big difference between the two models, totally in favor of the complete screening treatment. Regarding the influence of local lattice relaxations on the result, it is expected to be small in AgPd, while it could probably influence the result in CuPd, judging from the size difference of the atoms which constitute these alloys. At the same time, there is no big difference in the accuracy of our calculations in these two systems. This indicates that the influence of local lattice relaxations on the calculated CLS is not expected to be large in general.
68
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
Fig. 3. CLS for Ag 3d 5 / 2 in Ag 12x Pd x . The complete screening picture (filled boxes, dashed line) and the initial state approach (empty boxes, dot-dashed line) is compared to experimental values ¨ from the work of Steiner and Hufner [14] (empty circles).
Fig. 4. CLS for Pd 3d 5 / 2 in Ag 12x Pd x . The notation is the same as in Fig. 3.
4. Summary A way to interpret the influence of the final state effects on the calculated CLS within the complete screening approach is as follows: the orbital character of the screening charge plays an important role on the magnitude of the final state effect [1]. One would then expect that different orbital characters of the screening electrons in the pure metal and in the alloy would lead to a bigger effect than if they were of a similar character. In our situation this means that electrons at the Fermi level, EF , in pure Pd have more of a d-character, while the corresponding electrons in an alloy of Pd with Ag or Cu, have more of an sp-character. The density of states calculations for these alloys very much support this picture. Notice also that the final state effect is larger in the concentration interval 0–50% Pd in Figs. 2 and 4 and almost constant, while above 50% it decreases with higher concentration, if compared with the initial state approach.
We have carried out a calculation of the core level binding energy shifts in the random f.c.c. alloys CuPd and AgPd, and have shown that the model of complete screening gives good results compared to experiment. In this model, initial and final state effects are incorporated into one scheme, and the result for the Pd CLS in both alloys clearly shows that an initial state approach is not at all appropriate for describing the core level shift. The final state effects can not be excluded or approximated to be the same in the pure metal and in the alloy, particularly when considering Pd in the f.c.c. CuPd and AgPd random alloys.
Acknowledgements This work was supported by the Swedish Foundation for Strategic Research. IAA and BJ are grateful
W. Olovsson et al. / Journal of Electron Spectroscopy and Related Phenomena 127 (2002) 65–69
to the Swedish Research Council, Natural and Engineering Sciences for financial support.
References ˚ [1] B. Johansson, N. Martensson, Phys. Rev. B 21 (1980) 4427. [2] A. Rosengren, B. Johansson, Phys. Rev. B 23 (1981) 3852. ˚ ˚ [3] N. Martensson, P. Hedegard, B. Johansson, Phys. Scripta 29 (1984) 154. [4] M. Weinert, R.E. Watson, Phys. Rev. B 51 (1995) 17168. [5] R.J. Cole, N.J. Brooks, P. Weightman, Phys. Rev. Lett. 78 (1997) 3777; R.J. Cole, N.J. Brooks, P. Weightman, Phys. Rev. B 56 (1997) 12178. [6] J.S. Faulkner, Y. Wang, G.M. Stocks, Phys. Rev. Lett. 81 (1998) 1905. [7] J.S. Faulkner, Y. Wang, G.M. Stocks, Phys. Rev. Lett. 83 (1999) 3572.
69
[8] P. Weightman, R.J. Cole, Phys. Rev. Lett. 83 (1999) 3571. [9] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864; W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. ´ H.L. Skriver, B. Johansson, Phys. Rev. Lett. 71 [10] M. Alden, (1993) 2449; ´ I.A. Abrikosov, B. Johansson, N.M. Rosengaard, M. Alden, H.L. Skriver, Phys. Rev. B 50 (1994) 5131. [11] I.A. Abrikosov, H.L. Skriver, Phys. Rev. B 47 (1993) 16532. [12] I.A. Abrikosov, W. Olovsson, B. Johansson, Phys. Rev. Lett. 87 (2001) 176403. [13] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [14] O.K. Andersen, Phys. Rev. B 12 (1975) 3060; O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53 (1984) 2571. ˚ ´ [15] N. Martensson, R. Nyholm, H. Calen, J. Hedman, B. Johansson, Phys. Rev. B 24 (1981) 1725. ¨ [16] P. Steiner, S. Hufner, Acta Metal. 29 (1981) 1885.