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L2,3 edges of chromium: comparison between electron energy loss spectra in transmission and reflection mode
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Solid State Communications, Vol. 83, No. 11, pp. 921-925, 1992. Printed in Great Britain.
L2,3 EDGES OF CHROMIUM: COMPARISON BETWEEN ELECTRON ENERGY LOSS SPECTRA IN TRANSMISSION A N D REFLECTION MODE L. Lozzi, M. Passacantando, P. Picozzi and S. Santucci Dipartimento di Fisica, Universit~ de L'Aquila, 67010 Coppito (AQ), Italy M. Diociaiuti Istituto Superiore di Sanith, 00100 Roma, Italy and M. De Crescenzi
I
Dipartimento di Matematica e Fisica', Universit~i di Camerino, 62032 Camerino (MC), Italy
(Received 17 April 1992 by E. Molina) The extended fine structure above the Cr L2,3 edges observed in electron energy loss spectra taken both in reflection and in transmission mode has been carefully compared. The good agreement between the structural results obtained by the two measurements confirms the validity of the dipole approximation used to describe the cross section of the electron energy loss spectroscopy in reflection mode. This is particularly surprising because in reflection the primary beam energy is of the same order of the magnitude of the investigated energy loss. This effect is ascribed to the localized spatial extension of the L2~3 wave function. The number of non-dipole terms (monopole transitions) has been shown by a thorough measurement of the Li ionization edge intensity.
1. INTRODUCTION IN THE LAST few years a lot of work, both experimentally and theoretically, has been devoted to study the capability of Extended Energy Loss Fine Structure (EELFS) spectroscopy in reflection mode of studying the structural properties of surfaces and interfaces [1-6]. Due to the strong interaction between electrons and matter EELFS is an important technique in the study of adsorbates, clusters and thin films [2, 7, 8]. In this spectroscopy the features observed in the electron cross section above an ionization edge are interpreted as being due to an interference effect between the ejected electronic wave coming out from the excited atom and the backscattered part of this wave due to the presence of the surrounding atoms. This process is similar to that currently observed in the X-ray absorption spectra [9], which need high flux synchrotron radiation sources. The EXAFS theory is based on the dipolar selection rule for the core electron excitation. Instead, in an electron energy loss experiment, the cross section for the excitation of a deep core level has not only the dipolar term, but also :
other contributions (i.e., monopole, quadrupole, etc.) can also be present. In fact, the inelastic cross section for the excitation of core level by fast electrons, in the Born approximation, between an initial core state Ii) and final state If) is given by [10]: d2tr(E, q)
dEdq
871"e4 1
- l~2v2 q3 I ( f l e x p (iq" r)li)l 2,
(1)
where E is the energy loss, q is the momentum transfer, v is the incident electron velocity and r is the position operator of the atomic electron. Expanding the exponential, one obtains: exp(iq.r) = 1 + i q - r -
l/2(q.r) 2 + ....
(2)
Neglecting the first term, due to the orthogonality of the initial and final wave functions, the second term determines the dipole transitions, while the third causes monopole and quadrupole transitions. The weight of the different terms in the cross section depends on the q magnitude. For low q value the dipole term dominates, while at high q value the monopole and quadrupole contributions can not be neglected. In a scattering process with impinging electrons of energy Ep which lose energy equal to AE,
921
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L2, 3 EDGES OF C H R O M I U M
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the momentum transfer q ranges from a minimum T h e s e results underline 'that for localized core levels value qmin o~ Elp/2 - (Ep - AE) 1/2 to a maximum one (Is, 2p) the dipole contribution to the inelastic cross qmax 0¢ A E 1/2. Due to the 1/q 3 term in equation (1) section is still dominant even at low Ep, while the the main contribution to the cross section is other terms (monopole, quadrupole, etc.) are dominated by the q values around qmin. completely negligible. These last contributions are For EELFS in transmission mode, i.e. by using particularly evident for delocalized shells, like Li or very fast electrons with kinetic energy of 100- Ml, because their weight increases dramatically 300keV, since the minimum momentum transfer decreasing E e. 9min is very small (~ 0.1 A-t), the dipole approxi2. E X P E R I M E N T A L mation holds: this has been verified both :experimentally and theoretically [10,11]. Instead, for The E E L S spectra in reflection mode were EELFS in reflection mode, i.e. with low energy performed in an ultra high vacuum (UHV) apparelectrons (1-3 keV), due to the q magnitude (CR L 23 atus with a total pressure in the 10-SPa range. A edge, A E ~ 5 8 0 e V , qmin~3.6/~-'), the dipoi'e thick Cr film (,,~ 500~) was evaporated onto a approximation should be questionable [2,3]. In carbon rod in a UHV chamber at a pressure of order to estimate the amount of non-dipolar ,-~ 5 x 10 -8 Pa. The chamber was equipped with an contributions which are present in the cross section electron gun coaxial to a Riber single pass CMA for the excitation of core edges by low energy (cylindrical mirror analyzer) which was used for electrons, various theories have been developed. For Auger and EELS spectroscopies. All spectra were the K edge of silicon [21 and L2,3 edges of copper [3] it collected with an incident electron energy Ep between has been theoretically demonstrated that the dipole 1000 and 2000eV and a current of 5#Amm -2. A contribution to the cross section is the dominant one peak to peak modulating voltage of 10 V was used for and that the structural results obtained by means of the detection of the fine structure, while for the L2,3 EELFS in the reflection mode are very similar to edges a 2V modulation was chosen, in order to those calculated from EXAFS spectra. Instead, for increase the energy resolution A E / E ~ 0.3%. the M2,3 edges, the higher order terms seem to play an The experimental apparatus for EELS measureimportant role [3] and a sizeable difference between ments in transmission mode consisted of a magnetic the experimental nearest neighbour distance and the sector energy analyzer (Gatan 607) attached to a crystallographic value has been reported [12]. The Philips EM430 transmission electron microscope problem could be associated with the M2,3 ionization (TEM), equipped with a LaB6 electron gun, opersince it has been shown that the same discrepancy ating at a primary beam energy of 250keY. The arises in the analysis of the/142,3 EXAFS spectra [12]. sample was prepared by thermal evaporation of Another interpretation was given by Tran Thoai et al. chromium (99.99% pure) on a copper grid covered [13] on 11//2,3edges ofCu, Ni and Co and by Luo et al. with a carbon layer in a UHV chamber at a pressure on M2,3 edges of Cu [14] and N2,3 of Pd [15]. They of ,-~ 5 x 10-8 Pa. The nominal thickness, monitored have shown that this discrepancy could be due to the with a Inficon XTM quartz microbalance, was about use of the plane-wave approximation for the 500,~. The deposited film was protected against calculation of the backscattered phase shift and oxidation with a thin carbon film and then amplitudes. Instead, the use of the curved-wave transferred into the TEM. approximation leads to the exact nearest-neighbour distances. 3. RESULTS AND DISCUSSION The aim of this work is to assess with high Figure 1 shows the electron energy loss spectra for accuracy the validity of the dipole approximation for the excitation of L2,3 edges of chromium by EELFS the L2, 3 edges of chromium followed by the EELFS in reflection mode, i.e. when the primary beam energy oscillations recorded in transmission (upper curve) Ep is comparable with the energy loss (high q and reflection mode (lower curve). In the latter case transfer). We have compared the L2,3 edges and the the first derivative of the backscattered electron is reported. The L2 and fine structure observed above the same edges of distribution, - d N ( E ) / d E , polycrystailine Cr sample by using electron energy L 3 edges are located at 584 and 575eV energy loss spectroscopy (EELS) in reflection and trans- loss, respectively, while the structure at about mission modes. There is a good agreement between 695eV energy loss is due to the ionization of the Ll the structural results obtained with these techniques shell. It is interesting to note the difference in the in terms of Fourier transforms, back-scattering amplitudes, phase shifts and L2.3 edge intensities. LI/L2, 3 intensity ratio for the two measurements. In
Vol. 83, No. 11
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Energy Loss (eV) Fig. l, Electron energy loss spectra of the Cr L2,3 edges in transmission (upper curve, Er = 250keV) and reflection mode (lower curve, Ep = 2 keV). The latter spectrum has been taken in first derivative mode, -dN(E)/dE. In the reflection spectrum, we report the polynomial function drawn through the LI edge used to subtract it (dashed line). In the inset we report the Li edge recorded in both geometries (continuous line for transmission and dotted line for reflection). The reflection signal has been integrated and the spectra have been normalized at L 3 edge intensity.
2
4
6
k (A-')
8
10
Fig. 2. EELFS structures beyond the Cr L2, 3 edges obtained from the spectra shown in Fig. 1 after the background subtraction. The k wave vector is referred to the L 3 edge. The spectrum taken in reflection mode (curve b) has been numerically integrated and the L I structure has been removed. Curve c is the residual obtained by subtracting a and b spectra.
have been analyzed following the EXAFS standard method: (1) the energy loss has been referred to the L3 the inset of Fig. 1, comparison between the Li edge edge onset energy and then transformed into the kintensity in both geometries is reported. The reflec- wave vector; (2) a background has been subtracted to isolate tion signal has been integrated and the spectra have been normalized at the L 3 edge. This is a clear the modulating structures x(k). evidence of the importance of non-dipole transition After the background subtraction the data taken contribution to the cross section detected in reflection in reflection mode have been numerically integrated mode. It has been shown that for s core edges (such to obtain the x(k) EELFS curve. as L I o r MI, i.e. spatially delocalized wave functions) In Fig. 2 we report the x(k) obtained from the the monopole transition becomes more and more N(E) spectrum taken in transmission mode (curve a) important as a function of the increase of and that from the numerically integrated data of the the momentum transfer [2,3]. This contribution dN(E)/dE spectrum recorded in reflection mode decreases as the incident electron energy increases, (curve b). Figure 2(c) reports the residual curve as clearly demonstrated for the nickel MI edge [16]. obtained by subtracting curve (b) from curve (a) In order to minimize the influence of the LI edge on showing no characteristic frequency over the whole k the analysis of the reflection L2,3 EELFS spectrum we range. The x(k) spectra have been multiplied by k have subtracted this structure drawing a polynomial and then Fourier transformed using a Gaussian curve through the edge (shown in Fig. 1). Instead, in window in the range 2.5 < k(A -I) < 8.5 in order to both the experiments, since the spin-orbit splitting obtain the radial distribution functions F(R). In Fig. between the L2 and Ls edges is small (9eV) com- 3 we report the Fourier transforms FiR ) of the pared with the spacing of the extended fine- oscillations shown in Fig. 2. The theoretical F(R) structure maxima, it is reasonable to neglect the L 2 calculated by the EXAFS formula is reported in the edge [I0]. lower part of Fig. 3. We have included the first three The fine structure of both the experimental data coordination shells and the backscattered amplitudes
924
L2, 3 EDGES OF CHROMIUM
Vol. 83, No. 11
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and phase shifts are taken from McKale et al. [17]. The prominent peak at 2.25 A is due to the first and second coordination shells in the chromium bcc structure [too closed to be resolved in the F(R)] located, after the phase shift correction, at 2.49 A and 2.88 A respectively [18]. The peak at ,,~ 3.7 A is related to the third coordination shell (4.08 A). Note that the position of the main peak is the same in all the Fourier transforms and the overall shape of the F(R) is also very similar. The back-Fourier transform results of the main peak of the F(R) shown in Fig. 3 are reported in Fig. 4. In the upper part we show the back-scattering amplitude A(k) and the oscillating part of the x(k) for the transmission and reflection modes. In the lower part the phase shifts are compared with that extracted from the theoretical F(R). The theoretical phase shift takes into account only p ", ed final states [17]. So that the excellent agreement that we observe in all the k range ensures the applicability of the optical selection rule for the two experimental geometries. A confirmation of our conclusion is given by a careful analysis of the L2,3 line shapes. Within the dipolar approximation the near edge line shape of the L2,3 transitions gives us the density of the 3d empty states [10] (the matrix element for the transition p ~ s is about 50 times smaller than that for p ~ d
". ,
-182
R (A) Fig. 3. Fourier transforms F(R) of the fine structures shown in Fig. 2 (upper and central p a r t ) a n d the theoretical F(R) curve (lower part) obtained by Fourier transforming a calculated EXAFS spectrum, including the first three shells. The theoretical phase shifts, backscattered amplitudes [17] and the crystallographic distances [18] have been used.
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k CA-') Fig. 4.. (a) Back-Fourier amplitudes ,~(k) and oscillations obtained from the main peak of the F(R) of Fig. 3 for both experimental geometries. (b) phase shift functions calculated as in (a), compared with the theoretical phase shift reported by McKale [17] taking into account p ~ ed final states. [9]). In Fig. 5 we report the Cr Z2, 3 edges obtained by EELS in transmission (upper curve) and reflection (lower curve) mode. In the second case the spectrum has been numerically integrated. The characteristic sharp double peaks at threshold, called "white lines",
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Vol. 83, No. 11
L2,3 EDGES OF CHROMIUM
are due to transitions from the 2p3/2 (L3) and 2pl/2 (/.2) core levels towards the 3d empty states above the Fermi level EF. The intensity ratio between the L 3 and L 2 edges, obtained after the subtraction of a twostep function located at the edges and with a 2 : 1 intensity ratio considering the 2j + 1 degeneracy of the 2p initial states, is about 1.3 instead of 2 for both the spectra. This anomalous ratio has been observed both in EELS in transmission mode and iri X-ray absorption spectroscopy (XAS) across the 3d transition row [10] and it has been attributed to a breakdown of the one-electron picture [19]. In conclusion we have experimentally checked that for the Cr L2,3 edges the final states for the electron energy loss cross section are dominated by the optical selection rule in both experimental geometries. The results indicate that the E X A F S analysis can be used to exploit the EELFS data taken in reflection mode above highly localized shells like /-,2,3 or K. In this way the EELFS technique gives the same structural information obtained by the EXAFS and energy loss in transmission mode. The different weight of non-dipolar terms for delocalized shells (like L1) detected in reflection and transmission mode has been shown by a comparison between the features obtained with both geometries.
Acknowledgement - The authors are grateful to O. Consorte for valuable technical assistance. REFERENCES .
M. De Creseenzi, F. Antonangeli, C. Bellini & R. Rosei, Phys. Rev. Lett. 50, 1949 (1983).
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
925
M. De Crescenzi, L. Lozzi, P. Picozzi, S. Santucci, M. Benfatto & C.R. Natoli, Phys. Rev. B39, 8409 (1989). P. Aebi, M. Erbudak, F. Vanini, D.D. Vvedensky & G. Kostorz, Phys. Rev. 1341, 11760 (1990). A.P. Hitchcock & C.H. Teng, Surf. Sci. 149, 558 (1985). D.K. Saldin, Phys. Rev. Lett. 60, 1197 (1988). F. Mila & C. Noguera, J. Phys. C20, 3863 (1987). M. De Crescenzi, M. Diociaiuti, L. Lozzi, P. Picozzi & S. Santucci, Phys. Rev. B35, 5997 (1987), E. Chainet, M. De Crescenzi, J. Derrien, T.T.A. Nguyen & R. Cinti, Surf. Sci. 186, 801 (1986). P~A. Lee, P.H. Citrin, P. Eisenberger & B.M. Kincaid, Rev. Mod. Phys. 53, 769 (1981). R.D. Leapman, L.A. Grunes & P.L. Fejes, Phys. Rev. il26, 614 (1982). B.K. Teo & D.C. Joy, EXAFS Spectroscopy and Related Techniques, Plenum Press, New York (1980). M. De Crescenzi & G. ChiareUo, J. Phys. C18, 3595 (1985). D.B. Tran Thoai & W. Ekardt, Solid State Commun. 75, 143 (1990). B. Luo & J. Urban, Surf. Sci. 239 239 (1990). B. Luo & J. Urban, J. Elect. Spectrosc. Related Phenom. 57, 399 (1991). J. Cazaux & A.G. Nassiopoulos, Surf. Sci. 162, 965 (1985). A.G. McKale, B.W. Veal, A.P. Paulikas, S.K. Chan & G.S. Knapp, J. Am. Chem. Soc. 110, 376 (1988). R.W.G. Wyckhoff, Crystal Structures, Interscienee, New York (1980). G. Wendin, Phys. Rev. Lett. 53, 724 (1984).
Solid State Communications, Vol. 83, No. 11, pp. 921-925, 1992. Printed in Great Britain.
L2,3 EDGES OF CHROMIUM: COMPARISON BETWEEN ELECTRON ENERGY LOSS SPECTRA IN TRANSMISSION A N D REFLECTION MODE L. Lozzi, M. Passacantando, P. Picozzi and S. Santucci Dipartimento di Fisica, Universit~ de L'Aquila, 67010 Coppito (AQ), Italy M. Diociaiuti Istituto Superiore di Sanith, 00100 Roma, Italy and M. De Crescenzi
I
Dipartimento di Matematica e Fisica', Universit~i di Camerino, 62032 Camerino (MC), Italy
(Received 17 April 1992 by E. Molina) The extended fine structure above the Cr L2,3 edges observed in electron energy loss spectra taken both in reflection and in transmission mode has been carefully compared. The good agreement between the structural results obtained by the two measurements confirms the validity of the dipole approximation used to describe the cross section of the electron energy loss spectroscopy in reflection mode. This is particularly surprising because in reflection the primary beam energy is of the same order of the magnitude of the investigated energy loss. This effect is ascribed to the localized spatial extension of the L2~3 wave function. The number of non-dipole terms (monopole transitions) has been shown by a thorough measurement of the Li ionization edge intensity.
1. INTRODUCTION IN THE LAST few years a lot of work, both experimentally and theoretically, has been devoted to study the capability of Extended Energy Loss Fine Structure (EELFS) spectroscopy in reflection mode of studying the structural properties of surfaces and interfaces [1-6]. Due to the strong interaction between electrons and matter EELFS is an important technique in the study of adsorbates, clusters and thin films [2, 7, 8]. In this spectroscopy the features observed in the electron cross section above an ionization edge are interpreted as being due to an interference effect between the ejected electronic wave coming out from the excited atom and the backscattered part of this wave due to the presence of the surrounding atoms. This process is similar to that currently observed in the X-ray absorption spectra [9], which need high flux synchrotron radiation sources. The EXAFS theory is based on the dipolar selection rule for the core electron excitation. Instead, in an electron energy loss experiment, the cross section for the excitation of a deep core level has not only the dipolar term, but also :
other contributions (i.e., monopole, quadrupole, etc.) can also be present. In fact, the inelastic cross section for the excitation of core level by fast electrons, in the Born approximation, between an initial core state Ii) and final state If) is given by [10]: d2tr(E, q)
dEdq
871"e4 1
- l~2v2 q3 I ( f l e x p (iq" r)li)l 2,
(1)
where E is the energy loss, q is the momentum transfer, v is the incident electron velocity and r is the position operator of the atomic electron. Expanding the exponential, one obtains: exp(iq.r) = 1 + i q - r -
l/2(q.r) 2 + ....
(2)
Neglecting the first term, due to the orthogonality of the initial and final wave functions, the second term determines the dipole transitions, while the third causes monopole and quadrupole transitions. The weight of the different terms in the cross section depends on the q magnitude. For low q value the dipole term dominates, while at high q value the monopole and quadrupole contributions can not be neglected. In a scattering process with impinging electrons of energy Ep which lose energy equal to AE,
921
922
L2, 3 EDGES OF C H R O M I U M
Vol. 83, No. 11
the momentum transfer q ranges from a minimum T h e s e results underline 'that for localized core levels value qmin o~ Elp/2 - (Ep - AE) 1/2 to a maximum one (Is, 2p) the dipole contribution to the inelastic cross qmax 0¢ A E 1/2. Due to the 1/q 3 term in equation (1) section is still dominant even at low Ep, while the the main contribution to the cross section is other terms (monopole, quadrupole, etc.) are dominated by the q values around qmin. completely negligible. These last contributions are For EELFS in transmission mode, i.e. by using particularly evident for delocalized shells, like Li or very fast electrons with kinetic energy of 100- Ml, because their weight increases dramatically 300keV, since the minimum momentum transfer decreasing E e. 9min is very small (~ 0.1 A-t), the dipole approxi2. E X P E R I M E N T A L mation holds: this has been verified both :experimentally and theoretically [10,11]. Instead, for The E E L S spectra in reflection mode were EELFS in reflection mode, i.e. with low energy performed in an ultra high vacuum (UHV) apparelectrons (1-3 keV), due to the q magnitude (CR L 23 atus with a total pressure in the 10-SPa range. A edge, A E ~ 5 8 0 e V , qmin~3.6/~-'), the dipoi'e thick Cr film (,,~ 500~) was evaporated onto a approximation should be questionable [2,3]. In carbon rod in a UHV chamber at a pressure of order to estimate the amount of non-dipolar ,-~ 5 x 10 -8 Pa. The chamber was equipped with an contributions which are present in the cross section electron gun coaxial to a Riber single pass CMA for the excitation of core edges by low energy (cylindrical mirror analyzer) which was used for electrons, various theories have been developed. For Auger and EELS spectroscopies. All spectra were the K edge of silicon [21 and L2,3 edges of copper [3] it collected with an incident electron energy Ep between has been theoretically demonstrated that the dipole 1000 and 2000eV and a current of 5#Amm -2. A contribution to the cross section is the dominant one peak to peak modulating voltage of 10 V was used for and that the structural results obtained by means of the detection of the fine structure, while for the L2,3 EELFS in the reflection mode are very similar to edges a 2V modulation was chosen, in order to those calculated from EXAFS spectra. Instead, for increase the energy resolution A E / E ~ 0.3%. the M2,3 edges, the higher order terms seem to play an The experimental apparatus for EELS measureimportant role [3] and a sizeable difference between ments in transmission mode consisted of a magnetic the experimental nearest neighbour distance and the sector energy analyzer (Gatan 607) attached to a crystallographic value has been reported [12]. The Philips EM430 transmission electron microscope problem could be associated with the M2,3 ionization (TEM), equipped with a LaB6 electron gun, opersince it has been shown that the same discrepancy ating at a primary beam energy of 250keY. The arises in the analysis of the/142,3 EXAFS spectra [12]. sample was prepared by thermal evaporation of Another interpretation was given by Tran Thoai et al. chromium (99.99% pure) on a copper grid covered [13] on 11//2,3edges ofCu, Ni and Co and by Luo et al. with a carbon layer in a UHV chamber at a pressure on M2,3 edges of Cu [14] and N2,3 of Pd [15]. They of ,-~ 5 x 10-8 Pa. The nominal thickness, monitored have shown that this discrepancy could be due to the with a Inficon XTM quartz microbalance, was about use of the plane-wave approximation for the 500,~. The deposited film was protected against calculation of the backscattered phase shift and oxidation with a thin carbon film and then amplitudes. Instead, the use of the curved-wave transferred into the TEM. approximation leads to the exact nearest-neighbour distances. 3. RESULTS AND DISCUSSION The aim of this work is to assess with high Figure 1 shows the electron energy loss spectra for accuracy the validity of the dipole approximation for the excitation of L2,3 edges of chromium by EELFS the L2, 3 edges of chromium followed by the EELFS in reflection mode, i.e. when the primary beam energy oscillations recorded in transmission (upper curve) Ep is comparable with the energy loss (high q and reflection mode (lower curve). In the latter case transfer). We have compared the L2,3 edges and the the first derivative of the backscattered electron is reported. The L2 and fine structure observed above the same edges of distribution, - d N ( E ) / d E , polycrystailine Cr sample by using electron energy L 3 edges are located at 584 and 575eV energy loss spectroscopy (EELS) in reflection and trans- loss, respectively, while the structure at about mission modes. There is a good agreement between 695eV energy loss is due to the ionization of the Ll the structural results obtained with these techniques shell. It is interesting to note the difference in the in terms of Fourier transforms, back-scattering amplitudes, phase shifts and L2.3 edge intensities. LI/L2, 3 intensity ratio for the two measurements. In
Vol. 83, No. 11
L2, 3 EDGES OF C H R O M I U M
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Energy Loss (eV) Fig. l, Electron energy loss spectra of the Cr L2,3 edges in transmission (upper curve, Er = 250keV) and reflection mode (lower curve, Ep = 2 keV). The latter spectrum has been taken in first derivative mode, -dN(E)/dE. In the reflection spectrum, we report the polynomial function drawn through the LI edge used to subtract it (dashed line). In the inset we report the Li edge recorded in both geometries (continuous line for transmission and dotted line for reflection). The reflection signal has been integrated and the spectra have been normalized at L 3 edge intensity.
2
4
6
k (A-')
8
10
Fig. 2. EELFS structures beyond the Cr L2, 3 edges obtained from the spectra shown in Fig. 1 after the background subtraction. The k wave vector is referred to the L 3 edge. The spectrum taken in reflection mode (curve b) has been numerically integrated and the L I structure has been removed. Curve c is the residual obtained by subtracting a and b spectra.
have been analyzed following the EXAFS standard method: (1) the energy loss has been referred to the L3 the inset of Fig. 1, comparison between the Li edge edge onset energy and then transformed into the kintensity in both geometries is reported. The reflec- wave vector; (2) a background has been subtracted to isolate tion signal has been integrated and the spectra have been normalized at the L 3 edge. This is a clear the modulating structures x(k). evidence of the importance of non-dipole transition After the background subtraction the data taken contribution to the cross section detected in reflection in reflection mode have been numerically integrated mode. It has been shown that for s core edges (such to obtain the x(k) EELFS curve. as L I o r MI, i.e. spatially delocalized wave functions) In Fig. 2 we report the x(k) obtained from the the monopole transition becomes more and more N(E) spectrum taken in transmission mode (curve a) important as a function of the increase of and that from the numerically integrated data of the the momentum transfer [2,3]. This contribution dN(E)/dE spectrum recorded in reflection mode decreases as the incident electron energy increases, (curve b). Figure 2(c) reports the residual curve as clearly demonstrated for the nickel MI edge [16]. obtained by subtracting curve (b) from curve (a) In order to minimize the influence of the LI edge on showing no characteristic frequency over the whole k the analysis of the reflection L2,3 EELFS spectrum we range. The x(k) spectra have been multiplied by k have subtracted this structure drawing a polynomial and then Fourier transformed using a Gaussian curve through the edge (shown in Fig. 1). Instead, in window in the range 2.5 < k(A -I) < 8.5 in order to both the experiments, since the spin-orbit splitting obtain the radial distribution functions F(R). In Fig. between the L2 and Ls edges is small (9eV) com- 3 we report the Fourier transforms FiR ) of the pared with the spacing of the extended fine- oscillations shown in Fig. 2. The theoretical F(R) structure maxima, it is reasonable to neglect the L 2 calculated by the EXAFS formula is reported in the edge [I0]. lower part of Fig. 3. We have included the first three The fine structure of both the experimental data coordination shells and the backscattered amplitudes
924
L2, 3 EDGES OF CHROMIUM
Vol. 83, No. 11
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and phase shifts are taken from McKale et al. [17]. The prominent peak at 2.25 A is due to the first and second coordination shells in the chromium bcc structure [too closed to be resolved in the F(R)] located, after the phase shift correction, at 2.49 A and 2.88 A respectively [18]. The peak at ,,~ 3.7 A is related to the third coordination shell (4.08 A). Note that the position of the main peak is the same in all the Fourier transforms and the overall shape of the F(R) is also very similar. The back-Fourier transform results of the main peak of the F(R) shown in Fig. 3 are reported in Fig. 4. In the upper part we show the back-scattering amplitude A(k) and the oscillating part of the x(k) for the transmission and reflection modes. In the lower part the phase shifts are compared with that extracted from the theoretical F(R). The theoretical phase shift takes into account only p ", ed final states [17]. So that the excellent agreement that we observe in all the k range ensures the applicability of the optical selection rule for the two experimental geometries. A confirmation of our conclusion is given by a careful analysis of the L2,3 line shapes. Within the dipolar approximation the near edge line shape of the L2,3 transitions gives us the density of the 3d empty states [10] (the matrix element for the transition p ~ s is about 50 times smaller than that for p ~ d
". ,
-182
R (A) Fig. 3. Fourier transforms F(R) of the fine structures shown in Fig. 2 (upper and central p a r t ) a n d the theoretical F(R) curve (lower part) obtained by Fourier transforming a calculated EXAFS spectrum, including the first three shells. The theoretical phase shifts, backscattered amplitudes [17] and the crystallographic distances [18] have been used.
i
I
.
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,
I
,
,
.
i
6
4
,
,
8
,
10
k CA-') Fig. 4.. (a) Back-Fourier amplitudes ,~(k) and oscillations obtained from the main peak of the F(R) of Fig. 3 for both experimental geometries. (b) phase shift functions calculated as in (a), compared with the theoretical phase shift reported by McKale [17] taking into account p ~ ed final states. [9]). In Fig. 5 we report the Cr Z2, 3 edges obtained by EELS in transmission (upper curve) and reflection (lower curve) mode. In the second case the spectrum has been numerically integrated. The characteristic sharp double peaks at threshold, called "white lines",
L~ La
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,
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o , 5~5
'
'
'
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Energy Loss (eV)
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Fig. 5. Cr L2,3 edges taken in transmission (upper curve) and r e ~ t i o n ' m o d e (lower curve). The latter curve has been numerically integrated to allow a one to one comparison.
Vol. 83, No. 11
L2,3 EDGES OF CHROMIUM
are due to transitions from the 2p3/2 (L3) and 2pl/2 (/.2) core levels towards the 3d empty states above the Fermi level EF. The intensity ratio between the L 3 and L 2 edges, obtained after the subtraction of a twostep function located at the edges and with a 2 : 1 intensity ratio considering the 2j + 1 degeneracy of the 2p initial states, is about 1.3 instead of 2 for both the spectra. This anomalous ratio has been observed both in EELS in transmission mode and iri X-ray absorption spectroscopy (XAS) across the 3d transition row [10] and it has been attributed to a breakdown of the one-electron picture [19]. In conclusion we have experimentally checked that for the Cr L2,3 edges the final states for the electron energy loss cross section are dominated by the optical selection rule in both experimental geometries. The results indicate that the E X A F S analysis can be used to exploit the EELFS data taken in reflection mode above highly localized shells like /-,2,3 or K. In this way the EELFS technique gives the same structural information obtained by the EXAFS and energy loss in transmission mode. The different weight of non-dipolar terms for delocalized shells (like L1) detected in reflection and transmission mode has been shown by a comparison between the features obtained with both geometries.
Acknowledgement - The authors are grateful to O. Consorte for valuable technical assistance. REFERENCES .
M. De Creseenzi, F. Antonangeli, C. Bellini & R. Rosei, Phys. Rev. Lett. 50, 1949 (1983).
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
925
M. De Crescenzi, L. Lozzi, P. Picozzi, S. Santucci, M. Benfatto & C.R. Natoli, Phys. Rev. B39, 8409 (1989). P. Aebi, M. Erbudak, F. Vanini, D.D. Vvedensky & G. Kostorz, Phys. Rev. 1341, 11760 (1990). A.P. Hitchcock & C.H. Teng, Surf. Sci. 149, 558 (1985). D.K. Saldin, Phys. Rev. Lett. 60, 1197 (1988). F. Mila & C. Noguera, J. Phys. C20, 3863 (1987). M. De Crescenzi, M. Diociaiuti, L. Lozzi, P. Picozzi & S. Santucci, Phys. Rev. B35, 5997 (1987), E. Chainet, M. De Crescenzi, J. Derrien, T.T.A. Nguyen & R. Cinti, Surf. Sci. 186, 801 (1986). P~A. Lee, P.H. Citrin, P. Eisenberger & B.M. Kincaid, Rev. Mod. Phys. 53, 769 (1981). R.D. Leapman, L.A. Grunes & P.L. Fejes, Phys. Rev. il26, 614 (1982). B.K. Teo & D.C. Joy, EXAFS Spectroscopy and Related Techniques, Plenum Press, New York (1980). M. De Crescenzi & G. ChiareUo, J. Phys. C18, 3595 (1985). D.B. Tran Thoai & W. Ekardt, Solid State Commun. 75, 143 (1990). B. Luo & J. Urban, Surf. Sci. 239 239 (1990). B. Luo & J. Urban, J. Elect. Spectrosc. Related Phenom. 57, 399 (1991). J. Cazaux & A.G. Nassiopoulos, Surf. Sci. 162, 965 (1985). A.G. McKale, B.W. Veal, A.P. Paulikas, S.K. Chan & G.S. Knapp, J. Am. Chem. Soc. 110, 376 (1988). R.W.G. Wyckhoff, Crystal Structures, Interscienee, New York (1980). G. Wendin, Phys. Rev. Lett. 53, 724 (1984).