ELECTRON INTERACTION IN X-RAY EMISSION SPECTRA

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ELECTRON INTERACTION IN X-RAY EMISSION SPECTRA

B. Ekstig, E. Källne, E. Noreland, R. Manne

To cite this version:

B. Ekstig, E. Källne, E. Noreland, R. Manne. ELECTRON INTERACTION IN X-RAY EMISSION SPECTRA. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-214-C4-217.

�10.1051/jphyscol:1971440�. �jpa-00214641�

JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-214

ELECTRON INTERACTION IN X-RAY EM1 S SION SPECTRA

B. EKSTIG (*), E. KALLNE (*), E. NORELAND (*) and R. MANNE (**)

R6sum6. - La structure KDI P' a ete Ctudiee expBrimentalement pour tous les elements purs de la premikre sBrie de transition et pour quelques-uns de leurs combinaisons. Les energies et pro- babilitks de transition relatives ont kt6 calculQs dans une approximation

frozen-orbital

pour la transition d'un Btat K normal

des Btats uniquement ionises de la configuration 3 ps 3 d n 4 s2 pour les BlBments Sc-Ni. Les rksultats supportent 17interprBtation que la structure K , ~ I ^{j '} est due a I'interaction Blectronique entre les couches incompl6tes 3 p et 3 d.

Abstract. -The K/?I B' structure is investigated experimentally for all pure elements of the first transition series and for some of their compounds. Relative transition energies and probabilities are calculated in a frozen-orbital approximation for the transition from a normal K state to singly ionized states of the configuration 3 ps 3 dn 4 s2 for the elements Sc-Ni. The results support the interpretation that the Kj1 structure is due to the electron interaction between partially filled 3 p and 3 d subshells.

Introduction. - The K p satellite is an X-ray satellite which appears on the low energy side of the KP, line in the first series of transition elements.

Coster and Druyvesteyn, as early as 1927, proposed that the KP' structure originates from the interaction between a hole and the incomplete 3 d shell [I].

In this paper an account is given of a combined experimental-theoretical investigation of the KP' struc- ture. The full report of the investigation will be made elsewhere [2]. The KP' structure was investigated experimentally for the elements of the first transition series Sc, Ti, V, Cr, Mn, Fe, Co and Ni. In Fe and in the cubic phase of FeGe the structure is investigated at several temperatures above and below the transition points for magnetic phase transition. A study was also made of Fe,O,.

Theoretical calculations were performed for free- ion states and the results were compared with the experiments.

In recent years the hypothesis of Coster and Druy- vesteyn has been elaborated by Tsutsumi [3] and by Nefedov [4] who investigated the KP, P' structure in pure elements and in compounds of the first series of transition metals. Both of these authors have also performed calculations of the relative energies and intensities of the KP, p' structure in a model which assumes coupling of the spins only. In this way two

(*) Institute of Physics, University of Uppsala, Uppsala, Sweden.

(**) Department of Quantum Chemistry, University of Uppsala, Uppsala Sweden.

components are obtained for the 3 p hole states with approximately the correct splitting and intensity ratio.

Recently Fadley et al. [ 5 ] studied the 3 s and 3 p hole levels in Fe and Mn by X-ray excited photoelec- tron spectroscopy and were able to see the splitting of both these levels in analogy to the one studied here.

However, the high background intensity makes a detailed comparison of their results for 3 p and ours for KP, p' difficult.

Present experiments. - Unless otherwise stated, the X-ray spectra were recorded with a bent quartz crystal spectrometer (crystal radius 200 cm, photon counter registration, primary excitation). The samples used were of spectroscopical quality.

The spectra of V and Co are representative for the whole series and are presented under (a) in figure 1 and 3. In addition to these the spectrum of Mn is presented in figure 2 because of its special character.

The complete set of spectra will be published else- where [2].

Previous investigations by Tsutsumi and Nefedov have shown that the chemical environment of the emitting atom influences the shape of the KPIPf structure. For the present investigation we have recorded the KP, P' structure of Fe in Fe@,O, and in cubic FeGe. For Fe,O, the Kj3' intensity is enhanced v i s - h i s the pure metal in agreement with previous investigations. The spectrum of cubic FeGe was recorded in secondary excitation with a bent crystal spectrometer with the crystal radius 50 cm and with

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971440

ELECTRON INTERACTION IN X-RAY EMISSION SPECTRA C4-215

1

f

FIG. 1-3. - The Kb1P region of the elements V, Mn and Co, respectively. The experimental spectrum is represented by curve a. The calculated spectra are denoted b and c, where c includes configuration interaction. The calculated spectra are convoluted and normalized to the same height as the experimental

curve at maximum.

photographic registration. Two temperatures were used for the recording of FeGe, one above and one below the Curie temperature 280 K. No temperature effect was found.

A further search for temperature effects in the KPI P' structure was made for pure metals. Iron was investigated in primary excitation above and below the Curie temperature of 1 040 K and in the liquid state.

Our experiments show that the KP, p' structure is independent of (i) temperature, (ji) mode of excitation and (iii) solid or liquid state of the sample. In a separate experiment we also found that the satellite intensity was (iv) independent of the energy of the impact radiation.

Theoretical considerations. - In order to obtain further information concerning the origin of the KP1 B' structure in transition elements of the iron series we have undertaken some exploratory calcula- tions of X-ray term energies and transition energies using a purely atomic model. Schnopper [6] has shown that the structure is independent of the mode of production of the original 1 s hole state and that no 1 s hole states with excited valence electron confi- gurations are involved. It is therefore natural to describe the initial state of the emission process as consisting of the 1 s hole coupled to the ground term of the corresponding 3 dn configuration. Assuming that this dn term has the orbital angular molnentum Lo and the spin So the two new 1 s 3 dn terms can be described by the quantum numbers (Lo ; So + 3)

and (Lo ; So - +). The energy splitting between these two terms, estimated from Clementi's wavefunctions, is of,the order of 0.04 eV. It is obvious that this split- ting will not influence the experimental X-ray spectrum.

The final states of the KP, emission belong to the configuration 3 p5 3 dn, i. e. the original I s hole has been filled by a 3 p electron. In the general case 6 terms arise with the quantum numbers L = Lo - 1, Lo, or Lo + 1 and S = So - 3, or So -t +, respectively.

We describe all hole states in the frozen electron appro- ximation, i. e. with the same orbital wavefunctions as for the neutral ground state. Under these circumstances and neglecting the energy dependent factor one can then show that the relative transition probabilities are proportional to (2 S + 1) (2 L + 1). For Mn with the configuration 3 d5 4 s2 the ground term is 6S, i. e.

Lo = 0, So = 3. In this case the addition of a 3 p hole gives only two terms, 'P and 5P with the relative inten- sities given by the multiplicities. This result is the same at that obtained by Tsutsumi and Nefedov [3], 141.

Following Slater [7], the relative transition energies can be expressed in terms of the electrostatic integrals between 3 p and 3 d orbitals. These integrals were evaluated from Clementi's wave-functions for the neutral ground terms of the 3 dn 4 s2 configuration.

In order to simplify the comparison with experiment the resulting line spectra have been convoluted with a Lorentzian function with the full width at half-maxi- mum equal to 4 eV. The resulting spectra are shown under (b) in figures 1-3. The curves are all normalized to the same height of the highest point in the convolu- ted spectra. With the exception of Sc a complete treatment of the 3 p hole states within the chosen model necessitates the inclusion of other terms of the same symmetry arising from excited terms of the d, configuration. Transitions to these terms are forbidden by the selection rules but intensity is gained from mixing with the previously considered allowed terms.

Therefore, a configuration interaction calculation

including all 3 p5 3 dn 4 s2 terms with possible X-ray

emission intensity was performed. The energies of the

excited dn terms were taken from optical spectral data

where possible. Energies of terms not listed in Moore's

tables were estimated with the help of the empirical electrostatic integrals calculated by Orgel [8], while the p-d integrals were the same as in the previous case.

Results of this somewhat more complete calculation are given under ( c ) in figures 1-3.

Discussion. - The theoretical calculations of the KP, P' structure are in qualitative agreement with the experiments in the following respect : The lines cons- tituting the high energy part of the spectrum are in most cases the most intense and are collected within a narrow energy region, whereas the low energy compo- nents are distributed over a wider energy region. The resulting spectrum has thus one high energy line, corresponding to the KP, line and some less intense lines spread out over the low energy region, corres- ponding to the KB' satellite.

The KP,-Kj3' energy separation is on the whole too large for the calculated spectrum, particularly when configuration interaction is included. There are several reasons which can be given for the increased spread of the calculated spectrum. One is that in the metals the 3 d orbital population is higher than in the free atom states considered here and the 4 s populations are correspondingly lower. This would increase the nuclear screening leading to more diffuse outer orbitals.

Calculated 3 d-3 d electron interaction integrals are too large to give a good description also of the optical spectra of transition metal atoms and ions. In the present calculation we have tried to remedy this by using optical data for excited dn terms. Obviously, a still better result would be obtained if the 3 d-3 p interaction integrals were also reduced.

Our approach is very similar to that of Fadley et al. [5] who discuss the 3 p hole in Mn2+ (without 4 s electrons), and who performed calculations both with and without the frozen electron approximation, obtaining similar results in both cases. The differences which exist are of minor interest in the comparison with the experiments.

In the model considered by Tsutsumi and Nefedov only two components are obtained corresponding to S = So + 4 and S

So - 4. This situation is identical to that for Mn without configuration inter- action. In this picture the KP, line corresponds to the So + 3 term and the KP' structure to the So - +term.

The inclusion of the orbital angular momentum in the present calculations gives a further splitting to the two components of the spin-only model of Tsutsumi and Nefedov. In some cases this splitting causes a reassignment of the spectra since some low multi- plicity components are shifted to the same energy region as that of high multiplicity components which lie closer together. In this way the calculated relative K p intensity is reduced, particularly for the light elements. Such an intensity reduction is present in our experimental results and is there more pronounced than predicted theoretically.

The asymmetry of the I@, lines found experimen- tally is also reproduced by the calculations, especially when configuration interaction is included. Such an asymmetry does not arise from the spin-only model.

In our theoretical model we have neglected solid state effects. In a crystal the 3 d orbital degeneracy is partly removed by the atomic site symmetry.

((

Crystal Jield

effects are therefore likely to be present also in pure metal spectra but are more impor- tant for complexes where they give rise to characteristic optical spectra and also influence the magnetic pro- perties. Correlations between magnetic properties of transition metal complexes and the Kj3' intensity have previously been established by Nefedov and used as evidence for the spin-only model. In our opinion the crystal field effects will make this model more suitable for compounds than for pure metals. In this way we may explain why the Kj3' structure is often more pro- nounced in X-ray spectra of chemical compounds.

The absence of temperature effects was also noted by Fadley et al. [S] in their electron spectroscopy investigation of these 3 s and 3 d levels in iron and manganese. The results disprove the theory that the KP' satellite intensity is due to electron-phonon interac- tion. On the other hand it is somewhat surprising that no effect was seen of magnetic phase transitions.

Apparently these transitions involve only the coupling of spins between different atoms and have little influene on the local atomic electronic structure. Alternatively, we may speculate that the inner-shell ionization preceding X-ray emission is such a violent event that magnetic ordering is lost. In either case one is lead to localized atomic descriptions of the KP, j3' structure.

Although our calculated spectra exhibit conside- rable smearing of the low energy structure the expe- rimental KP' structures are still more diffuse. To some extent this may be due to the interaction with excited terms not included in the calculation e. g., of the 3 p5 3 dn+' 4 s configuration.

Conclusions. - The present experiments show that the Kj3' satellite is present in all pure elements of the first transition series. It is found to be independent of temperature, liquid or solid state of the sample, ferromagnetic or paramagnetic state, mode of excita- tion, and energy of impact radiation but is influenced by chemical combination.

An explanation of the observed features is offered in terms of the electron interaction between the partially filled 3 p and 3 d subshells of the configuration repre- senting the final state of the transition. Calculations have been made which include orbital angular momen- tum as well as spin and allow for mixing of terms of the same configuration with the same symmetry. They are in better agreement with experiments than previous calculations where only spin was accounted for.

Although the agreement still is largely qualitative

they offer a satisfactory explanation of the observed

features.

ELECTRON INTERACTION I N X-RAY EMISSION SPECTRA

References

[I] COSTER (D.) and DRUWESTEYN (M. J.), 2. Phys., 1927, 1964,2,724, J. Struct. Chem., 1964,5,603 ; 1964,

40, 765. 5,605 and 1966,7,672.

121 EKSTIG (B.), KXLLNE (E.), NORELAND (E.) and MANNE [5] FADLEY (C. S.), SHIRLEY (D. A.), FREEMAN (A. J.), (R.), Physica Scripta, 1970, 2, 38. BAGUS (P. S.) and MALLOW (J. V.), Phys. Rev.

[3] TSUTSUMI (K.), J. Phys. Soc. Japan, 1959, 14, 1696 Letters, 1969,23, 1397.

and 1968, 25, 1418 and Rontgenspektren und [6] SCHNOPPER ( H . W.), Phys. Rev., 1967,154,118.

Chemische Bindung (A. Meisel, ed. Leipzig 1966), [7] SLATER (J. C.), Quantum theory of atomic structzlre,

p. 336. McGraw Hill, 1960.

[4] NEFEDOV (V. I.), Bull. Acad. Sci. USSR, Phys. Ser., [8] ORGEL (L. E.), J. Chem. Phys., 1955,23, 1819.

DISCUSSION

Mr. JBRGENSEN. - Is it conceivable that scandium used and how sure are you of the purity of especially metal and titanium metal do not contain 3 d electrons the Sc and Ti targets.

in contrast to the neutral atoms ? It would be particu- Mr. EKSTIG. - The satellite structure is narrower larly valuable to compare with scandium oxide which and higher in oxides than in metals and traces of

most cannot oxides should therefore be observed in the spectra.

in the form of weak 3 d character of delocalized orbitals Besides, our elemental spectra are in agreement with on the oxygen atoms producing

crossed transitions D. the recordings made by other spectroscop~sts~

Mr. EKSTIG. - The Kfl satellite is definitely present in the Sc metal indicating the excistence of d electrons in this metal. The K,8' satellite is duly present in the transition elements but not in the elements Cu and Zn. We have not recorded the spectrum of ScO and I agree that it would be interesting to do that.

S. HAGSTROM. - What is the influence on the recor- ded spectra of the chemical composition of the targets

Mr. URCH. - Can you explain why the calculated

structure is so much more complex than that which is

observed and why the calculated structure covers a

wider energy range than the experimental spectrum ?

Mr. EKSTIG. - I have pointed out some of the rea-

sons for the discrepances between theory and experi-

ment. The main reason is evidently that we in the cal-

culations use an atomic model whereas the experiments

are made in the solid state.