X-ray EMISSION BANDS AND ELECTRONIC

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X-ray EMISSION BANDS AND ELECTRONIC

STRUCTURE OF SILICON AND OF SOME SILICON, SULPHUR, AND ALUMINUM COMPOUNDS

G. Wiech, E. Zöpf

To cite this version:

G. Wiech, E. Zöpf. X-ray EMISSION BANDS AND ELECTRONIC STRUCTURE OF SILICON AND OF SOME SILICON, SULPHUR, AND ALUMINUM COMPOUNDS. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-200-C4-206. �10.1051/jphyscol:1971437�. �jpa-00214638�

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JOURNAL DE PHYSIQUE Colloque C4, supplLment au no 10, Tome 32, Octobre 1971, page C4-200

X-ray EMISSION BANDS AND ELECTRONIC STRUCTURE OF SILICON AND OF SOME SILICON, SULPHUR,

AND ALUMINUM COMPOUNDS

G . WIECH and E. ZOPF

Sektion Physik der UniversitM Miinchen West-Germany

Rbume. - On presente les spectres X d'kmission Kj? et Lz, 3 du silicium pur, du silicium present dans les composes intermetalliques CaBi, CasSis, CaSi, CaSiz et Cao,75Sro, ~$32, de l'aluminium dans AlN et AlSb, enfin du soufre dans ZnS, CdS et FeS2.

Les rksultats expQimentaux relatifs au silicium sont compares aux recentes valeurs calculkes de la densit6 d'etats et de la distribution d'intensitk des bandes d'emission ^Ket L. Les distributions d'in- tensite theorique et experimentale sont en bon accord. Les bandes d'emission S ^KBet S Lz, ³du ZnS ont etC interpretkes en tenant compte des differentes valeurs des bandes d'energie, obtenues par le calcul.

Abstract. - X-ray Kj?- and L2,s-emission bands are presented for pure silicon, for silicon in the intermetallic compounds CazSi, CasSi3, CaSi, CaSiz and C ~ O , ~ S S ~ O , Z ~ S ~ Z , for aluminum in AlN and AISb, and for sulphur in ZnS, CdS and FeS2.

For pure silicon the experimental results are compared with recent calculations of the density of states and the intensity distribution of the K- and L-emission bands. The experimental and theoretical intensity distributions agree fairly well.

In the case of ZnS an interpretation of the S KB- and S Lz,~-emission bands is given taking into account different energy band calculations.

1. Introduction. - Experimental studies of the electronic structure of solids throughout the filled energy bands and within a considerable energy range of the conduction bands can be achieved by several methods : X-ray spectroscopy (emission, absorption, and isochromat spectroscopy), photoelectron spectroscopy, optical measurements, and to some extent ion-neutralisation spectroscopy. The photon or electron spectrum as measured by one of these methods depends on the electron density of states and on the transition probabilities. It is not possible to obtain information about only one of these two quantities from the experiment, and therefore much discussion is based upon simplifying assumptions.

In the interpretation of the spectra some progress has been achieved since the band structure of numerous elements and compounds, and in several cases also the density of states, have been calculated in recent years. As to X-ray spectroscopic studies only in a few cases have transition probabilities been computed ; e. g. for aluminum [I], copper 121, and silicon [3].

The most extensive theoretical results are available for silicon, where the band structure, the density of states, the transition probabilities, and the intensity distribution of the KP- and L-emission bands were calculated. Silicon is very suitable for a comparison between theory and experiment, because the density of states curve and the X-ray emission bands exhibit marked structural features.

in the first part of this paper the theoretical curves obtained by Klima [3] are discussed and quantitati- vely compared with new Si KP- and Si L,,,-emission band measurements.

In the following parts the X-ray data of a number of compounds of silicon (Ca2Si, Ca5Si,, CaSi, CaSi,, Cao,,5Sro,25Si2), sulphur (ZnS, CdS, FeS,), and aluminum (AIN, A1Sb) are presented. For all compounds, except CdS, the Ku-lines, the KP- and L,,,-emission bands of the third period elements - i. e. the complete X-ray spectrum of these elements - are available.

The results are discussed in relation to available band-structure calculations.

2. Experimental. - For the investigation of the L2 ,,-emission bands a grazing incidence grating spectrometer was used, and for the Ku-lines and the KP- emission bands a spectrometer of the Johann type.

Both instruments have been described in detail else- where [4], 151, and therefore only the more important points are outlined here.

In the concave grating spectrometer a grating with a blaze angle of 1°31', coated with aluminum, was used for the L,,,-band of sulphur and silicon ; and a grating with a blaze angle of 3031f, coated with gold, for the L2,,-bands of aluminum. Both gratings have a radius of 2 m and 600 lines/mm. The detector is a n open Bendix photomultiplier with a tungsten photo- cathode. The resolution of the instrument is 0,46

A

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971437

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X-RAY EMISSION BANDS AND ELEC 2TRONIC STRUCTURE O F SILICON C4-201

The compounds of silicon and aluminum were pressed, or rubbed into an anode of copper, the sulphides into an anode of gold. The X-rays were excited by bombarding with a 0,3

...

6,O mA beam of electrons, accelerated to 3 keV. The X-ray intensity varied from lo3 to lo5 countslmin. The anode consists of a wheel with 8 sectors to hold up to 8 specimens. The wheel can be rotated from outside the spectrometer, and in this way several compounds may be investigated without breaking the vacuum or rebaking the chamber.

Moreover it is possible to focus the electron beam onto different spots of the same specimen. The X-ray tube was operated at a pressure of some l o p 8 torr.

The calibration curves for the special gratings are based on the wavelengths of the MC-lines of 38 Sr to 47 Ag re-measured carefully and with high accuracy [6].

After changing a grating the position of the zero- order reflection and the peak position of the first three orders of the Y MC-line are measured as para- meters to provide the new calibration curve which can be obtained for the whole energy range of the spectrometer within a few hours.

In the Johann type spectrometer a quartz crystal (10i0 plane) was used, bent to a radius of about I m with a reflecting area of 8 x 30 mm2. The average dispersion in the range of the Si KP-band is 6,SX U/mm.

All measurements were performed with fluorescence excitation. The operating conditions of the X-ray tube were 300

...

400 mA and 10 kV at a pressure of about torr. The detector is a GM-counter. The time for recording a Si KP-band was about 1 hour (0,2 eV/min). The intensity of the different emission bands varied with the substance, from 1

..

.4 x lo3 counts/

min, with a background of 5...10

%

of the maximum intensity. Reference lines were Fe Kb, ,, (4. order) and Co Ka, (4. order) for the Si Ka-lines, Ni Ka, (4. order) and Cr Ka, (3. order) for the Si KP-bands [7].

All the compounds proved to be stable during the investigation, except for AlSb which slowly decompo- ses under the electron bombardement.

3. K- and L- emission bands of silicon : Comparison between theory and experiment. - Using the one- electron approximation Klima [3] recently calculated the intensity distribution Z(v) of the KP- and L-emission bands of elemental silicon. This intensity distribution is given by the formula

the integration is carried out over the first Brillouin zone BZ.

The starting-point for calculations of the density of states N(E), and the X-ray K- and L-emission intensi- ties, were the energy bands E(k) obtained by two different methods but leading to somewhat different results. In the first calculation Klima used the energy

bands obtained by Cardona and Pollak [8j wo adjusted the theoretical results to match a number of experimental data. This calculation we refer to as theory I.

In the second calculation, referred to here as theory 11, Klima used the energy bands and wavefunctions which he calculated from first principles using the kp-OPW method. Thus, using these two different energy band calculations Klima calculated the dCnsity of states N(E), and the shape of the Si KP- and Si L-emission bands, by applying the method of Gilat and Dolling [9] and Gilat and Raubenheimer [lo].

FIG. 1. - Valence band structure of silicon a) Density of states N(E) (after Klima [12]),

b) Calculated Si Lz,3-emission bands (after Klima [S]), c) Experimental Si La, 3-emission band,

d ) Calculated Si KB-emission bands (dashed and dotted lines ; after Klima [S]), and experimental Si KB-emission band (full

line ; after Lauger [5]).

14

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The theoretical results for the Si L- and Si KP- emission bands, according to theories I and I1 are shown in figures lb and Id, and in figure l a the density of states N(E) according to theory I. In figure l a the state densities for the 4 single bands v,, v2, v,, and v4 are included. The lower bands v, and v2 (mainly s-like) are almost completely separated, while the two upper bands v, and v, (mainly p- like) strongly overlap.

- To avoid complication the density of states according to theory 11 has not been drawn into figure la.

It might be mentioned that this density of states curve is in good agreement with an earlier calculation by Kane [Ill.

Comparing the density-of-states curves we see that the results from theory I differ in the following points from theory I1 and from Kane's results : the distance between the two maxima D and E is about 1 eV smaller, there is more overlap of v, and v,, and the low-energy fall-off of v, has shifted to lower energies. The band- widths are respectively 13 eV (theory I), 12.4 eV (theory If), and 12.2 eV (Kane).

As a consequence of the dipole selection rules, transition probabilities cause a considerable difference in shape between the N(E) curves and both the K- and L-emission bands. However, if one considers the k- dependance of the transition probabilities for the bands v, to v4 throughout the Brillouin zone [12], one can state that the positions of characteristic points in the N(E) curve are not influenced by transition probabilities - at least not in the case of Si ; i. e.

for the characteristic points in N(E) one finds corresponding points at the same energy in the calculated emission bands.

For a comparison with the experimental results Klima took into account, semiempirically, the width of the core state and lifetime of the final states (Auger effect).

In figures l c and I d respectively the experimental L2,,- and KP-emission bands are shown. The L2,,- band as previously measured [13] was scanned step- wise.

The region between 93 and 99 eV was divided into more than 100 steps, and at each step 4 x lo4 pulses were counted. Special care was taken to examine the influence of the third order C K-emission band which is superimposed on the Si L,,,-emission band in the region of 94 to 95 eV. In this way more structural details have been received than in an earlier measure- ment [14]. - The Si KP-emission band was measured in our Institute by Lauger [5].

By comparing the theoretical and the measured intensity distributions, one finds surprisingly good agreement between theory I and experiment ; this to some degree may be because more experimental data were applied to theory I than to theory 11.

4. Coumpounds of the system Ca-Si. - In figure 2 the Si KP- and Si L,,,-emission bands of Ca2Si,

Ca5Si3, CaSi, CaSi,, and Ca,,,,Sr,,25Si2 are presented.

The K- and L- bands in figure 2 (and in all following figures) are correlated in energy with the corresponding Ka,-lines. The energy positions of characteristic

Energy lev)

FIG. 2. - Si Lz,3-and Si KB-emission bands of Ca-Si compounds.

features of the emission bands, together with the Kx,- lines are listed in Table I.

The Si KP- bands are affected to some degree by the Ca Ka-lines. Since the influence of the Ca Ka- lines is limited to the high-energy edge of the Si KP- bands, there is a little uncertainty in this part of the band, as indicated by dashed lines. The small peakrat the high energy side of the Si L- bands of Ca2Si and Ca5Si3 (100

...

102 eV) is due to the third-order transition MI-L2,, in calcium.

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X-RAY EMISSION BANDS AND ELECTRONIC STRUCTURE OF SILICON TABLE I

Energy position of characteristic points in the Si K-and Si L-spectrum of Ca-Si-compounds (ia eV)

Compound L,,,-emission band Kb-emission band Kcc-line

- -

Ca2Si 90.50 92.50 -

-

1 831.8 1 836.5 1 739.96

Ca5Si, 90.65 92.55 - - 1 832.1 1 835.6 1 836.5 1 739.95

CaSi 89.85 92.10 95.6 97.2 1 829.4 1 832.2 1 836.2 1 739.93

CaSi, 89.70 92.15 95.6 97.0 1829.9 1832.1 1836.1 1 739.97

Cao,75Sro,25Si2 89.80 92.05 95.8 97.6 1829.4 1831.8 1835.9 1837.2 1 739.95

TABLE I1

Energy position of peaks in the S K- and S L-spectrum of sulphides (in eV) Compound

- ZnS (cubic)

CdS (hexagonal)

FeS 2

(pyrites)

Lz, 3-emission band main

Kj3-emission band (Ref. [16]) Ka I-line (Ref. [16])

-

main

peak peak

147.95 151.1 151.6 - 2 459.13 2 462.98 2 466.09 - 2 307.66

The Si KP-emission bands of Ca,Si, CaSi, and CaSi, were measured earlier by Kramer 1151, using photographic registration. His results largely agree with those reported here.

The K- and L-emission bands of the Ca-Si compounds relate closely to the corresponding emission bands of pure silicon (see Fig. l c and 14, indicating similar structures of the energy bands ; this is in agrrement with the fact that the Kcc- lines are not shifted or only to a very small amount. A more detailed examination however shows some small but characteristic differences between the investigated emission spectra.

5. Sulphides. - Figures 3, 4 and 5 respectively show the S L,,,-emission bands of ZnS, CdS, and FeS,, and also the S KP-bands of ZnS and FeS2 as measured in our Institute by Koppen [16]. The energies of the S Ka,-lines, and of the maxima of the K- and L-emission bands are given in Table 11. The intensity of the sulphide L-bands, especially of CdS (3 kV ; 0,25 mA ; 3 x 10, counts/min), is relatively high ; thus measurements with increased resolution are planned. In all measurements the influence of the second-order C K-band was less than 3

%

of the maximum intensity of the S L- band, and could therefore easily be eliminated.

The S L,,,-emission bands of ZnS and CdS, and a number of other sulphides were measured by Meisel, Steuer, and Szargan [17], and by Meisel and Szar- gan [18], using photographic registration. Their results are in agreement with those reported here.

A comparison between the S L,,,-band and the S KP-band of ZnS (Fig. 3) shows that in the valence band s- and p-electrons are almost completely separa-

FIG. 3. - S Lz,s-and S KB-emission bands of ZnS ; S Kjafter Koppen [16].

ted. The lowest part of the valence band (the v, band) is s-like, while in the upper part of the valence band there is only a small admixture of s- and/or d-electrons to the p-electrons. The S L2,,-band of CdS (Fig. 4) is very similar to that of ZnS. Due t o

CdS S L,,3

FIG. 4. - S L2.s-emission band of CdS.

Auger broadening both bands show a strong tailing-off to lower energies. This makes it difficult to determine the energy of the bottom of the valence band.

As has been found by the calculations of Stukel,

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Collins, and Euwema [19] the band structure and the

density of states for 11-VI compounds agree in general ,,,+ 4

features with those for silicon (Fig. 1). The individual bands (v, to v,) become narrower, and the gap between the v,-band and the v2-band increases from the covalent silicon to the more ionic 111-V and 11-VI

compounds, the total width of the valence band remai- ^gwiL u _ - - - -

z L

^,k5 ^*

ning nearly unchanged. In the X-ray KP- and L-emis

sion bands this tendency is clearly observed when one ^,lw; FeS2 S KP

A

goes from silicon, SiGe [20], SiC (IV-IV), to BP,

-

Alp, Gap, InP (111-V) [21], and ZnS, CdS (11-VI). 9"".

For ZnS the band structure was recently calculated

by several authors [22] [23] [24] ; the results are given -

2L55 2160 2 2 A 0 *

in Table 111. The valence band of ZnS consists of three E".C~Y WI

parts separated from each other by relatively broad gaps. The upper valence band is generated by Zn 4s- and S 3p-electrons, the middle and the lower valence band are attributed to the Zn 3d- and S 3s-electrons respectively.

Though these three parts are clearly reflected in figure 3, due to Auger broadening it is difficult to determine the width of the single parts. Alinearextrapolation of the intensity distribution of the S KP-emission band gives a width of 7,O eV for the upper valence band, this value perhaps being somewhat too large. The width at least is 5,5 eV, and thus still larger than the theoretical values (Tabl. III). For the total width the experiment yields a value 2 13,O eV (13,O eV is the distance between the high energy end of the S KP- emission band, as determined by linear extrapolation, and the main peak of the S L2,,-emission band), which is of the same magnitude as the results given by theory.

As is shown by the experiment the distance between the centre of the middle and the lower valence band is 3,5 eV ; the corresponding theoretical value is about 5,s eV [22]. Furthermore, if we take into account the distance between the centre of the middle valence band and the two peaks in the S KP-emission band, and compare it with theory, it seems that the theoretical value for the Zn 3 d- bands which are almost k-indepen- dent, is too high in energy for about 2 eV.

The emission bands of FeS, (Fig. 5, Table 11) when compared with those of ZnS and CdS show some remarkable differences : the peak at about 151 eV in the L2,,-emission band is absent ; at about 161 eV

FIG. 5. - S L2,3- and S KB-emission bands of FeS2 ; S Kfl after Koppen [16].

a new peak appears, with a corresponding peak in the KP-band. Besides this the Kb-band for FeS, is broader than that for the two other sulphides, indicating that the gap between the lower and upper part of the valence band is smaller.

6. Aluminum compounds. - The 111-V-compounds AlSb and AIN were investigated. The results for the A1 L,,,-emission bands together with the A1 KP-emission bands as measured in our Institute by Lauger [5] are reproduced in figures 6 and 7. The energies of the maxima of intensity are listed in Table IV.

The spectra of A1N agree on the whole with the results of Fomichev [25], but there are some differences in the intensity ratio of the two peaks especially in the A1 KP-band.

While the A1 KP- band of AlSb has an intensity distribution similar to that of elemental silicon, in the A1 L2,,- band there seems to be no plateau in the energy region of the main intensity of the A1 KP- band, i. e. between 69 and 72 eV. This means that at the top of the valence band p-electrons are dominant, concentrated in a relatively narrow energy range of about 4 to 5 eV.

For A1N the total width of the valence band (9 eV) is smaller than for AlSb (11.5 eV) ; and the shapes of the A1 KP- and A1 L2,,-emission bands of AlN are less similar to the bands already described than are

Theoretical and experimental values for the widtlzs of the valence bands in ZnS (in eV) Upper valence Gap Middle valence Gap Lower valence Total Authors

band band band width

- - - - - - -

3.6 2.6 0.5 4.9 0.7 12.3 Eckelt [22]

3.5 Rossler [23]

4.3 -+ 8.7 ---+ 1.2 14.2 Walter and Cohen [24]

7.0 13.5 Experiment

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X-RAY EMISSION BANDS AND ELECTRONIC STRUCTURE OF SILICON C4-205 AIN at the top of the valence band, p-like bands are A

100- I I not as predominant as for AlSb or for other compounds

with zincblende or wurzite structure.

W, -

-

AIN AILZl

65 70 ^C

50 W 70 . *

Energy (eV1

FIG. 7. - Al L2,3- and A1 Kj?-emission bands of AIN ; A1 after Lauger [51.

Energy (eV)

FIG. 6. ^-A1 ^L2,3-and A1 Kj?-emission bands of AlSb ; Al Kj? Acknowledgements. - The are greatly after Lauger [5]. indebted to Dr. H. Schafer of the Institut fiir Anorga- nische Chemie der Universitat Miinchen for offering the bands of AISb. The two peaks in the A1 K-band of the Si-Ca compounds. Thanks are also due to AlN have nearly the same energy within the valence Mr. F. Widera and Mr. G. Melchart for assistance band as the two peaks of the A1 L-band. Thus, for during the course of the measurements.

Energy position of characteristic points in the A1 K- and Al L-spectrum of AlSb and AIN (in eV) Compound L2,,-emission band Kj?-emission band (Ref. [5]) Ka,-line (Ref. [5])

- -

AlSb - 63.7 67.35 1 552.3 1 554.1 1 557.6 1 486.67

AIN 55.9 64.9 68.3 1 543.3 - 1 555.5 1 486.74

DISCUSSION M. URCH. - The data presented for sulphur L2,, M

and Kfl emission spectra for iron pyrities can be inter- preted using a simple molecular orbital model. This model describes the bonding interactions of the atomic orbitals in the S i - unit. The ionisation energies of S 3 s and 3 p orbitals are approxirrrately 20.2 and 10.4 eV respectively. The rather clear separation of the Kj?

and L2,, M spectra relative to the Fermi level suggests that there is little hybridisation of the s and p valence orbitals of sulphur. The main broad feature of the L2,, M spectrum will therefore be due to electrons in a and a* (asterisk for antibonding) molecular orbitals of fairly pure 3 s character. The two weak maxima at higher energies may be due to either 3 s or 3 d participation in other orbitals which are principally 3 p in nature. The 3 p interactions will be both ^a(i. e.

* *

along the S-S bond) and n. Orbitals n,, n,, n,, n,, and a, will be occupied but or will be empty. The

highest energy peak may be ascribed to electrons in the n* orbitals and the main peak to electrons in the n orbitals ; the low energy shoulder will then be due to electrons in the S-S o, (3 p) bond. Some interaction between this orbital and the ^o,orbital of 3 s character will be possible, hence the weak peak at 155 eV in the L2,, M spectrum, which can be aligned with the shoulder in the Kj? spectrum. If this interpretation is correct the great difference in intensity between n and n* peaks presents a difficulty. It would be antici- pated that 3 d interaction will be greater with the n*

orbitals than with the n orbitals. Thus the n* orbitals may have considerable 3 d character and less 3 p character ; i. e. 3 p participation will be greater in n than in n* and therefore the transition at 2 466 eV is greater than that at 2 469 eV. The closeness in energy of these two n systems is probably also due to 3 d - n"

interaction causing the ionisation energy of n* to be

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increased. The highest energy peak in the L2,3 M spectrum is therefore associated with 3 d participation in the z * orbitals.

It is hoped that this interpretation shows now molecular orbital theory can be applied to X-ray emission spectra and conversely now such spectra provide invaluable information about the nature of chemical bonds for chemists.

M. WIECH. -I thank you very much for this interesting remarks.

M. FABIAN. - T O what extent did Klima take account of transition probability effects in his calculations of the emission curves for Silicon ?

M. WIECH. - Klima took into account the transition probabilities according to the formula mentioned in this paper. H e calculated the transition probabilities for the 4 bands v,, v,, v3 and v, of silicon along several symmetry lines of the Brillouin zone.

M. JBRGENSEN. - The similarity of the L emission curves for a variety of calcium silicides to that of crystalline silicon might invite the slightly heretical comment that the energy band structure may be of minor importance compared with effects of local order.

Thus, it would be interesting to study liquid silicon (theorists sometimes seem t o forget the existence of liquid metals) or to compare two crystalline modifications of the same stoichiometry such as pyrite and marcasite. Would the various modifications of silicon dioxide have spectra highly different from your silicides ?

M. WIECH. - Yes. the Si L2,3 emission band as well as the Si KP-emission band of SiO, differ markedly from the corresponding bands in pure silicon. In our institute the Si KP-bands were measured by Lauger for quartz, coesit and stischowit. The bands of the first two compounds differ only sightly, but the Si KP-band of stischowit shows a quite different intensity distribution.

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