X-RAY SPECTRA AND ENERGY BAND STRUCTURE OF ALKALI FLUORIDES

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X-RAY SPECTRA AND ENERGY BAND STRUCTURE OF ALKALI FLUORIDES

T. Zimkina, A. Vinogradov

To cite this version:

T. Zimkina, A. Vinogradov. X-RAY SPECTRA AND ENERGY BAND STRUCTURE OF ALKALI FLUORIDES. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-278-C4-281.

�10.1051/jphyscol:1971451�. �jpa-00214652�

X-RAY SPECTRA AND ENERGY BAND STRUCTURE OF ALKALI FLUORIDES

T. M. ZIMKINA and A. S . VINOGRADOV Leningrad State University

Resum6. - I. Les spectres d'absorption des fluorures des metaux alcalins et alcalino-terreux au voisinage de la discontinuite K (1 s) du fluor ont 6tk mesures [I].

La structure fine prononcee de ces spectres est attribuee k des transitions k partir du niveau interne K du fluor vers des niveaux particuliers de la bande de conductibilitk.

11. Les spectres d'kmission et d'absorption du fluor sont compares avec le spectre d'absorption K du lithium dans LiF [2]-[4] et avec les spectres d'absorption K et LII,III du sodium dans NaF 151, [6].

I1 est souligne que I'interaction coulombienne entre I'electron excite et le trou produit dans le

C(RUI de l'ion positif (cation) peut jouer un r61e important pour la dktermination de la structure fine de la discontinuite d'absorption du cation. La presence d'excitons X emp6che d'obtenir des infor- mations sur la structure de la bande d'energie des electrons k partir des spectres d'absorption X.

111 VINOGRADOV (A. S.), ZIMKINA (T. M.), MALZEV (U. F.) Fizika Tverdogo (1969), Tela 11,3354,

&I VINOGR~DOV (A. S.), ZIMKINA (T. M.), F. T. T., (1970)12, N 5.

[31 LUKIRSKII (A. P.), ERCHOV (0. A.), ZIMMNA (T. M.), SAVMOV (E. P.), FTT (1966), 8, 1787.

[4] HAENSEL (R.), KUNZ (C.), SONNTAG (B.), Phys. Rev. Letters (1968), 20, 262.

[5] RULE (K. C.), Phys. Rev. (1944), 66, 199.

[6] HAENSEL (R.), KUNZ (C.), SASAKI (T.), SONNTAG (B.), Phys. Rev. Letters (1968), 20, 1463.

Abstract. - I. Absorption spectra of alkali fluorides and alkalai-earth fluorides near the K (1 s) fluorine edge have been measured [I].

The pronounced fine structure of these spectra is attributed to transition from K fluorine core level to critical points in conduction band.

11. K fluorine emission and absorption spectra arec ompared with K lithium absorption spectrum in LiP [2]-[4] and with Kand LII,III sodium absorption spectra in NaF [51,[6].

It 1s marked that Coulomb interaction between excited electron and hole left behind in core level of positive ion (cation) can play an important role in determining the fine structure near the cation absorption edge. The presence of X-ray excitons makes impossible to get information about the electronic energy band structure of X-ray absorption spectra.

[I] VINOGRADOV (A. S.), ZIMKINA (T. M.), MALZEV (U. F.), Fizika Tverdogo (1970), Tela 11,3354.

121 VINOGRADOV (A. S.), ZIMKINA (T. M.), F. T. T. (1970), 12, N 5.

[31 LUKIRSKII (A. P.), ERCHOV (0. A.), ZIMKMA (T. M.), SAVINOV (E. P.), F. T. T. (1966), 8,1787.

[41 HAENSEL (R.), KUNZ (C.), SONNTAG (B.), Phys. Rev. Letters, (1968), 20, 262.

[5] RULE (K. C.), Phys. Rev. (1944), 66, 199.

161 HAENSEL (R.), KUNZ (C.), SASAKI (T.), SONNTAG (B.),"Phys. Rev. Letters, (1968), 20, 1463.

At present we have managed to overcome conside- rable experimental difficulties of studying absorption spectra in the soft X-ray range 18-20 rf and have obtained the K absorption spectra of fluorine in five alkali fluorides and four alkali-earth fluorides (LiF, NaF, KF, RbF, CsF, MgF,, CaF, and BaF,). The inves- tigations of the fine structure near the K absorption edge of fluorine were carried out by using X-ray spec- trometer-monochromator RSM-500 [I] operating with a gold coated concave diffraction grating, which has 600 lines per millimeter and its radius is 6 meter.

X-ray tube with tungsten target was used as a source of continuum spectrum. The tube was running at 5 kV, 90 mA. The intensity registred at 18 rf with a slit width 10 mkm was approximately 1 000 imp/s. A proportional counter was used as a detector. In the spectrometer there was a special focusing reflector with polystyrene coating, mounted at the grazing angle of l o 26'. It cuts off the short wavelength radiation with A less than 9 A. The thin films for studying absorp- tion spectra were prepared by vacuum evaporation of fluorides on nitrocellulose films inside of the spectro- meter. The alkali-earth fluorides were evaporated in a separate vacuum volume and then placed into the

spectrometer. The thickness of layers (about 1 000- 5 000 rf) was not measured and the results are presented in arbitary units px (p-linear absorption coefficient, x-thickness).

The energy resolution near absorption edge (about 690 eV) was equal to 0,9 eV. In figure 1 the absorp- tion spectra of alkali fluorides are shown and in figure 2 the spectra of alkali-earth fluorides are shown.

Let us consider, first of all, the characteristic features of the spectra obtained in the region of the K absorp- tion edge of the fluorine. In all spectra there is a sharp absorption edge and fine structure, extending approxi- mately to 60 eV and consisting of separate distinct maxima. In all cases the initial part of the absorption spectrum contains more intensive and more strongly pronounced maxima, than the next part.

In the majority of the spectra the initial part of the curve is separated from the next part by the deep minimum (e. g. minimum p in spectrum of LiF and a in spectrum of MgF,). The length of the initial part was estimated by the distance between the K-point and the deep minimum. It was equal to 13-15 eV in all spectra.

The sharp change of the fine structure is observed

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971451

X-RAY SPECTRA AND ENERGY BAND STRUCTURE OF ALKALI _C4-279

FIG. 1.

-

when one goes from the NaF to the KF spectrum and from the MgF, to the CaF, spectrum. In both cases transition from the third to the fourth period of the periodical table results in considerably more changes of the absorption spectra than transition from the fourth to the fifth period.

It is easy to see that there is an obvious similarity of the fine structures of the alkali fluorides KF, RbF,

CsF on the one hand and of the of alkali-earth fluorides CaF,, SrF,, BaF, on the other hand in spite of diffe- rence between their crystallic structures (face centered cubic lattice of NaC1-type and that of CaF,-type respectively).

There is once more common feature in spectra of fluorides, The onset of absorption shifts to low energy side while going from LiF to CsF and from MgF, to BaF,. This long-wave length shift of the absorp- tion K-edge of the fluorine is in accordance with an idea about increase of ionicity in rows LiF-CsF and MgF,--BaF, and apparently depends on decrease of a binding energy of 1 s electrons of fluorine.

The K-emission bands of fluorine, which had already been studied for the majority of fluorides [2], [3], can be used for interpretation of the spectra under consideration. The absorption spectrum and emission band of fluorine in LiF are produced for example in figure 3.

The emission band consists of the main maximum

A

A',

n

⁵

FIG. 3. - X-ray spectra of LiF.

1 . - K-absorption spectrum of lithium 121 ; 2. - K-absorption spectrum of fluorine ; 3. - K-emission spectrum of fluorine.

The bottom of the conduction band was taken as the origin of the energy scale.

t( a H and the two maxima (( b >> and (( c v, lying at the high energy side from maximum tt a D. These maximas are the multiple ionization satellites [4]. The main maximum ⁽⁽ a ^a,) corresponds to the electron transition from the valence band to the vacancy in the K-shell.

In LiF spectrum the energy distance from the emission maximum (t a >> to the middle point of the increasing part of the absorption curve (the K-point of the

IS

18 spectrum) is equal to 13,9 eV. This value is in a good

f6 agreement iwith the width of the energy gap in LiF

C

G crystal, which is estimated at 13,6 eV from the optical data [ 5 ] , [6].

Such analysis of the emission and the absorption spectra was carried out for the other fluorides and in the table I the distances between the maximum of emission band the onset of absorption in the X-ray

1

4

energy gaps obtained from optical data [5]-[9].

E

670 & 650 mo 7fi 7A7 740 50 -zw 7a the optical data. This gives the basis to conclude that

FIG. 2. - The h e structure of K-absorption spectra of fluorine the onset of the absorption in the K-spectra of fluorine in the alkali-earth fluoride crystals. is connected with the transition of 1 s-electrons to the

TABLE I

Energy gaps (in eV), obtained from the X-ray and the optical spectra

EX-ray Eoptieal EX-rrty Eogtical

- - - - - -

LiF 13,9 13,6[5],[6]

NaF 11,s 12,O [7] MgF2 13,7 12,2 191

KF 10,4 10,8 181 CaFz 11,O 11,3 [91

unoccupied states lying above the bottom of the conduction band.

At present the band structure for the majority of alkali halide crystals is calculated and optical spectra of this crystals are broadly interpreted on the basis of these calculations. Maxima in the optical absorp- tion spectra are related to transitions to excited states, arising near singularities of the conduction band [lo].

Such point of view is used for the interpretation of the X-ray absorption spectra of alkali-halide crystals.

Recently the interpretation of the X-ray absorption K-spectrum of Li in LiF (Fig. 3, curve 1) was carried out by Kunz, Miyakawa and Oyama [ I l l .

The authors have calculated the LiF band structure and determined the energies of the X-ray transitions from the K-level of lithium ion to the singularities of conduction band. From comparison of the experimen- tal data obtained by different methods with the theoretical data they have concluded that the first two maxima A' and A are due to transition of I s electron of lithium to the exciton states associated with the critical points of the conduction band. The other maxima B', B" and B are attributed to the direct transition of the 1 s electron of lithium to the states of the conduction band.

This interpretation does not take into account the effect of the exciton influence on the energy band structure. At the same time, Milgram and Givens [12]

already in 1962 noted that the energies of two the most intensive and narrow maxime A and B in the K-spec- trum of Li in LiF correspond to the energies of transitions of 1 s-electrons to two p-symmetry excited states of lithium ion

/ Is2 lS -+ 1s 2 p 2 P and Is2 lS ^-+ Is 3p lP /

Really, the energy of the maxima A in the LiF- spectrum is equal to 61,9 eV and the maximum B 69,6 eV. At the same time, the energies of the transi- tions, mentioned above, are 62,6 eV and 69,5 eV 1131.

Besides the energy of the first maximum A' coincides with the energy of the quadrupole transition Is2 lS + 1s 2s 'S in the free Li+- ion (61,O eV and 60,s eV respectively).

Further, the energy position of the deep minimum P

coinsides with the ionization potential of Li+-ion (75,9 eV and 75,6 eV respectively). So, the main fea- tures of the initial part of the absorption K-spectxm

of lithium in LiF are related directly with the excited states of the free Lii-ion.

The analogous correlation can be established also by the consideration of the absorption Ll,,I,l-spectrum of Na in NaF (Fig. 4, curve 1) 1141. In the table I1 are given the energies of transitions of 2 p-electrons in a free Naf-ion [13] and the energy positions of maxima in the L

,,,,,,

It is evident from this table, that the energy of the first excited state in a free Na+-ion is in a good agree- ment with the first maximum A in the spectrum of NaF.

The positions of the other maxima in the NaF-spec- trum are shifted to a low-energy side with respect to the position of excited states in a free Na+ ion, due to the influence of the crystal lattice. Therefore, the exci- ted states of the free positive ion reveal clearly in the absorption spectrum of the ionic crystal. As we have seen, all maxima near the edge in the absorption spec- trum of the positive ion in the ionic crystal are origina- ted from the transitions to excited states of the free ion. Some maxima due to these states overlap the continuum absorption and therefore the excited states arise in the conduction band of the crystal. It proves that Coulomb interaction between an ejected electron and a hole in the absorbing shell of an atom plays an important role in determination of the fine struc- ture near the absorption edge. Hence in the case of ionic crystal we can not receive the proper informa- tion about the energy structure of the conduction

FIG. 4. - X-ray spectra of NaF. The bottom of the conduction band was taken as the origin of the energy scale.

Energy positions (in eV) of maxima in the spectrum of the free ion Naf and that of the crystal NaF

Transition 2 p 6 ISo + 2 p6 IS,, 3 2 p6 ISo -, 2 p6 ISo ^-+

2 p 5 3 s lP1 2 p 5 3 p lP1 2 p 5 3 d , 4 s 1 P 1

- 2 p5 4 d, 5 s 'PI

- - -

Na ⁺ 33,3 37,2 41,2 43,9

NaF 33,l 35,5 39,15 41,6

X-RAY SPECTRA AND ENERGY BAND STRUCTURE OF ALKALI C4-281 band from the X-ray absorption spectrum of a posi-

tive ion. At the same time in the X-ray absorption spectra of negative ions the influence of excited states is, probably, less noticeable. Indeed, one can assume, that ⁽⁽ effective charge ^)> of the ion nucleus is increased by one after ejection of 1 s-electron. The outer electron shell of the negative ion correspondes to that of the next element. Therefore, the system of K excited F- (K-hole)

+

+

However, in the crystal lattice such ⁽⁽ excited node ⁾⁾ is surrounded octahedricaly by the positive ions of alkali metal and so the behaviour of the Is-electron, moved away, ressembles behaviour of electron on F-center of alkali-halide crystals. Hence, one can expect the arising of excited states of the 1 s-electron under the bottom of conduction band and with a less confi- dance in the conduction band 1151. However, as it was shown above, in all fluorine K-spectra the absorp- tion maxima before the K-edge are absent and the beginning of the absorption coincides with transitions to states near the bottom of conduction band.

The maxima above the threshold are connected rather with transitions to states of conduction band of the crystal than to excited states of a negative ion.

It is proved by difference between KF, RbF, CsF- spectra on the one hand and LiF, NaF-spectra on the other hand.

The calculations of band structures of alkali- halides [ll], [16] showed that the band structure of

Li and Na-halides considerably differs from band structure of other halides owing to absence of d-states near the bottom of the conduction band of Li and Na-halides. Unfortunately, the calculated band struc- ture with which the obtained spectra can be compared is published at present only for LiF crystal [Ill.

According to the calculation the nearest to the bottom of the conduction band singularities Xi, K1, K, and X; with an admixture of p-states are at 3 - 3,5 eV and 10 - 10,7 distance from the bottom. In LiF- spectrum the maxima A and B are disposed at 2,l eV and 9,8 eV correspondingly. These singularities can be associated with those maxima and the energy dis- tances are in a good agreement. It is difficult of course to draw conclusion on the basis of one example, that the structure of the K-spectra of fluorine reflects the structure of the conduction band. It is desirable besides to have theoretical data about probabilities of transitions.

Because one can't fully confident that the maxima in the spectra are directly connected with the maxima of density of states in conduction band, since the probability of transition has also the great influence on the cross-section of photoionization.

Finally, one can come to the conclusion that the absorption K-spectra of fluorine in the crystals of alkali and alkaline-earth fluorides give apparently more information about conduction band, than the absorption spectra of metals in those compounds.

References [I] LUCKIRSKII (A. P.), BRYTOV (I. A.), KOMJAK (N. I.),

cc Apparatura i metody rentgenovskogo analiza )),

1967, N 2, p. 4.

[2] FISCHER (D. W.), J. Chem. Phys., 1965, 42, 3814.

[3] MATTSON (R. A.), EHLERT (R. C.), c( Advances in X-ray Analysis ^)), 1966,9, p. 471.

[4] ABERG ^(T.), Phys. Letters, 1968, 26A, 515.

[S] CREUZBURG (M.), 2. Physik, 1966, 196, 433.

[6] ROESSLER (D. M.), WALKER (W. C.), J. Phys. Chem.

Sol., 1967, 28, 1507.

[7] REIJI SANO, J. Phys. Soc. Japan, 1969, 27, 695.

[8] TAKEO MIYATA, TETSUHIKO TOMIKI, 3. Phys. Soc.

Japan, 1968,24,954.

[9] STEPHAN (G.), LE CALVEZ (Y.), LEMONNIER (J. C.), ROBIN (S.), J. Phys. Chem. Sol., 1969, 30, 601.

[lo] PHILLIPS (I. C.), ⁽⁽ The fundamental optical spectra of solids B. Solid State Physics, 18. Academic Press, New York-London, 1966.

[ll] KUNZ (A. B.), MIYAKAWA (T.), OYAMA (S.), Phys.

Stat, Sol., 1969, 34. 581.

[12] MILGRAM (A.), GIVENS (M. P.), Phys. Rev., 1962, 125. 1506.

[13] MOORE'(C~. E.), ((Atomic Energy Levels)), 1 , Circ.

NBS 467, 1949.

[I41 HAENSEL (R.), KUNZ (C.), SASAKI (I.), SONNTAG (B.), Phys. Rev. Letters, 1968, 20, 1463.

[l5] L ~ ~ T Y (F.), 2. Physik, 1960,160,l.

[16] KUNZ (A. B.), Phys. Stat. Sol., 1968, 29, 115. Phys.

Rev., 1968,175,1147 ; 1969,180,934.

DISCUSSION Mr JORGENSEN. - Seen from the point of view of

M. 0. theory, it is not surprising that fluorine 1 s allows the detection of many more excited M. 0.

than the central atom 1 s. Thus, in SF, having the point group Oh, sulphur 1 s has only electric dipole-allowed transitions to M. 0. of symmetry type t,, (and there is an infinity of such orbitals) and the six fluorine 1 s would form linear combinations of the symmetry types a,, (from which the selection rules would be the same) and t,, (able to go to a,,, e,, ti,) and e, (from which transitions would be allowed to t,, and t,,.

However, the physically interesting question is whether one-electron substituted M. 0. configurations would be strongly mixed by the two-electron operator of interelectronic repulsion corresponding to an almost well-defined 1 s + 3 p excitation of one definite fluorine atom.

Madame Zimkina should be congratulated for having produced structures frequently assumed to be connected with the repetition of a unit cell in a crystal lattice Careful experimental work is good t o keep the theorists awake.