ENDOR MEASUREMENTS OF S-CENTRES IN ALKALI HALIDES

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ENDOR MEASUREMENTS OF S-CENTRES IN

ALKALI HALIDES

B. Eilebrecht, L. Schwan

To cite this version:

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C7-162 JOURNAL DE PHYSIQUE Colloque C7, supplément au n° 12, Tome 37, Décembre 1976

ENDOR MEASUREMENTS OF S" CENTRES IN ALKALI HALIDES

B. EILEBRECHT and L. SCHWAN

Physikalisches Institut (Teil 2), Universitat Stuttgart D 7000 Stuttgart 80, Pfaffenwaldring 57, FRG

Résumé. — La propriété essentielle des centres S~ est le trou de caractère p qui correspond à

l'absence d'un électron de la configuration du gaz rare Argon. A cause de cette structure simple, ces centres peuvent être regardés comme systèmes modèles pour l'étude d'électrons en défaut et leur traitement théorique. La validité des calculs fondamentaux effectués pour des systèmes mono-électroniques peut être testée également aux systèmes de trous. La distribution de l'électron non couplé sur plusieurs couches d'ions voisins a été déterminée dans KC1 par ENDOR. Quelques résultats expérimentaux sont présentés et comparés avec les calculs théoriques.

Abstract. — The characteristic feature of the S~ centres is the p-hole, which corresponds to the lack of one electron to the Ar configuration. Because of this simple structure these centres can be regarded as model systems for the study of defect electrons and for their theoretical treatment. The validity of calculations from first principles made for one-electron systems can be tested for defect-electron systems too. The distribution of the unpaired electron over several shells of neigh-bour ions was determined by ENDOR measurements in KC1. Experimental data are presented and compared with theoretical calculations.

In the study of colour centres we wish to obtain information about the wavefunctions of the localized electrons. One of the best known centre is hydrogen at various lattice sites. For the theoretical calculation of its wavefunction we know several methods that enable us to understand the observed data quantita-tively.

In order to examine the universal applicability of these methods we are now going to use them for a more complicated system, the S~ centre. S- has five

elec-trons in its 3p-orbitals and due to this one hole confi-guration it is complementary to neutral hydrogen. For a theoretical treatment of this centre one can use both a one electron model and a many electron model.

We will consider S~ in KC1, for which experimental results from optic and EPR by Fischer, Griindig and Hausmann [1, 2] are known. In figure 1 you can see

[0011 ^ ^ ^ ,41111

CDT

(off" oi °

K

*

Of—y> ©

m-

( M

"

FIG. 1. — Lattice surroundings of the S~

their model of the centre. It is confirmed by our ENDOR measurements. The sulfur ion is in an anion

site of the lattice surrounded by 6 potassium ions in the first shell and 12 chlorine ions in the second shell. In EPR the centre shows an axial symmetry about the [111] direction. Along this axis the value of the g-factor is 10 % smaller than perpendicular to it.

This orientation of the centre influences the interac-tion of the sulfur ion with the neighbouring nuclei. Only in the first shell all potassium nuclei have iden-tical interaction. In the second shell we can distin-guish between two types of chlorine neighbours : six nuclei are close to the [111] axis and six are in a plane perpendicular to this axis. In the further discus-sion I wish to denote these two types by Clz and CL;.

In the third shell we have two types of potassium. Only the two potassium nuclei lying in the [111] direc-tion are shown in the figure.

Our ENDOR measurements are made with a K-band spectrometer. The figure 2 shows a part of a typical ENDOR spectrum. At temperatures below 20 K the S~ centre shows an ENDOR spectrum which consists of more than 120 peaks. The peaks are extre-mly sharp — the typical half-width is about 5 kHz.

There is a big peak located near 3.5 MHz, which corresponds to the NMR frequency of the free chlo-rine isotope 35.

In order to determine the angular dependence of the hyperfine and quadrupole interaction we carried out two sets of ENDOR measurements rotating the= crystal around two distinct axis, [Oil] and [001].

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ENDOR MEASUREMENTS OF S- CENTRES IN ALKALI HALIDES

ENDOR

Spectrum

Boll C1101:

8.424

kG

I

3.0

3.2

3.4

3.6

3.8

FIG. 2. - Typical ENDOR Spectrum.

In figure 3 you can see the angular variation of the ENDOR peaks. The peaks are represented by triangles in a plot of the rotational angle versus the ENDOR frequency. The crystal was rotated around [oil].

The curves in this figure are the result of the interaction with the chlorine neighbours of the second shell. In order to distinguish the components, in figure 4 we have added the result of a computer simulation. C1, is plotted for the isotopes 35 and 37 (Fig. 4b). We recognize the sum lines (index Z) and a part of the difference lines (index A ) . The ratio of intensity between the isotopes is 3 : 1. We also see the lines of Clp. The lines of both types are split by quadrupole interaction, C1, being split much less than Clp. Look- ing only at the middle lines of these triples we notice, that the hyperfine interaction of the sulfur ion with the two chlorine types is of the same magnitude. In the same way we analysed the potassium nuclei of

the first and the [I 1 I] nuclei of the third shell (Fig. 4a). The simulated curves agree with the experimental results. We verified the simulations by our second set of measurements, so there is no doubt about the correct correspondence between the simulated and the mea- sured lines. The experimental results are compiled in table I.

For a theoretical interpretation of the experimental results we have to determine a model for the wavefunction of the sulfur defect electron. The most obvious orientation for this p-type hole is along the [ I l l ] direction. In this case the CIp nuclei, which are located perpendicular to this axis, would lie in the plane of vanishing probability density of this p-orbital. Because of their non-vanishing isotropic hyperfine constant, we cant to exclude this orientation of the orbital. We propose an orientation of the p-hole perpendicular to the [I 111 direction. In this model the orbital

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C7-164 3. EILEBRECHT AND L. SCHWAN

FIG. 3.

-

Angular variation of the ENDOR signal. The crystal was rotated around [oil].

..I

I .IIJ(LY I I I .a 1 I 1 1 1 1

.

1 1 a . . . . . a . a &I u . 1

.a

.

..adIra 86 u. 8

.

I U I I I I . . a

..I

...

..a. -.u.111

lies in the plane of the six C1, rotating around [Ill]. Since this rotating is fast compared with the EPR frequency we measure an average over the probability density of the hole.

In this model we carried out calculations for the isotropic hyperfine constant a . We used the method of the Loewdin orthogonalisation considering the outer shell electrons of the sulfur ion and the twenty next neighbours. The experimental data and the result of our calculations are compiled in table 11. We obtain the right order of magnitude for all Loewdin values in the middle column. The theoretical value for the first shell potassium nuclei is too large by a factor of 5. This correspondence is nearly as good as in interstitial hydrogen, where even the extended cova- lence theory yields values for the next neighbours

- 30°- [0111- - 60°- lilll-

Comparison of the experimental and theoretical values of the isotopic hyperfine constant (in MHz)

1 ,

.

& I 1 l l Y ( Y ,Ill,. 1. u

.

1 1 1 1 1 1 I I I

.

1 .

.

1 1 . 0. 1 - a . a , . .Iu I i 1 . i a ,.

..

I . . I J U ~ I . I I . a 1 . a . I & , . I 11 r . . . a . . . a

.

a11.1111 c ,

.".

a h a i ~ - . u . , , , ,a , 1 a, I 1 1 4 1...,11

..

1. ~ a 1 l 8 . 1 , U; a ..-1,aW1&.ru.-.r. •

.

a 6 . r a 1 8 1 au a 1 6 1 1

-

t a - a a a . . - d u u 6 1 . - a

..

4 I I 0.

.

. . . a 1 1 . . 1 1 1 1 l . 1 1 a . . I l r u . . . I l l r . . , l . - r .,I..IIIIIIUL. h 1 . a I.), 1 a a 1 r a 1 6 I 181 I I 1 1 r a . I

.

8 . 8 . I

. a u&.&ldu& .as1 & & 1 1

.

..

.

r r a * I - 1 I a I 1 1 . 1, I 1 1 .al,.. ..a. '11

.

r h a . - ., .I.IIIYII.,I .,,,

.

,

.

11. 1 1 11 I .I I 11 I h l .I& a d a d I . .I lid... I

,,, ..n~i-,a a , ., a a

.,

1 1 I I 8 r

.

I 8

.

I t 1 6 .

I..,

1 . 1 . 1 1 1 1 I a 1 t . . . ,

...

1. -

-, r l l a k u r .

.

. & I 1 1 6 I 8

.

a m * t A r r l r 4 r r l 1 a r v l r a .,la.

I , , a ' 1 . 6 a 1.11 1 1 1

.

1 I I 6 h . I a 1 1 .a. .1118. I61

.

1. a ;

I l lL 8 .

..

.

1

.

1 1 1 . 1 1 .I, I .ll . 1 ~ . l . 1 , , 1 1 I I l l 8 4 , ,, 1 u ..

alh

Nucleus Exp. Lowdin LCAO

-

- -

-

3 9 ~ 1 1.39 7.49 6.79

35Cl~la 0.85 0.54 0.89

3 5 C l ~ ~ p 1.25 1.62 2.45

39K11~ 0.007 8 0 0

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ENDOR MEASUREMENTS OF S- CENTRES IN ALKALI HALIDES C7- 165

a>

FIG. 4. - simulation of the angular variation. The crystal was rotated around [011].

than those of the other nuclei. This is a satisfying result for a one electron method like the Lodewin orthogonalisation. In a similiar manner we carried out many electron calculations with an LCAO method

[3] (table 11, right column). The results do not differ

essentially from those of the Loewdin method. Let us summarize the most important facts of my talk : for the first time ENDOR measurements were made at atomic hole centres in alkali halides. We determined the hyperfine and quadrupole constants of the neighbouring nuclei in the first, second and partially in the third shell.

Using the model of the rotating orbital for the para- magnetic hole we are able to interpret the isotopic hyperfine data quite accurately. Applying the Loew- din one electron approximation and a many electron LCAO method to this system, we got comparable results. The validity of our model will be proved by further investigations in equivalent systems.

AcknowIedgments. - The authors wish to thank

Prof. Dr. H. Pick for the possibility to perform these investigations. This work was supported by Deutsche Forschungsgemeinschaft.

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B. EILEBRECHT AND L. SCHWAN

References

[I] FISCHER, F., GRUNDIG, H., 2. Phys. 184 (1965) 299. [2] HAUSSMANN, A., 2. Phys. 192 (1 966) 3 13.

[3] SCHWAN, L., J. Physique Colloq. 37 (1976) C 7...

DISCUSSION

0. SCHIRMER.

-

Unless you have other information than presented in your talk one cannot conclude from the isotropic hyperfine interaction of the nodal plane nuclei in model I, that this model is incorrect :

exchange polarisation of the S- and the overlap electron density, as known for the V,-centers from the works of Ikenberry, Jette and Das, and of Gaz- zinelli and Mieher, will also lead to sizeable nodal plane isotropic hyperfine interaction. The very small

~ 1 1 ' isotropic hyperfine interaction can also be

understood in your model I along lines given in a paper by myself three years ago.

B. EILEBRECHT. - At this moment we cannot determine which part exchange polarization plays for

the S- centre. Transferring the results of the V,-centre to this centre is a questionable procedure because of the fundamental difference between molecular and atomic centres. For the V,-centre the direction of the p-hole is determined by the geometric structure of the molecule, whereas the hole of the S--centre itself influenced the orientation of the centre by the Jahn-Teller-Effect.