THE SOFT X-RAY SPECTRA OF SOME METALS AND ALKALI HALIDES

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THE SOFT X-RAY SPECTRA OF SOME METALS AND ALKALI HALIDES

T. Sagawa

To cite this version:

T. Sagawa. THE SOFT X-RAY SPECTRA OF SOME METALS AND ALKALI HALIDES. Journal

de Physique Colloques, 1971, 32 (C4), pp.C4-186-C4-192. �10.1051/jphyscol:1971435�. �jpa-00214636�

JOURNAL DE PHYSIQUE Colloque C4, suppl&ment au no 10, Tome 32, Octobre 1971, page C4-186

THE SOFT X-RAY SPECTRA OF SOME METALS AND ALKALI HALIDES

T. SAGAWA,

Department of Physics, Faculty of Science, Tohok University

RBsumB. - Nous avons Btudie les aspects des spectres des rayons X mous relevant du probleme B N corps au moyen des satellites de grande Bnergie des bandes d'emission mktalliques de Li K, Be K et A1

du spectre d'absorption Na+

des halogBnures de sodium et du spectre d'absorption Cl-

des chlorures alcalins et mBtalliques. Nous discutons Bgalement le satellite de basse knergie de la bande K du graphite en relation avec le plasma habituellement observe dans les bandes d'kmis- sion de rayons X mous des mktaux.

Abstract. - Many body aspects appearing in the soft X-ray spectra were examined by the high energy satellites of metallic Li K, Be K and A1

emission bands, the Naf La,

absorption spectra of sodium halides and the C1- Lz,

absorption spectra of alkali and metal chlorides. Some discus- sions are also given to the low energy satellite of graphite K band in connection with the plasmon satellite observed usually in the soft X-ray emission band of metals.

1. Introduction. - In the soft X-ray spectra of solids it seems to appear the structures due to both the simple electronic process and the many body effects. The former reflects the usual one-electron band picture of solids in unperturbed form and the latters are due to the transient core-hole appearing inevitably in the electronic processes involved.

The influences due to such a core-hole to the soft X-ray spectra can not be negligible even in metals.

Nozieres [I] et al. pointed out that the gradual rising of profile at the Kedge and the small hump at the sharp L2,, edge of metals are typical many body effects due to the transient core-hole. On the contrary, Stott and March [2] showed that these profiles at the edge can be explained by density of states times the tran- sition probabilities. It was also shown by Longe et al. [3] that the electronic decaying process emitting a soft X-ray quantum may give rise to a partial energy loss due to plasmon excitation with a little bit of probability, and results in a low energy satellite called as plasmon satellite. Hedin et a1 [4] suggested further that the interaction of the plasmon with the hole should result in plasmaron satellite at lower energy position than that of the plasmon satellite.

The plasmon satellite was found experimentally for the L2,, emission band of metallic Na, Mg and A1 by Rooke [5], while the plasmaron satellite was not found yet. These many body effects in the spectra of metals are only a small fraction in their intensities of that due to one-electron process.

In insulators, it might be expected that the many body effects due to the core-hole may appear in various features with more enhanced probabilities than in

metals, i. e., the core-excitons for instance. In semi- conductors, where band gaps are narrow compared with the widths of valence or conduction bands and dielectric constants are large, the soft X-ray spectra might be dominated by band-to-band transitions and show rather smooth profiles reflecting densities of states and van Hove singularities. In molecularcrystals, on the other hand, dielectric constants are small and electronic wavefunctions are fairly localized on each molecule. Then the soft X-ray spectra might be dominated by the creation of core-exciton of Frenkel- type and the band-to-band transition may be consi- derably weak. Alkali halide belongs to the intermediate case, and both the excitonic and band-to-band natures will be expected to appear in the spectra.

These properties are treated theoretically by Toyo- zawa et al. [6] for the fundamental optical transitions and the features mentioned above are the analogous speculations to the soft X-ray spectra. In practice, Sagawa et al. [7] examined to explain the sharp absorp- tion bands appearing near the threshold of the Cl- L,,, absorption spectra of NaCl and KC1 as due to these core-excitons, in their early paper. However, Brown et al. [8] interpreted the similar spectra of alkali halides by only the densities of states in the conduction bands.

Under these circumstances, it may be worth-while to examine whether such many body effects as mentioned above exist really or not.

For the case of metals, the high energy satellites, which are emitted from doubly ionized core-state, are investigated, because the satellite bands should reveal a similar profile as main band if one-electron

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971435

THE SOFT X-RAY SPECTRA O F SOME METALS AND ALKALI HALIDES C4-187 process is dominated and should be resulted in modi-

fication of profiles if many-body processes occur with certain probability. Such an attempt has been done by Catterall and Trotter [9] for the K satellite emission bands in lithium and beryllium and they concluded that no modifications of profiles of satel- lites in comparing with the main band are found except small broadening in the band widths. We have re- examined these experiments for the K satellites in Li and Be and the L,,, satellites in Al. As a result, the K satellite in Li showed a general agreement with that of CatteraIl and Trotter. However, the K satellite in Be and the L,,, satellites in A1 have not necessarily similar profiles as their main bands. These non-simi- larities between the main and satellite bands seem to present a new problem to be solved, although it is not clear as yet for us whether the many body processes expected above take a role for these modifications or not.

Plasmon satellite in the emission bands of metals are expected theoretically with very low intensity, which is amounted as about 1 % or less of that of main band. Accordingly, it was not so easy to detect the plasmon satellites with high accuracy. On the other hand, it was interesting for us, whether such a low energy satellite can be found also in semi-metals like graphite or not. Fortunately, the K emission band of graphite has in general so large intensity that the measurement is comparatively easy even for a satel- lite with very low fraction of the intensity of main band if it really exist. As a result, we were able to find out the low energy satellite, which might correspond to the plasmon satellite in metals.

As a representative substance for the case of the insulators, the alkali halide, which is typical substance in order to see the local and non-local natures in its electronic excitation processes, was employed as the specimens. Especially, the shape and the wavelength position of the sharp and large absorption bands near the threshold and their temperature dependences were investigated in detail. It was found that these sharp bands reveal many excitonic natures theoretically expected. Haensel et al. [lo] have also concluded that these bands in the Na+ L,,, absorption spectra of sodium halides are due to core excitons with its hole in 2 p level of Naf in terms of their elegant photo- emission studies.

2. Experimental. - The Na+ L2,, absorption spec- tra was taken by a grazing incidence spectrograph with a concave grating of 2 m radius and a vacuum spark source of Vodar type [ll]. Other measurements were performed by a grazing incidence spectrometer with a convave grating of 2 m radius, where the source for absorption measurements were the bremsstrahlung emitted from tungsten target for the soft X-ray tube specially designed and the emission spectra were taken by the ultra-high-vacuum soft X-ray tube with low target loading. The Siegbahn glass gratings were

employed for whole measurements. The numbers of signal counts were plotted digitally in the step of suitable time intervals except for photographic measu- rements. Further details of the light sources and the procedure for the measurement were described in previous papers [12].

3. Results and Discussions. - Figures 1 to 3 show the comparisons of the profiles of the high

I

-

S A T E L L

. I ^X

FIG. 1. - The high energy satellite band (solid line) compared with the K emission band (broken line) of metallic lithium.

FIG. 2. - The high energy satellite band (solid line) compared with the K emission band (broken line) of metallic beryllium.

>

I-

-

(0 Z W C Z

-

HIGH ENERGY S A T E L L IT E

l , , , , l . * c a l < m a * l ~ ~ ~ . J

- 1 5 -1 0 - 5 0 5 eV

Be

H l GH ENERGY S A T E L L I TE

-0-

--

I . . . . I .

. . .

FIG. 3. - The high energy satellite band (solid line) compared

with the

emission band (broken line) of metallicaluminium.

C4-188 T. SAGAWA

energy satellites in Li, Be and A1 [I31 with those of the main K and L2,, bands, respectively, in normaliz- ed energy scales, where the solid lines are the satel- lites, the broken lines are the main bands, the energy scales were shifted so as t o coincide at the edges each other and the intensities were normalized at the peak height. Similarity between the profiles of both bands is excellent in Li, while the cases of Be and A1 are not so good. The steepness a t the high energy edges are lower in satellites than that of main bands, which are consistent with the theory of edge anomalies in K bands but inconsistent in L,,, bands. It may be possible to be smeared out the edge anomaly in the satellite of A1 by the large life-time broadening in doubly ionized core state. It should be remarked, on the other hand, that the low energy part of the satellite bands in Be and A1 are greatly enhanced in comparing with the main bands. Since the selection rules involved in the electronic transition processes are the same for both the main and satellite bands the origins of such enhanced profiles can not be ascrib- ed to the transition probabilities and also to the den- sity of states, and still remains for us as a problem to be solved.

Figure 4 shows the low and high energy satellites of the K emission band of graphite [14], where the

. .,

(D)

...

...

...

- ... ..._.... ____._....-

240 JW 320 ^{5 -L-}

220 260 280 340

PHOTON ENERGY lev)

FIG. 4. - The high and low energy satellites of the K emission band of graphite (a) and the bremsstruhlung emitted from the tungsten target (b). No structures are found in the photon

energy range of the satellites.

satellites are shown in enlarged intensity scale. The high energy satellite might be due to doubly ionized core-state, while the low energy satellite is not neces- sarily clear at present. In connection with this, the electron energy loss spectra of graphite measured by Zeppenfeld [15] shows the loss structures at about 7 eV and 25 eV low energy positions, where the former is ascribed as due to the plasmon loss for n-electrons and the latter for n and o electrons. Energy difference between the peak positions of main band and that of the low energy satellite observed here is 29.8 eV, which corresponds comparatively well to the loss value, 25 eV, for the n and o electrons. I n general, the plasmon satellites in metals are observed with larger loss energies than the plasmon energies themselves, which

is reasonable also in theoretical point of view. It seems to be reasonable by the reasons mentioned above that the low energy satellite appearing in the K band of graphite is due to the plasmon satellite.

Figure 5 shows major parts of the Nai L,,, absorp- tion spectra in NaCl [16], which is shown as a repre-

NaCL

- L N T

I

3 2 33 3 4 3 5 3 6 3 7

P H O T O N E N E R G Y

FIG. 5. - Na+

absorption profile of NaCl near the thres- hold measured at the room (broken line) and liquid nitrogen

(solid line) temperatures.

sentative of the soft X-ray absorption structures in

alkali halides. Solid line and broken line in the figure

represent the results measured at liquid nitrogen and

room temperatures, respectively. The result shown

here was refined more than previous one [12] by mini-

mizing the effect of scattering light from the diffrac-

tion grating and by correcting the effect of second order

light. Similar profiles were obtained also for NaF,

NaBr and NaI. Absorbance on the low energy side

of band A, which corresponds to the intensity of the

background continuum, is larger than that on the

high energy side of band B. It should be remarked

that the intensity of the doublet, A and B is high

compared with other portion of the spectra. A rough

estimation of the cross section under the absorption

curves in figure 5 shows that the fraction of the

intensity of the doublet to the total cross section

below 41 eV at liquid nitrogen temperature is

about 0.48. As is obvious in figure 5, absorp-

tion band sshift their locations and become nar-

rower when specimen is cooled. The changes of

peak positions and of band widths are tabulated in

Table I and Table I1 for all sodium halides. It is

interesting to note that band E makes red-shift upon

cooling the specimen. The width of the band E is

much wider than that of band A or B. The shape of

the band is asymmetric at liquid nitrogen temperature,

and a minimum on the low energy side of band E

appears to be in a diplike shape. In order to show

the change in the shape of the first doublet upon

cooling the specimen, figure 6 shows the profile of

the doublet of NaCl in expanded scale. In figure

shown absorption curve measured at room tempera-

THE SOFT X-RAY SPECTRA OF SOME METALS AND ALKALI HALIDES C4-189

The shift of the location of various absorption maxima.

R T stands for room temperature and L N T for liquid nitrogen temperature

Peak NaF NaCl NaBr NaI

(ev) (ev) - (ev) - (ev) -

RT 33.21 33.00 32.84

A LNT 33.07 33.29 33.10 32.87s

Difference 0 . 0 8 ~ 0.10 0.035

RT 33.13 33.46 33.27 33.13

B LNT 33.20 33.55 33.365 33.18

Difference 0.07 0.09 0.095 0.05

RT 34.60 34.38 34.00 33.70

C LNT 34.65 34.44 34.12 33.78

Difference 0.05 0.06 0.12 0.08

RT 35.34 34.75 34.30 34.15

D LNT 35.34 34.70 34.36 34.19

Difference 0.00 - 0.05 0.06 0.04

RT 39.08 36.60 36.20 35.54

E LNT 39.08 36.58 36.19 35.51

Difference 0.00 - ^{0.02 - 0.01} - 0.03

The change of the half height width of absorption bands upon cooling specimens. R T stands for room temperature and for liquid nitrogen temperature

Peak NaF

(ev) _- RT

A LNT

Ratio RT

B LNT

Ratio

NaCl (eV> _-

0.21 0.1 I 0.52 0.21 0.12 0.57

NaBr NaI (eV) - (ev) 0.21 0.16 0.10 0.09 0.48 0.56 0.22 0.26 0.12 0.15 0.55 0.58

RT 1.48 0.56 0.76 0.84

E LNT 1.48 0.40 0.52 0.48

Ratio 1.00 0.71 0.68 0.57

ture, Gaussian-curves is shown as well, and in figures showing absorption curve measured at liquid nitrogen temperature Lorentzian-curve are shown as well.

The figure seems to indicate that the band is well approximated by a Gaussian curve at room tempera- ture. The profile measured at liquid nitrogen tempera- ture is nearly Lorentzian in shape although the fitting is not so well as in the case of the fitting to Gaussian at room temperature. Deviation occurs on the high energy side of peak B, which may be due to the presence of the dip between band B and hump C .

We have attributed bands A and B to the creation of excitons at r point in the Brillouin zone. The shape of the absorption band due to the exciton with the hole in the 2 p level of sodium is Gaussian at room temperature. Since the width of the band is reduced as much as 50 percent upon cooling specimen to liquid nitrogen temperature, it is obvious that the

I

3 3

3 3 5 3 3

3 3 5 3 3 6

P H O T O N

FIG. 6. - The shapes of the &st exciton doublet in Na+ Lz.3

absorption spectra of NaCl. The left is the one measured at the room temperature and the right at the liquid nitrogen tempera- ture. Fine line shows the Gaussian for the left and the Lorent-

zian for the right.

shape of the band is governed by the electron-phonon interaction. It was pointed out by Toyozawa [I71 that the shape of the exciton absorption band is Gaussian when the coupling between electrons and phonons is strong. The strong coupling occurs when temperature is high, many defects are present, or the effective mass of the exciton is large. Thus the observed band shape is consistent with Toyozawa's theory.

When the temperature of the specimen is lowered, the electron-phonon coupling tends to be weak. In the weak coupling limit, the exciton absorption band has an asymmetric Lorentzian. In the present case, the Lorentzian shape of the exciton bands in Na+ L2,, spectra can not be explained in terms of the electron- phonon interaction only. Since the effective mass of a 2 p core exciton is large, the electron-phonon interac- tion does not seem to be treated in the weak coupling limit even at liquid nitrogen temperature. According to Toyozawa et al. [6], the coexistence of local and band aspects will lead to the exciton line shape being likely of asymmetric Lorentzian, and a dip similar to an antiresonance dip seen in the autoionization spec- trum of atomic excitation [18] may be observed in solids. A similar result can be caused by the inter- ference of excitonic states with continuous band states [19]. In the present case, the core exciton state occurs in energy in the continuous band-to-band region, and this kind of the electron-electron interac- tion may possibly be caused. Thus, the Lorentzian shape of the core exciton band observed at liquid nitrogen temperature will be ascribed to the electron- electron interaction described above. A dip found on the high energy side of the first doublet may be related to antiresonance.

The amounts of the spin-orbit splitting of the 2 p

T. SAGAWA

Exchange energies and

the amounts of spin-orbit splitting for the r : exciton with the hole in the 2 p level of sodium, I : absorption intensity, E : energy of absorption maximum, A : exchange energy,

52 : unit cell volume,

A : magnitude of spin-orbit splitting. Values were obtained at liquid nitrogen temperature

Material Spectrum A152 x Refe-

( e ~ . ~ m - ~ ) rence Na+

NaF

fundamental Na+

NaCl

fundamental Na+

NaBr

fundamental Naf

NaI

fundamental ("). SANO, Preprint.

( b ) T. T O M I K I , J. Phys. Soc. Japan, 1968, 24, 1286.

("1 Y. ONODERA and Y . TOYOZAWA, J. Phys. Soc. Japan, 1967,22, 833.

( d )

J. E. EBY, K. J . TEEGARDEN and D. B. DUTTON, Phys. Rev., 1959, 116, 1099.

(") Calculated by the present authors on the basis of reference d.

level of sodium do not vary much among different sodium halides, as shown in Table 111. This means that the core level is not much affected by surround- ings, and then the overlap affecting the spin-orbit

: :

;

VUV ABS. f:

WHITE-STRALEY ,'

I

1968 ! /)

NaCL

L3 ABS.

Fonp- Cohen

I

I

- SCOP 1965 --- BASSANI-KNOX - FOWLER 1965

FIG. 8. - C1-

absorption profile of AgCl near the thres- hdld (solid line). Broken line is the fundamental absorption profile obtained by White and Straley. The E-k diagram shown in lower part is the ones calculated by Bassani et al. [24] and

Scop [251.

FIG. 7. - C1-

absorption profile of NaCl near the thres- hold (middle), Upper histogram is the density of states in the conduction band of NaCl and lower one is the E-k diagram,

which are calculated by Fong and Cohen [22].

THE SOFT X-RAY SPECTRA OF SOME METALS AND ALKALI HALIDES C4-191 splitting in crystal is small. According to Onodera

and Toyozawa [20], the exchange energy is given by A = z J / F ( o ) ( ~ Q .

Here J i s the exchange and excitation transfer integrals, F(0) is the envelope function of exciton at the origin, and D is the volume of unit cell. The value of A/Q does not vary much among different sodium halides in comparing with the case of r exciton in the funda- mental absorption spectra, as seen from Table ITS.

This means that the core exciton in Na' L2,, may occur approximately within the sodium ion, while in the case of fundamental absorption, the electron to be excited is transferred from the halogen ion to the sodium ion. These results are compatible with the view that the bottom of the conduction band of sodium halides probably consists of the 3 s function of sodium.

The fact that a large part of the oscillator strength is concentrated to the 1 st exciton doublet is attri- buted to the localization of excitation, which makes the oscillator strength so as to concentrate on exciton

absorption as pointed out by Toyozawa et al. [6].

On the basis of the band calculations for NaCl by Kunz 1211 and Fong and Cohen [22], band E is assi- gned as X-exciton in the Brillouin zone. The large width and the asymmetric shape of band E suggest that the X exciton is metastable. The backgroun- absorption for band E consists of the core-level-to- band as well as the band-to-band transitions, which may makes the X exciton less stable.

Figure 7 shows the C1- L2,, absorption spectra of NaCl as a representative of alkali chlorides, where the energy band diagram and the density of states calculated by Fong and Cohen [23] are also shown.

The data were obtained by gas counter and more refined than that of previous paper 171. I t might be obvious from the figure that both the excitonic and band natures coexist in the spectrum. Figure 8 shows the C1- L2,, absorption spectra of AgC1, where the tentative assignments of the structures are done in comparing with the fundamental absorption in vacuum UV region 123) and with the band calculation by Bassani et al. [24] and Scop [25].

References [I] NOZIERES (P.) and DE DOMINICIS (C. T.), Phys. Rev.,

1969, 178, 1097. MIZUNO (Y.) and ISHIKAWA (K.), J. Phys. SOC. Japan, 1968, 25,627.

[2] STOTT (M. J.) and MARCH (N. H.), Phys. Letters, 1966, 23,408.

[3] GLICK (A. J.) and LONGE (P.), Phys. Rev. Letters, 1965, 15, 589. BROUERS (F.), Phys. Letters, 1964, 11,297. MORITA (A.) and WATABE (M.), J. Phys.

SOC. Japan, 1968,25, 1060.

[4] HEDIN (L.), Solid State Commun,, 1967, 5, 451.

LUNDQVIST (B. I.), Phys. kondens. Materie, 1967, 6,193.

[5] ROOKE (G. A.), Phys. Letters, 1963, 3, 234.

[6] TOYOZAWA (Y.) et al., J. Phys. Soc. Japan, 1967, 22, 1337.

[7] SAGAWA (T.) et al., J. Phys. Soc. Japan, 1966, 21, 2587,2602.

[8] BROWN (F. C.) et al., Preprint to be published.

[9] CATTERALL (J. A.) and TROTTER (J.), Phil. Mag., 1959, 4, 1164.

[lo] HAENSEL (R.) et al., Phys. Rev. Letters, 1969, 23, 530.

[ll] VODAR (B.) and ASTOIN (N.), Nature, 1950, 166,1029.

DAMANY (H.), RONCIN (J.-Y.) and DAMANY- ASTOIN (N.), Applied Optics, 1966, 5, 297.

[12] NAKAI (S.) and SAGAWA (T.), J. Phys. Soc. Japan, 1969, 26, 1427. AITA (0.) and SAGAWA (T.), J.

Phys. SOC. Japan, 1969, 27, 164.

1131 ICHIKAWA (K.), KONO (S.), AITA (0.) and SAGAWA (T.), to be published.

[14] AITA (0.) and SAGAWA (T.), to be published.

[IS] ZEPPENFELD (K.), Phys. Letters, 1967, 25A, 335.

[16] NAKAI (S.), ISHII (T.) and SAGAWA (T.), to be published.

[17] TOYOZAWA (Y.), Prog. theor. Phys., 1958, 20, 53.

[18] FANO (U.), Phys. Rev., 1961, 124, 1866, ibid., 1965, 140, A 67.

[19] PHILLIPS (J. C.), Phys. Rev. Letters, 1964, 12, 447.

HOPFIELD (J. J.), J. Phys. Chem. Solids, 1961, 22, 63. JAIN (K. P.), Phys. Rev., 1965, 139, A544.

[20] ONODERA (Y.) and TOYOZAWA (Y.), J. Phys. Soc.

Japan, 1967,22, 833.

[21] KUNZ (A. B.), Phys. Status solidi, 1968, 29, 115.

[22] FONG (C. Y.) and COHEN (M. L.), Phys. Rev., 1969, 185, 1168.

[23] WHITE I11 (J. J.) and STRALEY (J. W.), J. Opt. SOC.

Am., 1968, 58,759.

[24] BASSANI (F.), KNOX (R. S.) and FOWLER (W. B.), Phys. Rev., 1965,137, A 1217.

[25] SCOP (P. M,), Phys. Rev., 1965,139, A 934.

DISCUSSION

Dr. WIECH. - YOU mentioned that in the case of length region were the absorption coefficient is cons- aluminium the disagreement between the slape of the tant ? In this case the influence of selfabsorption could main band and the short wave length satellite might be neglected.

be due to selfabsorption. In the absorption spectra

presented Dr. Kunz we have seen that there are T. SAGAWA. -In the cases of the satellite bands strong fluctuations of the absorption coeffcient. This of Li and Be, we have not observed any underlying may affect the intensity distribution of the satellite.

high energy tail like as in the case of

The question now is : Do the satellites lie in a wave

C4-192 T. SAGAWA Mr. JORGENSEN. - I certainly agree that the sharp bands A and B of sodium chloride are separated by effects of spin-orbit coupling in the sodium 2 p shell.

Do you know any explanation why A originating in the excitation of two Kramers doublets ( j = 312) is weaker than B originating from only one Kramers doublet ? Perhaps triplet-singlet separation of compa- rable size ?

T. SAGAWA. - There is the theory of Toyozawa

about the changes in both intensity ratio and spin-

orbit splitting, in the absorption spectra of alkali

halides. By his theory, these changes in the intensity

ratio and in spin-orbit splitting are due to the exchange

interaction between the electron-hole created in the

inner hole and the excited electron. His theory fits

to our experimental results very well.