X-RAY ABSORPTION SPECTROSCOPY (L3 EDGES, XANES, EXAFS) ON 4f MIXED-VALENT COMPOUNDS

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X-RAY ABSORPTION SPECTROSCOPY (L3 EDGES, XANES, EXAFS) ON 4f MIXED-VALENT

COMPOUNDS

G. Krill

To cite this version:

G. Krill. X-RAY ABSORPTION SPECTROSCOPY (L3 EDGES, XANES, EXAFS) ON 4f MIXED-VALENT COMPOUNDS. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-907-C8-914.

�10.1051/jphyscol:19868176�. �jpa-00226081�

X-RAY ABSORPTION SPECTROSCOPY (Lg EDGES, XANES, EXAFS) ON 4f MIXED-VALENT COMPOUNDS

G. KRILL

Laboratoire d e Physique du Solide (U.A. C.N.R.S. 155), Universit6 de Nancy I, F-54506 Vandoeuvre-1Bs-Nancy Cedex, France

and

L.U.R.E. (L.P. C.N.R.S.). Universite Paris-Sud, F-91405 Orsay Cedex, France

Resume. - L'utilisation de la spectroscopie d'absorption X 2 l'etude des compses 2 valence intermediabe est r e s h e . Cette technique experimentale, qui p m e t la d6- termination absolue du t a m d'occupation 4f, est souvent critiquee,etant donne l'exis- tence possible de processus mlti6lectroniques qui peuvent fausser les r6sultats.

Aussi, dans cet article, une attention toute particulihe sera portke 2 ce problhe ainsi qu'a son influence 2 la fois dans le cas des composes de terres rares 18g2res (La, Ce), et lomdes (Sm, Eu, %I, Yb). D'autres m&anismes, pouvant GSre confondus avec les processus multi6lec-troniques, semnt envisages. Finalement , ¹ 'utilisation de L'EXAFS et du XANES pour l a determination des relaxations atomiques dans les com- poses 2 valence intddiaire sera envisag5e.

A b s t r a c t . - The use of X-ray absorption spectroscopy (XAS) in the study of mixed- valence (MV) compounds is reviewed. %is technique which allows an absolute deter- mination of the 4f occupancy is often criticized because of the possible existence of rmiltielectmn pmcess in the final state which m y falsify the results. Therefo- re a special attention will be paid in this paper to this problem and on its possi- ble influence both in the case of light rare-earth (KE) (La, Ce) and heavy RE (Sm, Eu, Tm, Yb) compounds. Pzrticularly, several other mechanisms, which m y be confused with final state effects, are discussed. Finally the use of EXAFS and XANES for the determination of atomic relaxations in PV compounds is investigated.

1. 1ntroduction.-

The possibility that the 4f orbitals in RE campounds m y hybridize with the conduction electrons has open, since a decade. a wide and interesting field of research both in Solid State Physics and i n the Chemistry of Solids. - - S fascina- ting results have been obtained for the so-called mixed-valent ( W ) mterials and recently for the heavy-fermions compounds (1, 2, 3 ) . k both cases the particular properties of the ground state are the consequence of the presence at the Fermi level (or very close from it) of degenerate 4f levels which are, more or less, hy- bridized with the conduction electrons (4). I shall reswict myself in this paper to discuss the case of M I compounds.

Due to the hybridization the 4f electrons form a "band" and thus, m y fluctuate between localized and extended states according to : 4 fn (5d 6 ~ + ) ~ 4 ~ - 1 (5d The characteristic timy fox this24f charge fluctuation (~f) deii pends directly on the hybridization. ( T - ~ = A = rVkf Po) (5). For MV compounds, A is typically 0.1 + 1 eV and thus

is 10- - 10-l4 sec. These quantum-mechanical fluctuations yield a non-integraL 4f occupation number (nf) which may be in a simple way related to the mean valence V. (The valence of a RE ion is, by definition, the number of ( 5 4 6s) electrons, i. e. m). Because the X-ray absorption process takes place on a very short time scale (10-l6 s < rf) both the 4fn (5d 6sIm and

4fn-I (5d 6sIm+l configurations are directly observed in the absorption spectrum of a MV compound ( 6) .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868176

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If the hybridization dmps to zero (Vkf

0) thus ~f tends to infinity.

In this last situation the MV state, if it occurs, IS static and often labelled as inhomgeneous. However, as all the intermediate situation m y occur, the distinction between homogeneous (dynamic) and/or inhomgeneous (static) M I states m y be, in some cases, quite mificial.

The pmblem of W compounds r e s w s to the "old" and diffkult situa- tion, currently encounted in Solid State mysics, where the hybridization (1) is of the same order as the intraatomic Coulomb interaction (Uff and/or Udf). Tne ana- logy with highly correlated systems is striking (e. g. Yott-Hubbard insulators (7) ).

For the 4f compounds the problem is not straightforward because the degeneracy of the 4f orbitals and the spin-orbit coupling (including relativistic corrections) must be taken into account.

The aim of this paper is to discuss, from an experimental pint of view, how high energy spectroscopies m y give valuable infonration on the fundamental pa- rameters of the MV problem (particularly nf (8) and the hybridization). The paper js divided into two m i n parts. In the first one (sections 2 and 3 ) the direct use of Lg spectroscopy in the detemFLnation of 7 (nf) will be presented, paying a spe- cial attention to the pmblem of mltielectron process which are often invoked to minimize the quantitative use of high enwgy spectroscopy (8, 9, 10). A comparison with other experimental techniques will be given. In the second prt (section 4), the information that m y be obtained from the XANES (20 + 100 eV above the Lg edge) and the MAFS (100 + 1000 eV) experiments will be presented. I shall focus on the problem of atomic relaxations (i. e. how the lattice responds to a change in the 4f occupancy) which are sensitive to the hybridization parameter.

2. L3 edges spectroscopy on mixed-valent materials : comparison with other experi- mental techniques.-

In the last decade L3 absorption spectroscopy has widely been applied in the field of MV compounds. Particularly the valence transitions induced by pres- sure (Cerium metal (IT), Srn S (12) ) temperature (Eu Pd2 Si2 (13) , ^Eu Gun Sin (14) or by alloying effects (15, 16) have been investigated.

The basic idea for the use of L3 edge spectroscopy in MV mterials is simple. If we suppose that at a qiven time two types of 4f configurations (say 4fn (5d 6sIm and 4fn-I (5d 6s)m+ ) coexist in a compound and if their lifetimes are longer than 10-l6 sec, then, because the screening of the nucleus charge is m r e efficient for a 4f electron than for a 5d, the Lg absorption edges (and m r e generally all core-level excitations) will be made of two well-separated contribu- tions (7-10 eV) corresponding to the two 4f configurations (17). In principe we need iust to weight the intensities of the two contributions to get the mean valen- ce : V = 2 + (I (4fn-l)/(1 (4fn) + I (4fn-l)) . The m i n advantage of this high ener- gy spectroscopy is the possibility to get an &solute determination of V. For all the other experimental techniques which m y be used to deduce (M6ssbauer effect, sus- ceptibility or lattice parmter measurements) references for the integral valent states are needed.

In table I the values of V, obtained from several experimental techni- ques, on various MV (or Integral Valent) systems are reported.

Table I V

a-Ce Ce Nis Sm S (HP)

Sm Bg Eu W3 EuPd2Si2 Eu Pd2 P2

L 3

3.1 (11) 3.3 (17) 2.57 (12) 2.65 (21) 3. (25) 2.3 (13) 2.2 ( 8 )

XPS

<3.04 3.12 (18)

-

2.65 (22) 2.5 (26)

-

2.2 ( 9 )

Latt. con

3.5 4.0 2.77 (19) 2.77 (23) 3. (27) 2.3 (28) 2.4 (29)

Suscept.

non mag.

non mag.

-

-

3 (27) non mag.

2 (8)

Cdssbauer

-

-

2.61 (20)

2.65 (24)

3. (27)

2.2 (13)

2- (8)

effects complicates seriously the pmblev (30). (However such surface effects are absent in the cerium compounds (17)). For the lattice constant the relationship between volume and valence is non linear (30, etc. However in some other cases the results are definitively umeconciliable. For instance in all the cerium AW compounds the values obtained from the Lg (or XPS) differ completely from those deduced from lattice constant and/or ~mgnetic susceptibility measurements. This point has been verified in nmrous cerium systems (6). Even i n the case of heavy FE compounds the- re are some puzzling situations. For instance Eu Pdn P2 is zdoubtly purely divalent in its p u n d state whereas it appears to be mixed-valent (V = 2.2) from the high energy spectroscopies results.

At evidence such discrepancies must be explained if we want to be confi- dent in the results obtained from high energy spectroscopy. In order to underline the possible sources of ermrs let us first describe the mechanism of a L3 absorption process and the usual approximations which are made for the data analysis.

A Lg absorption process is a 2 P312 + 5 E d (or 2 p312 * ⁺ 6 ^E s*) transi- tion. Because of the dipolar selection rules (1 = 2 1) only empty states with d or s symmetries can be reached in the final state. (E means that there may be some ad- mixture with other symmetries in the 5d or 6s initial state and the *is simply here to underline the fact that we are in a final state with one m r e electron in the 5d

(or 6s) states and a core hole on the 2p level). As the transition probability mtrix elements for a 2p3/2 + 6s transition are two order of magnitude weaker than those for a 2 P3/2

5d transition they can be neglected in the physical description of a L3 absorption process. In principle if we want to describe correctly an experiment it is necessary to calculate the transition probability mtrix elements P (E) =

I ^< +* 1 ^exp (?%?)?I + ^> 1 ^where I $I* ^> is the wave function of the final state

(i. e. in the presence of the core hole) and their energy dependence. This is an impossible challenge and thus several simplifications must be mde.

a) The most important (and probably the m r e delicate) is to suppose that a one-electron picture can be used. In the final state all the orbitals which are not directly involved in the abs~rption process are passive. It means that they are insensitive to the creation of the core hole. For 4f metals recent calculations have shown that this single electron picture works strikingly well ( 3 2 ) . However in the case of MV mterials the situation is a little bit more complicated.

b) Often an overshplified mdel is used. Tt supposes that the sane L3 profile m y be used for the 2 P3,2 (4F) + 5 e d? and the 2p3l2 (4fn-l) + 56 d*

transitions. This approxhtion is not correct because i) there is no reason to suppose that the P (E) are identical and ii) the shape of the 5d density of empty states m y be rather different. The procedure becomes particularly hazardous if one tries-b~eproducethe Lg edge of a given RE atom using that obtained for an other FE even if the local environments are quite identical.

The pmblem of multielectron process (i. e. the breakdown of the one- electron picture) will be discussed in section 3. Let us now consider in details what kind of errors m y result from the second point we mentionned just above (b).

In the one-electron approxinntion a Lg edge m y be fairly well repro- duced (14) by i) the convolution of a Lorentzian (traducing the core hole lifethe) with a 5 ~ d x density of empty states weighted by P (El, ii) adding an arctang curve to take into account the transition towards the continuum, iii) a final convolution with a Gaussian reproducing the experimental broadening. Tt is thus possible to deduce experimentally the product N (E) = P (El . ^{(5 E} d*) by several deconvolutions process (33).

The corehole lifetimes for all the RE: elements are well Icnown and the

experimental resolution m y be precisely deduced by taking the rocking curve of the

mnochmmtor used for the experiment. Such a procedme needs low noise data and it

supposes that all other experimental difficulties (thickness and homogeneity of

the samples, absence of holes, etc.) have been overcomed. All these parameters af-

fect drastically the shape of the white line.

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The r e s u l t s obtained f o r several Eu/Pd and Eu Pd2 S i n compounds a r e shown on f i g u r e 1. The shapes of N (E) a r e s i g n i f i c a n t l y d i f f e r e n t f o r E U ~ + (4f 7, and E U ~ + (4f 6 , ; mreover they a r e highly dependent f m t h e chemical environment.

It i s i n t e r e s t i n g t o notice t h a t , i n t h e case of Eu Pds(fig. 1 a ) t h e shape we found f o r N (E) well agrees with t h e BIS experiments ( 5 3 ) . bhether, f o r E U * + / P ~ , t h e par- t i c u l a r shape o f N (E) m y be due t o a modification of t h e density of s t a t e s o r t o t h e occurrence of a shake-up e f f e c t (see section 3) i s s t i l l an open question.

Fig. 1 : N (E) for several Europium compounds (see t e x t ) (a means m q h o u s compounds). The v e r t i c a l bars in f i g . 1 a f o r Eu Pd3 indicate t h e positions and i n t e n s i t y of t h e 5d density o f s t a t e s a s deduced f r o m BIS experiments ( 53 ) .

Any f i t t i n g procedure which w i l l use iden'tical o r unappmpriate valces f o r N (E) yields, t o a m r e o r l e s s extent, uncorrect r e s u l t s . It i s possible t o es- t h t e t h e error one can make. Let us suppose t h a t , instead of t h e c o r r e c t N (El f o r Eu Pd3 , we use t h e dashed symmetric shape shown on f i g . 1 a. The new f i t is shown on figure 2 . I n order t o bring some i n t e n s i t y i n t h e 5 ^-+ 10 eV region, one m y try t o intmduce a s m l l component ( 7 %) above t h e E U ~ + edge. This i s exactly t h e energy position expected f o r E U ~ + . Such a configuration has never been observed i n any Eu compound.

The f i n a l conclusion of such an experiment w i l l be t h a t Eu _{Pd3 i s mixed-} valent with V = 3.07 ( ! ! ). Thus even i n t h e one-electron picture, without involving any experimental f a l s i f i c a t i o n it i s possible t o get wrong r e s u l t s .

Let us mention here a n additionnal complication which m y come from t h e W S structu- res. I n some cases (34) t h e multiple s c a t t e r i n g of t h e photoelectron m y give an extra contribution

near t h e edge s t r u c t u r e (10 eV) contributing t o

t h e m r we can rrake on V. Before t o invoke any

multielectron process it i s thus important t o check

t h e following points : a ) Are we sure t h a t t h e sam- ,

p l e i s homgeneous, exempt of any contamination

(oxidation, e t c . ) ? b) Are we confident i.h t h e

N (E) used f o r the f i t t i n g pmcedure ?

C ) Can we a s c e r t a i n t h a t

there i s no W S contribution i n t h e energy range ,,

where t h e 4fn-I is expected ?

I f t h e answers t o these questions a r e a l l p o s i t i v e then multielectron process m y ke

suspected.

^{k v )}

Fig. 2

died how the electrons react to the sudden creation of a core hole, it has been a lot of theoretical and experimental jobsonthis subject particularly in the case of 4f mterials (36, 37). As this pint will be extensively discussed at this con- ference it is not necessary to enter the details of the subtil mechanisms which are at the origin of the multielectron process. Let us just underline the main fea- tures :

- Due to the attractive potential of the core hole a 4f level, unoccu- pied in the initial state, is lowered below the F e d level in the final state. De- pending on the hybridization this 4f state will be either occupied or unoccupied in the final state. This is the shake-down process encounted in metallic materials.

- In the case of insulating compounds, because there are no conduction electrons, such shake-down process becomes unpmbable and in such a case a shake-up process takes place. This m y be also the case even in metallic compounds if, for instance, the shake-down process is energetically unfavourable.

For the 4f mterials a shake-down means that there is one more 4f electron in the final state and the shake-up one electron less. At evidence we will have some problem in the determination of V. For the purpose of this paper it is interesting to answer briefly the following questions :

1) Is it possible to predict the occurrence of such mltielectron process ?

2) Are they important for L3 spectroscopy ?

Shake-down satellites have been clearly observed in the XPS core level spectra of numerous La and Ce compounds (18, 38). For instance the intensity of this satellite is 40 % in La Pd3 and 20 % in Ce Pd3. Light RE elements like Ia or Ce are good candidates for multielectron process because the 4f wave function is extended in real space and thus the hybridization with the conduction electrons is enhanced. As shown by the recent theoretical calculations of GUNNARSSON and

SCHONWMMER (36, 37) the XPS spectra (and also the BIS and MV edges) are well repro- duced if the hybridization is properly taken into account both in the initial and final states. It means that the (nf) values obtained from high energy spectros- copy are roughly correct. In these cases lattice constant or magnetic measurements are unable to yield the correct value of nf. The concept of valence breaks down in this high hybridization limit. For heavy RE elements (Sm, Eu, ?m, Yb), because the hybridization becomes smller (the 4f orbitals are more localized) , such multi- electron processes are less probable. It explains why the agreement between high energy spectroscopy and other experimental techniques is better (see table I).

Except the puzzling case of Eu Pd2 P2 and more generally that of divalent Eu, where atomic calculations (39) have shown that the shake-down processes are impos- sible, there is no direct experimental evidence of shake-up process in metallic compounds.

Up to now we discuss essentially the way by which the electrons will react to the sudden creation of a core hole. In fact if this situation is exactly that encounted in XPS (or in EXAFS), it differs a lot for an absorption process.

There m e at least two f u n b n t a l differences :

i) the photoelectron has an almost zero kinetic energy ; thus we are in an adiabatic limit where the electrons will have time enough to relax in order to screen the core hole,

ii) the photoelectron stays on the atom and plays a role in the scree- ning of the 2p core hole. For these reasons mltielectrons satellites m e weaker in XAS than in XPS and it is always difficult to show their existence (40). This is well illustrated on fig. 3 where the XPS (3d) and XAS (L3) of La in L3. Pd3 have been repoeed. The L3 data are deconvoluted f m n -the core hole Iffeeime (3.4 ell) in order to enable the comparison wlth XPS, The intensity of the 4f shake-down is considerably reduced in XAS. Similar conclusions have been-obtafned for numemus La and Ce compounds (41, 42). It explains simply why the nf (V) deduced from the L3 well agrees with the values calculated in the Gunnwsson and Sch6nnhanmerrs nodel.

We do not really understand in this context why for Eu Pd2Pnthe same "shake-up" inten-

sity is observed both in XAS and XPS.

JOURNAL DE PHYSIQUE

1 1.

Fig. 3 : Lg of La in La Pd3 (The re- sults have been deconvoluted from the core hole lifetime) The vertical bars give the intensity observed in XPS for

A L.M*

4r'

r

at*

the La3 d512 core level.

- 6 - 4 2 0 2 4 6

-XAS (LJ)

b E

k") 4. XANES and EXAFS experiments on mixed-valent compounds.-

Only a few CXAFS experiments have been performed on MV mterials (43, 44, 45, 25) and there are no XANES results (except a recent paper we published on this subject (46). This is well explained by the difficulty to analyse the EXAFS results in that particular cases (47) and the lack of XANES theory for 4f mterials.

However the information we can get from such experiments are important. A MV com- pound m y be written as [(FZ 4F), (RE 4fn-1)1-x1 X where X is any chemical ele- ment involved in the fomtion of the MV material. The situation resembles that en- counted, for instance, in [Gal-x Inx] As where EXAFS experiments have shown the exis- tence of atomic relaxation (48) : The &-As and In-As distances are quite similar to those of pure Ga As and In As compounds and thus'differ f m t h o s e obtained from X-ray diffraction where the average lattice constant follows 2 Vegard's law. It is quiee obvious that such a situation m y be encounted in MV compounds, at least in the static limit (small hybridization). The difficulty in the I?V case is that it is impossible to perform independent EXAFS experiments above the Lg edges of a RE ei- ther in the 4 F of 4fr1-l configurations. (They are seprated by a few eV).

Before to process any EXAFS data on MV mterials one must solve the

"Energy Threshold Puzzle" (49) ; is it necessary to consider one or two threshold energies for the data processing ? In the static case there is no doubt that two thresholds must be taken into account (25); in the dynamic one the conclusion is not so evident. However our recent studies (46, 47) support the two-threshold mdel in all MV situations. A justification may be found simply by camparing the EXAFS and XPS processes : in XPS the photoelectmn leaves definitively the solid whereas in EXAFS it is backscattered by the surrounding atoms. 341 an XPS experiment performed on a MV mterial the (measured) kinetic energies of the photoelectrons (i. e. k) are different for the 4 F and 4F-1 photoemission process. (The difference is rough- ly the energy splitting between the two structures in the L3 edges). Then two dif- ferent kinetic energies (i. e. two different thresholds) m s t be considered in the EXAFS process. At evidence the EXAFS results are highly dependent from this hypothesis.

In the static case (inhomogeneous) the a-tomic relaxation, that we defined by ^6R = d (RE: 4fn - X) - d (RE 4fn-I - X) where d are the intwatomic distances is large (up to 0.15 8 for a first neighbow shell) whereas in the dynamic (hormgeneous) case it drops on the 0.04 8 range (25, 47) . (i. e. in the sensitivity limit of EXAFS experiments). The atomic relaxation is the result of a competition between the elas- tic energy and che hybridization energy (50). The reduction of the atomic relaxation in the homogeneous case is due to the importance of the hybridization energy and, m principle, EXAE'S experiments should be able to test the hybridization via these ato- mic relaxations ; however, due to the difficulty in the data pmcessbg, it is un- likely to use them except in a few simple situations (sinrple cristallographical structures, binary systems , ^{etc. )}

One m y ask the question if XANES experiments (20 + 100 eV) are not

able to yield more directly the importance of the atomic relaxation. At first

sight XANES seems to be m r e difficult (and indeed it is) than EXAFS. However

several simple arguments m y be used for a preliminar approach of the problem.

structure) rescaling t h e energy by a factor ( dl/d2)2 where dl and d2 a r e the in- teratomic distances of compounds 1 and 2 (51).

2 ) This procedure i s strikingly correct, even f o r 4f m t e r i a l s (32) and has been successfully applied t o the Ce,% transition (52).

The XANES spectra X (E) of MV materials , i n t h i s simple m d e l , m y be written a s :

4fn 4fn-1 (E)] (1)

X (E) = x [XIref (E)I+ (1 - x) [Xrref where

-

4fn i s obtained from the XANES spectrum of the integral valent (4fn)cornpound. rescaling the energy by t h e factor (d 4f-n /d4fn 2

r e f ⁾ 4fn-1 i s obtained Iran the XANES spectrum of t h e integral valent

- ^"ref

4fn-I /d4fn-1) 2 (4fn-1)cowound rescaling t h e energy by the factor (d ef

I n order t o take i n t o account t h e energy s p l i t t i n g , t&s contribu- t i o n i s shifted by 7 eV t o higher energy.

- x i s the intensity of the 4f component i n the edge. lb

In principle the strength of the atomic relaxation m y be deduced from such experiments. I r e f e r the lector t o t h e papers we present a t t h i s conference (BEAURFPAIRE e t al. and MALERRF: e t a l . ) i n which t h i s simple f o m l i s m has been ap- plied t o several homogeneous and inhomgeneous MV cases. The r e s u l t s we obtained are i n good agreement with those given by EXAFS measurements.

5. Conclusion.-

X-ray Absorption Spectroscopy i s a powerful tool f o r the study of Mixed-Valent compounds and it yields valuable i n f o m t i o n about the ground s t a t e properties. The effect of m l t i e l e c t r o n process i s almost non important f o r L3 spectroscopy; however such mechanisms cannot be completely ruled out i n some par- t i c u l a r cases. W e need more experimental studies on t h e subject befor!e any defini- t e conclusion. Nevertheless it appears t h a t Solid State effects m y be confused with m l t i e l e c t r o n process and a p e a t care must be given t o the f i t t i n g procedure of an absorption edge i f we want t o be able t o separate these different contributions.

EXAFS and XANES experiments should be m r e systerratically performed on MV m t e r i a l s because they can give interesting i n f o m t i o n on t h e strength of t h e hybridization parameter. Up t o now it was c o m n l y accepted t h a t it was impossible t o deduce the nature of a M V s t a t e fmm Lg spectroscopy (either s t a t i c o r dynamic). It i s possible t o get t h i s piece of i n f o m t i o n d i r e c t l y from the XANES spectra which a r e always recorded with the L3 edges.

Acknowledgements - I thank Drs. BEAUREPAIRE, GODART, KAPPLER, MALTERRE and Prof.

GAUTTER f o r t h e i r exciting collaboration during t h i s work.

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( 8) Sampathkumran E. V. , Kaindl G. , ^{Kmne W.} , Persheid B. and V i jayaraghavan R.

Phy. Rev. L e t t . 54 (1985) 1067

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(10) Sampthkumran E. V. Hyp. I n t . 27 (1986) 183

(11) Rohler J., Wohlleben D., Kappler J. P. and K r i l l G. F'hy. Lett. A 103 (1983) 220 (12) Rohler J., K r i l l G., Kappler J. P., Ravet M. F. and Wohlleben D. i n r e f 2, p. 215 (13) Kedy R. , ^{Croft M.} , ^{Murgai V.} , Gupta L. C. , Godart C. , Parks R. D. and Segre C.U.

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