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ATOMIC RELAXATION IN MIXED-VALENT SYSTEMS DEDUCED FROM EXAFS
SPECTROSCOPY
N. Wetta, G. Krill, P. Haen, F. Lapierre, M. Ravet, C. Godart, F. Holtzberg
To cite this version:
N. Wetta, G. Krill, P. Haen, F. Lapierre, M. Ravet, et al.. ATOMIC RELAXATION IN MIXED- VALENT SYSTEMS DEDUCED FROM EXAFS SPECTROSCOPY. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-965-C8-969. �10.1051/jphyscol:19868185�. �jpa-00226091�
Colloque C8, suppl6rnent au n o 12, Tome 47, dkcembre 1986
ATOMIC RELAXATION IN MIXED-VALENT SYSTEMS DEDUCED FROM EXAFS SPECTROSCOPY
N. WETTA*, G. KRILL*', P. HAEN"', I?. LAPIERRE"*
M. F. RAVET" , C. GODART' and F . HOLTZBERG+ +
'LMSES ( U A 306 CNRS), ULP, 4, Rue Blaise Pascal, F-67070 Strasbourg Cedex, France
* * ~ a b o r a t o i r e de Physique des Solides ( U A 155 CNRS),
Universite d e Nancy I , BP 239, F-54506 Vandoeuvre-les-Nancy Cedex, France
* * *
CRTBT, Avenue des Martyrs, F-38042 Grenoble Cedex, France 'Laboratoire de Chimie & Metallurgie des Terres Rares,
( E R 209 CNRS), F-92190 Meudon, France
and LURE, Universite Paris-Sud, F-91405 Orsay Cedex, France
" I B M , Thomas J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
Resum6 - Nous presentons une methode dlanalyse des spectres EXAFS permettant de mettre en evidence les effets de relaxation atomique mzme dans le cas de compos6s 2 valence intermCdiaire homogene pour lesquels ces relaxations sont tres faibles. L'EXAFS peut donc Etre utilis6 pour prdciser la nature homogene ou inhomogene de 116tat mixte. Enfin, nous appliquerons notre proc6d6 au sys- t h e W S e pour conclure B la prdservation du caractere homogkne de la valence dans les compos4s non-stoechiom6triques. X
Abstract - We will present how it is possible, from EXAFS spectroscopy, to es- timate atomic relaxation effects even in homo.geneous mixed valent compounds, for which these relaxations are known to be very small. EXAFS experiments, analysed by our procedure, can then be used to decide if the ground state is homogeneous or inhomogeneous. At least, the procedure will be applied to the Tm Se system. We conclude that the homogeneous character of the mixed valent stzte is preserved in the non-stoichiometric compounds.
1. INTRODUCTION
Mixed-valent states can either be homogeneous (i.e. due to fast 4f charge flucta- tions) or inhomogeneous (i.e. due to local environment effects with an "infinite"
life time). Because X-ray absorption process takes place on a very short time scale (T ,$, sec), much shorter than the time of atomic motion, EXAFS is expected to be an accurate method for atomic relaxation effects (i.e. 4f electron/phonon coupling) investigation. Up to now, EXAFS data analysis performed on homogeneous mixed-valent (HMV) compounds are not consistent with the assumption of strong rela- xations (comparable to the difference of pure ionic radii) and of two threshold energies.Thus, it is generally admitted that the single threshold energy and the mean distance hypothesis is the best choice for analysing HMV compounds, although many other solutions with strongly reduced relaxation effects may also be possible / I / . Such solutions are expected in HMV compounds, as the consequence of the competition between hybridization and elastic energies.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868185
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The aim of this paper is to present a new way of analysing EXAFS data which will allow us to conclude, without ambiguity, to the occurence of small atomic relaxation effects in the HMV TmSe.
2. EXAFS DATA ANALYSIS
In the energy range of EXAFS spectroscopy, the sudden approximation is valid and the L absorption spectrum is then the result of the convolution of the spectral densiEy associated to "2p" photoemission with L absorption spectrum calculated in a band structure model. Assuming that the ph5EoIemission spectrum is mainly the sum of two Lorentian lines, the EXAFS spectrum is the superposition of two spectra associated to both electronic configuration of the rare earth ion :
~ ( k ) =
el
(k)~in(2kR~++~ (k)) + ~~(k')sin(2k'~~++~(k'))= A(k) sin (2kR + $(k))
with = (R + R )/2 AE is the splitting between the two threshold energies, and k1
=*:
EXAFS spectra above L edge of the rare earth are here considered rather than the spectra above K edge &$'the neighbour, although the latter case seems "a priori" less complicated. In fact, we should in this case consider two different back scattering amplitudes on the two subshells (in addition to two different phase shifts !). Such a problem, like all problems of amplitude, is much more difficult to solve than compli- cations arising from phases.
In order to test the validity of an EXAFS analysis, in relation with the present stu- dy of Tm Se compounds, we simulate the EXAFS of both pure trivalent (our "reference compoundK) and mixed-valent TmSe, with cubic NaCl structure. We used the following parameters for the first shell :
- For the trivalent TmSe : 6 Se atoms are located at R=2.81 from the Tm3+ ions and '~m- ~e =0.05 A, X (200 eV) = 8 A.
- For the mixed-valent TmSe we assume that 2.4 Se atoms are located at R =2.88 A from the Tm2+ ions and 3.6 Se are located at R2=2.84 A from the Tm3+ iod. The Debye- Waller factors are assumed to the same value as the reference i.e. :
First, we tried to fit these spectra with the usual procedure and starting with the four following hypothesis : one distance and one threshold (solution ( I ) ) , one dis- tance and two thresholds (2), two distances and one threshold ( 3 ) , two distances and two thresholds (4). The results we obtained are in agreement with EXAFS data analysis performed earlier on simulated mixed-valent SmS compound /I/, and can be swarized as follows :
a) It is impossible to deduce from the agreement factor (A ) what is the best solution, b) Unphysical solutions with one mean distance can be obtahed by enhancing the value f of the Debye-Waller factors (we obtained 5 = 0.057 A). In this fitting procedure, a small difference between bond lengths cannot be distinguished from a Debye-Waller fac- tor in the usual energy range (4 8-1 5 k < 10 h1 -t 14 A-') which is too limited.
If we%try to reproduce separately the phase (2kR + $(k)) and the amplitude ratio Aref/A(k) w i t h 5 fixed to the value of oref we obtain the following results :
+Table I
The amplitude is highly sensitive to the exis- tence of a single or double threshold energy and to the occurence of atomic relaxation around the fluctuating Tm ions.
The solution (4) which is in agreement with the parameters introduced for the simulation, is the only solution that reproduces correctly the amplitude.
experimental situation, because the noise level on the data we will analyse in section 3 is typically of this order. The existence of this low level of noise doesn't change our conclusions : the best solution is still the two threshold energies and two dis- tances one, and the values obtained for the parameters (R, = 2.87 A, R2 = 2.838 A, AE = 5 eV) are still very close to those introduced in our simulazions.
If there exists a reference compound isostructural (i.e. with the same chemical en- vironment) to the studied mixed-valent compound and if its EXAFS is measured exactly under the same experimental conditions, we can then use th's method for EXAFS deta analysis, consisting a separate fit of both phase (Zk~+$(k)) and ratio Are£/*(*), the plot of Log(Ar £/A) vs k2 fixing the Debye-Waller factors in our equations. The phase shift 4 (k) for one of the electronic configurations is extracted from the
reference phase. According to Teo and Lee 1 131, the central atom phase shift for the other configuration can be deduced from the preceeding one by adding a constant cor- rection factor C and then : 92(k') = ~$~(k') + C. More details about this method will be given in a further publication.
3. ATOMIC RELAXATION EFFECTS IN MIXED-VALENT Tm,Se :
Fig. 1 : Fig. 2 :
EXAFS spectra for the trivalent TmSe (solid Radial distribution function (RDF) line) and the MV stoichiometric TmSe (-.- ) for the trivalent TmSe (solid line)
and the MV stoichiometric TmSe (-.-)
Fig. 3 :
Fit of the amplitude for the off-stoichiometric sample
--- : false solutions
- : solution B
insert : 'I,
Plot of LO~(A,,~/A) vs k2 for the MV TmSe
o : stoichiometric sample
1 x : off-stoichiometric sample
.. *r The TmxSe compounds exist on a
6 8 10 12 wide ranae of stoichiometry with
k (2' ) the cubic NaCl structure and with x extending about 0.8 to 1 depen- ding on the author 141. Near the stoichiometric composition (x : I), the characte- ristic properties of HMV materials are observed. When vacancies are introduced in
C8-968 JOURNAL DE PHYSIQUE
the Tm sublattice, all the physical properties change drastically, and in particu- lar, the valence changes from 2.6 (for the stoichiometric compound) to a value very close to 3 and the homogeneous character of the MV state becoming doubtful 151.
Earlier EXAFS experiments have concluded to the absence of relaxations in the stoi- chiometric TmSe 161. Our aim is to show the occurrence of atomic relaxations in stoichiometric TmSe and to follow their possible change with stoichiometry.
0
We consider the EXAFS Spectra of bgth stoichiometric TmSe (a = 5.7122 A) and off- stoichiometric sample (a = 5.6766 &) and the spectra of a nearly trivalent off- stoichiometric sample (a = 5.6277 A). We will design these three compounds by their lattice parameters.
Fig. 1 and 2 present the EXAFS spectra and the Fourier transform in R space for both trivalent and stoichiometric samples. We will show below (insert of Fig. 3) that there is no reason to suspect a change in the Debye-Waller factor between the two samples. Thus, the decrease of the RDF's magnitude for the stoichiometric MV TmSe as compared to the trivalent one (observed for each atomic shell ! ) may be a first evidence for the occurrence of atomic relaxation effects in the stoichiometric sample. This point will be confirmed in the following by our data analysis.
1. The choice of a reference compound :
We believe that for our EXAFS study, the nearly trivalent (a=5.62 i) samole is the best choice for our reference compound, because (1) several simulations performed when taking into account the small divalent character of this sample (v=2.95) showed that such an effect can be easily compensated by a slight change of the threshold energy AEo ; (ii) the EXAFS contribution of the first Se shell surrounding the Tm ions in this compound is easily reproduced w h ~ n assuming a pure octahedral local environment of theoTm ions (6 Se at R = 2.806 A in accordance with the lattice parameter and o = 0.058 A). All attempts trying to reproduce a slight rhomboedrisa- tion of the Se octaedron /7/ yield bad results.
2. Experimental results :
Following the procedure described in section 2, we tried to fit independently the phase and amplitude on each sample. First, we must precise the variation of the Debye-Waller factor in the Ease of MV TmSe as compared to the reference. The inva- riance with k2 of Log(Aref/A) for both samples, reported on Fig. 3, is the evidence that the Debye-Waller factors for the two MV compounds have to be taken equal to that of the reference in our adjustements. Nl,N2, AE are also fixed to values dedu- ced fromL111 edges. The results are summarized in Table 2. For clarity, we only report the better and the worse fits.
Hypothesis A : 1 mean distance and 1 threshold energy Hypothesis B : 2 distances and 2 threshold energies.
Sample HYP. N1 R1 (A) N2 R2 (A) AEo (eV) A (%I Agfk ( % ) gf+
TmSe A : 6 2.837 - - 2.3 0.9 12
a = 5.7122 ft B : 2.4 2.851 3.6 2.836 -2.4 0.9 4
TmxSe A : 6 2.815 - - 1.1 2 13
a = 5.6766 4! B : 1.5 2.84,, 4.5 2.810 4.9 2 4
Table 2
On Fig. 3, we report the fits on the amplitude obtained on the sample (a=5.67). The
atomic relaxation that we obtained are very small for all compounds (AR 2 3 ~ 1 0 - ~ A), confirming that the Tm ions still keep their HMV character in the TmxSe compounds through the valence changes with non-stoichiometry (in fact, such a conclusion de- pends strongly on sample preparation technique). EXAFS experiments on the K-edge of Se have also been performed and we checked that the results obtained on the Tm edge are consistent with the data above K-edge. These last points will be discussed in detail in a forthcoming paper.
We have shown in this paper the EXAFS experiments at the LIII edge of the RE in mixed-valent systems may give valuable information about the importance of atomic relaxation even in the case of homogeneous systems. The existence of two threshold energies has to be considered both in the IMV 111 and HMV systems. This conclusion is in agreement with recent XANES study of MV materials 181. In the homogeneous case the atomic relaxations, as expected, are very small, and it is absolutely necessary to use high quality EXAFS data (the noise level must be less than 1% per point if we want to be confident in the data analysis of HMV systems). Thus, the use of EXAFS experiments must be limited to the study of simple crystallographical structure
(NaC1, AuCu3).
ACKNOWLEDGEMENTS : We thank Prof. F. Gautier for his constant interest in this work.
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