Local environment effects in mixed valent rare-earth systems studied by EXAFS

Journal

190

INVITED

and Magnetic

Materials 47&4X (19X5) 190- 196 North-Holland, Amsterdam

PAPER

LOCAL ENVIRONMENT BY EXAFS G. KRILL L.M.S.E.S.

of Magnetism

EFFECTS IN MIXED VALENT

*, J.P. KAPPLER

*, M.F.

RARE-EARTH

SYSTEMS

STUDIED

RAVET

(LA CNRS no. 306) UniuersiiC Louis Pasteur, 4, rue Biarse Pascal, 67070 Strashourg Cedex, France

C. GODART

*

ER CNRS 209, Place A Briand, 91290 Meudon, France

and J.P. SCNATEUR I.E.G. (ER CNRS 155) Domaine Uniuersitaire, BP 46, 38042 St. Murtin d’Hhes,

France

The possibility to study the local environment of an intermediate valent rare-earth ion by EXAFS spectroscopy is reviewed. The strength and limitation of EXAFS as compared to X-ray diffraction are discussed. We show in this paper that the local environment effects are different for inhomogeneous and homogeneous mixed valent systems: in the former case. atomic relaxation occurs whereas in the latter the atoms adopt single average position. It means that the Virtual Crystal Approximation (VCA) can be used for the description of the local environments in the homogeneous phases. This conclusion is quite paradoxal because usually the VCA does not apply to random solid solutions.

1. Introduction Extended X-ray Absorption Fine Structure (EXAFS) refers to oscillations of the absorption coefficient on the high-energy side of an absorption edge. These oscillations are the result of an interference process between the outgoing and the backscattered waves of the photoelectron emitted after the absorption process [l]. therefore they can be used for the determination of the local environment of an ion even in the absence of Long Range Order (LRO) [2]. Because EXAFS takes place on a very short time scale (7 5 lo-” s), i.e. shorter that the time of atomic motion, the dynamical response of the atoms surrounding an unstable 4f ion may be considered. Earlier EXAFS experiments [3-61 have suggested that in Homogeneous Mixed Valent materials (HMV) all the atoms adopt single-average positions rather than dynamically distorded environments with two different stable positions corresponding to the two valence state of the RE ion. This implies that the Virtual Crystal Approximation (VCA) which assumes that all atoms * LURE,

Universite

Paris-Sud,

Bat.

209

C, 91405

Orsay.

France.

0304-8853/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

occupy the average lattice positions deduced from X-Ray Diffraction (XRD), can be applied to the HMV systems. The aim of this paper is to discuss precisely this hypothesis, answering the following questions: i) Are EXAFS experiments able to give a definite conclusion in HMV systems? ii) Is the VCA picture appropriated for describing the nanostructure of an admixture between 4f n and 4f * * ’ ions randomly distributed on lattice sites? In the following we shall first examine how EXAFS experiments can give informations about the parameters in which we are interested, discussing particularly the strength and the limitation of the technique, as compared to XRD experiments (section 2). Next we shall present the EXAFS results we obtained on several Mixed Valent (MV) materials both in the HMV and Inhomogeneous (IMV) states.

2. EXAFS: strength and limitation .?.I General The finality of any EXAFS study is to reproduce as well as possible the experiment by using the general

G. Krill et al. /

formula:

x(k)

= * 7

$em2’jk2 e-2R~h(k)lfin,(k)l J

sin(2kR,+4,(k)), N,: the number of neighbours on the jth shell; R,: the average distance between central and scattering atoms on the jth shell; u,‘: the mean square average of the difference of displacement; X(k): the mean free path of the photoelectron; I&( 71,k) I: the backscattering amplitude of the atoms on the jth shell; q,(k): the phase shift of the photoelectron wave due to the backscattering and central atoms; k: the photoelectron wave vector. k = h-‘fim( E - IT,), where E, is the threshold energy. The overall sign is (-) for excitation from an s state (K or L, edge) and (+) from a p state (L,,, or L,, edges). As this general formula, on its simplest form, well describes the experiment on integral valent materials, we believe that all the effects which are not taken into account (multielectron scattering, core hole relaxation, p + s transition for EXAFS on the L,,, edges) have no importance for the study of MV systems. The parameters in which we are interested for MV systems are the mean distances (or the distribution of distances) R, and the Debye-Waller type factor u,‘. For simple structures (NaCl or AuCu,) the successive shells are well separated in R space, then by Fourier filtering it is possible to isolate the EXAFS contribution of each shell and the data analysis is considerably simplified. In order to fit the data, two procedures can be used: (i) either we use theoretical phase shifts and backscattering amplitudes [7], (ii) or, using more sophisticated Fourier transforms [8], we isolate separately for each shell the phase (2kR, + Ir;( k)) and the amplitude (N,/kRf . . ), the precise knowledge of the distances in a reference compound allows the determination of #,(k) which can then be transferred to other cases. Unfortunately the second approach cannot be used as soon as there is more than one atomic specie on a given shell. 2.2. Accuracy of EXAFS

191

EXA FS studies of mixed valenl systems

presence of the L,, edge; (iii) the nature of both central and scattering atoms. It has been shown [9] that for high quality data recorded on 12 A’ after the edge in a material with heavy central atoms (Z > 40) and light scattering atoms (Z < 20), the lower limit for the determination of the distance is AR = 0.03 A. For 0, the relative error is at least 5%. In the case of MV compounds, several other parameters may be important, particularly for EXAFS performed after the L,,, absorption edges. First we can ask if it is correct to use the same phase shifts for 4f” and 4f n*1 ions, secondly because all the L,,, absorption edges of MV materials present a double structure (J. Rohler, this conference, p. 175), the use of a single threshold energy is questionable. It is beyond the scope of this paper to discuss in details these points and let us just here make several comments. There is a priori no reason to suppose that the central atom phase shifts for 4f n and 4f” *I ions are identical. On the contrary, as shown by Teo and Lee [7] they are different but this can be taken into account by changing slightly E,, which in EXAFS formalism is a free parameters. However, it implies that for MV materials different #,(k) should be used for 4f” and 4f” *’ ions, thus complicating the data analysis. The second point is still rather more complicated [4,5,10,11], and we will discuss it qualitatively, considering several situations which may be encountered in MV systems. In fig. 1 the EXAFS for the first shell of a fictious MV SmS( V = 2.5) has been simulated using one threshold energy (located on the Sm2’ edge), 6 sulphur atoms located at Rs,_s = 3 A and a realistic value for u, = 0.07 A. On the same figure, we report what we

32lE u On' x -I-

results -2-

It is extremely important to understand the limits of EXAFS both in the general case and in the particular one of MV materials. The accuracy on the EXAFS parameters (R,, u,~.. . ) depends (with decreasing importance) from (i) the “quality” of the experimental data; (ii) the extend of EXAFS in k space (in the case of Sm or Eu we are limited to 12 A-’ because of the

-3I

4

6

8 K(INV

Fig. 1. Simulation of first neighbour mixed-valent compounds (see text).

10

12

EXAFS

spectrum

%

in

192

G. Krill et al. / EXAFS studies of mixed valent systems

should expect if two distances (AR = 0.15 A) were present either considering one single ,?a(-+-) or two threshold energies separated by AE = 7.1 eV (- - -). There is no doubt that EXAFS is able to distinguish between these three hypothesis. However, if now we suppose that AR becomes smaller (= 0.04 A) (we expect this situation for HMV systems [12]), that u, may be slightly changed (_t5%) and that the threshold energy E, (the free parameter) may move +2 eV around the Sm*+ edge (keeping the energy splitting between Sm2’ and Sm3’ constant), then one can verify that good fit to the data can be obtained (the agreement factor drops to 2%). Our conclusion is that in these limits, using a mean distance and a single threshold energy yields one of the possible solutions. 2.3. Difference between EXAFS

and XRD

The h(k) factor which never exceeds 10 A gives to EXAFS its local picture only sensitive to short-range order. We obtain an instantaneous “snapshot” of the atomic configuration averaged on all configurations. On the contrary XRD gives us informations averaged on all the unit cells of the crystal and is only sensitive to long-range order. Therefore the informations deduced from both experiments may be quite different. This has been well illustrated by recent EXAFS studies on Ga, _,In,As [13]. In this system where Ga and In ions

are randomly distributed on a given sublattice, EXAFS experiments show that the Ga-As and In-As distances are different, whereas XRD yields the conclusion that they are equal, as expected from Vegard’s law. It means that the VCA pictures does not give a correct description of the local environment of the ions in this alloy. The analogy with MV materials is straightforward, indeed we deal with 4f” and 4f” * 1 ions, randomly distributed on the sublattice of a RE(4f”), _,RE(4fn *‘),X compound. The EXAFS a,* which is analog to a Debye-Waller (DW) factor is not identical to the XRD DW factor. Indeed in EXAFS it represents the mean square average of the difference of displacement instead of the mean square average displacement in XRD. As a consequence only the vibrations which involve out of phase longitudinal displacement will contribute to the EXAFS o,~. This is important if we want to discuss phonon anomalies in the MV compounds.

3. Application

to MV

systems - results and discussion

All the experiments we discuss now have been performed by the transmission technique [2], using the synchrotron radiation delivered by the DC1 storage ring at L.U.R.E. (Orsay). Several experiments have been done on a “inlab” spectrometer from GSK Scientific

v-295 7

E(eV) Fig. 2. L,,, absorption edges at 300 K of Eu ions in EuPd,A

1:compounds

G. Krill et al. / EXAFS studies of mixed valent systems Inc. [14] using a RU-200B rotating anode (in this case the counting time is 3-4 h for an EXAFS spectrum). As the transmission technique needs thin samples (30-50 p) we check carefully that powdering the samples (< 20 p) does not induce any phase transformation of the compounds. 3.1. Inhomogeneous mixed valent systems: the EuPd,A, system (A = B, Be,Si):

Table 1 Data analysis for the first shell (Eu-Pd) in EuPd,A, pounds. (A, is the agreement factor of the fit) d Eu-Pd

EuPd, EuPd,Be,,, EuPd,SioZ5 EuPd,Bo.,

EuPd, crystallizes in the cubic AuCu, structure where each Eu atom is surrounded by 12 Pd located at a/ fi (a is the lattice constant). As shown by the L,,, absorption edges (fig. 2) the valence of Eu ions changes from - 3 to 2.5 when Boron atoms are introduced in the unit cell, whereas no measurable change occurs for Si or Be insertion. For our EXAFS study, the main point is that recent Mossbauer experiments [15] have shown the inhomogeneous character of the MV state of Eu in EuPd,B,. The Radial Distribution Function (RDF) obtained by a direct Fourier tranform of the EXAFS data are reported in fig. 3. The magnitude of the main structure changes drastically, particularly in the IMV compounds. Such behaviour cannot be explained by the presence of an extra-atom in the unit cell still it is not observed for Si or Be insertion. In order to obtain quantitative informations, we have isolated by Fourier filtering the main structure of the RDF (2 + 3.2 A). The data have been fitted using the general EXAFS formula and all the results are summarized in table 1. As for EuPd,, the

2

6 I R(A) Fig. 3. RDF functions for the EuPd,A,

compounds at T= 77 K.

193

EuPd,B

Lattice constant at RT(A)

Ai

(A)

:A)

2.87 2.92 2.90 2.93 3.00 2.91 (6E 7eV) 2.94 2.99

0.045 0.015 0.02 0.065 0.02 0.02 1 0.06 0.02

2.91 (6E 7eV)

0.02 )

com-

5% 4.10, 8% 4.14, 8% 4.11, 7% 7%

4.180 I

7% 5sg 4.193 I

best fit is obtained supposing a well-ordered AuCu, structure, we have considered in all cases that each Eu ion was surrounded by 12 Pd atoms. When Be or Si is inserted we observe a small but significant increase in the Eu-Pd distances, in good agreement with the lattice constant behaviour. The main effect here is the decrease of u,, which means that the lattice becomes more “hard”. On the contrary, for the IMV samples the uj must be enhanced if only one distance is taken into account. This can be analyzed as the result of static disorder, but as shown on table 1, an other solution exists, still better, if we suppose the coexistence of two Eu-Pd distances and two threshold energies shifted by 7 eV. We believe that this solution is correct because (i) the two distances we found correspond roughly to those expected for

194

G. KriN et al. / EXAFS studies of mixed ucrlent system picture can only be true if the impurity concentration is small enough to avoid the percolation transition of trivalent Samarium ions on the fee sublattice. (ii) After the volume collapse (_u > c,.) the samples present all the characteristic properties of HMV compounds. As our EXAFS results for SmS under pressure and SmS, tO, have been already published [5,6], we only present here those for SmS, _.I’, and Sm, I-As,. including our previous results in the discussion, The RDF are reported in fig. 4a, b. The first (6 anions) and second (12 samarium) shells are well separated in R-space as expected for a NaCl structure. Because sulphur ( Z = 16) and phosphorus ( 2 = 15) have nearly the same backscattering amplitude and phase shift, a direct comparison between the magnitude of the RDF peaks is possible for SmS, _ ,P, (this does not apply to the first shell of SmS,_,As,). In the case of phosphorus substitution, although all the samples are in the MV state (see table 2). the RDF look alike, except a small increase of the magnitude which can be well explained by a slight decrease of the 0, factors observed previously in SmP [lo]. We don’t observe the effect described in the EuPd,B, MV compounds. We believe that this difference has its origin in the nature of the MV state, either homogeneous or inhomogeneous.

Eu2+-Pd and Et?+-Pd in a lattice where Boron is present; (ii) the u, values are the same as for EuPd,Be,,, supporting the hypothesis that the inor EuPd,Si,.,,, trinsic effect of Boron (i.e. in the absence of valence change) is identical to that of Be or Si. If our hypothesis is correct, it means that in the IMV materials atomic relaxation occurs. The situation should be then rather similar to that of the GalIn,YAs system discussed above, implying that the VCA picture cannot be applied to such materials. 3.2. Homogeneous compounds

mixed

valent systems:

the S&-type

The volume collapse which occurs at the semiconductor to semimetal transition in SmS compounds can be induced by applying pressure or by chemical substitution either on Sm or S sublattice [16]. In the case of sulphur substitution by Arsenic or Phosphorus, we know from earlier studies [17,18] that two different regions must be considered: (i) before the critical concentration x,,, where the volume collapse occurs (x,, = 0.05), there is strong experimental evidence that the samples are in an IMV state. The model proposed in refs. [17,18] supposes that all the six Samarium ions surrounding the impurity (As, P) become trivalent whereas all the others remain divalent. Obviously, this

Table 2 Data analysis

for the first and second shells in SmS, ~.‘;P, and SmS, _ , As 1 systems 1st shell

d

2nd shell

N atoms

(A) SmS SmS0

9Po,,

*

Sm%7PO3 *

0

Al

(A) 0.09

5%

4.25

12Sm

0.08

6%

2.1

5.97

2.875

6S

0.085

8%

4.03

12 Sm

0.09

7%

2.60

5.70

2.87 2.88

4.2 S 1.8 P

4.04

12 Sm

0.08

5%

2.75

5..70

2.89

3.6 P

0.085 }

4.05

12 Sm

0.075

5%

2.81 2.89

2.4 S 3.6 P

0.08 0.08

2.85

5.72

2.25

5.89

6~0

> 23%’ I

2.4 S

0.085 0.1 0.08

2.88 2.90 2.89

5s

SmSo.~sAsO.,s * KofAs

1 As 6Sm

0.08

7%

SmAs

2.94

6 As

0.08

8%

**

L,,, of Sm

‘4,

(r\)

6S

6S 2S 4s

*

0

Lattice parameter at KT in (A)

2.96

2.89

SmS,,,As,,,,

N atoms

(A)

2.95 2.85 2.95 (6E’= 7eV)

SmS0.4P06

d

Valence deduced for L,,,

>

7% 3g

4.20

12 Sm

0.11

10%

4.08

12 Sm

0.08

5%

2.60

5.74

4.2

12 Sm

0.08

68

3

5.92

G. Krill et al. / EXAFS studies of mixed valent systems

2

4

195

6

R(;i)

Fig. 4. RDF function

at T = 77 K (a) for the SmS, _,P,

compounds;

The data analysis results are reported in table 2. The symbols (* or **) mean that either a HMV (*) or IMV (**) is expected from their physical properties. For pure SmS and SmAs the distances we found well agree with those deduced from the lattice constant. In the HMV state (*) for all cases the best fits are obtained considering one mean distance and one single threshold energy (in the limits we discussed in section 2.2) both for the first and second shells. For SmS,,,As,,, such an hy-

(b) for the SmS, _,As

compounds.

pothesis is supported by the EXAFS experiments we have performed both on the L,,, edge of Sm and the K edge of As. As shown on table 2, an attempt has been made for the nearly trivalent SmS,,~,P,,, compound to investigate the possibility of atomic relaxation around S or P atoms. The distances we used are those expected for Sm3+-S (= 2.81 A) and Sm3+-P (= 2.89 A); obviously such an hypothesis gives a bad fit of the data. Once again, it appears that the main effect is ob-

G. Krill et al. / EXAFS studies of mixed valent systems

196

served for the IMV SmS,,,,AsO,O~ sample. Indeed, if the hypothesis of one simple mean distance for Sm-S pairs may be correct for the first shell, it cannot be applied to the second, even if we increase the a, up to 40% (0.11 instead of 0.08 A in the other cases). Therefore, as for IMV EuPd,B,, we believe that the second solution given in table 2, assuming the coexistence of both Sm*+-S (= 2.95 A) and Sm3+-S (= 2.85 A) distances and two threshold energies, is better. In principle, it should be possible to test the validity of this solution by fitting the second Sm-Sm shell, however this is difficult because we should take into account three distances (Sm*+-Sm*+, Sm3+-Sm3+ and Sm2+-Sm3+) with different threshold energies (Sm’+-Sm3+ pairs become non-equivalent to Sm3+-Sm*+ pairs). The number of free parameters is too important, therefore we did not try it. For the first neighbours shell the present results agree completely with those obtained for SmS under pressure and SmS, _,O, [5,6]. Some differences are found for the second neighbours shell, namely a damping effect is observed for SmS at high pressure (10 I P 2 40 kbar) and SmS,,,,O,,,,, i.e. in the HMV regime. Since this damping is not present for HMV SmS,_,P, or SmS, _xA~,, we must now conclude that it is not a characteristic feature of the HMV state. Recent neutron scattering experiment performed on SmS at high pressure have shown a large softening of the LA phonons branches in the HMV state [19]. The EXAFS u, of the second neighbours shell in a NaCl structure is strongly dependent from these phonons modes, therefore it may be possible to correlate the damping effect (high u,) with the softening of the LA branches. A similar effet could not be observed on the first neighbours shell since only optical phonons contribute to its 0;. Further investigations are needed in order to clarify this point.

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[61

[71 PI [91

[lOI

IllI

u21 [I31 1141

[I51 [I61

Acknowledgements u71

want to acknowledge the collaboration of J. Riihler during this work. The authors are grateful to Professors D. Wohlleben and F. Gautier for their constant interest in this work. We

iI81 [I91

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