Studies of lattice distortions in AuNi solid solutions by EXAFS and computer simulations

Solid State Communications, Printed in Great Britain.

Vo1.63,No.7,

pp.569-572,

1987.

0038-1098/87 $3.00 + .OO Pergamon Journals Ltd.

STUDIES OF LATTICE DISTORTIONS IN AuNi SOLID SOLUTIONS BY EXAFS AND

COMPUTER SIMULATIONS G. Renaud, N. Motta’, M. Belakhovsky F. LanGon, L. Billard Centre d’Etudes Nucleaires, Departement de Recherche Fondamentale, Service de Physique 85 X, 38041 Grenoble Cedex, France On leave from Dipartimento di Fisica. II Universita di Roma , Via 0. Raimondo 00173 Roma, Italy l

(Received by E.F.Bertaut 25 february 1987)

We report on EXAFS analysis and computer simulations of the topological disorder in concentrated AuNi solid solutions, in relation to the marked difference in size between Au and Ni atoms. The mean nearest - neighbours interatomic distances were derived in a large composition range. It is shown that the atoms are strongly displaced with respect to the average lattice. The three partial pair correlation functions were found to be asymmetric.

In crystalline alloys in which constitutive elements have a marked difference in size, the resulting elastic distortions may play a major role in determining the physical and thermodynamical properties’. This appears to be the case in AuNi solid solutions. In particular, the enthalpy of mixing and composition fluctuations or magnetic clustering which develop during low temperature ageing2 are strongly influenced by the unusually large lattice distortions. Interestingly. prior work has brought valuable information about the atomic displacements which take place, with respect to the normal lattice siting, for the &60Ni40 composition, in the high temperature, disordered conditior?. However,more extended work is still required to get a better understanding of the general, low temperature , structural behaviour of the solid solutions considered. For this purpose, we have performed new experiments based on analysis of AuNi alloys, with particular reference to the existing state of order frozen-in by a fast quench from the miscibility domain. The present work is based on use of the EXAFS which is most appropriate to the spectroscopy, determination of the nearest-neighbour (NN) distances (AuAu, AuNi and NiNi)4. This communication reports on the results obtained on the two absorption edges of Ni with O
experimentally determined and the simulated shapes and positions of the PPCF. The model EXAFS spectra calculated from the computed PPCF support the view that the above mentioned asymmetry is required for a proper derivation of the physical parameters studied, in particular the mean NN distances. 1. Experimental Great care was taken to homogenize the samples by a two day anneal at 1120K. They were then rolled to the appropriate thickness (4 to 5 pm) with several intermediate anneals, and finally quenched from 1050K to room tern erature in Helium vapour at an approximate rate of 10 B K/s. A previous study of short-range ordering kinetics in these solid solutions5 together with more recent resistivity measurements?, enabled to determine that a further 20mn anneal at 630K is sufficient to restore the homogeneity from the point of view of short-range order. It avoids the complications due to the eventual advent of a spinodal decomposition between 400 and 500K2. We measured the fine structure above the K-edge of Ni and the Lll,-edge of Au at L.U.R.E. ( Orsay, France ). The spectra where recorded using a Si(200) double-crystal monochromator. Harmonics where rejected by detuning the two crystals in order to keep 40% of the maximum intensity of the rocking curve on the Ni edge, and 70% on the Au-edge .The energy resolution was about 2eV on the Ni-edge,4eV on the Au-edge. The samples were hold at 77K during measurements, in order to minimize the phonon damping of the spectra. An X-ray diffraction study was also made on the same samples, to determine the lattice parameters at 77K. 2. Analysis simulation

of

EXAFS

data

and

computer

The kX(k) interference function was extracted following the procedure proposed by Lengeler and 569

570

STUDIES

OF LATTICE

DISTORTIONS

IN AuNi SOLID SOLUTIONS

Vol. 63, No. 7

Eisenberger7. The first peak of the Fourier transform, containing a mixture of the two NN distances on the edge of interest, was filtered and backtransformed into k-space, the resulting k*X( k) signal being fitted with a two shell model:

AuSONi50

Au

symmetrcc

Edge G(r)

k2X.(k)=(-t)‘+‘kSa2(k)CbFb(k)Jdr4apbg,b(r)

PI

x sin(2kr+2s,(k)+bb(k))

where’a’ denotes the absorbing atom, ‘b’ its neighbours, I=0 on the Ni-edge, I=1 on the Au-edge, S,*(k) is the probability for the photoabsorption process to produce an electron at the incident photon energy, Fh(k) and bh(k) are the amplitude (including mean free path damping factor) and phase of the backscattering factor of the b species; 2 6,(k) is the phase shift introduced by the absorber a ; p,, is the atomic density of the b atoms and g (r) is the “reduced partial pair correlation function (l@CF) related to the radial distribution function kDF,h(r) by: RDF,b(r)=

Total phases (absorber+backscatterer) and amplitudes (including mean free path and Debye-Waller factor terms) were extracted from the spectra of Au and Ni pure metals. Theoretical calculationsa of the absorber phases enabled to derive the backscattering phases from the experimentally extracted total ones. The Au-Ni distances obtained with these hybrid phase shifts are in perfect agreement with the ones obtained using long-range ordered AuCua as a standard (after a correction of 0.006 A to account for the difference between the backscattering phases of Cu and Nigslo ).The spectra were first fitted using the customary expression for EXAFS, based on the small disorder approximation of the PPCF’ I. The EXAFS determined distances were too small, as were the total coordination numbers. These errors are usual when analysing EXAFS from amorphous materials. It was deduced that the asymmetry of the PPCF has to be taken into account. For the Au-edge spectra, the widths of the AuAu and AuNi distributions deduced from the above mentioned fits were reasonably small. An expansion of the RDF to the third order with respect to the distances was sufficient to include their asymmetry. The EXAFS function used was, following Eisenberger and Brown’*: [31 k2X,(k)=(-l)t+1kS,2(k)ZbN,bFb(k)exp(-2k)

x

.u+26,(k)+eu(k)+arctgC,b(k))

where Cab(k) is expressed moments of the RDF:

as a function

&b(k)=-4k/rab

of the three first

-(8/f5)k3

141

rab being the centroid of the distribution, and the second and third shifted moments. On the Ni-edge spectra, the asymmetry of the NiNi distribution was too large to apply the above We introduced a fully asymmetric approximation distribution of the form13: g(R)=A(R-R”)*exp(-B(R-R”)) g(R)=0 , if RIR” where,

The Au,,Ni,,

, if R>R”

as a result of the normalisation

A=NBMnP(l

h

Au50Nc50

PI

4s r2P, g&(r)

(1 +C,b(k))1’2sin(2kr

8

2+6R”B+2R02B2)

151

of 4rcr*pg(r): [61

Fourier transform of the Au-edge spectrum of is plotted on Fig.1 , together with the result of

0 Fig. 1

12 Fourier

Rd

)

L

Au

Edge

5

6

transform of the Au-edge spectrum in and its best fit with the pair of Eq. [S].

Au$oNi50 distnbution

the best least-squares fit obtained using k-squared weighting and non-Gaussian pair distribution functions. As the Au concentration is increased the region of the fitted data extends to higher k values (typical range from k=2.5 A-’ to k=l6.5 A-‘) and the residual of the least squares fit is improved. In concentrated alloys Au _ Nix (0.3 I x 5 0.5). (1 (j’ the correction on the NN distances ue to the asymmetry of the pair correlation functions is +0.02 A for the AuAu distances, +0.03 A for the AuNi distances and +0.05 A for the NiNi ones. The first two mean distances are determined with 0.01 A accuracy, whereas the accuracy on the mean NiNi distances is only 0.02 A for three reasons: i) the asymmetry of the NiNi distribution is more pronounced ii) the two distances involved (AuNi and NiNi) are quite near each other (Ar=0.05 A). iii) the experimental data are restricted to km, =14AV1. In fact, we are unable at present to analyse tie Ni-edge spectra for alloys with less than 20 at.% Ni, since the difference between the two distances presumably becomes too small (less than 0.03 A). In order to help the understanding of EXAFS and X-ray diffraction results, a computer simulation was performed. Since the existing data about the WarrenCowley parameters in these solid solutions indicate only a either towards orderingI or towards slight tendency clustering3, no chemical order has been introduced in the simulations. An initial configuration of 1372 Au and Ni atoms randomly distributed on a FCC lattice in proportion x was first built. Then , the structure was relaxed15, by moving all the atomic positions and by changing the density, until a minimum of the total potential energy is

reached. Only pair interactions were considered. For each composition, pair potentials of the three types: Lennard-Jones , Johnson16 and Morse , have been used. For consistency with the above hypothesis of a chemically random alloy, the depths of the potentials used for the three pairs (AuAu, AuNi and NiNi) were chosen equal. The distances R”Ni i and R” uAu corresponding respectively to the minima o r the NI.FpI and AuAu pair potentials were chosen such that the relaxation of the pure element gives the corresponding FCC lattice at 77K (dNiNi=2.486 A and d AuAu=2.876 A);the R’A an~~~~~~~r,n~a~ot~~ mean value of R” .TAU the Morse potentra : +(r)=D(

exp(-2&

(R-R”))-2exp(-cu

(R-R”))

171

was fixed at 6 for the three pairs. The Lennard-Jones and the Morse potentials were truncated at a distance rt equal to 1.2 A and 1.8 A respectively. Fifth order polynomials were used between rt and a cut off distance , rc , at which the interactions are set to zero, so that the pair potentials and their two derivatives are continuous at rt and rc. The distance ro equals 1.6 A and 2.1 A respectively. 3. Asymmetry EXAFS spectra

571

STUDIES OF LATTICE DISTORTIONS IN AuNi SOLID SOLUTIONS

Vol. 63, No. 7

of

the

a requirement

PPCF:

for

fitting.

For the various potentials and compositions , the three PPCF were reconstructed from the final topological configuration obtained. The corresponding EXAFS spectra were calculated from these distributions using equation [l]. These model spectra were then fitted using different EXAFS functions. The EXAFS formula based on the Gaussian form of the PPCF led to a wrong determination of the NN the maximal radial distance of the parameters, distribution being obtained instead of the mean one. This confirms that the distances deduced with that formula from experimental data were too small. Only use of a non-Gaussian distribution EXAFS formula to fit these model spectra yields the right coordination numbers (with 5% accuracy), together with the true mean NN distances ( with 1% accuracy) and the second and third momenta (with 10% and 20% accuracy respectively), as was deduced by comparison with the same parameters directly calculated-on the radial pair distribution functions used to generate the spectra. For instance, the three PPCF obtained after numerical relaxation using Morse potentials in Au50Ni50 are plotted in Fig.2. Also reported is griNi calculated using equation [5] with B=14.8 A- and

R “=2.45 A, values derived from the fit of the reconstructed Ni-edge EXAFS spectrum. The mean r value (2.65 A\ and the maximal r value (2.58 A, of the two gNiNi(r)‘distributions are equal. Good agreement is also found in less concentrated alloys,which shows that the modelled PPCF are adequate. Thus experiments and simulations (whatever the pair potential ) lead to the conclusion that the distribution of the AuAu distances is narrow and weakly asymmetric, in contrast with the distribution of the NiNi distances, which is wide and exhibits a highly asymmetric character in the concentrated alloys. Indicatively, the width of the latter is comparable to the one in amorphous metallic alloys. The AuNi distribution width is intermediate. It is noted that the results concerning the widths of the partial distributions aaree with the conclusion of Wu and Cohen3 drawn from their diffuse scattering experiment in the 40 at.% Ni solid solution. But their study was restricted to a single composition, and the shape of the distributions had not been taken into account. 4.

Interatomic

distances.

The partial mean NN distances and the average one (calculated as the interatomic distance in the perfect FCC crystal with the alloy atomic density) deduced from simulations were compared to the experimental results of EXAFS and X-ray diffraction, respectively. Neither the Lennard-Jones potential, nor the Johnson one have been found to give appropriate results: mean values derived from the former were significantly different from the experimental ones, whereas the distributions widths obtained with the latter were too large with respect to the ones resulting from the fits of experimental spectra. In contrast, the Morse potential was found to give satisfactory agreement with both diffraction and EXAFS results. Fig.3 shows the experimentally determined (squares) and simulated (continuous lines) NN distances. For comparison the average distances are also shown. The

2.5 1111111111111111111-

0

Fig. 3

2.LO

2.60

2.80 R(;

Fig. 2

The three calculated

R”=2.45 line).

A

3.00

)

PPCF gAuA.u(‘), after numerrcal

is also plotted’

gAuNi(‘)vgN’ r(r) relaxation wrt ‘“c; a

for comparison

(thick

.2

.4

.6

mole fraction

EXAFS measured (squares) (continuous lines) NN distances

x

.8

1

and simulated in AuNi alloy.

agreement is remarkable, though only pair interactions were considered, neglecting higher order ones. It appears that, although the solid solutions considered are crystalline, the atoms are strongly displaced with respect to their regular location in an undistorted lattice. It is also seen that the size of the alloyed atoms is intermediate between the one in the host monoatomic structures and the one that they would retain in the undistorted close-packed FCC structure. Surprisingly, the difference between the AuAu and the AuNi distances (about 0.1 A) is larger than

572

STUDIES OF LATTICE DISTORTIONS IN AuNi SOLID SOLUTIONS

between the AuNi and the NiNi ones. In their diffuse scattering study, Wu and Cohen found smaller AuAu and AuNi displacements from the average lattice, but larger NiNi ones . The question arises whether this discrepancy might be related to the different ways of averaging the displacements in the two techniques . It is recalled that EXAFS measures the true radial distribution functions, whereas the mean values of the projections of the pair displacements are obtained in the analysis of x-ray diffuse scattering data. In conclusion, the present study shows that the partial pair displacements are far from being negligible in the AuNi solid solutions. Moreover, the structural static disorder is unusually large: it must be taken into account in EXAFS analysis in order to derive the mean NN distances.

Vol. 63, No. 7

The small spread of AuAu pair distances is confirmed, which contrasts with the wide distribution of the Ni atoms. Further work is in progress to extend this study over the entire composition range, and to use the more appropriate approach of the cumulantsll to describe the asymmetry of the PPCF when analysing the EXAFS spectra. 5.

Acknowledgement

We would like to acknowledge Dr J. Hillairet (CENG-DRF) for his continuous interest and support during this work, for the characterization of the samples made by resistivity measurements, and for critical reading of the manuscript. One of us (N.M.) wishes to acknowledge the CENG for hospitality and financial support.

References: 1. H.E. Cook and D. de Fontaine, Acta. met. 17, 915 (1969). P.Letardi, N.Motta and A.Balzarotti, J.Phys. C in press. 2. O.F. Kimball and J.B. Cohen , Trans. Met. Sot. A/ME, 245 . 661 (19691 F. Hdfer and P. Warbichler , 2. Metallkde. 76, 11 (1985) C.M. Hurd, S.P. McAlister and I Shiozaki, J.Phys. F: Metal. Phys., 11, 457 (1981). T.B.Wu and J.B. Cohen, Acta Met. 31, 1929 (1983) 3. D. Raoux, Z. Phys. 6, Condensed Matter 61,397 4. (1985) E. Balanzat, M. Halbwachs, J. Hillairet, C. Mairy, 5. P. Guvot and J.P. Simon, Acta. Met. 31, 883 (1983) G. Renaud and J. Hillairet, unpublished results. 6. B. Lengeler and P.Eisenberger, Phys. Rev. B, vol. 21, 7. 4057 (1980)

8.

The phase shifts calculations were made using the EXCURVE program developed at the SERC Daresbury

g, ~by~~!~,t?$W 10. 11. 12. 13. 14. 15. 16.

International Conference on fX4FS and Near-kdge structure, Fontevraud, 1986. B.K. Teo and-P.A.Lee, J. Am. Chem. Sot. 101, 2815 (1979) G. Bunker, Nuclear Inst. and Met. 207, 437 (1983) P. Eisenberger and G.S. Brown, Solid State Comm. 29, 481 (1979) E.D. Crozier and A.S. Seary, Can. J. Phys., 58, 1388 (1980) P.A. Flinn. B.L. Averbach and M. Cohen, Acfa. Met. 1, 664 (1953) F. Lancon, L. Billard, J. Laugier and A. Chamberod, J. Phys. F: Met. Phys. 12, 259 (1982). R.A. Johnson, Phys. Rev. A 134, 1329 (1964)