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Correlated Chemical and Positional Fluctuations in the Gold-Nickel System: a Synchrotron X-Ray Diffuse
Scattering Study
G. Renaud, M. Belakhovsky, S. Lefebvre, M. Bessière
To cite this version:
G. Renaud, M. Belakhovsky, S. Lefebvre, M. Bessière. Correlated Chemical and Positional Fluctua- tions in the Gold-Nickel System: a Synchrotron X-Ray Diffuse Scattering Study. Journal de Physique III, EDP Sciences, 1995, 5 (9), pp.1391-1405. �10.1051/jp3:1995199�. �jpa-00249389�
Classification Physics Abstracts
61.10 61.55H 07.85
Correlated Chemical and Positional Fluctuations in the Gold- Nickel System: a Synchrotron X-Ray Diffuse Scattering Study
G. Renaud(~), M. Belakhovsky(~), S. Lefebvre(~) and M. Bessibre(~)
(1) CENG, D4partement de la Recherche Fondarnentale sur la MatiAre Condens6e, SP2M/PI,
17 rue des Martyrs, 38054 Grenoble Cedex 9, France (~) LURE, Universit6 Paris-Sud, 91405 Orsay, France
(Received 7 November 1994, accepted 29 May 1995)
Rksum4. Nous pr6sentons une analyse quantitative de la diffusion diffuse des rayons X par
un monocristal Au8oNi2o, dans son 4tat m4tastable, homogbne, caract4ristique d'un recuit h 520 K. Il est frappant que l'intensit4 due I l'ordre I courte distance est d'un ordre de grandeur
inf4rieure I l'intensitd due aux d4placements atomiques. La solution solide est presque al4atoire du point de vue de l'ordre local, mars des fluctuations de composition existent d4jh le long des
directions < loo >, de longueur d'onde cS 1 nm, qui sont les pr6curseurs des modulations de composition qui se d6veloppent lors d'un recuit en dessous de la courbe spinodale coh6rente. Les ddplacements de paire du premier ordre ont 4galement 4td ddduits de l'analyse. Des fluctuations de position sont observ4es le long des directions < loo >, corr416es aux fluctuations de composi-
tion. Ces rdsultats sont discut6s en relation avec le comportement anormal des solutions solides Aui-~Ni~ h basse temp4rature.
Abstract. A quantitative analysis of the X-ray diffuse intensity scattered by an Au8oNi2o single-crystal was performed, in its metastable, homogeneous state, characteristic of the temper-
ature of 520 K. An important feature is that the intensity due to chemical short-range order is
one order of magnitude smaller than the intensity due to atomic displacements. The solid solu- tion is nearly random from the point of view of short-range order, but composition fluctuations along < loo > directions
are already present, of characteristic wavelength m 1 nm, which are precursors of the composition modulations which develop when annealing bilow the coherent spinodal decomposition boundary. The first-order mean pair displacements were also obtained.
Positional fluctuations along < 100 > directions are found, which are correlated with composi-
tion fluctuations. These results are discussed in connection with the anomalous low-temperature
behavior of Aui-~Ni~ solid solutions.
1. Introduction
Binary solid solutions form an important class of metallic alloys for which, in general, theoret- ical models are well developed. However, many fundamental problems still remain when the
constitutive elements differ in size. In particular, size effects are known to stabilize some inter- mediate phases with respect to infinitesimal composition fluctuations, although these phases
Q Les Editions de Physique 1995
are out of thermodynamical equilibrium. The Au-Ni system was chosen because it is charac- terized by a very large size effect (cS 15 il), and because several results indicate that elastic interactions are dominant. Among many unusual properties connected to this effect are the very deep depression of the coherent spinodal boundary [1-4], the blocking of composition
modulation growth during spinodal decomposition [3] and exceptionally slow vacancies [5].
Au-Ni solid solutions have been the subject of two kinds of studies. The first ones [6-10]
aimed at characterizing the Short-Range Order (SRO), that is whether an atom has a tende/cy
to surround itself with like or unlike species (note that here, SRO may also mean clustering).
Of interest was the homogeneous high temperature state, retained at lower temperatures by
a fast quench, and its evolution during annealing above the coherent spinodal boundary, I-e-
above
mw 500 K. Although most studies were restricted to the determination of the nearest
neighbor SRO tendency, no clear picture has emerged because chemical effects were not prop- erly separated from positional ones. Some studies indicated a homocoordination tendency [8,9],
but others indicated a heterocoordination tendency [6, 7]. The second kind of investigations
used different techniques [11-16] to study the ageing below the coherent spinodal decomposi-
tion boundary. For 15 at.% <
xNj < 60 at.%, composition modulations of short wavelength
and small amplitude were found to develop along < 100 > directions [3]. In all cases, the
development of these modulations was found to stop rapidly. It was recently shown [17] that this blocking is not due to kinetic limitations, but rather to thermodynamic reasons, since a
metastable state could be reached reversibly. This thermodynamic limitation is believed to arise from the elastic energy induced by structural distortions correlated in those systems to
composition modulations.
In order to develop adequate theoretical models which explicitly include elastic interactions, it is fundamental to measure both chemical and positional correlations in a state which is well
characterized. An X-ray diffuse scattering study [18] conducted at high temperature (1023 K),
above the miscibility gap, concluded that the Au6oNi4o solid solution is nearly random for
nearest neighbors, but that there is a strong clustering tendency for next nearest neighbors.
In the frame of an extensive study of these binary alloys by microscopic and macroscopic mea-
surements and computer simulations, we present here quantitative information on short-range
order and structural distortions in the Au8oNi2o solid solution. Residual resistivity measure-
ments, which are described elsewhere [17], showed that the SRO tendency in the metastable state (above the coherent spinodal phase transition, but below the miscibility gap) is a pre-
cursor state of the low temperature composition modulated state, and allowed a very precise
characterization of the necessary metallurgical treatments to retain the alloy in this well defined state. It was thus chosen to measure quantitatively the SRO tendency in this homogeneous
metastable state, characteristic of the temperature of 520 K.
We first describe in some details the experimental conditions, and especially the sample preparation, since it determines the precise metallurgical state of the sample. Then we present the information contained in the X-ray diffuse intensity. Chemical and positional fluctuation
parameters deduced from the analysis are next given. The results are finally discussed in light
of the known low-temperature behavior.
2. Experimental
2.1. SAMPLE PREPARATION. An ingot of Au8oNi2o was first prepared by hyperfrequency melting in UHV, starting from 99.9995$lo-pure Au supplied by ASARCO and 99.999%- pure Ni obtained by zone refining. The single crystal was then grown by the Bridgman technique
in a high purity alumina crucible. The following conditions were selected to obtain a large single crystal: cooling rate of 25 K/min between 1323 K and 973 K with an external gradient
of 30 K/cm. The oven was removed at 973 K to avoid unmixing. The compositional homo-
geneity was checked by X-ray diffraction and by Scanning Electron Microscope (SEM) X-ray
fluorescence analysis. The first study yielded the lattice parameter a = 4.000 + 0.0005 I,
which corresponds exactly to x = 20 +1 at.% Ni. This value was confirmed by SEM, which also showed that the total concentration variation along the growth direction was less than 1 at.%. An additional X-ray fluorescence analysis was performed, proving that Fe, Al and Cu impurity levels were negligible. The sample was spark-cut parallel to the (311) atomic planes.
A 1 mm thick monocrystalline disc was then mechanically polished with diamond paste and
chemically polished with a mixture of hydrochloric and nitric acids. In order to get rid of the growth structure, the sample was annealed for 3 days at 1223 K (I.e. mw 10 K below the melting point). The sample was next slowly cooled down to 900 K, and quenched to room temperature
by water cooling the quartz capsule. This slow quench was selected to avoid retaining a high
concentration of supersaturated vacancies, which would have induced further evolution at room
temperature. The X-ray diffuse scattering, measured after the last polishing as a function of detector angle 2@, in constant small incident angle IQ = 7°) conditions, was monotonic, which proved that surface hardening was negligible. Finally, the sample was annealed for 30 min at 520 K, in order to reach the metastable state characteristic of this temperature.
Due attention was paid to the thermal treatment. By comparison with an extensive study of
short-range ordering kinetics in Aui-~Ni~ solid solutions, over the whole composition range, residual resistivity measurements were performed on thick polycrystalline samples having exer-
cized the same high temperature treatment as the single crystal, followed by various quenches.
Isochronal and isothermal resistivity measurements were then performed and compared to pre- vious results on thin samples. These resistivity measurements showed that: I) unmixing during
the initial quench from 900 K was avoided, it) the metallurgical condition chosen for the single crystal was indeed the metastable state characteristic of 520 K after a 30 min anneal at this
temperature. This state, located just above the spinodal decomposition boundary, is homoge-
neous both locally and over large distances, iii) any later evolution at room temperature was
avoided.
2.2. MEASUREMENTS AND DATA REDUCTION. Measurements were carried on the D23
station at LURE, which has been described elsewhere [19, 20]. It was equipped with a fixed- exit sagitally focusing double crystal monochromator with Si(1ii crystals, which focused the beam onto a mw 1 mm spot at the receiving slits position, and with a horizontal axis 4-circle goniometer. The sample was cooled down to mw 93 K by means of a special system of Cu wires [21], with one degree temperature regulation accuracy. The scattered beam was detected by a Si(Li) solid-state detector, through a single-channel pulse-height analyzer which rejected
harmonics and spurious fluorescence emission. To avoid excitation of fluorescences from Au
and Ni, and resonant Raman transitions from Ni, the wavelength was ~set to 1.9 I (6 526 eV).
In fact, at the time of the experiment, no mirror system for harmonic rejection was available,
so that the third and fourth harmonics did excite fluorescences. Since the penetration depth
(mw 1.8 ~Jm) was very small, it was essential to check that the surface roughness was low enough
so that the data were not altered. This was done by monitoring the Au La (1
= 1.28 I)
fluorescence during an R-scan starting at Q
= 6°. No variation larger than 2% were observed, thus implying that the surface roughness was low enough to avoid enhanced absorption at low incident and exit angles. The diffuse intensity was measured at 2 200 different reciprocal lattice locations, with 0.1 rlu steps. The monitor count was selected so that the signal was
-~
10~
counts, which yields
-~
3% counting statistical accuracy.
For the sake of normalization, the experimental scaling factor, which relates the experimental
count rate to the corresponding number of Laue units was evaluated. The absolute intensity
at sample position,
-~ x 10~ photons/(s mm~) was estimated by measuring the integrated intensity from several Bragg peaks of an untextured Al powder, and subsequent fitting of the Debye-Waller factor. Calculated values were used to estimate the Compton correction [22],
and the Laue intensity [23], including anomalous corrections [24]. In this alloy, because of the widely differing scattering powers of the two species, the Laue intensity is more than one order of magnitude larger than the Compton scattering intensity. The total scattering factors
were corrected for the Debye-Waller factor, using values estimated from phonon dispersion relations measurement on the same sample [17] (rms displacement < u( >= 2.5 x 10~~ i~
at 93 K). These last data were also used to calculate the Thermal Diffuse Scattering (TDS)
contribution [25], and correct for it. Note that the TDS was already reduced (I.e. always smaller than 10% of the total intensity) by the low temperature, 93 K. The intensity was thus
placed on an absolute scale, in electronic units.
3.. Data Analysis
We briefly recall first the information which is contained in the diffuse intensity scattered by
a binary solid solution. More details concerning the data analysis can be found elsewhere [26, 27]. After subtraction of the thermal diffuse scattering intensity ITDS, and normalization in electronic units, the diffuse intensity can be written as a function of the momentum transfer k according to:
1(~) " lBragg(k) + lLaue(k) (ISRO(~) + ii (k) +12(~))
where ILaue(k)
= NCaCb(f( f()~ is a monotonic function of the momentum transfer. N is the number of scattering atoms, f[ and f( are the respective atomic scattering factors of atoms a and b, corrected for the Debye-Waller term, Ca and Cb are the atomic fractions of a and b atoms, respectively. IsRo(k) is the Fourier transform of the Warren-Cowley parameters ai~nn which describe the short-range order in the solid solution. They are defined by: ai~nn = 1- J~f~/Cb
where Pif~ is the probability of finding a b atom at the end of the interatomic vector [lmn]a
if there is an a atom at the origin of the vector. For a random alloy, (f~
= Cb and all
ai~nn = 0, except oooo, which is always unity, since Pf)
= 0. There is a tendency towards heterocoordination (that is for a given atom to be surrounded by unlike neighbors) when ai~nn is
negative, and a tendency towards homocoordination (that is for a given atom to be surrounded by like neighbors) when ai~nn is positive. Ii(k) and 12(k) are the first-order and second-order
displacement intensities, respectively. They can be written as:
Ii(k) = ~j ha £ Fp(k)Q$~(k)
a=~,y,z P=a,b
and
12(k)= L hl L Fp(k)FQ(k)Rf~(k)+ L hnhp L Fp(k)FQ(k)S$f(k)
""~~Y,~ P,Q"a,b a, fl
= (x, y), P,Q=a,b
(Y,z),(z,x)
fl (~) jl(~)
~~~~~ ~ ~~~ ~ ~~~ ~~~~~~ ~~ ~~~~~ /~(~~~ /~(~) ~~~ ~~~~ /~(~)~~ /~(~) ~~~~~ ~~~
/lz are the redUced reciprocal lattice Coordinates Ofk. The Q$~(k), R$~(k) and S$f(k) terms are also three-dimensional Fourier transforms of the first-order, < U$)~~ >, and second-order,
< (U$)~~)2 > and < U$)~~U()~~ >, average interatomic displaceljlents for each pair PP or
PQ (P,Q " Au or Ni), respectively. The aim of a diffuse scattering study in a binary alloy is to obtain separately the 25 different components IsRo(k), Q$~(k), RfQ(k) and S$f(k), so
that the chemical, aimn, and positional < (U$)~~ >, < (U$)~~)2 > and < U$)~~U()~~ >
partial pair correlations can be deduced from in inverse Fouiier transform. ' '
In order to obtain the different components of the diffuse intensity in the whole unit cell,
it is sufficient to determine them in a minimum volume, Vm, of the reciprocal lattice, which, for the fcc lattice, is 1/96 of the whole reciprocal unit cell. For each k-point in this volume,
the intensity is measured at M other points deduced by reciprocal space symmetry operations, where the different components of the diffuse intensity have either identical or exactly opposite values than in the minimum voluIne. This leads, for each point in Vm, to M linear equations with n unknowns, namely the intensity components. A powerful method to solve the equations system, referred to as Georgeopoulos and Cohen (G-C) method, has been used [27]. A least
squares fit to the redundant linear system is performed. However, since the variations of the
Fa(k) and Fb(k) factors are very similar, the system is bad-conditioned, and the stabilization of the solution relies on additional symmetry constraints and use of a Householder transform.
An advantage of this method over previous ones [28] is that it minimizes the uncertainties
on each intensity components and that the variances of the correlation parameters can be calculated [29]. This method has been used successfully to study the precipitation of Guinier- Preston zones in Al-1.94 at.% Cu [33], the arrangement of non-stoechiometric defects in fl- NiAl [34], and the short-range ordering in Au3Cu [20].
Since Au atoms scatter about eight times more than Ni ones, and since Au is the majority coInponent, an approximation was made which allowed us to reduce the number of unknown from 25 to 13. This was achieved by grouping together the second order displacement terms for the three types of pairs, while keeping the FAU factor in front. The intensity 12(k) was thus
rewritten according to:
12(k)
=
£ h$F(~(k)R[(k) + ~ hahpf(~(k)S[~(k)
°"~~~~~ Off = (x>z),
(Y>z),(z,x)
with:
~~(~) ~
" ~~~~~(~) + ~~(~)~l~~~(~) + @(~)~~~~~(~)
Au Au
and a similar expression for S[~(k). The approximation relies on the hypothesis that R[ (k) has the same symmetry properties as the three individual terms RfQ(k). This can be justified if one
assumes that the three mean square pair displacements < (U$)~~)2 > have similar magnitudes,
so that contributions from AuNi and NiNi pairs can be neglected. Indeed, the ratio of AuNi and NiNi contributions to the AuAu one are respectively of the order ~~~ ~~~
-~ 8 x 10~~ and
CAU FAU
~~~ ~~~
-~
2.5 x 10~~ Another justification can be found by considering that the ratios
CAU FAU
FNiIFAU and F(~/F(~ are constant over the measured volume. Their variations are actually respectively 14% and 20%.
Successive analysis were performed, from rougher to finer approaches, characterized by the total reciprocal space volume chosen, the number of unknowns, and the approximations used.
All analysis in which the second order pair displacements contributions were neglected yielded
an ao value -~ 1.44, much larger than the expected value of1. The introduction of the second order displacement intensity was thus required and yielded an ao value very close to the ideal value of 1.
(300)
2
(000) (010) (020)
Fig. 1. Iso-intensity Curves, in the (h~h~o) reciprocal plane, of the measured total intensity (at
93 K), corrected for thermal diffuse scattering, and normalised in Lade units.
4. Results and Discussion
General trends regarding short-range order tendency can be obtained by visual inspection of the data. Figure I shows the total intensity in the (001) plane, corrected for calculated thermal
diffuse scattering [25] and normalized in electronic (Laue) units. There is clearly no marked tendency towards heterocoordination, since the intensity remains very low and monotonic away from the Bragg peaks. By contrast, the intensity is large in the neighborhood of Bragg peaks.
This may arise either from SRO clustering, or from large displacement intensities. The intensity is strongly asymmetric with respect to Bragg peak positions, which shows that it arises mainly from displacements of the atoms with respect to the nodes of the regular lattice. Similar
qualitative conclusions were reached in earlier studies of the Au6oNi4o solid solut16n [8,18].
IsRo(k) contours, represented in Figure 2, exhibit a pronounced minimum around h~n = 0A in the (hh0) directions and a broad, weak satellite in the (h00) directions, with a maximum for the same h~n value. The diffuse maximum around (0.40 0) reveals the existence of composi-
tional fluctuations of small amplitude and
-~ 1 nm wavelength in the < 100 > directions. This
