A DIFFUSE NEUTRON SCATTERING STUDY OF CLUSTERING IN CuNi-ALLOYS

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A DIFFUSE NEUTRON SCATTERING STUDY OF

CLUSTERING IN CuNi-ALLOYS

J. Vrijen, E. van Royen, D. Hoffman, S. Radelaar

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C7, supplkment au no 12, Tome 38, dkcernbre 1977, page C7- 187

A

DIFFUSE NEUTRON SCATTERING STUDY OF CLUSTERING IN CuNi-ALLOYS

J. V R I J E N

Netherlands Energy Research Foundation ECN, Petten, The Netherlands

E. W. V A N R O Y E N

Laboratorium voor Fysische Metaalkunde, Rijksuniversiteit Groningen, Groningen, The Netherlands D. W . H O F F M A N

Scientific Laboratory, F o r d Motor Company, Dearborn, Michigan.48121, U.S.A. and S. RADELAAR

Laboratorium voor Experimentele Fysica, Rijksuniversiteit Utrecht, Utrecht, The

ether lands

RBsumC. - Le degrk de clustering d'alliages CuNi de compositions comprises entre 20 et 80 % atomique de Ni, a CtC dktermink par diffusion de neutrons. Les conditions expkrimentales optimums ont 6th obtenues en utilisant les isotopes 62Ni et 6 5 C ~ . Les parambtres de Warren et Cowley ont Btk dkterminks en fonction de la tempkrature (entre 400 et 700 oC) et en fonction de la composition. Ces parambtres prksentent une forte asymktrie en fonction de la composition. Cette asymktrie dkpend de la temperature (en rkalitk elle augmente si la tempkrature de recuit dkcroit). Les rksultats expkri- mentaux sont cornparks 9 diffkrents moditles thkoriques (Clapp-Moss, Hoffman et Tahir-Kheli) et 9 des rksultats de simulation. Cette comparaison montre que les interactions ri plusieurs corps jouent un r61e important dans la formation d'amas des alliages CuNi. La localisation de la lacune de miscibilitk cohkrente est calculke h partir de donnkes expkrimentales. Evidemment, la lacune de miscibilitk

prkdite est elle aussi asymktrique, ce qui est en bon accord avec les donnkes relatives aux chaleurs de mklange.

Abstract. - The amount of clustering in CuNi-alloys, ranging in composition from 20 to 80 at. % Ni, has been determined by means of diffuse neutron scattering. Optimum experimental conditions were achieved by the use of the isotopes 62Ni and 6 5 C ~ . The Warren-Cowley parameters were determined both as a function of temperature (between 400 and 700 OC) and as a function of composition. The cluster parameters show a rather strong asymmetry as a function of composition. The asymmetry is temperature dependent (in fact it increases with decreasing annealing temperature). The experimental results will be compared with various theoretical models (Clapp-Moss, Hoffman and Tahir-Kheli) and with the results of a computer simulation. This comparison shows that many- body interactions play an important role in the clustering of CuNi-alloys. The location of the coherent miscibility gap in CuNi is calculated from the experimental data. Obviously the predicted miscibility gap is also asymmetric, which is in good agreement with data of the heat of mixing.

Introduction. - Numerous detailed studies of the atomic arrangements in alloys exhibiting short-range

order (s.r.0.) have been published. Comparatively few such studies have been carried out for clustering sys- tems. As was convincingly demonstrated by Mozer et al. [l] the CuNi-system is ideally suited for the study of clustering phenomena by means of neutron diffraction, provided one makes use of the isotope 62Ni, which has a negative scattering length. Through the use of this isotope it is possible to strongly enhance the diffuse component of the scattering while simulta- neously reducing the fundamental (Bragg) scattering. I n this paper we will present measurements of the Warren-Cowley parameters obtained from the diffuse

scattering of CuNi-alloys as a function of temperature and composition. The results will be compared with the predictions of various statistical theories, viz. the Clapp-Moss approximation [2, 3, 41 (henceforth called CMA), the spherical model approximation (SMA) presented by one of the authors [5] and the high temperature expansion of Tahir-Kheli [6] (TKA). We will also present computer simulations of clustering in the 43.5 at. perc. C u alloy. In this paper we will limit ourselves t o the consideration of pair-wise interactions only.

Experimental procedure. - The differential cross- section for the elastic scattering of thermal neutrons

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C7-188 J. VRIJEN, E. W. VAN ROYEN, D. W. HOFFMAN AND S. RADELAAR

from a binary system with only short range correla- tions between the occupation of the sites can be written as

analogous to that for X-ray scattering. N is the number of lattice sites in the system, c, and c, are the atomic fractions of the components A and B, b, and bB their effective scattering lengths, a, the Warren-Cowley s.r.0. parameters, K the scattering vector and rn the

position vector of site n. For simplicity the Debye- Waller factors and the size-effect modulation of the diffuse intensity have been omitted. The first term of eq. (1) describes the diffuse scattering and it will be clear that for optimal observability the factor (b, - bB)2 should be as large as possible. The use of 62Ni (bslNi = - 0.87 X 10-l2 cm) together with

6 5 C ~ (b,,,, = 1.1 1 X 10- l 2 cm) instead of naturpl Ni

and Cu increases this factor considerably. The second term represents the fundamental Bragg reflections of the lattice with atoms with an average scattering length of (c, b,

+

c, b,). An account of the experimental procedure, data handling, corrections, etc. was given in [7]. Starting with the null-matrix (the alloy with zero Bragg-scattering) a total of nine different alloys was made. The (polycrystalline) samples were homo- genized at temperatures ranging from 1 050 to 1 200 OC (depending on their Ni-content). Equilibrium in the amount of clustering was achieved by annealing at 700 OC and at lower temperatures. Data were taken at room temperature.

FIG. 1. - Diffuse neutron scattering pattern of 6 5 C ~ 0 435 6ZNi0.565, quenched from 400 OC after a 30 hours anneal.

represented by 9 s.r.0.-parameters. Only slight devia- tions at higher K-values occur. Also evident is the complete absence of Bragg-reflections at the indicated positions. Values of the Warren-Cowley parameters for the first nine shells are given in table I for the null-matrix.

Figure 2 gives the values of a, as a function of composition for three different temperatures. The increasing asymmetry of the composition dependence of the clustering with decreasing temperature is to be noted. As is evident from the plots in figure 2 the temperature dependence of the clustering for low Ni-concentrations is rather small in the temperature region studied.

Results. - A typical experimental result is pre- In figure 3 we have plotted a, as a function of T - '

sented in figure 1, which shows the diffuse scattering for all compositions studied. A linear T - l dependence

of the null-matrix 65C~0.,,5 62Ni0.565 annealed of a, would be expected at least for very high tem- at 400 OC. The experimental data can be accurately peratures. The plots on the left hand side show that the

Warren-Cowley parameters for theJirst nine shells describing the clustering in 65C~o.435-62Nio.565 as a function of temperature. Each heat treatment was ended by quenching the specimen. The standard deviation A is given in units of the last decimal.

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A DIFFUSE NEUTRON SCATTERING STUDY O F CLUSTERING IN CuNi-ALLOYS C7-189

FIG. 4. - Crit~cal temperature for thc null-matrix as a function of annealing temperature. calculated with CMA ( a ) and SMA (6).

at. perc. Ni

FIG. 2. - - a , as a function of concentration for thrcc d~lfrrent anneahng tempcmtures.

FIG. 3. -Temperature dependence of a , for the nine alloys studied. The Ni content is given in atomic per cent.

extrapolated straight lines do not pass through the origin (i.e. T = CO). However, the plots on the right

hand side (for high Ni-content) do extrapolate to a, = 0 for T = CO.

Discussion. - We calculated the critical temperature for decomposition of the null-matrix using the CMA and the SMA. A comparison of the CMA and SMA with an exact series expansion by Fisher and Burford [g] showed [S] that the critical temperature is overestimated in the CMA and underestimated in the SMA. Figure 4 shows the calculated Tc for the different annealing temperatures. Apparently the calculated TCys decrease with decreasing annealing temperature. At that time (the null-matrix was the

first to be studied) we did not realize the importance of the many-body interactions which are responsible for the fact that the a's do not extrapolate to a = 0 for infinite T. We attributed these discrepancies to the inadequacies of the CMA and SMA in the temperature range studied. To test this hypothesis we carried out computer simulations using a model of 4 000 atoms with both first and second neighbour pair interactions. Details of this Monte Carlo vacancy diffusion model will be discussed elsewhere [g]. The results of these computer simulations are shown in figure 5. The values below T = 340 OC presumably do not correspond to equilibrium states. A slight increase in the value of a , was observed even after 20 jumps per atom. The interaction energies ( + 10 meV and - 4 meV) were determined from a best fit of the CMA to the measurements. The simulated data lie consistently below the curve representing the CMA. Using the CMA to obtain interaction energies from the simulated data

I

o neutron scattering

slmulations

FIG. 5. - - - Results of the computer simulations and the neutron diffraction experiments for the 43.5 at. perc. Cu alloy. Also shown

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C7- 190 R. DE KIDDER, G. VAN TENDELOO, D. VAN DYCK AND S. AMELINCKX

we found that V , was lower (+ 9.5 meV) and the ( V, (

was higher ( V , = - 4.5 meV) than the original values. Both the CMA and the SMA now produced a constant value of Tc (470

+

40 K and 290 10 K respecti- vely). The values of Tc calculated with the aid of

the CMA using the 700 OC data (which most closely appsoach the conditions under which the CMA is valid) are shown in figure 6. Due to the effects men- tioned above the maximum of this miscibility gap is at least 100 OC too high. However, the shape is in excel- lent agreement with data on the heat of mixing [10, 1 l].

Kheli [6]. Figure 5 shows that the third-order result agrees very well with the computer simulations. The CMA-curve deviates from the simulated data at fairly high temperatures ( T r 2 Tc).

The results presented above convincingly show that the composition dependence of clustering in CuNi cannot be described with pair-wise interactions only. There are very few methods available which can deal with many-body interactions in binary alloys. Kikuchi's cluster-variation method can handle these kinds of problems. An analytical procedure based on a high temperature expansion was given by [12]. Preliminary calculations based on the latter model indicate that one has to take into account both first and second nearest neighbour pair interactions and a many-body (triplet) interaction.

Conclusions. - The asymmetry of the composition dependence of the amount of clustering in the CuNi-system indicates fairly strongly many-body interactions. Due to this effect the temperature dependence of the Warren-Cowley parameters cannot be satisfactorily explained by theories which take only pair interactions into account.

The shape of the calculated miscibility gap shows a remarkable resemblance to the measurements of the heat ofmixing [10, l l].

Acknowledgments. - We wish to thank Mr. H. J. Bron of the Laboratorium voor Fysische

at. perc. Ni Metaalkunde, Rijksuniversiteit Groningen, for his

co-operation in preparing the specimen, and

FIG. 6. - Miscibility gap calculated using the 700 OC data. _{Mr. W. van der Gaauw for his technical assistance}

in the experiments. The FOM (Stichting Funda- We also calculated the Warren-Cowley parameters menteel Onderzoek der Materie) sponsored this work using the high temperature expansions of Tahir- with a grant for the isotopes.

References

[ l ] MOZER, B., KEATINC;, D. T. and Moss, S. C., Phys. Rev. [7] VRUEN, J., VAN DIJK, C. and RADELAAR, S., Proceedings of

175 (1968) 868. the Conference on Neutron Scattering, Gatlinburg (1976), 121 CLAPP, P. C. and Moss. S. C., Phys. Rev. 142(1966) 418. ed. R. M. Moon, 1976, p. 92.

181 FISHER, M. E. and BURFORD, R. J., Phys. Rev. 156 (1967) 583.

131 CLAPP, P. C. and Moss. S. C., Phys. Rev. 171 (1968) 754. [9i VAN ROYEN, E. W. and RADELAAR, S., to be published. [4] Moss, S. C and CLAPP. P. C.. phys. Ret>. 171 (1968) 764. ORIANI, R. A. and MURPHY, W. K., eta et. 8 (1960) 23.

[l11 RAPP, R. A. and MAAK, F., Acta Mer. 10 (1962) 63. 151 HOFFMAN, D. W., Met. Trans. 3 (1972) 3231. _[l21

.

_TAGGART._{G. B. and}_TAHIR-KHELI,_{R. A.,}_{Progr. Theor. Phys.}

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