A small angle neutron scattering study of the δ′-Al3Li coarsening in an AlLi alloy

Physica B 156 & 157 (1989) 68-71 North-Holland, Amsterdam

A SMALL ANGLE NEUTRON IN AN Al-Li ALLOY S. ABIS’, R. CACIUFFO*,

SCATTERING

F. CARSUGHI*,

STUDY OF THE 6’-Al,Li

COARSENING

R. COPPOLA3, R.K. HEENANZ

R. OSBORN4,

and M. STEFANON’ ‘Elettrochimica Marco Ginatta, Torino, Italy ‘Dipartimento di Scienze dei Materiali e della Terra, Universid di Ancona, Italy ‘E.N.E.A., C.R.E. “Casaccia”, Roma, Italy 4Neutron Division, Rutherford Appleton Laboratory, Oxon, OX11 OQX, UK ‘E. N. E. A., C. R. E. “E. Clementel”, Bologna, Italy

Time of flight Small Angle Neutron Scattering was used to investigate the coarsening process in an AI-Li (3 wt%) alloy annealed at 463 K for different times. The size distribution and the growth rate of the 6 ‘-Al,Li precipitates have been determined and compared with the predictions of coarsening theories. The position and the intensity of the interference peak observed in the scattering pattern have a time dependence which is in good agreement with the predictions of phase separation theories based on Ising model simulations. The time scaling characteristics of the structure function have been verified

1. Introduction

Isothermal ageing below the critical temperature of binary Al-Li alloy results in the decomposition of the supersaturated solid solution in a two-phase mixture of 6 ‘-Al,Li precipitates in an (YAl-Li solid solution matrix, before reaching the equilibrium phase &AlLi. Because the precipitation of the 6’ phase is always present in the commercial alloys, having in fact typical content of 3 wt% Li, the nucleation, growth and coarsening of these precipitates have previously been the object of numerous, detailed studies [l, 51. In this paper we present the results of a Neutron Small Angle Scattering (SANS) study of an Al-Li (3 wt%) binary alloy aged at 463 K for various amount of time. The aim of the experiment was to study the mechanism governing the precipitation process of the 6 ‘-Al,Li phase and, in particular, to observe the time dependence of the S ’ particle size distribution. In fact, while earlier experimental results (mostly obtained by Transmission Electron Microscopy, TEM) are in a satisfactory agreement [l] with the predictions of the different theoretical coarsening models so far as the time dependence of the average size of the precipitates is concerned, a wider size range

is usually theories.

observed

2. Experimental

than

predicted

by

the

results and discussion

The experiment was performed on high purity Al-Li 3 wt% samples quenched from 833 K and thermal aged at 463 K for different amounts of time ranging from 1 to 90 hours. The measurements were carried out on the LOQ time of flight SANS diffractometer at the UK spallation source ISIS of the Rutherford Appleton Laboratory. A Q range from 0.05 up to 1.8nm-’ was spanned using incident wavelength between 0.3 and 1 nm. The results obtained are shown in fig. 1 where SANS intensities Z(Q) corrected for sample transmission, detector effeciency and background are plotted as a function of the momentum transfer Q. A diffuse interference peak may be observed, whose position Q, shifts towards small Q values while its height I,,, increases as the ageing time progresses. In order to deduce the distribution of particle sizes, the presence of the interference effects (which indicate the existence of spatial correlation between the precipitates) must be taken into account. A complete analysis

0921-4526/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

S. Abis et al. I SANS study of coarsening in an Al-Li

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0.1

0.2

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Q W-l) Fig. 1. SANS intensities observed for AI-Li 3 wt% samples, aged at T = 463 K for various amounts of time.

about this point will be published later. Only the main results obtained under the assumption of uncorrelated particles will be presented here. The application of the Guinier law to the central part of the scattering curves leads to the determination of the gyration radii R, of the 6’ particles. Values ranging from 6 to 23 nm are found for annealing times 1 between 1 and 90 hours, respectively. The cube of the Guinier radii increases linearly with the time in agreement with the prediction of the LifshitzSlyosov-Wagner (LSW) theory [6,7] and with the observations of previous TEM studies [l]. However, a ratio K/K(O) = 7 is found between the observed slope K of the R: vs. t straight line and the growth rate K(0) calculated, in the frame of the LSW theory, using a value y = 0.014 J/m2 for the surface energy [S] and D = 1.84 x lo-l9 m*/s for the diffusion coefficient [9]. This discrepancy is to be attributed to the effect of the volume fraction Cr, of precipitates. The LSW theory is in fact strictly valid only for systems for which Cr tends to zero and modified theories must be used to describe the behaviour of systems with C, # 0 [lo]. The observed ratio K/K(O) = 7 is in reasonable agreement with the MLSW model [ll] which predicts values around 6 for C, of the order of lo%, while too small a value (-1.32) is given by the Lifshitz-Slyosov encounter modified (LSEM) theory including the possibility of particle coalescence [lo]. The average radius of the precipitates R can be obtained from the position Q, of the first modulation of the Q”Z( Q) vs. Q curve, by using

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69

the relation [12] Q,,R = 2.75. This gives values in good agreement with the Guinier radii and, in particular, a time dependence of the form tQ with (Y= 0.29 is found. As suggested in ref. [13], an estimate of the number of scattering precipitates per unit volume N can also be obtained from the position of the interference peak, in the framework of a simple model for the spatial interparticles correlation. A power law of the type N = ii&-’ (p = 0.81) is obtained with values rangin 9 from about 10” cmm3 at 1 hour to 2 x 1015 cmat 90 hours (these values must however be considered with care because of the approximation of the model we used). The volume fraction of precipitates should then have an order of magnitude given by 4nR3N/3 which is found to be about 10% for all the investigated annealing time (a power law Cr a to.” is obtained for the time dependence of the volume fraction), again in agreement with the predictions of the coarsening theories. An asymptotic Q -4 dependence of Z(Q) is observed, as predicted by the Porod law. The total precipitate surface per unit sample volume S, may then be calculated if the absolute values of the SANS cross-section are known [14]. In the present case, no calibration measurements were performed so that only the time behaviour of Sr may be checked. As expected for a coarsening process with constant Cr, S, appears to be approximatively proportional to R -‘(S, 0: teY with y = 0.34). Although the presence of a strong interference peak creates problems in deducing particle size distributions from scattering data, an indication on the time evolution of the particle dimensions may be obtained with the procedure described in [15,16] using the intensity measured above Q,, where the interference term can be approximated to one. For ageing times greater than 5 hours, the size distribution functions N(Rlfi) so obtained are almost stabilized on a unique curve. This is in agreement with coarsening theories which predict (for sufficiently long times) a universal distribution of particle sizes, independent of all material parameters. In fig. 2, the N(RIl?) curves for t = 5 and 90 hours are shown as an example and compared with the theoretical LSW curve. It can be noted that the

S. Abis et al. I SANS

70

study of coarsening

in an AI-Li

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Fig. 2. Normalized particle size distributions N(RIR) for 5 and 90 hours ageing time at 463K, compared with the theoretical LSW curve.

experimental distributions are more symmetrical than the LSW curve. Their shapes recall those of the LSEM model [lo], but this theory is not able to predict the observed growth rate. Moreover, the root-mean-square width of the experimental curves (s -0.30-0.36) is larger than the LSW value (s = 0.215) but in better agreement with the predictions of a recent model [17] where the effect of diffusive interactions on Ostwald ripening are taken into account (s - 0.28 for C, 10%). Finally, we have checked the dynamical scaling behaviour of the intensity distributions Z( Q, t) measured at different times t [18]. This quantity is directly proportional to the structure function S( Q, t), i.e. to the Fourier transform of the composition correlation function of the alloy at a given time t after the quench. Monte Carlo simulations of the tridimensional Ising model [19], used to describe the segregation in homogeneous systems quenched into the miscibility gap, predict a time-independent shape for the scaling function F(q)

= @(t)

Qm_

r(QT

,-

J

Q2Z(Q,

’

t,

t> dQ

Qnun

where q = Q/Q, and Q,(t) being the nth moment of Z( Q, t). As shown in fig. 3, such behaviour (already observed in other systems [20]) is well verified in our case for ageing time larger than 1 hour. Moreover, the time evolution of the

Fig. 3. Scaling function F(Q/&,) scaling behaviour of the measured

showing intensities.

the

dynamical

Z(Q) moments is also in line with the Ising model predictions [18]. In fact, we found Q, 0:t-‘9 wit_h u = 0.27 and an almost constant value for Q,(t)R,(t) (2.6-3.2). A stationary state for the unmixing of the alloy is further supported by the constant Q2(t) l&,‘(t) - 1.3 ratio. Concerning the time evolution of the interference of peak Z(Q), power laws of the type Q, m t-“’ and Z, cctan are also well verified for exponent values (a’ - a - 0.27 and a”lu’ - 3.57) which compare favorably with the Ising model simulations.

Acknowledgement

We are indebted to F. Rustichelli for helpful suggestions and discussions.

References [I] K. Mahalingam, B.P. Gu, G.L. Lied1 and T.H. Sanders Jr., Acta Metall. 35 (1987) 483. [2] R. Kauel, A.R. Ah and Z. Farid, Phys. Status Solidi A 45 (1978) 47. [3] D.B. Williams and J.W. Edington, Acta Metall. 24 (1976) 323 and refs. quoted therein. [4] T.H. Sanders Jr., E.A. Ludwiczak and R.R. Sawtell, Mater. Sci. Engin. 43 (1980) 247 and refs. quoted therein.

S. Abis et al. I SANS study of coarsening in an Al-Li [5] B.P. Gu, J.H. Kulwicki, G.L. Lied1 and T.H. Sanders

Jr., Mater. Sci. Engin. 70 (1985) 217. [6] I.M. Lifshitz and VV. Slyosov, J. Phys. Chem. Solids 19 (1961) 35. [7] C. Wagner, Z. Electrochem. 65 (1961) 581. [8] S.F. Baumann and D.B. Williams, Scripta Metall. 18 (1984) 611. [9] L.P. Costas, USAEC report DP 813, U.S. Atomic Energy Commission (1963). [lo] C.K.L. Davies, P. Nash and R.N. Stevens, Acta Metall. 28 (1980) 179 and refs. quoted therein. [ll] A.J. Ardell, Acta Metall. 20 (1972) 61. [12] F. Livet, in: Phase Transformations in Solids, Mat. Res. Sot. Symp. Proc., vol. 21, T. Tsakalakos, ed. (Elsevier, Amsterdam, 1983) p. 507

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[13] M. Roth, Ecole d’Ete d’Aussois (1981) p. 239. [14] A. Boeuf, R. Caciuffo, R. Coppola, S. Melone, P. Puliti and F. Rustichelli, Nucl. Instr. Meth. A 234 (1985) 562. [15] S. Abis, R. Caciuffo, R. Coppola, M. Magnani, F. Rustichelli and M. Stefanon, Physica B 136 (1986) 469. [16] M. Magnani, P. Puliti and M. Stefanon, Nucl. Instr. Meth. B, in print. [17] M. Marder, Phys. Rev. B 36 (1987) 858. [18] P. Fratzl, J.L. Lebowitz, J. Marro and M.H. Kales, Acta Metall. 31 (1983) 1849 and refs. quoted therein. [19] J.L. Lebowitz, J. Marro and M.H. Kalos, Acta Metall. 30 (1982) 297. [20] J.P. Simon, P. Guyot and A. Ghilarducci de Salva, Phil. Mag. A 49 (1984) 151 and refs. quoted therein.