On the mechanism of lamellar spacing adjustment in eutectic alloys

Journal of Crystal Growth 42 (1977) 526—535 © North-Holland Publishing Company

ON THE MECHANISM OF LAMELLAR SPACING ADJUSTMENT IN EUTECTIC ALLOYS T. CARLBERG and H. FREDRIKSSON Department of Casting of Metals, Royal Institute of Technology, 10044 Stockholm, Sweden

Well controlled unidirectional solidification experiments with continuous increased solidifcation rate were performed for eutectic alloys in the systems Ag—Cu, Al—Zn, Al—Cu and Al—Ni. In the Ag—Cu and Al—Zn alloys it was observed that discontinuous changes in the lamellar spacing occured at low solidification rates. At high solidification rates such discontinuities could not be observed. Anyway the lameliar spacing was always larger than that observed at constant rate experiments. In Al—Cu alloys discontinous changes in the lamellar spacing with increasing solidification rate were also observed. However, after each change the lamellar spacing increased gradually up to a lamellar distance of 20% lower than before the abrupt decrease. Al—Ni eutectic alloys gives a rod like eutectic structure. In this alloy no discontinuous changes could be observed. A theoretical analyses ofthe observation based on well known theoretical models are discussed.

1. Introduction

2. Experimental method

A variety of mechanisms for establishing the optimum lamellar spacing in eutectic reactions are discussed in the literature. Hunt and Jackson [1] and O’Hara and Hellawell [2] suggest that lamellar terminations play a decisive part by either developing into complete lamellae or disappearing. Double [3] performed experiments in which he progressively increased the speed of solidification and then studied sections at right angles to the direction of solidification. He found that the movement of incomplete lamellas was of minor significance. The decisive factor was the movement of areas of mismatched lamellas in a way that favoured the growth of areas of optimum lamellar spacing at the expense of other areas. Hunt and Jackson [1,4] investigated the solidification of fault-free eutectic structures by allowing transparent organic materials to solidify in thin layers. With increasing solidification speeds it was not possible to obtain a continuous reduction of the lamellar spacing. Instead, the solidification front became unstable and the lamellar spacing suddenly decreased by half. In order to investigate whether the latter mechanism was

The experiments were carried out in a gradient solidification device shown schematically in fig. 1. A steep temperature gradient, 300°C/cm,was chosen to ensure a stable, smooth sohdification front. The

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also possible in three-dimensional systems containing faults, we performed the following experiments.

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T. Carlberg, H. Fredriksson

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Fig. 2. Longitudinal section of the Ag—Cu eutectic. showing the start of the solidification on the left side of the picture, 2. drastic decrease in lamellar spacing in the centre, X 80. Acceleration 7.4 X 10~ cm/sec

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A1 203 tubes had an inner diameter of 2 mm and were drawn out of the furnace by means of a drawing device driven with a stepless variable motor. This made it possible to subject the test samples to continuous accelerations. The rate of acceleration could also be varied by means of a gear mechanism,5,and 3.7the X following accelerations were used: 1.48 X i0 i05, and 7.4 X i05 cm/sec2. The experiments were carried out as follows: The samples were first held motionless for 5 mm to allow the solidification front to stabilize, and then drawn out of the furnace at a continuously increasing speed. Experiments were done using the following eutectic alloys: Ag—Cu, Al— Zn, Al—Cu, and Al—Ni.

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3. Results In the case of the Ag—Cu alloy, discontinuous changes in the lamellar spacing were observed in the experiments using the two highest accelerations. In the sample subjected to the highest acceleration, the lamellar spacing dropped by half all at once. Fig. 2 shows this sample under low magnification. Alter the starting point on the left, there can be seen a zone of wide lamellar spacing, which suddenly decreases to

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~ Fig. 3. Longitudinal section of the Ag—Cu eutectic, showing a drastic decrease in lamellar spacing, X 400. Accelaration 7.4

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7’. Carlberg, H. Fredriksson / Mechanism of lamellar spacing adjustment in eutectic alloys

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Fig. 4. Longitudinal section of the Ag—Cu eutectic, showing two drastic decreases in lamellar spacing, X 400. Acceleration 3.7 X 2. lO~cm/sec

one-half in the middle of the photograph. Fig. 3 shows the discontinuity under higher magnification. In the sample subjected to the next highest acceleration, the lamellar spacing decreased in two steps of about one-quarter each, fig. 4. By recording the position of the samples as a function of time, it was possible to calculate the speed of solidification at each point along the sample. Further, lamellar spacing

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measurements were made on sections extracted at various distances from the starting point. This enabled us to plot the lamellar spacing X against the rate of solidification V. Figs. 5 and 6 shows these curves for the highest and second-highest accelerations. By using data on X as a function of V obtained from experiments carried out using a constant speed,

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IKI~ V ~iO~cm/sec Fig. 5. Interlamellar spacing as a function of growth rate, for a Ag—Cu eutectic solidified with increasing growth rate with an acceleration of 7.4 X i05 cm/sec2. The dashed curve shows the same function, but from experiments with constant growth rate after Livingston et al. [5].

v 10~cm/sec Fig. 6. Interlamellar spacing as a function of growth rate, for Ag—Cu eutectic solidified with increasing growth rate with an acceleration of 3.7 X iO cm/sec2. The dashed curve shows the same function, but from experiments with constant growth rate after Lvingston et al. [5].

T. Carlberg, H. Fredriksson / Mechanism of lamellar spacing adfustment in eutectic alloys ~

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Fig. 7. Transverse section of the Ag—Cu eutectic, in the beginning of the specimen just after the start of solidification, showing 2. both regular and irregular lamellar arrangement, and lamellar faults, X 800. Acceleration 3.7 X io~ cm/sec

we were able to include curves showing the lamellar spacings that establish themselves after a long period at the same solidification rate. These curves, extracted from Livinston et al. [5], are drawn as dashed curves on the graph. Repetition of the experi. ments gave the same results, although the discontinuities did not always occur at the same distances from the starting point. The sections were also studied to find what types of faults the structures contained, Fig. 7 shows a section of a sample accelerated at 3.7 x iO~cm/sec2 just before the first discontinuity. We can see both terminations and mismatched surfaces. It can also be seen that much of the structure is not lamellar but more irregular, with lamellar planes running in two mutually perpendicular directions. These structures have been previously described by Cooksey et al. [6]. The proportion of irregular, rod-like structures was greater at the beginning of the sample than after the major part of the sample had solidified. It should be pointed out that the lamellar spacings were measured only in areas of regular lamella formation. In the Al—Zn system, a discontinuous decrease in the lamellar spacing was also observed. It occurred in the sample subjected to the highest acceleration and caused a doubling of the number of lamellas. The point of difference from the Ag—Cu system was that

in the present case the jump came much sooner after the starting point (fig. 8). The zone of thick lamellas was too short to allow measurement of the lamellar spacing within it, and in a repetition of the experiment no discontinuity occured (fig. 9). Curves of the same type as for Ag—Cu are shown in fig. 10, which displays data from the sample of fig. 9. It can be seen from this graph that the curves from experiments using acceleration and from experiments performed with constant speeds are very close, which was not the case with Ag—Cu (figs. 5 and 6). Studying the sections, we see that in this case, too, there are a number of areas of rod structure at the beginning of the sample just after the starting point. After a few mfflimeters, however, the rod structure disappears and the structure becomes entirely lamellar. In the case of the Al—Cu eutectic, no discontinuities were observed when the experiments were performed in the same way as for the other systems. The reason for this was that these samples solidified with a cellular solidification front right from the start, probably due to a change of composition caused by sedimentation on the phase boundary before the experiments began. To avoid this, experiments were carried out with a low, constant solidification rate maintained for a long time. This enabled a smooth

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T. C’arlberg, H. Fredriksson / Mechanism of lamellar spacing adjustment in eutectic alloys

Fig. 8. Longitudinal section of the Al—Zn eutectic. showing the start of the solidification at the very left of the picture. Just after 2. the start there is a drastic decrease in lamellar spacing. X 800. Acceleration 7.4 X l0~ cm/sec

solidification front to stabilize, and the speed could then be increased progressively. Discontinuities were then obtained, all of them having the appearance shown in fig. 11. There is a sudden doubling of the number of lamellas, but many of the new lamellas dis-

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appear again almost inimediately. The net result is a decrease of about 20% in the lamellar spacing and a number of such discontinuities occur in succession. The Al—Ni experiments were performed in order to investigate whether similar effects could also arise

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lig. 9. Longitudinal section of the Al—Zn eutectic, showing the start of the solidification, without any drastic decrease in lamellar spacing, X400. Acceleration 7.4 X io~ cm/sec2.

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this century. However, it proved difficult to treat this problem in quantitative terms. It was not until the mid 1940s that Zener [71pointed out a way to deal with eutectic reactions quantitatively. His theoretical treatment has since been applied and developed further for eutectic reactions by a number of workers, inclduing Hillert [8], Tiller [9], and Jackson and Hunt [1]. All these models assume that the supercooling is composed of a component to keep the dif. fusion going plus a component for forming new surfaces. Following Tiller and Kirkaldy’s treatment of this problem, we find the following expression for the

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2 3 4 5 v”lO cm/sec Fig. 10. Interlamellar spacing as a function of growth rate, for a Al—Zn eutectic solidified with increasing growth rate 5 cm/sec2. The dashed with an acceleration of 7.4 X10

undercooiing ~T: ~T=K 1vX+K2/X

curve shows the same function, but from experiments with constant growth rate after Livingston et al. [5].

4. Quantitative treatment of eutectic reactions The theory of eutectic growth has been dealt with many times in the literature since the beginning of

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where ST” undercooling, u = growth rate, X = lamellar spacing, K1 = constant according to table 1, K2 = constant according to table 1. At a given rate of solidification, ~T and X vary as shown in fig. 12 below. It can be seen from the figure that eq. (1) does not uniquely determine the choice between undercooling and the lamellar spacing corresponding to a given rate of solidification. Zener proposed that the lamellar spacing would assume a value such that the reaction would take place at the fastest rate or with the minimum of undercooling. It has

in a system which solidifies into a rod eutectic. No such tendency could be discovered, however.

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Fig. 11. Longitudinal 2. section of the Al—CuA12 eutectic, showing a drastic decrease in lamellar spacing, X 800. Acceleration 3.7 X i0~cm/sec

7’. Carlberg, H. Fredriksson I Mechanism of lamellar spacing adjustment in eu tectic alloys

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Table 1 Constants used in the calculations

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2 X 106 K K1 (°Csec/cm 5 6 x i0~ 2 (°Ccm) 5.1 X i0~ The constants for the Al—Cu system are calculated and the constants of the other systems are chosen with respect to expected differences in D, a and m:

A Fig. 12. Undercooling as a function of the interlamellar spacing for an eutectic alloy at a certain growth rate.

K 1 (1 — ka)Ce/4D(lIm,3 — I/mn) K2 2a~Te/MI Ce = eutectic composition D = diffusion coefficient Te = eutectic temperature LiH = heat of fusion ~ = partition ratio of the n-phase ma = the liquidus slope of the n-phase m13 = the liquidus slope of the 13-phase = surface energy

shown on table 1 and assuming a wavelength of 1OX0. X0 was assigned the value 2X~,where X~is the critical lamellar spacing and 2X~gives the minimum of undercooling. The calculation results are shown in fig. 13. The figure shows calculations for two different values of ~X. It is apparent from the figure that the solidifi-

been shown in a number of studies over the last decade [3,10] that this criterion is not generally valid. This led Puls and Kirkaldy [11] to point out that Zener’s criterion should instead by revised to state that the eutectic will contain a spectrum of lamellar spacings lying in the region of the minimum, Following this theory, we are then able to write the following expression for the variation of the lamellar spacing: X = X0 + ~z~Xsin(2ir/nX)x.

(2)

cation front becomes smoother as ~X decrease. With the object of investigating the effect of the choice of system on the character of the solidification front, we carried out similar calculations substituting other values of K1 and K2 in eq. (3). The values of K1 and K2 were based on the systems Ag—Cu and Al— Zn. The values of the constants assumed are shown on table 1. The results of the calculations are shown in table 2, line 1. It appears from the table that the smoothness of the solidification front, given the same lamellar spacing, increases as the ratio of K1 to K2 decreases. We can therefore draw the conclusion that the solidification front should be smoother in the Ag—Cu system than in the Al—Zn system.

Substituting this expression in eq. (1), we obtain: =

K1v [X0+ ~X sin(2ir/nX)x] K2

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where X0 is a selected lamellar spacing and ~X denotes the spread of the lamellar spacing about the value X0. nX denotes the magnitude of the wavelength. the the aid of the above we are enabled to With describe character ofequation, the solidification front. We have chosen to do this for the case of a eutectic Al—Cu alloy which was allowed to solidfy at a rate of i0~ cm/sec in a temperature gradient of 100°/cm. The calculations were performed using the constants

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IJIIJJ11~1j1E[11I] (b) Fig. 13. Calculated shape of the solidification front for a Al—Cu eutectic at a growth rate of 1 X 10~ cm/sec: (a) ~X = 2 X i0~ cm, (b) ~x = 4 X l0~ cm.

7’. Carlberg, H. Fredriksson / Mechanism of lamellar spacing adjustment in eutectic alloys

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5. Stability of solidification front The variations in the lamellar spacing will be related to the fault density of the eutectic structure. With the aid of the theory presented in the preceding paragraph, we are therefore able to account for the observation by Double [31 that the change in the lamellar spacing is related to the fault density. It was apparent from fig. 13 that areas having the extreme value 2X~lead the solidification process. During the solidification process there is a competitive relationship between the different parts of the solidification front. This competition has the effect that the areas that lead the process of growth are able to spread out ahead of the others. In our case, this results in a gradual alteration of the lamellar spacing towards the value 2X~.This would be a comparatively slow process, and it would also be strongly influenced by the stability of the system. Ic)

6. Effect of solidification rate on the character of the solidification front If the solidification rate is gradually increased from a given initial rate under constant conditions, the lamellar spacing will deviate from the extreme value of 2X~.It is therefore of interest to follow the changes in the solidification front while continuously increasing the solidification rate. Calculations of this type were performed. As the initial values we took the solidification rate and the lamella distribution that had been used as the basis of the calculations presented in fig. 13 and table 2, line 1. The results are shown in fig. 14 and table 2. In table 3 the corresponding results are shown from calculations with two different &‘~, but with constant values of K1 and K2. Both the period and the amplitude of the roughness increase, because the areas with the smallest lamellar spacing grow faster than other areas. The solidification front becomes unstable. The amplitude is a function of the lamella variations, table 3, and of the values of the constants K1 and K2, table 2. A larger value of i~Xresults in a greater increase in amplitude, and so does a larger value of the ratio of K1 to K2. Due to the instabffity of the solidification front, areas of faster growth spread out ahead of other areas, which permits a modification of the

Fig. 14. Calculated shape of the solidification front at increasing growth rate for the case shown in fig. 1 3b with ~X = 4 X i0~ cm: (a) V’~1.1 X 10 cm/see; (b) V 1.25 X 10 cm/see; (c) V 1.5 x i0~ cm/sec.

lamellar spacing. The rate at which this process takes place probably depends on the magnitude of the variations in the lamellar spacing. This magnitude is determined by the experimental conditions, including the solidification rate and the convection pattern in the melted metal.

7. Change in lamellar spacing with increasing solidification rate In the systems Ag—Cu and Al—Zn it was possible to observe discontinuous changes in the lamellar spacing as the solidification rate progressively increased. In every case, these changes occurred at the beginning of the samples, where the rate was low and the spacing wide. The mechanisms proposed in the preceding paragraph, based on the assumption that variations in the lamellar spacing and faults in the structure are capable of modifying the lamellar spacing towards its optimum value, evidently operate too slowly under

7’. Carlberg, H. Fredriksson / Mechanism of lamellar spacing adjustment in eutectic alloys

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The discontinuous change in the lamellar spacing is probably explicable in terms of the mechanism proposed by O’Hara and Hellawell [2]. This process will

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conditions of high accelartion at the lower speeds. Instead, the solidification front becomes unstable and a sudden decrease occurs in the lamellar spacing. This will be connected with the number of faults and with the magnitude of the variations in larnellar spacing in the structure. As the rate of solidification increases, the variations in the lamellar spacing become greater [10], with the result that modification towards the optimum value can thenceforth proceed continuously. This is easily seen in figs. 5,6 for Ag—Cu and in fig. 10 for Al—Zn. A comparison of these figures shows that the lamellar spacing is more easily modifled in Al—Zn than in Ag—Cu alloys. The reason for this is probably that the ratio of K1 to K2 in eq. (3) is greater in the Al—Zn system than in the Ag—Cu systern, resulting in a rougher solidification front and hence greater opportunity for modification of the lamellar spacing in the former case.

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A — Fig. 16. Curves showing the undercooling as a function of the interlamellar spacing for different growth rates, where V3 > V2> V1. The artows shows the changes in undercooling with increasing growth rate. At a certain growth rate there is a sudden decrease in lamellar spacing, immediately followed by an increase, which also gives an decrease of the undercooling.

be associated with a drastic change in the supercooling at the solidification front, in the manner illustrated in fig. 15. In a gradient solidification experiment, this results in a sudden, discontinuous increase in the rate of growth. In the case of Al—Cu alloys it was shown that a sudden change in the number of larnellas does not necessarily result in the lamellar .

spacing assuming the value 2X~.In this system, it assumed a smaller value. The change in the supercooling at the solidification front associated with the change in the lamellar spacing in the Al—Cu system is illustrated in fig. 16.

8. Conclusions Unidirectional solidification with increasing solidification rate was performed for some eutectic alloys. It was found in experiments with high acceleration that the interlamellar spacing decreased discontinously. The systems investigated were Ag—Cu, Al—Cu, Al—Zn and Al—Ni, and the discontinuous steps were found in all systems except Al—Ni. The latest was solidified to a rod eutectic, and that is probably the reason to the discrepancy. By measurements of the lameliar spacing along the specimens, it was found that the adjustment of the lamellar spacing was faster in the Al—Zn system than in the Ag—Cu system. With the assumption that the distribution of the lamellar spacings was sinusoidal shaped, it was possible to calculate the shape of the solidification front. The calculations were made with different amplitudes on the assumed sinus distribution, and with different material constants. The result from the calculations was that a larger amplitude gave a rougher solidification front, and the constants corresponding to the Al—Zn system, gave a rougher front than those from the Ag—Cu system. It was also possible to calculate the shape of the solidification front at increasing rate, but with the same distribution of the lamellar spacing. Those calculations gave a rougher front at increasing solidification rate. It was suggested that a rougher front makes it easier for the lamellar spacing to adjust a favourable .

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T. Carlberg, H. Fredriksson I Mechanism of lamellar spacing adjustment in eutectic alloys

535

value, and that made it possible to explain that the adjustment of the lamellar spacing in the Al—Zn systern was faster than in the Ag—Cu system.

[4] J.D. Hunt and K.A. Jakcson, Trans. AIME 236 (1966) 843. [51se~Ada Met. 18(1970)399. E.F. Koch and R.R. Rus-

References

[6] D.J.C. Cocksey, D. Manson, M.P. Wilkinson and A. Hellawell, Phil. Mag. 10(1964) 745. [7] C. Zener, Trans. AIME 169 (1946) 550.

[1] J.D. Hunt and K.A. Jackson, Trans. AIME 236 (1966) 1129, [2] S. O’Hara and A. Hellawell, Scripta Met. 2 (1968) 107. [3] D.D. Double, Mater. Sci. Eng. 11(1973)325.

[8] M. Hillert, Jernkontorets Ann. 141 (1957) 757. [9] WA. Tiller, in: Liquid Metals and Solidification (ASM) p.276. [10] AS. Yue, Trans. AIME 224 (1962) 1010. [11] M.P. Puls and .J.S. Kirkaldy, Met. Trans. 3 (1972) 2777.