Effects of Electrodiffusion on the Pb-Sn Eutectic Growth

EFFECTS OF ELECTRODIFFUSION ON THE Pb-Sn EUTECTIC GROWTH

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(Received: October 10, 1997; Accepted: March 9, 1998)

Abstract - In the growth of a binary eutectic alloy, the formation of two new solid phases results in an unusual solute segregation process. In order for growth to happen, one of the solid phases must experience a decrease in the initial melt concentration of one of the alloy constituents and an increase in the amount of the other element. An analogous phenomenon occurs with respect to the other phase. The lateral composition gradient gives rise to mass transport parallel to the growth direction and across the solid/liquid interface, which controls the liquid interfacial composition field. The presence of an electric field during solidification can change the interfacial liquid composition distribution and thereby the growth condition. In this work, the Pb-Sn eutectic alloy was directionally solidified under the influence of an electric field normal to the growth direction. The results obtained show that electrodiffusion due to the electric field can change the eutectic lamellar spacing, the lamellar growth orientation and the eutectic microstructure regularity.

Keywords: Electrodiffusion, eutectic growth, solid faces.

INTRODUCTION

The growth mechanisms involved in eutectic solidification have been studied in detail within the last decades. Several theoretical and experimental studies have been done in order to understand the effect of transport phenomena's parameters on the growth of eutectic microstructure (Verhoeven and Homer,1970; Quenisset and Naslain,1981; Baskaran and Wilcox,1984; Eisa and Wilcox,1986). In eutectic reaction, transformation of liquid phase into two solid phases involves simultaneous diffusion of eutectic system components. Such a phenomenon is called diffusion-coupled growth (Jackson and Hunt, 1966) and gives rise to a two-phase solid with anisotropic properties. The array of solid phases in eutectic microstructure suggests that eutectic alloys are potentially useful materials in obtaining structural composites. Besides mechanical properties, eutectic microstructure may exhibit unique electric, magnetic and optic properties (Galasso, 1967; Ditchek et al., 1990; Rossoni et al., 1991).

The primary parameter in eutectic microstructure, which controls many of its properties, is the distance between solid phases. In eutectic lamellar growth such distance is called lamellar spacing, and it is basically a function of solute distribution in liquid phase near solid/liquid interface, which is, essentially, a result of growth rate, diffusion coefficients and eutectic system characteristics. Then, for a particular growth condition, the microstructure spacings are already determined. Generally, it is desirable to be able to control such spacings. To obtain such control, it is necessary to alter the mass transfer in the liquid phase near the solid/liquid interface. Variation in lamellar spacing is limited to the change in growth rate which is usually limited to a narrow band of rates where lamellar growth is stable. The solute distribution in the liquid near solid/liquid interface depends on the mass transport due to the movement of solid/liquid interface and the flux due to atomic diffusion given by Fick's law. In addition to such fluxes, the presence of a mass flux in the liquid, parallel to the solid/liquid interface, will change the solute profile at interfacial liquid. A change in liquid solute distribution produces a variation in the interfacial liquid undercooling, which, consequently, changes the lamellar spacing.

A mass flux normal to the growth direction and parallel to solid/liquid interface can be obtained by applying a transverse electric field to the melt during the eutectic growth. Such a phenomenon is called mass transport by electrodiffusion. The phenomenon of electrodiffusion, which is also termed electrotransport or electromigration, is the atomic movement produced by an electric field applied to a solid or liquid metal (Verhoeven, 1966). According to Angus et al. (Angus et al., 1961), a metallic conductor shows a small component of ionic conductivity. The exposition of a molten metallic sample to an electric field induces ionic mass transport.

The main objective of this paper is to examine the influence of an electric field normal to growth direction on lamellar eutectic growth.

EUTECTIC GROWTH WITH A TRANSVERSE ELECTRIC FIELD

According to classical eutectic growth theory (Jackson and Hunt, 1966), lamellar spacing, l , depends on liquid undercooling at solid/liquid interface, which is given by the summation of two parts: one associated with the deviation of liquid composition from the eutectic composition and the other related to the curvature of solid/liquid interface. The relationship between lamellar spacing and liquid undercooling is obtained from (Seetharaman and Trivedi, 1988):

(1)

where D T is the liquid undercooling, K₁ and K₂ are constants of the eutectic system, C_I is the liquid composition at solid/liquid interface, and C_e is the eutectic composition. The value of lamellar spacing during eutectic growth is the one that minimizes the liquid undercooling at solid/liquid interface. Lamellar spacing is obtained by applying the" extremum condition" principle, which is found by making dD T/dl =0:

(2)

The term d(C_I-C_e)/dl in equation 2 is obtained by determining the liquid solute distribution in eutectic growth. To calculate lamellar spacing it is necessary to find the solute distribution in the liquid phase near solid/liquid interface, which is a consequence of atomic fluxes during eutectic growth, as shown in Figure 1.

In directional solidification of a eutectic alloy at steady-state, according to Figure 1.a, two types of mass flux are present: flux related to composition gradient in liquid phase and flux related to movement of solid/liquid interface (Caram and Wilcox, 1992; Caram et al., 1990). The flux due to liquid composition gradient is given by:

(3)

where x is the direction normal to the growth direction, y is the growth direction, C is the composition and D is the molecular diffusion coefficient of solute in the liquid. The flux due to the movement of solid/liquid interface is obtained from:

(4)

where V is the growth rate. If a sample is solidified under the influence of a transverse electric field, as shown in Figure 1.b, a third flux (due to electrodiffusion) is observed, and it is given by (Angus et al., 1961):

(5)

where E is the electric field, U is the solute ionic mobility in x-direction, near solid/liquid interface and assumed to be constant in this problem. The net mass flux, J_T, is defined by:

(6)

The liquid solute distribution is found by making a mass balance in a liquid differential element. At steady-state, solute distribution may be obtained from:

(7)

Equation 7 allows one to calculate liquid composition during directional solidification with the influence of a mass transport due to electrodiffusion, acting normal to growth direction. By analyzing such an equation one is able to observe that electrodiffusion may change solute distribution in the liquid near the interface, and hence, the lamellar spacings.

Figure 1:
Mass fluxes during directional solidification: (a) without electrodiffusion; (b) with electrodiffusion.

EXPERIMENTAL METHODS

The experimental work was performed by directionally solidifying the Pb-Sn eutectic alloy. Such an alloy was chosen due to its large amount of results and information accessible in the literature. The sample of the growth alloy was prepared by weighing the proper eutectic amount of 99.99% purity Pb and Sn, corresponding to 61.9 wt % Sn - 38.1 wt % Pb. Quartz ampoules containing Pb-Sn alloy were filled with argon.

The variation of the mass flux normal to the growth direction was obtained by inserting two small graphite electrodes connected to a power supply and in contact with alloy into ampoules. To avoid oxidation, the graphite electrodes were bonded to the ampoule with special cement, as shown schematically in Figure 2. Several values of current were used: from 0 to 8A. Such values resulted in current density across the graphite/alloy contact section from 0 to 1,000 A/cm^-2. The contact area was close to 8.0 x 10^-3 cm² and the applied voltage varied from 0 to 0.05 V.

Figure 2:
Experimental setup to study eutectic lamellar growth with electrodiffusion.

To obtain directional solidification, a Vertical Bridgman-Stockbarger crystal growth unit was used. It consisted of two heating zones (hot and cold zones) separated by an adiabatic zone. The sample with Pb-Sn alloy was moved from the hot zone to the cold zone to induce solid growth. To examine the effect of electrodiffusion on eutectic growth, ingots of 10.0 cm in length and 0.8 cm in diameter were directionally solidified at 1.0 cm/hr. A thermal gradient at the solid/liquid interface of 45^oC/cm was determined using K-type thermocouples. Longitudinal and radial samples were taken from several locations near the graphite electrodes. Slices of the directionally solidified alloy were cast in a resin mold, mechanically polished and chemically etched in a solution of glycerol, acetic acid and nitric acid for 15 sec to reveal the lamellar structure. The lamellar microstructure of longitudinal and radial samples was examined using optical microscopy technique.

RESULTS AND DISCUSSION

The growth condition without electrodiffusion was verified by solidifying eutectic Pb-Sn samples at several growth rates and by using two types of samples: ampoules with and without the graphite electrodes. Since the sample was lowered from the hot zone to the cold zone, natural convection was reduced. Then, eutectic solidification without electrodiffusion was considered to be a pure diffusion growth process. The relationships between lamellar spacing and growth rate obtained using both types of ampoules, with and without electrodes, showed good agreement with data found in the literature (Caram et al., 1991; Mollard and Flemings, 1967). Such a control test led to the result that the sample thermal conditions were not altered by the graphite electrodes.

A series of ten experiments was carried out using d.c. from 0 to 8A. The effects of electrodiffusion on lamellar microstructure were studied by analyzing the samples near the graphite electrodes. In all the electrodiffusion experiments the samples were exposed to the electric field during the entire processing time. However, electrodiffusion affected eutectic growth only at the moment that solid/liquid interface reached the graphite electrodes region. At this point, the ionic flux altered the pure diffusion growth process, and hence the liquid solute distribution at solid/liquid interface. Changes in the solute distribution altered interfacial liquid undercooling and, consequently, changed lamellar spacing. When low values of currents were employed, a slight or no variation in lamellar spacing was noted. As the current was increased, the lamellar spacing also increased. Figure 3 presents several microstructures and their positions near graphite electrodes obtained in experiments using 8A. Compared with experiments without electrodiffusion, lamellar spacings were not altered in the region far from the graphite electrodes. However, it increased with the decreasing distance from the graphite electrodes. At the region in the middle of the graphite electrodes, the microstructure was coarser than when solidification was performed without electrodiffusion, but it was finer than the microstructure obtained between the graphite edges. This region was exposed to the action of electrodiffusion. Although such behavior was not expected, it has a reasonable explanation. Consider three locations at the region of the graphite electrodes, as shown in Figure 3. In region 1, far from the electrodes, ionic current is negligible, and lamellar spacing is constant, and it is a result of pure diffusion growth conditions only. In region 2, between the graphite electrodes edges, the ionic flux is high due to the edge effect, which increased lamellar spacing. Finally, in region 3, between the graphite electrodes, ionic current is greater than the current in region 1, but smaller than the current in region 2, which led to lamellar spacing values between those found in region 1 and region 2.

To measure the lamellar spacing variation, longitudinal samples may be used occasionally. However, to measure spacing at different locations, cross-sectional samples were utilized in this work. As eutectic microstructure grows with many grains at several orientations, it is necessary to use a cross-sectional sample to avoid mismeasurement of the lamellar spacing. The lamellar spacing variation at locations near the graphite electrodes for several values of current is shown in Figure 4.

The reason for such variation is found by analyzing the mechanism of regular eutectic growth. Besides molecular diffusion during eutectic growth, electrodiffusion flux in the melt near the solid/liquid interface works as an additional means of mass transport. Electrodiffusion flux helps the diffusive flux of eutectic constituents, which increases the efficiency of cross-diffusion of solutes in the melt ahead of solid phases.

Figure 3
: Lamellar eutectic microstructure at graphite electrodes region obtained with several values of current and V=1,0cm/hr.

Figure 4:
Lamellar spacing variation obtained near graphite electrodes.

One could affirm that variations in the lamellar spacing could be due to the Joule heating caused by the current through the sample. To determine whether or not the changes observed were due to the electrodiffusion, the electrical contact at the graphite/alloy interface and the current polarity effects were investigated. When the graphite was in contact with a solid region in the sample, the value of the electrical resistance between the graphite and the alloy was found to be very large. In such a case, the Joule heating could be significant, and hence, would alter the eutectic structure. On the other side, when the contact was with the molten alloy, as in the case of a directional solidification, the electrical resistance was found to be negligible. Besides the variation in lamellar spacing, in all experiments a slight change in the lamellar growth orientation was observed. When the current polarity was modified, the growth orientation changed too. Such a fact confirms that the main reason for spacing changes was the electrodiffusion.

CONCLUSIONS

Based upon the results obtained in this work it can be affirmed that a transverse electric field applied during eutectic growth could be a different technique for changing lamellar eutectic growth condition. During directional solidification, Pb-Sn eutectic lamellar spacings increase with the influence of a transverse electric field. The electric field produces a mass transfer by electrodiffusion that alters the solute distribution in the liquid near solid/liquid interface. Such a change alters the interfacial undercooling and therefore the lamellar spacings. However, change in lamellar microstructure depends on the intensity of electrodiffusion. Also, the presence of electrodiffusion reduced the lamellar eutectic microstructure regularity and slightly changed the lamellar growth direction.

NOMENCLATURE

C_e Eutectic composition

C_I Interfacial melt composition

D Diffusion coefficient in melt, m² s^-1

E Electric field, V m^-1

J Mass flux, atoms m² s^-1

K₁ Constant of the eutectic system

K₂ Constant of the eutectic system

T Temperature, K

U Solute ionic mobility, m² s^-1 V^-1

V Growth rate, m s^-1

x Distance along the solid/liquid interface, m

y Distance into the melt from the interface, m

l Lamellar spacing, m

ACKNOWLEDGEMENT

This research was supported by CNPq, FAEP-UNICAMP and FAPESP.

REFERENCES

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Publication Dates

• Publication in this collection
  09 Oct 1998
• Date of issue
  Mar 1998

History

• Accepted
  09 Mar 1998
• Received
  10 Oct 1997