Determination of thermal conductivity and interfacial energy of solid Zn solution in the Zn–Al–Bi eutectic system

https://doi.org/10.1016/j.expthermflusci.2010.11.001Get rights and content

Abstract

The equilibrated grain boundary groove shapes for solid Zn solution (Zn–3.0 at.% Al–0.3 at.% Bi) in equilibrium with the Zn–Al–Bi eutectic liquid (Zn–12.7 at.% Al–1.6 at.% Bi) have been observed from quenched sample with a radial heat flow apparatus. Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy for solid Zn solution in equilibrium with Al–Bi–Zn eutectic liquid have been determined to be (5.1 ± 0.4) × 10−8 K m, (80.1 ± 9.6) × 10−3 and (158.6 ± 20.6) × 10−3 J m−2 from the observed grain boundary groove shapes, respectively. The thermal conductivity variation with temperature for solid Zn solution has been measure with radial heat flow apparatus and the value of thermal conductivity for solid Zn solution has been determined to be 135.68 W/km at the eutectic melting temperature. The thermal conductivity ratio of equilibrated eutectic liquid to solid Zn solution, R = KL(Zn)/KS(Zn) has also been measured to be 0.85 with Bridgman type solidification apparatus.

Introduction

The solid–liquid interfacial energy, σSL, is recognized to play a key role in a wide range of metallurgical and materials phenomena from wetting [1] and sintering through to phase transformations and coarsening [2]. Thus, a quantitative knowledge of σSL values is necessary. However, the determination of σSL is difficult. Since 1985, a technique for the quantification of solid–liquid interfacial free energy from the grain boundary groove shape has been established and measurements have been reported for several systems [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21]. The grain boundary groove shape formed at the solid–liquid interface in a thermal gradient can be used to determine the interfacial energy and the interface near the groove must everywhere satisfyΔTr=1ΔSfσSL+d2σSLdn12κ1+σSL+d2σSLdn22κ2where ΔTr, is the curvature undercooling, ΔSf is the entropy of fusion per unit volume, n(nx, ny, nz) is the interface normal, κ1 and κ2 are the principal curvatures, and the derivatives are taken along the directions of principal curvature. Eq. (1) is valid only if the interfacial free energy per unit area is equal to surface tension per unit length, σSL = γ. When interfacial free energy differs from surface tension, the problem is more complicated and the precise modification of the Gibbs Thomson equation is not yet established [21]. When the solid–liquid interfacial free energy is isotropic, Eq. (1) becomesΔTr=σSLΔSf1r1+1r2where r1 and r2 are the principal radii of the curvature. For the case of a planar grain boundary intersecting a planar solid–liquid interface, r2 =  and the Eq. (2) becomesΓ=rΔTr=σSLΔSfwhere Γ is the Gibbs–Thomson coefficient. This equation is called the Gibbs–Thomson relation [13].

Gündüz and Hunt [13] also developed a finite difference model to calculate the Gibbs–Thomson coefficient. This numerical method calculates the temperature along the interface of a measured grain boundary groove shape rather than attempting to predict the equilibrium grain boundary groove shape. If the grain boundary groove shape, the temperature gradient in the solid (GS) and the ratio of thermal conductivity of the equilibrated liquid phase to solid phase (R = KL/KS) are known or measured the value of the Gibbs–Thomson coefficient (Γ) is then obtained with the Gündüz and Hunt’s numerical method.

One of the common techniques for measuring solid–liquid interfacial free energy is the method of grain boundary grooving in a temperature gradient. In this technique, the solid–liquid interface is equilibrated with a grain boundary in a temperature gradient as shown in Fig. 1, and the mean value of solid–liquid interfacial free energy is obtained from the measurements of equilibrium shape of the groove profile. The grain boundary groove method is the most useful and powerful technique at present available for measuring the solid–liquid interface energy and can be applied to measure σSL for multi-component systems as well as pure materials, for opaque materials as well as transparent materials, for any observed grain boundary groove shape and for any R = KS/KL value. Over last 25 years, the equilibrated grain boundary groove shapes in variety of materials have been observed and the measurements of the solid–liquid interfacial free energies were made from observed grain boundary groove shapes [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21].

The phase diagram of Zinc (Zn)–Aluminum (Al)–Bismuth (Bi) eutectic system has been evaluated [22]. Some thermal properties such as solid–liquid interfacial energy, Gibbs–Thomson coefficient, grain boundary energy and thermal conductivity of solid and liquid phases in the Zn–Al–Bi eutectic system have not been well known. The values of solid–liquid interfacial energy, Gibbs–Thomson coefficient and grain boundary energy could be of use to people doing comparisons between experimentally observed solidification morphology and predictions from theoretical models. Thus the aims of the present work were to observe the equilibrated grain boundary groove shapes for solid Zn solution in equilibrium with Zn–Al–Bi eutectic liquid and to determine the thermal conductivity of solid and liquid phases, the Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy for solid Zn solution in the Zn–Al–Bi eutectic system.

Section snippets

Experimental apparatus

In order to observe the equilibrated grain boundary groove shapes in opaque materials, Gündüz and Hunt [13] designed a radial heat flow apparatus. Maraşlı and Hunt [14] improved the experimental apparatus for higher temperature. The details of the apparatus and experimental procedures are given in Refs. [13], [14], [15], [16], [17]. In the present work, a similar apparatus was used to observe the grain boundary groove shapes in the Zn–Al–Bi eutectic system and the block diagram of the

Determination of Gibbs–Thomson coefficient

If the thermal conductivity ratio of equilibrated liquid phase to solid phase, the coordinates of the grain boundary groove shape and the temperature gradient of the solid phase are known, the Gibbs–Thomson coefficient (Γ) can be obtained using the Gündüz and Hunt’s numerical method described in detail Ref. [13]. The experimental error in the determination of Gibbs–Thomson coefficient is the sum of experimental errors in the measurement of the temperature gradient, thermal conductivity and

Conclusions

A radial temperature gradient on the sample was established by heating from the centre with a single heating wire and cooling the outside of the sample with a heating/refrigerating circulating bath. The equilibrated grain boundary groove shapes for solid Zn in the Zn–Al–Bi eutectic alloy were observed from a quenched sample. The Gibbs–Thomson coefficient, solid–liquid interfacial energy and grain boundary energy of solid Zn in the Zn–Al–Bi eutectic system have been determined from the observed

Acknowledgement

This project was supported by Erciyes University Scientific Research Project Unit under Contract No.: FBD–08–580. The authors are grateful to Erciyes University Scientific Research Project Unit for their financial supports.

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