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Predicting the Density of Solid and Liquid Near-Eutectic Ga–In–Sn Alloy

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Abstract

Europe has set itself the goal of reducing net greenhouse gas emissions to zero by 2050. This requires innovative concepts for the transfer of thermal energy. One of these could be the use of liquid metals and alloys as heat carriers. For this purpose, the precise knowledge of the thermophysical properties of these materials is of great importance. This study therefore aims to model the temperature dependent density of solid and liquid near-eutectic gallium-indium-tin alloys. Three approaches—weighted fitting of experimental data, modelling based on atomic volumes of alloying elements, and an approach that accounts for possible excess density—are utilised. Details of these strategies with respect to the thermophysical properties of the alloying elements, and the binary sub-alloys, are discussed. The resulting correlations are validated using six independent experimental data sets. The study concludes that, currently, the fitting polynomials are the most reliable models. The estimates based on atomic volumes are in close agreement with these functions. This is true for both the solid and liquid states. This marks the first time that the density of the solid state of this particular alloy has been modelled. The difficulties associated with modelling the density excess are manifold. This includes the lack of precise thermophysical properties for the alloying elements. The study paves the way for near-eutectic liquid gallium-indium-tin alloy as a heat carrier. In the view of the potential importance of heat transfer employing liquid metals, these findings highlight the need for further investigations in this field.

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Abbreviations

c p :

Isobaric heat capacity [J·kg−1·K−1]

G :

Gibbs energy: [J]

H :

Enthalpy of mixing [J·mol−1]

L xy :

Interaction parameters [J·mol−1]

T :

Temperature [K]

V i :

Atomic volume of component i [m3·mol−1]

X i :

Molar fraction of component i [–]

β :

Expansion coefficient [K−1]

ρ :

Density [kg·m−3

EGaInSn:

Near-eutectic gallium-indium-tin alloy

eu:

Eutectic

fit:

Fitting approach

Ga:

Gallium

GaIn:

Binary gallium indium alloy

GaSn:

Binary gallium tin alloy

In:

Indium

InSn:

Binary indium tin alloy

liq:

Liquid

m:

Melting

Sn:

Tin

sol:

Solid

exc:

Excess

i…0, 1:

Constant and linear interaction parameters

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Acknowledgements

The Bundesministerium für Wirtschaft und Klimaschutz der Bundesrepublik Deutschland supports the study financially under the research grant 49MF200081. The author thanks Maria José V. Lourenço and Carlos Nieto de Castro (University of Lisbon, Portugal) for the fruitful discussions that supported this work.

Funding

The author has no competing interests to report. The Bundesministerium für Wirtschaft und Klimaschutz der Bundesrepublik Deutschland supports the study financially under the research Grant 49MF200081.

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  1. Institut für Luft- und Kältetechnik gGmbH Dresden, 01309, Dresden, Germany

    Matthias H. Buschmann

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M.H.B conceived and authored the paper.

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The un-expanded correlations for Eqs. 8 and 24 are available upon request from the author.

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Buschmann, M.H. Predicting the Density of Solid and Liquid Near-Eutectic Ga–In–Sn Alloy. Int J Thermophys 45, 10 (2024). https://doi.org/10.1007/s10765-023-03295-y

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