Model for Surface Tension of Pure Liquid Metals: Revisit to Iida’s Model

Abstract

Abstract In the present study, a well-known Iida’s equation for surface tension was modified to improve the predictivity of the surface tension of pure liquid metals. A semi-empirical equation for the surface tensions ( $${\sigma }_{m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> ) of liquid metal at its melting temperature proposed by Iida et al. uses a generalized $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> value of 0.51 to represent the ratio of the distance required to separate one atomic pair from its equilibrium distance. This study improved the predictability of the equation by refining the $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> value using the equilibrium interatomic distance ( $${r}_{e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> ) and atomic radius ( $${r}_{a}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:math> ). Assigning an accurate $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> value for each element greatly improves the prediction accuracy of the surface tension for liquid metals. Furthermore, the critical temperature ( $${T}_{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> ) was calculated based on the interatomic distance ( $${r}_{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> ) at $${T}_{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> and temperature coefficient of density ( $$d{\rho }_{T}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:mrow> </mml:math> / $$dT$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dT</mml:mi> </mml:mrow> </mml:math> ) and used to predict the temperature dependence coefficient of surface tension ( $$d{\sigma }_{T}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:mrow> </mml:math> / $$dT$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dT</mml:mi> </mml:mrow> </mml:math> ). As results, more accurate surface tensions of 42 liquid metals were predicted over the entire liquid state temperature. Graphical Abstract

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