Linear isotherm regularities of liquid gallium under pressure

Huaming Li,Yongli Sun,Mo Li,Yanting Tian,Hao Ding

doi:10.1063/5.0074623

Huaming Li, Yongli Sun + Show 3 more

Open Access

https://doi.org/10.1063/5.0074623

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Abstract

Several new regularities in liquid gallium have been obtained from both the available experimental data and calculated thermodynamic properties along the isothermal lines with the equation of state (EoS) of a power law form. The quantity Z−1V3 is linearly proportional to V3 for all isotherms at high temperatures. Both the calculated reduced isothermal bulk modulus B*=BTVRT and the parameter Zint=PintVRT derived from the available experimental data and EoS of a power law form are observed to be linear with respect to V−3 with the temperature T and gas constant R, which is verified by the derived analytical expression from the derived linear isothermal regularity (LIR) EoS. By using the analytical expression from the LIR EoS, the calculated isobaric thermal expansion coefficient, isochoric heat capacity, isobaric heat capacity, Grüneisen parameter, and Anderson–Grüneisen parameter show quite different behavior with pressure at a constant temperature compared with those values from EoS of a power law form. In addition, analytical expressions of thermodynamic properties of liquid gallium are derived from the LIR EoS, such as adiabatic bulk modulus, sound velocity, entropy, internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy, which have the same tendency with pressure at a constant temperature as the numerically integrated values from EoS of a power law form.

Highlights

Gallium is one of the polyvalent metals with a number of unusual properties
We explore the simple empirical regularities from both the calculated properties of liquid gallium with the power law form of the equation of state and the experimental data, which include pressure–volume data, isothermal bulk modulus, and internal pressure along different isotherms under pressure
Simple new empirical regularities have been derived in liquid gallium under pressure on the basis of the calculated data from modified measured results and an equation of state (EoS) of the power law form

Summary

INTRODUCTION

Gallium is one of the polyvalent metals with a number of unusual properties. It has a low melting point under ambient conditions, and with increasing pressure, there is a minimum value existing at 1.2 GPa on the melting curve.[1,2,3,4] In the crystalline state, it exhibits rich solid phases with the variation of the pressure and temperature. An equation of state (EoS) in the power law form proposed by Baonza et al.[26,27] on the pseudospinodal hypothesis has been used to explore the thermodynamic properties in liquid indium,[28] liquid sodium,[29] and liquid potassium[30] under pressure through a limited number of measurements along different isothermal lines, and the calculated pressure–volume data showed good agreement with the experimental results. We explore the simple empirical regularities from both the calculated properties of liquid gallium with the power law form of the equation of state and the experimental data, which include pressure–volume data, isothermal bulk modulus, and internal pressure along different isotherms under pressure. We find the same new linear regularities from both the calculated values and the measured results under pressure

THEORETICAL BASIS

Linear isotherm regularities

Thermal expansion coefficient and heat capacity

DISCUSSION AND CONCLUSION