Thermodynamic Characterization and Equation of State for Solid and Liquid Lead

Abstract

A high-temperature equation of state (EoS) for the fcc phase of solid lead and liquid lead was developed herein using experimental data on thermodynamic properties, volumetric thermal expansion, compressibility, temperature-dependent bulk modulus, and sound velocity from ultrasonic measurements and melting curve. The whole totality of experimental data was optimized using the temperature-dependent Murnaghan EoS over a pressure range of 0–130 kbar. The temperature dependences of thermodynamic and thermophysical parameters were described herein using an expanded Einstein model. The resultant EoS describes well the whole set of available experimental data within measurement uncertainties of individual parameters.

Thermodynamic Properties and Equation of State for Tungsten

“…The optimization of the thermophysical and thermodynamic parameters of tungsten was performed taking account of the suggestions reported in [8] by using a model that approximates well and reproduces experimental data for lead [9], aluminum [10], and copper [11] in a wide temperature and pressure range.…”

“…The Tait equation was used for the description of the pressure-dependent molar volume of tungsten [12,13]. Unlike the studies [9][10][11], and accounting for the very high melting temperature of tungsten (T m = 3687 ± 7 K [14]), a temperature dependence of the pressure derivative of the isothermal bulk modulus was incorporated into the equation. The final form of the equation is written as:…”

“…The function chosen in the studies [9][10][11] to describe lead, aluminum, and copper was employed in this study for the description of the isothermal bulk modulus of tungsten. This function is based on the equation that calculates the isothermal compressibility, as suggested in [16].…”

Multiple Glass Transitions in Bismuth and Tin beyond Melting Temperatures

“…Density varies linearly with increasing temperature, T (K), above T m in liquid elements [3,[57][58][59][60][61]:…”