Thermodynamic Properties and Equation of State for Solid and Liquid Aluminum

Abstract

High-temperature equations of state for solid and liquid aluminum were constructed herein using experimental data on thermodynamic properties, thermal expansion, compressibility, bulk modulus and sound velocity measurements, supplemented with phase diagram data (melting curve). The entire set of experimental data was optimized using the temperature-dependent Tait equation over a pressure range of up to 800 kbar and over a temperature range from 20 K to the melting point for solid aluminum and to 3800 K for liquid aluminum. The temperature dependence of thermodynamic and thermophysical parameters was described by an expanded Einstein model. The resultant equations of state describe well the totality of experimental data within measurement errors of individual variables.

The Physics of the Thermodynamic Entropy

“…There is nothing particular about the elements represented in Figure 4 other than that they have moderate to low melting points. They were otherwise chosen because an internet search produced a complete range of data for each of the three metals, aluminium [11], indium [12] and lead [13]. It is noticeable that, with the exception of lead, all four have a mean reduced heat capacity below three.…”

“…Transformation to constant volume is straightforward given knowledge of the compressibility as well as the thermal expansivity [7] and reduces the heat capacity slightly, but without doing the calculations it is not possible to say for certain that the mean reduced heat capacity at constant volume will stay below 3. [12], Al [11], Pb [13] and Si [8] from 0K to their respective melting points. The specific heat of Ge [10] is shown over a limited range of temperature range, but including the melting point, for direct comparison with silicon.…”

“…Figure 4. The specific heat of three different metals, In[12], Al[11], Pb[13] and Si[8] from 0K to their respective melting points. The specific heat of Ge[10] is shown over a limited range of temperature range, but including the melting point, for direct comparison with silicon.…”

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.…”

THERMODYNAMIC PROPERTIES AND THE EQUATION OF STATE OF Α-Alumina

“…Определение параметров уравнения состояния оксида алюминия проведено на основе модели, использованной в статье [10] для нахождения уравнения состояния алюминия. Оптимизированные значения всех параметров определены аналогично с использованием симплексного метода мультиразмерной минимизации.…”