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Caloric and isothermal equations of state of solids: empirical modeling with multiply broken power-law densities

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Abstract

Empirical equations of state (EoSs) are developed for solids, applicable over extended temperature and pressure ranges. The EoSs are modeled as multiply broken power laws, in closed form without the use of ascending series expansions; their general analytic structure is explained and specific examples are studied. The caloric EoS is put to test with two carbon allotropes, diamond and graphite, as well as vitreous silica. To this end, least-squares fits of broken power-law densities are performed to heat capacity data covering several logarithmic decades in temperature, the high- and low-temperature regimes and especially the intermediate temperature range where the Debye theory is of limited accuracy. The analytic fits of the heat capacities are then temperature integrated to obtain the entropy and caloric EoS, i.e. the internal energy. Multiply broken power laws are also employed to model the isothermal EoSs of metals (Al, Cu, Mo, Ta, Au, W, Pt) at ambient temperature, over a pressure range up to several hundred GPa. In the case of copper, the empirical pressure range is extended into the TPa interval with data points from DFT calculations. For each metal, the parameters defining the isothermal EoS (i.e. the density–pressure relation) are inferred by nonlinear regression. The analytic pressure dependence of the compression modulus of each metal is obtained as well, over the full data range.

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Correspondence to Roman Tomaschitz.

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Tomaschitz, R. Caloric and isothermal equations of state of solids: empirical modeling with multiply broken power-law densities. Appl. Phys. A 126, 102 (2020). https://doi.org/10.1007/s00339-019-3256-7

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Keywords

  • Multi-parameter equation of state (EoS)
  • Caloric EoS of carbon allotropes
  • Specific heat of vitreous silica
  • Thermal EoS and compression modulus of metals
  • High-pressure regime
  • Multiply broken power laws