TY - JOUR

T1 - Revisiting the Extension of SGTE Heat Capacity Data to Zero Kelvin

T2 - Combining Classical Fit Polynomials with Debye–Einstein Functions

AU - Gamsjäger, Ernst

AU - Wießner, Manfred

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/11/4

Y1 - 2024/11/4

N2 - It is demonstrated in this work that a four parameter Debye–Einstein integral is an excellent fitting function for heat capacity values of pure elements from zero Kelvin to room temperature provided that there are no phase transformations in this temperature range. The standard errors of the four parameters of the Debye–Einstein approach are provided. As examples the temperature dependent molar heat capacities of Fe, Al, Ag and Au are calculated in the temperature range from 0 to 300 K. Standard molar entropies, enthalpies and values of a molar Gibbs energy related function are derived from the molar heat capacities and the values are compared to literature data. The next goal focuses on a seamless transition of these low temperature heat capacities to SGTE (Scientific Group Thermodata Europe) unary data. This can be achieved by penalyzing deviations in the heat capacity values and in their temperature derivatives at the transition point. Whereas the constrained heat capacities of Fe and Al mimic the experimental data, the calculated values deviate considerably in case of Ag and Au. As an alternative a smooth transition in the heat capacities and the temperature derivative is achieved by a switch function employed close to the transition region.

AB - It is demonstrated in this work that a four parameter Debye–Einstein integral is an excellent fitting function for heat capacity values of pure elements from zero Kelvin to room temperature provided that there are no phase transformations in this temperature range. The standard errors of the four parameters of the Debye–Einstein approach are provided. As examples the temperature dependent molar heat capacities of Fe, Al, Ag and Au are calculated in the temperature range from 0 to 300 K. Standard molar entropies, enthalpies and values of a molar Gibbs energy related function are derived from the molar heat capacities and the values are compared to literature data. The next goal focuses on a seamless transition of these low temperature heat capacities to SGTE (Scientific Group Thermodata Europe) unary data. This can be achieved by penalyzing deviations in the heat capacity values and in their temperature derivatives at the transition point. Whereas the constrained heat capacities of Fe and Al mimic the experimental data, the calculated values deviate considerably in case of Ag and Au. As an alternative a smooth transition in the heat capacities and the temperature derivative is achieved by a switch function employed close to the transition region.

KW - Debye–Einstein model

KW - heat capacities

KW - regression analysis

KW - thermodynamic modeling

KW - unary systems

UR - http://www.scopus.com/inward/record.url?scp=85208100273&partnerID=8YFLogxK

U2 - 10.1007/s11669-024-01159-y

DO - 10.1007/s11669-024-01159-y

M3 - Article

AN - SCOPUS:85208100273

VL - 45.2024

SP - 1194

EP - 1205

JO - Journal of phase equilibria and diffusion

JF - Journal of phase equilibria and diffusion

SN - 1547-7037

IS - 6

ER -