ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Modeling of thermo‐physic properties for pure elements using segmented regression methodology

Date: 05.06.2014
Place: CALPHAD XLIII, State Key Lab of Powder Metallurgy, Central South University, Changsha, China

Irina Roslyakova
Bo Sundman, Department of Materials Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden
Holger Dette, Mathematik III, Ruhr-Universität Bochum, Bochum, Germany

Currently in CALPHAD applications the temperature dependence of the heat capacity is described by high-order polynomials [1] with adjustable parameters fitted to experimental data. This approach to fit coefficients that lack physical meaning is restricted to high temperatures above 298.15K. The CALPHAD community discussed this problem in 1995 during a Ringberg Workshop and proposed a “universal” model to describe the thermodynamic properties over the whole temperature range from 0K to 6000K [2]. The first attempt in this direction was performed by Chen and Sundman in [3] applied to bcc, fcc, liquid and amorphous phases for the pure Fe.

Following the ideas from [2], [3], and [4], in this work we propose a new model for pure elements which consider several physical effects (e.g. electronic, vibrational etc.) and valid from 0K up to the melting temperature. The proposed model is based on segmented regression methodology, since these contributions appear in different temperature ranges and can be described by different functions. The preceding approach has been applied for several pure elements as Fe, Cr, Al, and Ge and results shows good agreement with experimental data.

We also performed the comparison of the segmented regression model with SGTE model [1]. Additionally we calculated corresponding confidence intervals for estimated model parameters using the bootstrap method.


[1] Dinsdale, AT. "SGTE Data for Pure Elements." CALPHAD 15 (4) (1991): 317-425.

[2] Chase, M.W., Ansara, I., Dinsdale, A., Eriksson, G., Grimvall, G., Höglund L, Yokokawa H. "Group 1: Heat Capacity Models for Crystalline Phases from 0 K to 6000 K." CALPHAD 19 (4) (1995): 437-447.

[3] Chen, Q., Sundman, B. "Modeling of Thermodynamic Properties for Bcc, Fcc, Liquid, and." J. Phase Equil 22 (6) (2001): 631-644.

[4] M. Palumbo, B. Burton, A. Costa e Silva, B. Fultz, B. Grabowski, G. Grimvall, B. Hallstedt, O. Hellman, B. Lindahl, A. Schneider, P. E. A. Turchi, and W. Xiong, “Thermodynamic modelling of crystalline unary phases” Phys. Status Solidi B, 1–19 (2013)

Supporting information:

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