ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


Statistical modelling of thermo-physical materials properties using segmented regression: application to chromium (Cr), aluminum (Al) and germanium (Ge)

Date: 07.10.2013
Time: 3:50 p.m.
Place: Sino-German Cooperation Group "Microstructure in Al alloys" Bilateral Symposium 2013, Changsha, China

Irina Roslyakova
Holger Dette, Mathematik III, Ruhr-Universität Bochum, Bochum, Germany

Traditionally in applied thermo-physics the temperature dependence of the heat capacity is described by high-order polynomials [1] with adjustable parameters fitted to experimental data. This approach led to fitting coefficients that lack physical meaning and are not valid below 298.15K.

To overcome this problem we propose a more physical approach that requires the modeling of several contributions (e.g. electronic, vibrational, etc.). Since these contributions appear in different temperature ranges [1, 2], the segmented regression methodology [3, 4] is applied for developing of mathematical model for heat capacity of materials.

We applied our approach to three elements: Al, Cr and Ge, and investigated the reliability of underlying fitting results for Cr by calculating other physical properties of interest, such as the enthalpy (H) that can be derived directly from the heat capacity of the studied material. Finally, based on the results, we constructed Gibbs energy function for these materials in the temperature range from 1K up to melting point and compared it with traditional SGTE description.


[1] B. Sundman, H. Lukas, S. Fries (2007). Computational Thermodynamics: The Calphad Method.

[2] G. Grimvall (1986). Thermophysical properties of materials.

[3] G. A. F. Seber, C. J. Wild (1989). Nonlinear Regression.

[4] Chui G. (2002). Bent-Cable Regression for Assessing Abruptness of Change. PhD-Thesis

Supporting information:

201Roslyakova_3d-Sino-German-Bilateral-Symposium 2013.pdf
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