Using first-principles results to calculate finite-temperature thermodynamic properties of the Nb–Ni μ phase in the Bragg–Williams approximation

Abstract

Results of first-principles (FP) total energy calculations for 32 different configurations of the μ phase in the binary system Nb–Ni are used in the compound energy formalism (CEF) to model finite-temperature thermodynamic properties. A comparison with Cluster Expansion Hamiltonian–Cluster Variation Method (CEH-CVM) calculations indicates that the CEF describes temperature-dependent site occupancies as well as the CEH-CVM within the temperature range of interest for applications. This suggests that the Bragg–Williams–Gorsky approximation (BWGA) used in the CEF is sufficient to describe site occupancies and thermodynamics of the μ phase. A phase diagram is calculated using the μ phase description derived in the present work together with a previous Calphad description for the other phases of this system. The FP-CEF approach significantly improves the description of the thermodynamic properties as a function of composition compared to the Calphad procedure generally used up to now.

Acknowledgements

This work is partially supported by DFG (Deutsche Forschungs Gemeinschaft) within the Collaborative Research Center 370 ‘Integrated Modelling of Materials’ and by the Deutsche Zentrum für Luft-und Raumfahrt e.V. (DLR), grant number 50WM 0043 and by a grant from the Swedish Strategic Research Foundation (SSF). Part of this work (MS) was performed under the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research of Matter), and was made possible by financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek NWO (Netherlands Organisation for scientific Research). The authors gratefully acknowledge PHYNUM at LPMMC for computational resources on the PC cluster (AP).

Notes

‖Current address: Laboratoire de Chimie Métallurgique des Terres Rares, ISCSA, CNRS, 2-8 rue Henri Dunant, F-94320, Thiais Cedex France.

○Laboratorium voor Materiaalkunde, Delft University of Technology, 137 Rotterdamseweg, Delft, 2628 AL Netherlands.

Additional information

Notes on contributors

J.-M. Joubert‖

‖Current address: Laboratoire de Chimie Métallurgique des Terres Rares, ISCSA, CNRS, 2-8 rue Henri Dunant, F-94320, Thiais Cedex France.

M. H. F. Sluiter○

○Laboratorium voor Materiaalkunde, Delft University of Technology, 137 Rotterdamseweg, Delft, 2628 AL Netherlands.