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Thermodynamic modeling of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr system
Affiliation:1. School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China;2. General Research Institute for Non-ferrous Metals of Beijing, Beijing 100088, China;1. Escola Politécnica da Universidade de São Paulo, Metallurgical and Materials Engineering Department. Av. Prof. Mello Morais, 2463, CEP 05508-030 São Paulo – SP, Brazil;2. Instituto de Física da Universidade de São Paulo, CP 66318, 05315-970 São Paulo – SP, Brazil;3. Escola de Engenharia de Lorena da Universidade de São Paulo, Materials Engineering Department, Lorena – SP, Brasil;1. Forschungszentrum Juelich, IEK-2, 52425 Juelich, Germany;2. Now with: TU Wien, Institut of Materials Science and –Technology, Getreidemarkt 9, E308, 1060 Vienna, Austria;3. Thermochemistry of Materials Scientific Research Centre, NUST MISIS, Leninsky prosp. 4, 119049 Moscow, Russia;4. Institute for Materials Applications in Mechanical Engineering, RWTH Aachen University, Augustinerbach 4, 52062 Aachen, Germany;1. State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, China;2. Hunan Provincial Key Defense Laboratory of High Temperature Wear-Resisting Materials and Preparation Technology, Hunan University of Science and Technology, Xiangtan, 411201, China;3. College of Metallurgy and Materials Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412008, China;1. State Key Laboratory of Powder Metallurgy, Central South University, Hunan 410083, PR China;2. Collaborative Innovation Center of Steel Technology, University of Science and Technology Beijing, Beijing 100083, PR China;3. College of Metallurgy and Materials Engineering, Hunan University of Technology, Zhuzhou 412007, China;4. College of Mechanical and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China;5. MSI, Materials Science International Services GmbH, Am Wallgraben 100, 70565 Stuttgart, Germany
Abstract:The total energies of Laves phases in the Cr–Nb and Zr–Cr systems have been calculated by the pseudo-potential VASP code with a full relaxation of all structural parameters. The special quasirandom structures (SQSs) have been constructed and their total energies have been calculated by the VASP code to predict the enthalpies of mixing for bcc and hcp solid solution phases. The phonon calculations for the C14 and C15 Laves phases have been performed to analyze the phase stability at elevated temperatures. The experimental study on the Zr–Cr system has been carried out at different temperatures to determine the phase boundaries. Based on these results, thermodynamic models of Cr–Nb and Zr–Cr with extension to the ternary Zr–Nb–Cr systems have been developed in this work by using the CALPHAD approach.
Keywords:First-principles calculations  CALPHAD
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