B2-disorder phase boundary calculations in Fe rich region of Fe-Si binary system with tetrahedron approximation of CVM

Naoya Kiyokane, Ying Chen, Takako Yamashita, Masayasu Nagoshi, Takaaki Iguchi, Tetsuo Mohri

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The phase boundary between B2 ordered and disordered phases in the Fe-rich region of the Fe-Si binary system is calculated by Cluster Variation Method (CVM). The configurational entropy is formulated within the tetrahedron approximation of CVM, and the internal energy is derived by Cluster Expansion Method (CEM) operated on a set of total energies calculated by DFT. The Debye Gruneisen model is employed to introduce the vibrational effect. The second order transition for the B2 order-disorder transition is confirmed, which is in agreement with the published phase diagram data and the results of previous CALPHAD calculations. The calculated transition temperature in the present study is higher around the stoichiometric composition and lower in the Fe-rich region compared to the experimental transition temperature. One reason for this overestimation and underestimation of the transition temperature may stem from the facts that the local atomic displacement and wide range atomic correlations are not considered in the present study. The transition temperature is also determined using Thermo-Calc software with the SSOL4 database. The transition temperature obtained by Thermo-Calc calculations accurately reproduces the experimental results. Hence, it is considered that the interaction parameters and the ordering parameters of CALPHAD free energy implicitly include the contributions of short range ordering and local atomic displacement.

Original languageEnglish
Pages (from-to)207-214
Number of pages8
JournalCalphad: Computer Coupling of Phase Diagrams and Thermochemistry
Publication statusPublished - 2017 Mar 1


  • Cluster Expansion Method
  • Cluster Variation Method
  • Fe-Si alloy
  • First-principles calculations
  • Order-disorder transition

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Computer Science Applications


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