Tetrahedron Approximation Of Cluster Variation Method Research Articles

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

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.

Site preference of atoms in the relaxed (111) APB of Ni3Al(X) alloys

The cluster variation method (CVM) has been widely used for solving many problems of phase equilibrium in metals and alloys. In the present study, we extend the original CVM so as to perform the calculations of the energy and profile of antiphase boundaries in the intermetallic compounds such as Ni-Al-X systems (X is chosen to be Fe). We calculate the site preference of ternary elements in the relaxed (111) APB region forLl2-type Ni3Al(X) alloys, based on the tetrahedron approximation of CVM. We have found that the peak of the calculated (111) APB energy appears at an alloy composition deviating slightly to the Al-rich side from stoichiometry. This deviation is considered to result from the short-range effect between Ni and Al at the APB region.