Papers by Keyword: Cluster Variation Method

Abstract: Continuous Displacement Cluster Variation Method is employed to study binary phase equilibria on the two dimensional square lattice with Lennard-Jones type pair potentials. It is confirmed that the transition temperature decreases significantly as compared with the one obtained by conventional Cluster Variation Method. This is ascribed to the distribution of atomic pairs in a wide range of atomic distance, which enables the system to attain the lower free energy. The spatial distribution of atomic species around a Bravais lattice point is visualized. Although the average position of an atom is centred at the Bravais lattice point, the maximum pair probability is not necessarily attained for the pairs located at the neighboring Bravais lattice points. In addition to the real space information, k-space information are calculated in the present study. Among them, the diffuse intensity spectra due to short range ordering and atomic displacement are discussed.

Abstract: Cluster Variation Method (CVM) has been widely recognized as one of the most reliable theoretical tools to study phase equilibria in metallic alloy systems. The conventional CVM, however, does not allow atomic local displacements and, therefore, calculated results often encounter various inconveniences such as the overestimation of transition temperatures. Continuous Displacement Cluster Variation Method (CDCVM) was proposed to circumvent such deficiencies of the conventional CVM. Preliminary studies on an order-disorder phase diagram based on CDCVM indicate that the transition temperature is shifted downward reproducing experimental tendencies. In the present study, lattice thermal vibration effects are also incorporated through Morse potential. It is concluded that the local lattice distortion effects are quite effective to reduce the transition temperature.

Abstract: Multi-scale simulation of ordering process from electronic, atomistic scales to microstructural scale was carried out by hybridizing Phase Field Method (PFM) and Cluster Variation Method (CVM). The hybrid model was applied to disorder-L10 ordering process in Fe-Pd system. Furthermore, computation of relaxation constants in the PFM was attempted based on Path Probability Method (PPM) which is the time evolution version of the CVM, within a linearized analysis of order-order relaxation process.

Abstract: The thermodynamic properties and phase transformations of metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The thermodynamic quantities, like thermal lattice expansion coefficients, specific heats, Grüneisen constants, elastic constants calculated by using the SMM are compared with those of other theoretical schemes and the experimental results. The hcp-bcc structural phase transformations observed for IVB elements, Ti, Zr and Hf, are discussed in terms of the anharmonicity of thermal lattice vibrations. The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys. In addition, the temperature dependence of the elastic moduli C11, C12 and C14 and those of the ideal tensile and shear strengths of the bcc elements Mo, Ta and W are studied: We also discuss the melting transitions of metals and alloys within the framework of the SMM and estimate the melting temperatures through the limiting temperature of the crystalline stability.

Abstract: The detailed behavior of the free energy of Cluster Variation Method in the vicinity of spinodal ordering transition is examined. The generalized phase diagram proposed in the previous study is modified and spinodal ordering transition is reinterpreted as a limiting case of the ideal glass transition.

Abstract: The thermodynamic properties of high temperature metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by using the tetrahedron cluster approximation of the cluster variation method (CVM). The energetics of the binary (Ta-W and Mo-Ta) alloys are treated within the framework of the first-principles TB-LMTO (tight-binding linear muffin tin orbital) method coupled to CPA (coherent potential approximation) and GPM (generalized perturbation method). The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys.

Abstract: Phase Field Method is combined with the Cluster Variation Method within the square approximation, and the multiscale ordering behavior from atomistic to microstructural evolution process of ordered domains in the two dimensional square lattice is investigated. The transition temperature is determined at 1:1 stoichiometric composition and it is confirmed that the transition is of the second order. The growth process of the ordered domains is visualized and it is revealed that the sharp decrease of the free energy takes place during the process.

Abstract: A calculation of the interface energy for the Ni-Al binary alloy, including the inter-phase boundary (IPB) energy and the anti-phase boundary (APB) energy, has been performed using the Cluster Variation Method (CVM) with the tetrahedron approximation within the temperature range of 600°C~1300°C. The calculated IPB energies range between 8 and 13 mJ/m2, while the APB energies range between 24 and 46 mJ/m2. Additionally, the dependence of the average composition and the order parameter on distance with the compositionally diffuse interfacial regions has been computed. The calculation also shows the width of the diffuse IPB increases with the temperature linearly.

Abstract: First principles calculations have been applied in various fields in Materials Science. The authors have been attempting to reproduce a binary phase diagram by combining FLAPW electronic structure total energy calculations with Cluster Variation Method of statistical mechanics. Such a first principles calculation for static equilibrium has been quite successful for a series of Febased alloy systems. Recently, main attention is directed towards the extension of the first principles calculation to phase transformation dynamics by incorporating Phase Field Method. A series of preliminary calculations on disorder-L10 ordering in Fe-Pd and –Pt are satisfactory and the evolution process of Anti-Phase Boundaries was reproduced. In the present report, first-principles calculations of phase equilibria and phase transformation are briefly reviewed. Particular focuses are placed on coarse graining operation which authors developed and and time scaling as a remaining problem.

Abstract: Modeling of Glass transition is attempted based on the Cluster Variation Method. Free energy functional of an L10 ordered phase is employed to describe the first order nature of the transition. Free energy contour surface calculated as a function of temperature and an order parameter which simulates an amount of defects provides a generalized stability diagram in which the ideal glass transition temperature is identified as a critical point. Transition kinetics is investigated by Path Probability Method which is the kinetics version of the CVM to time domain. Continuous cooling behavior is calculated by explicitly incorporating the temperature dependent viscosity term based on VFT (Vogel-Fulcher-Tamman) formula. The glass transition is realized as the freezing of the order parameter due to the enhanced viscosity. The extension of the present theoretical scheme to non-Bravais lattice is attempted by Continuous Cluster Variation Method.