K. Masuda-Jindo

Application of Statistical Moment Method to Thermodynamic Properties of Metals at High Pressures

The moment method in statistical dynamics is used to study the thermodynamic properties of metals taking into account the anharmonicity effects of the lattice vibrations and hydrostatic pressures. The explicit expressions of the lattice constant, thermal expansion coefficient, and the specific heats C v and C p of cubic (fcc) metals are derived within the fourth order moment approximation. The thermodynamic quantities of Al, Au, Ag, Cu, and Pt metals are calculated as a function of the pressure, and they are in good agreement with the corresponding experimental results. The effective pair potentials work well for the calculations of transition and noble metals, compared to those of the s p -valence metals. For obtaining better agreement of the thermodynamic quantities of metals like Al, it is required at least to use the more sophisticated electronic many body potentials. In general, it has been shown that the anharmonicity effects of lattice vibration play a dominant role in determining the thermodynamic...

Calculation of alloy phase diagrams by continuous cluster variation method

Abstract The continuous displacement (CD) formulation of the cluster variation method (CVM) is applied to study the phase stability of the binary alloys. The present theory is a generalization of the conventional CVM and the basic idea is to treat an atom which is displaced by r from its reference lattice point as a species designated by r . The applications are presented to two-dimensional as well as three-dimensional binary alloys. For phase-separating binary alloys, the change of lattice constant with the composition and the reduction of the transition temperature are shown. We also investigate the order–disorder phase transition of BCC alloys within the pair approximation of the CD scheme of the CVM.

The continuous displacement CVM treatment of alloy systems

Abstract The continuous displacement (CD) formulation of the CVM allows atoms to be displaced from the reference rigid lattice points. When an atom displaced at r is regarded as a species r , the system is an alloy of an infinite number of species and the CVM entropy can be applied to the system. This paper presents the basic concepts behind the method and its applications. After the method is introduced, applications are presented to 2-dimensional systems including the single component case, surface relaxation and binary alloys of phase separating kind. In the surface studies, the angle dependence of the displacements is plotted in the polar coordinates and a snapshot of the displacements is simulated. In the surface layer, calculations showed inward or outward shift of the layers. For phase separating binary alloys, the change of lattice constant with the composition and the reduction of the transition temperature are shown. Comments are made on future applications.

Application of the statistical moment method to thermodynamic quantities of silicon

The lattice constants, thermal expansion coefficients, specific heats at constant volume and those at constant pressure, Cv and Cp, second cumulants, and Lindemann ratio are derived analytically for diamond cubic semiconductors, using the statistical moment method. The calculated thermodynamic quantities of the Si crystal are in good agreement with the experimental results. We also find the characteristic negative thermal expansion in the Si crystal at low temperatures.

Cluster Variation Method in the computational materials science

Abstract Cluster Variation Method (CVM) has been very successful in the computations of alloy phase diagrams as well as in many problems of the materials science related to the phase transitions. Originally, CVM was developed in the framework of the so-called rigid lattice approximation, but it has recently been extended to include continuous atomic displacements due to thermal lattice vibration and local atomic distortion due to size mismatch of the constituent atoms. In the present study, we focus our attention on the latter continuous displacement treatment of CVM. The continuous displacement (CD) formulation of the CVM is applied to study the phase stability of the binary alloys. The basic idea is to treat an atom which is displaced by r from its reference lattice point as a species designated by r . The effects of continuous atomic displacement on the thermodynamic quantities and phase transitions of binary alloys are investigated in detail. We also discuss the extension of the CD treatment of CVM to the calculations of solid-liquid and gas liquid phases transitions.

Atomic theory of fracture of brittle materials: Application to covalent semiconductors

Using the lattice Greens function approach and LCAO (linear combination of atomic orbitals) electron theory, we investigate the atomistic configuration and lattice trapping of cracks in Si. The LCAO electron theory coupled to second order perturbation theory (SOP) has been used to derive explicit expressions for the bond breaking nonlinear forces between Si atoms. We calculate the cracked lattice Greens functions for a crack on the (111) plane and lying in the (110) direction. With the nonlinear forces acting in a cohesive region near the crack tips, the crack structure is then calculated. The calculated structure possesses a crack opening at the Griffith load which should allow penetration of typical external molecules to the crack tip at the Griffith loading. Other consequences for chemical reactions at the crack tip are discussed in the light of these results. The lattice trapping is low, only a few percent of the Griffith load.

Study of Self-Diffusion in Metals by Statistical Moment Method: Anharmonic Effects

The self-diffusion in metals is studied using the moment method in the statistical dynamics including the anharmonicity effects of lattice vibrations. The Gibbs free energy of a metal lattice containing thermal vacancies is derived using the fourth order moment approximation. The interaction energies between the atoms in metals are estimated by using the effective pair potentials. The activation energy Q and pre-exponential factor D 0 of the self-diffusion coefficient are given in closed forms. The activation energy Q and pre-exponential D 0 values are calculated for Fe, Ag, Ta, and W metals at high temperature region near the melting temperature as well as at low (liquid Helium) temperatures, and they are shown to be in good agreement with the experimental results.

First-principles calculations for point-defect energies in metals and phase diagrams of binary alloys

Abstract We discuss the present status of the first-principles electronic-structure calculations for defect energies in metals. The calculations apply density functional theory in the generalized-gradient approximation of Perdew and Wang, together with a full-potential version of Korringa–Kohn–Rostoker Greens function method, developed by the Julich group. It is shown that: (1) the present calculations reproduce very well the experimental results for vacancy formation energies in metals, as well as the bulk properties such as equilibrium lattice parameters and bulk moduli of metals; and (2) the type of the phase diagram of a binary A–B alloy can be characterized by the interaction energies between a pair of impurity B (A) atoms in the host metal A (B). The observed temperature dependence of the solid solubility limit of Rh in Pd is also reproduced very well by the free-energy calculations based on the cluster variation method with the pair- (up to the eighth neighbor) and many-body (up to a tetrahedron of first-nearest neighbors) interaction energies, all of which are determined by the present first-principles calculations.

Tight-binding calculation of the solute−dislocation interaction energy in nickel: effect of atomic relaxation

Abstract The solute-dislocation (S-D) interaction energies for various kinds of transition-metal (TM) and of B-subgroup (B-sub) solutes in nickel (Ni) have been calculated using tight-binding theory, taking account of lattice relaxation around the solute atom. It turns out that the S-D interaction energy for TM solutes becomes almost equal to that for B-sub solutes at an equal value of size-misfit in nickel. This means that the extra contribution of TM solutes to the S-D interaction (which has been observed for certain alloy systems such as Ni3Al-based alloys) does not exist for Ni-based f.c.c. alloys. We will show that such a contribution depends very sensitively on the character of the solute-lattice-defect interaction and the materials; it can be expected to occur in intermetallic compounds like Ni3Al.

Study of Self-Diffusion in Silicon at High Pressure

The process of self-diffusion in semiconductors at high pressure is studied using the statistical moment method including the anharmonicity effects of the lattice vibration. The activation energy, Q , and pre-exponential factor, D 0 , of the self-diffusion coefficient are given in an explicit form. The thermodynamic relationships so obtained permit the direct calculation of the activation energy, Q , and pre-exponential factor, D 0 , in Si at high pressure, both in the high temperature region near the melting temperature, and at low (room temperature) temperatures. The calculated results are shown to be in good agreement with the experimental data.