Theoretical calculation of the free energy of mixing of liquid transition-metal alloys using a bond-order potential and thermodynamic perturbation theory (original) (raw)

Tight-binding potentials for transition metals and alloys

Physical Review B, 1993

The parameters of many-body potentials for fcc and hcp transition metals, based on the secondmornent approximation of a tight-binding Hamiltonian, have been systematically evaluated. The potential scheme, cast in analytical form, allows us to reproduce correctly the thermal behavior of transition metals making use of a small set of adjustable parameters. The large cutoff, which extends the range of the interactions up to the fifth-neighbor distance, ensures good quantitative agreement with the experimental data up to temperatures close to the melting point. The ability of the potentials to describe real systems has been checked by calculating point-defect properties, lattice dynamics, and finite-temperature behavior, and by comparing the results with other potential schemes. Application of this scheme to bcc transition metals has proved unsuccessful. Examples of derivation of many-body potentials for a few transition-metal alloys with cubic structure are also reported.

Effect of the ordering potential on the structure of liquid alloys

EPJ Web of Conferences, 2011

Rep. Prog. Phys. 60 (1997) 57-150) enables the understanding of the different kind of alloys: hetero-coordinated one's leading to compounds, homocoordinated ones leading to miscibility gap systems and substitutional alloys. The ordering potential is based on the comparison of identical atom interionic potentials (V 11 and V 22) and different atom interionic potential (V 12) It allows the description of the demixing properties of some alloys. In order to understand the concepts, we developed our calculations by using a Lennard-Jones potential, the atomic structure being calculated by molecular dynamics simulation. We obtained surprising and unexpected results putting in evidence the time of simulation and the strength of the ordering potential.

Orbital free ab initio study of static and dynamic properties of some liquid transition metals

Several static and dynamic properties of liquid transition metals Cr, Mn and Co are studied for the first time using the orbital free ab-initio molecular dynamics simulation (OF-AIMD). This method is based on the density functional theory (DFT) which accounts for the electronic energy of the system whereas the interionic forces are derived from the electronic energy via the Hellman-Feynman theorem. The external energy functional is treated with a local pseudopotential. Results are reported for static structure factors, isothermal compressibility, diffusion coefficients, sound velocity and viscosity and comparison is performed with the available experimental data and other theoretical calculations.

Combined Pauling Bond Valence-Modified Morse Potential (PBV-MMP) model for metals: thermophysical properties of liquid metals

Physics and Chemistry of Liquids, 2017

We develop a new quasi-crystalline approach, combined Pauling Bond Valence-Modified Morse Potential (PBV-MMP), in which the Pauling's classical relationship between bond valence (BV) and bond length (BL) is incorporated within a modified Morse Potential (MMP) description of the potential energy of interaction between two metal atoms in the bulk, along with the assumption that these interactions are limited to the nearest neighbours with a coordination number n M. This semi-theoretical approach only needs metal-metal bond energy for a specified valence to provide predictions. For the kinetic and diffusion steps, we utilise Eyring's transition-state theory and free volume model to estimate entropy changes. The PBV-MMP approach for bulk liquid metals is in the spirit of Unity Bond Index-Quadratic Exponential Potential (UBI-QEP), which has been successful in predicting thermodynamics and kinetics of solid metal surface catalysed reactions. Our model reliably predicts selfdiffusivity, viscosity, surface tension that agrees with experimental results for several liquid metals, including gallium.

Thermodynamics and structure of liquid binary alloys calculated using an analytic pair potential

Physical Review B, 1994

Analytic pair potentials proposed by Pettifor and Ward are developed using the Heine-Abarenkov pseudopotential for Li-Na, ¹K, and Na-Cs liquid binary alloys. The corresponding partial structure factors are calculated using the random-phase approximation. The calculated thermodynamic and structural properties using this real-space formalism are in good agreement with experiments.

Composition-dependent interatomic potentials: A systematic approach to modelling multicomponent alloys

Philosophical Magazine, 2009

We propose a simple scheme to construct composition-dependent interatomic potentials for multicomponent systems that when superposed onto the potentials for the pure elements can reproduce not only the heat of mixing of the solid solution in the entire concentration range but also the energetics of a wider range of configurations including intermetallic phases. We show that an expansion in cluster interactions provides a way to systematically increase the accuracy of the model, and that it is straightforward to generalise this procedure to multicomponent systems. Concentration-dependent interatomic potentials can be built upon almost any type of potential for the pure elements including embedded atom method (EAM), modified EAM, bond-order, and Stillinger-Weber type potentials. In general, composition-dependent N-body terms in the total energy lead to explicit N + 1-body forces, which potentially renders them computationally expensive. We present an algorithm that overcomes this problem and that can speed up the calculation of the forces for composition-dependent pair potentials in such a way as to make them computationally comparable in efficiency and scaling behaviour to standard EAM potentials. We also discuss the implementation in Monte-Carlo simulations. Finally, we exemplarily review the composition-dependent EAM model for the Fe-Cr system [PRL 95,075702, (2005)].

Electronic theory for the metal-nonmetal transition in simple metal alloys

Journal of Physics C: Solid State Physics, 1978

The metal-non-metal transition in liquid alloys such as Csx_~Au ~ and Lia_~Pb~ is explained as resulting from concentration dependent electron charge transfer causing short range atomic order and a change from metallic to ionic bonds. Numerical results for the electronic density of states, the electron charge transfer, the free energy of mixing and the volume change are given.

Efficient atomistic approaches to thermodynamic quantities for solid-liquid equilibria in alloys

2010

Two important thermodynamic quantities are bulk solid and liquidfree-energy as a function of composition G (x) and the solid-liquidinterfacial free-energy? sl. For both, an accurate determination isrequired for modelling crystallisation and melting processes. In thisthesis, I combine statistical mechanics and atomistic simulations todevelop new approaches to calculate G (x) and? sl. In the case of G (x), a method based on a Free Energy Perturbation (FEP) technique is proposed, which allows to achieve ab initio accuracyat a fraction of the ...

Model potential based on tight-binding total-energy calculations for transition-metal systems

Physical review, 1995

A semiempirical model potential to simulate properties of fcc transition metals is proposed. The attractive part of the potential has been obtained from a tight-binding Hamiltonian that takes into account the symmetry of the d orbitals and leads to a 2/3 power dependence on the effective coordination (or second moment of the local density of states) instead of the usual square-root dependence. The repulsive interaction is assumed to be of the Born-Mayer type. In order to use this potential for specific materials, four parameters are adjusted with experimental data. We present two different parametrizations and calculate bulk, defect, surface, and cluster properties comparing with experiment, ab initio calculations, and the usual second-moment approximation.