Anab initiopair potential applied to metals

Scaling of Phase Diagram and Critical Point Parameters in Liquid-Vapour Phase Transition of Metallic Fluids

The first objective of this paper is to investigate the scaling behavior of liquid-vapor phase transition in FCC and BCCmetals starting from the zero-temperature four-parameter formula for cohesive energy. The effective potentials between the atoms in the solid are determined while using lattice inversion techniques as a function of scaling variables in the four-parameter formula. These potentials are split into repulsive and attractive parts, as per the Weeks–Chandler–Anderson prescription, and used in the coupling-parameter expansion for solving the Ornstein–Zernike equation that was supplemented with an accurate closure. Thermodynamic quantities obtained via the correlation functions are used in order to obtain critical point parameters and liquid-vapor phase diagrams. Their dependence on the scaling variables in the cohesive energy formula are also determined. An equally important second objective of the paper is to revisit coupling parameter expansion for solving the Ornstein–Zernike equation. The Newton–Armijo non-linear solver and Krylov-space based linear solvers are employed in this regard. These methods generate a robust algorithm that can be used to span the entire fluid region, except very low temperatures. The accuracy of the method is established by comparing the phase diagrams with those that were obtained via computer simulation. The avoidance of the ’no-solution-region’ of the Ornstein-Zernike equation in coupling-parameter expansion is also discussed. Details of the method and complete algorithm provided here would make this technique more accessible to researchers investigating the thermodynamic properties of one component fluids.

A generalized method for the inversion of cohesive energy curves from isotropic and anisotropic lattice expansions

Cohesive energy curves contain important information about energetics of atomic interactions in crystalline materials, and these are more often obtained using ab initio methods such as density functional theory. Decomposing these curves into the different interatomic contributions is of great value to evaluate and characterize the energetics of specific types of atom-atom interactions. In this work, we present and discuss a generalized method for the inversion of cohesive energy curves of crystalline materials for pairwise interatomic potentials extraction using detailed geometrical descriptions of the atomic interactions to construct a list of atomic displacements and degeneracies, which is modified using a Gaussian elimination process to isolate the pairwise interactions. The proposed method provides a more general framework for cohesive energy inversions that is robust and accurate for systems well-described by pairwise potential interactions. Results show very good reproduction of cohesive energies with the same or better accuracy than current approaches with the advantage that the method has broader applications.

Embedded-atom-method interatomic potentials from lattice inversion

The present work develops a physically reliable procedure for building the embedded-atom-method (EAM) interatomic potentials for the metals with fcc, bcc and hcp structures. This is mainly based on Chen-Möbius lattice inversion (Chen et al 1997 Phys. Rev. E 55 R5) and first-principles calculations. Following Baskes (Baskes et al 2007 Phys. Rev. B 75 094113), this new version of the EAM eliminates all of the prior arbitrary choices in the determination of the atomic electron density and pair potential functions. Parameterizing the universal form deduced from the calculations within the density-functional scheme for homogeneous electron gas as the embedding function, the new-type EAM potentials for Cu, Fe and Ti metals have successfully been constructed by considering interatomic interactions up to the fifth neighbor, the third neighbor and the seventh neighbor, respectively. The predictions of elastic constants, structural energy difference, vacancy formation energy and migration energy, activation energy of vacancy diffusion, latent heat of melting and relative volume change on melting all satisfactorily agree with the experimental results available or first-principles calculations. The predicted surface energies for low-index crystal faces and the melting point are in agreement with the experimental data to the same extent as those calculated by other EAM-type potentials such as the FBD-EAM, 2NN MEAM and MS-EAM. In addition, the order among the predicted low-index surface energies is also consistent with the experimental information.

First-principles pair potentials across the metal-ceramic interface

Systematic approaches are presented to invert the first-principle binding energy to obtain the pair potentials across the metal/ceramic interfaces. The conformation characteristics of two virtual interface models suitable for the inversion are summarized: (1) the positions of one kind of ceramic ions stay unchanged, but those of the other change; or, (2) there is no change in the relative positions of the ceramic ions to the metal atoms but the positions of two kinds of ceramic ions are all exchanged each other. As an example, we derive the pair potentials of Ni-Zr(4+) and Ni-O(2-) across the Ni/ZrO(2) interface with this method, which exhibit comparable accuracy to the first-principle results. This provides direct evidence that the interfacial potentials obtained from this method can reasonably describe the general features of bondings across the metal-ceramic interface. The limitation of this method is also discussed.

Type of inversion problem in physics: an inverse emissivity problem

Inversion problems have recently drawn vast amounts of attention from the physics community due to their potential widespread applications. In this Rapid Communication, a different type of inversion problem in physics is proposed: an inverse emissivity problem, which aims to determine the emissivity g(nu) by measuring only the total radiated power J(T). Like other inverse problems, this one has potential for important practical applications. An exact solution is obtained for the proposed inverse problem. A unique existence theorem and techniques for eliminating divergences are also presented. A universal function set (UFS) suggested for numerical calculations is shown to be very useful in a numerical example. The UFS makes this inversion method practical and convenient for realistic calculations.

Exact solution of the specific-heat-phonon spectrum inversion from the Mobius inverse formula

The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main difficulty arises from the fact that the Mobius function &mgr;(n) is not completely known for large n in practice. In this paper, some exact solutions of SPI are obtained by using the Mobius inversion formula, most importantly the Debye spectrum as a special case, and the problem of the unknown Mobius function &mgr;(n) for large n is avoided. It is shown that the Mobius inversion formula can be useful for exact solutions to spectral inversion problems.