The Embedded-Atom Model

The embedded-atom model was developed by Daw and Baskes [20] and was originally intended to describe metallic systems. In general, the potential takes the 

More recently, a particularly interesting new formulation of the embedded-atom model, called the force-matching method has been published by Ercolessi and Adams [21]. In this work, no prior assumptions were made on the actual functional forms in Eqs. 4.34 and 4.35. All functions were described by splines, and the splines were fitted such that the difference between the forces predicted by the 

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Figure 15 Melting temperature and latent heat for sodium clusters of different sizes. Open and closed symbols mark results for the singly charged and the neutral clusters, respectively, and the squares and the circles represent results from calculations using the tight-binding and the embedded-atom model, respectively. Finally, experimental results are shown with the triangles. Reproduced with permission of American Institute of Physics from 52...

Foiles, S.M. Chapter 3, Calculation of the surface segregation of alloys using the embedded atom model. In Surface Segregation Phenomena (ed. Dowben, P.A. and Miller, A.). Boca Raton, FL CRC Press, 1990, pp. 79-105. 

Chapter 11 deals with the tight-binding and the embedded-atom models of solid state. The method of the local combination of atomic orbitals is described. We present examples of the technique application. Description of atom systems in the embedded-atom method, embedding functions and applications are considered. In conclusion the reader will find the review of interatomic pair potentials. 

Although the embedded atom model proved to be a good potential for metallic systems, it fails to describe covalent materials, such as semiconductors. The reason for this is that the electron density in Eq. 4.35 is assumed to be isotropic, which is a good approximation in close packed systems, like fee crystals, but in the case of covalent bonds, the electron density is higher along the bonds. In order to correct this, an angle-dependent density term was introduced by Baskes [22] for silicon... 

Garcia-Rodeja, J., Rey> C.> Gallego, L. J.> Alonso, J. A. (1994). Molecular-dynamics study of the structures, binding energies, and melting of clusters of fee transition and noble metals using the voter and chen version of the embedded-atom model. Physical Review B, 49, 8495. 

The chemical potentials have been evaluated numerically by Hagen using embedded atom models for the defect energies [10]. An important finding was that good quantitative... 

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. 

Haftel Ml, Rosen M. 2001. Surface embedded atom model of the electrolyte-metal interface. Phys Rev B 64 195405. 

An alternate approach, which has proven to be extremely useful for metals, has been developed by Daw, Baskes and Foiles - (and to a lesser extent, by Ercolessi, Tosatti and Parrinello ). Called the embedded atom method (EAM) (or the glue model by the second group), the interactions in this approach are developed by considering the contribution of each individual atom to the local electron density, and then empirically determining an energy functional for each atom which depends on the electron density. This circumvents the problem of defining a global volume-dependent electron density. 

Here, Iq is the electron affinity of C60 (Iq = 2.65 eV [50]). Thus, the 5-potential model ignores the finite thickness nature of the carbon cage within the model, A = 0. Furthermore, in the framework of this model, the size of the embedded atom ra is considered to be so small, compared to the size of C60, that the ground state electronic wavefunctions of the embedded atom coincide exactly with those for a free atom. In other words, the model assumes no interaction between the ground state encaged atom and the carbon cage at all. Therefore, the model is applicable only to the deep inner subshells of the encaged atom. As for the carbon atoms from... 

The basic idea of this model is to assume the embedded atom to reside in a cavity inside the liquid helium, the dimension of the cavity being determined by the intermolecular interaction between the bulk liquid and the central atom. The total energy is partitioned into three parts namely, liquid energy, energy of the free atom and the interaction between the liquid and the atom [254,255]. The total Hamiltonian is thus... 

S. J. Plimpton and B. A. Hendrickson, Mater. Theory Modeling, 291, 37 (1992). Parallel Molecular Dynamics with the Embedded Atom Method. 

There are many theories on the mechanism of the segregation effect that suggest either a chemical or an electronic mechanism or both types of mechanisms. However, it seems that the most reliable mechanism is electronic as proposed by Mukheijee and Moran [35]. This electronic model calculates the chemical properties of the pure constituents from their physical parameters and then estimates those of the alloys. It employs the tight-binding electronic theory, the band filling of the density of states, and the bandwidth of the pure components for the calculations. However, it seems that the 2D Monte Carlo simulations produce better results by using the embedded atom and superposition methods. The latter allows for the calculation of the compositions from the relative atom positions, and the strain and the vibrational energies has been reviewed for 25 different metal combinations in [36]. It was also possible to predict composition oscillations as a consequence of the size mismatch. 

The embedded-atom method [Daw and Baskes 1984] is an empirical embodiment of a simplified quantum mechanical model for bonding in solids called effective medium... 

Both the Finnis-Sinclair and the embedded-atom potentials (together with others that we have not considered here) can be represented using a very similar functional form. However, it is important to realise that they differ in the way that they connect to the first-principles, quantum mechanical model of bonding. They also differ in the procedures used to parametrise the models, so that different parametrisations may be reported for the same material. 

For larger Au NPs many theoretical calculations have been made using empirical interatomic potentials. A number of different models have been developed to represent the many-body character of bonding in metals, for example, Finnis-Sinclair, Gupta, and glue models. Here, we discuss the embedded atom method (EAM), which has many similarities with the models mentioned above but can be considered as more... 

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