Embedded-atom method

Lutsko J F ef a/1989 Molecular-dynamic study of lattice-defect-nucleated melting in metals using an embedded-atom-method potential Phys. Rev. B 40 2841... 

Daw M S and M I Baskes 1984. Embedded-atom Method Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Physical Review B29 6443-6453. 

A full-scale treatment of crystal growth, however, requires methods adapted for larger scales on top of these quantum-mechanical methods, such as effective potential methods like the embedded atom method (EAM) [11] or Stillinger-Weber potentials [10] with three-body forces necessary. The potentials are obtained from quantum mechanical calculations and then used in Monte Carlo or molecular dynamics methods, to be discussed below. 

We have used the embedded-atom method (EAM) to develop interatomic potentials suitable for the simulation of iron-nickel alloys. In this method the total energy of the alloys can be written as... 

M.S. Daw and M.I. Baskes, Embedded-atom method Derivation and application to... 

Table 5 Surface energies, calculated from the tight-binding theory (TB), by the embedded-atom method (EAM), or by modified embedded atom method (MEAM), compared to experiment. Energies are given in units of ijm .

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. 

Theoretical Study of Icosahedral Ni Clusters within the Embedded Atom Method. 

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. 

While the embedded atom method has been formally derived by Daw and Baskes the functions used in computer simulations are t3pically empirically determined. The description presented here will therefore treat this approach as an empirical method. The first step in determining the potential is to define a local electron density at each atomic site in the solid. A simple sum of atomic electron densities has proven to be adequate, and so in most cases a sum of free atom densities is used . The second step is to determine an embedding... 

The structure and dynamics of clean metal surfaces are also of importance for understanding surface reactivity. For example, it is widely held that reactions at steps and defects play major roles in catalytic activity. Unfortunately a lack of periodicity in these configurations makes calculations of energetics and structure difficult. When there are many possible structures, or if one is interested in dynamics, first-principle electronic structure calculations are often too time consuming to be practical. The embedded-atom method (EAM) discussed above has made realistic empirical calculations possible, and so estimates of surface structures can now be routinely made. 

For systems with metallic bonds, the empirical embedded atom method (EAM) suggested by Daw and Baskes [69] is widely used. In this method, the bond energy is expressed as a function of the density at the site of... 

Now that the top-down internal state variable theory was established, the bottom-up simulations and experiments were required. At the atomic scale (nanometers), simulations were performed using Modified Embedded Atom Method, (MEAM) Baskes [176], potentials based upon interfacial atomistics of Baskes et al. [177] to determine the conditions when silicon fracture would occur versus silicon-interface debonding [156]. Atomistic simulations showed that a material with a pristine interface would incur interface debonding before silicon fracture. However, if a sufficient number of defects were present within the silicon, it would fracture before the interface would debond. Microstructural analysis of larger scale interrupted strain tests under tension revealed that both silicon fracture and debonding of the silicon-aluminum interface in the eutectic region would occur [290, 291]. 

M.S. Daw, M.I. Baskes Embedded-atom method Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443-6453 (1984)... 

Y. Li et al Embedded-atom-method tantalum potential developed by the force-matching method. Phyl. Rev. B Cond. Mattr Matls. Phys 67, 125101 (2003)... 

M.I. Baskes Application of the embedded-atom method to covalent materials a semiempi-rical potential for silicon. Physl. Rev. Lett. 59, 2666-2669 (1987)... 

B. Jelinek et al Modified embedded-atom method interatomic potentials for the Mg-Al alloy system. Physl. Rev. B 75, 054106 (2007)... 

Although a valence-type force field of the type illustrated by Eq. [1] is most suitable for modeling molecular systems, the electronegativity equalization approach to treating polarization can be coupled equally well to other types of potentials. Streitz and Mintmire used an EE-based model in conjunction with an embedded atom method (EAM) potential to treat polarization effects in bulk metals and oxides. The resulting ES + EAM model has been parameterized for aluminum and titanium oxides, and has been used to study both charge-transfer effects and reactivity at interfaces. 

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

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