Potential_Part_4

Potential_Part_4 - Embedded-atom and related methods for...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Embedded-atom and related methods for metallic systems (I) As we discussed above, pair potentials, even with an additional density-dependent term cannot provide an adequate description of metallic systems. An alternative simple but rather realistic approach to the description of bonding in metallic systems is based on the concept of local density that is considered as the key variable. This allows one to account for the dependence of the strength of individual bonds on the local environment which is especially important for simulation of surfaces and defects. Many methods, that have been proposed since early 1980s, have different names (e.g. embedded-atom method - EAM, effective medium theory, Finnis-Sinclair potential, the glue model, corrected effective medium potential - CEM, etc.) and are based on different physical arguments (e.g. tight-binding model, effective-medium theory), but result in a similar expression for the total energy of the system of N atoms: () + = i j ij ij i i i ) (r φ 2 1 ρ F E Interpretation and functional form of F, f, and φ depend on a particular method. From the point of view of effective medium theory or the embedded-atom method, the energy of the atom i is determined by the local electron density at the position of the atom and the function f describes the contribution to the electronic density at the site of the atom i from all atoms j. The sum over function f is therefore a measure of local electron density ρ i . The embedding energy F is the energy associated with placing an atom in the electron environment described by ρ . The pair-potential term φ describes electrostatic contributions. The general form of the potential can be considered as a generalization of the basic idea of the Density Functional Theory – the local electron density can be used to calculate the energy.
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This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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Potential_Part_4 - Embedded-atom and related methods for...

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