Finnis-Sinclair method

Fig. 7. Maps of the electronic charge density in the (110) planes In the ordered twin with (111) APB type displacement. The hatched areas correspond to the charge density higher than 0.03 electrons per cubic Bohr. The charge density differences between two successive contours of the constant charge density are 0.005 electrons per cubic Bohr. Atoms in the two successive (1 10) planes are denoted as Til, All, and T12, A12, respectively, (a) Structure calculated using the Finnis-Sinclair type potential, (b) Structure calculated using the full-potential LMTO method.

In the perfect lattice the dominant feature of the electron distribution is the formation of the covalent, directional bond between Ti atoms produced by the electrons associated with d-orbitals. The concentration of charge between adjacent A1 atoms corresponds to p and py electrons, but these electrons are spatially more dispersed than the d-electrons between titanium atoms. Significantly, there is no indication of a localized charge build-up between adjacent Ti and A1 atoms (Fu and Yoo 1990 Woodward, et al. 1991 Song, et al. 1994). The charge densities in (110) planes are shown in Fig. 7a and b for the structures relaxed using the Finnis-Sinclair type potentials and the full-potential LMTO method, respectively. 

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... 

The Finnis-Sinclair analytic functional form was introduced at about the same time as two other similar forms, the embedded-atom method > and the glue model." ° However, the derivation of the Finnis-Sinclair form from the second-moment approximation is very different from the interpretation of the other empirical forms, which are based on effective medium theory as discussed later. This difference in interpretation is often ignored, and all three methods tend to be put into a single class of potential energy function. In practice, the main difference between the methods lies in the systems to which they have been traditionally applied. In developing the embedded-atom method, for example, Baskes, Daw, and Foiles emphasized close-packed lattices rather than body-centered-cubic lattices. Given that angular interactions are usually ig-... 

For high computational efficiency, a pair potential such as the LJ or the Morse potential is used. With the increasing demand on accuracy and available computational power, many-body potentials such as the Finnis-Sinclair potential and the EAM (embedded atom method) have been commonly used [79]. 

Table 9. Calculated surface free energy y of metals for various orientations. The subscripts A and B refer to the two possible surface terminations of (1010) surfaces of hep crystals [910ve], where the termination with the smaller lattice spacing is denoted A [98Vit]. Calculations were performed for T = 0 K. The method of calculation is indicated FS empirical n-body Finnis-Sinclair potential, PSP total energy pseudopotential, EAM embedded atom method, DFT density functional theory, FPLAPW full potential linear combination of augmented waves, FPLMTO full potential linear combination of muffin tin orbitals.

All of the nonbond potential functional forms that have been presented to this point take into account the effect that one particle has on another particle based solely on the distance between the two particles. However, in some systems like metals and alloys as well as some covalently bonded materials like silicon and carbon, the nonbonded potential is a function of more than just the distance between two particles. In order to model these systems, the embedded-atom method (EAM) (Daw and Baskes 1983,1984 Finnis and Sinclair 1984) and modified embedded-atom method (MEAM) (Baskes 1992) utilize an embedding energy, f j, which is a function of the atomic electronic density pi of the embedded atom I and a pair potential interaction 0// such that... 

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