Central force potentials

The Finnis-Sinclair type potentials (Finnis and Sinclair 1984) are central-force potentials but have a many-body character in that the energy of a system of particles is not merely a sum of pair interactions between individual atoms. In this scheme, modified for binary alloys by Ackland and Vitek (1990), the total energy of a system of N atoms is written as... 

Similarly, in studies of lamellar interfaces the calculations using the central-force potentials predict correctly the order of energies for different interfaces but their ratios cannot be determined since the energy of the ordered twin is unphysically low, similarly as that of the SISF. Notwithstcinding, the situation is more complex in the case of interfaces. It has been demonstrated that the atomic structure of an ordered twin with APB type displacement is not predicted correctly in the framework of central-forces and that it is the formation of strong Ti-Ti covalent bonds across the interface which dominates the structure. This character of bonding in TiAl is likely to be even more important in more complex interfaces and it cannot be excluded that it affects directly dislocation cores. 

Stillinger FH, Rahman A (1978) Revised central force potentials for water. J Chem Phys 68(2) 666... 

The problem of evaluating the encounter rate of two particles has been treated in a wide variety of contexts for a wide range of conditions. Consider the case of two particles A and B interacting by a central force potential K(R). When... 

There are three general points applicable to any central force potential that emerge from this analysis ... 

The reason why a central, long-ranged ionic potential can successfully model directional and short-ranged covalent forces in silica is attributed to the fact that Si-0 bonds are so rigid that the Si-Si (or 0-0) distances and Si-O-Si (or O-Si-0) angles are almost perfectly correlated [9]. This explanation suggests that one try even simpler central force potentials in molecular simulations of partially covalent structures. In Ref. [20] Mie s potential... 

F. H. Stillinger and A. Rahman, /. Chem. Phys., 68, 666 (1978). Revised Central Force Potential for Water. 

Jancso G, Bopp P, Heinzinger K (1984) Molecular dynamics study of high-density liquid water using a modified central-force potential. Chem Phys 85 377-387... 

A reasonable central force potential for ion-neutral elastic scattering is the Morse potential given by... 

Remember that the U r) is a central force potential and must be modified in order to obtain a unidirectional force. A unit cell with a NaCl structure contains 54 nearest neighbor bonds that would have to be stretched to expand this cell in three dimensions. However, to expand it in one dimension only requires stretching 18 bonds. Therefore, since only 1/3 the number of bonds need to be stretched in a linear expansion, the stress can be written as... 

We now turn our attention to the s and s-p bonded metals, or the elements in groups lA-IVA. We include the IVA elements even though they are not metals because their elastic properties behave similar to the simple metals because of their s and p bonds. Lacking a rational model for their attractive potential, such as the Coulomb potential model that can be used for the ionically bonded salts, the best that can be done is to try to fit one of the empirical potential functions such as the Morse potential, the Buckingham potential, or the Mie potential that were discussed in Chapter 3 to their measured properties. However, since it is necessary to use most of the observed properties to calculate the parameters needed to fit the potential, there is little left to predict. Also, it should be mentioned that the relation between the 1-D and 3-D central force potential, based on the number of bonds between the ions in the NaCl structure, would not be the same for fee, hep, or bcc structures. Hence the relations develop for the NaCl system. Equations 7.34 through 7.37 are not valid for other systems. 

---