What are the issues concerning the development of interatomic potentials, when the number of elements increase ( as most of the interatomic potentials seem to be fitted for elements, binary alloys or at most for ternary systems)?
Unfortunately, the development of interatomic potential for multi-component systems demands anew to create "pure" potential functions. For instance, if you have two EAM-potential for two different elements you will not create correct EAM-potential for binary system only by adding one new cross-function. The change of all potential functions is needed.
From the statistical thermodynamic perspective(Bose-Einstein or Fermi-Dirac), the interaction potential can be estimated by the relationship between partition function and thermodynamic functions.
If you have the potentials for the pure elements, you can take an average of them as an estimate for the interaction between two atoms of different species. See Gomez et al., Phys. Rev. Lett. 84, 4397 (2000) -file attached- and reference 19 within.
Unfortunately, the development of interatomic potential for multi-component systems demands anew to create "pure" potential functions. For instance, if you have two EAM-potential for two different elements you will not create correct EAM-potential for binary system only by adding one new cross-function. The change of all potential functions is needed.
This can be a fairly involved process if you carry out such task on your own. In short, you would need to perform a series of first principles calculations with respect to elemental-metals, alloys, defects, etc. Then using the formalism of M. Baskes, Finnis-Sinclair, or Sutton-Chen go about the fitting procedure. In addition, you might find that the Modified-EAM is a better descriptor for the atomic interactions. The paper below, by L. Ward et al., highlights an approach to developing Finnis-Sinclair EAM parameters for alloy systems using single element data; there is also a website dedicated to this formalism. The generator also provides "quality" of fit information with regards to Enthalpy, Bulk Modulus, and lattice parameter for various crystalline phases. Hope this helps.
http://atomistics.osu.edu/eam-potential-generator/index.php
Article Rapid Production of Accurate Embedded-Atom Method Potentials...
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