# 2.1.2. Potentials of internuclear interaction for metal systems: a method of the diped atom and potential of strong communication

At modelling of metal systems with use of program LAMMPS the multipartial potentials answering to a method of diped atom (embedded atom method) [58, 62] as a rule are applied. Further reduction MPA will be used.

By present time many variants of the yielded method and a number parametrizatsy used potentials are offered. In this method potential energy of i th atom of a grade zadayotsja the equation

Where F_{a} - the energy of submergence which is function of nuclear electronic density - potential energy of twin interaction

Between elements of grades and and β.s the purpose of acceleration of calculations for potential MPA, as well as for potential of strong communication (PSS) which is applied in program CSEG, enters radius scraps r_{cut} outside of which interaction energy of atoms is necessary a wound to zero. Both summations in the formula resulted above are manufactured on all atoms j, the distance between which does not exceed radius potential scraps r_{cut}. Multipartial, instead of twin character of potential MPA is defined by a member considering energy of submergence. Among the multipartial potentials offered for the description of internuclear interaction in metal systems, MPA most adequately considers what even singl-component metal represents a binary mixture, i.e. the basis and electronic gas consists from ionic. Follows, at the same time, to notice, that each type of a crystal lattice will answer certain function of submergence, i.e. Same MPA the potential cannot be used for the description of internuclear interaction in metals with different types of a crystal lattice. Various variants MPA of potentials are discussed in the monography [58].

At use of program CSEG it was applied PSS (tight-binding potential) which also name potential Gupta as it has been offered and used for the first time in R.P.Gupta's work [63]. We will note specific features and advantages of this potential which also is used at modelling of metal systems, nevertheless, much less often, than MPA. Though PSS is semiempirical, it has kvantovomehanicheskoe a substantiation, i.e. is based on kvantomehanicheskom approach of strong communication. Within the limits of this approach energy of / / atoms E_{i}рассматривается as function of distance to other atoms, i.e. does not consider in the form of the separate contribution energy an electron - ionic and an electron-electronic of interactions. Thus the same potential function can be applied not only to GTSK-METALS, but also to OTSK-METALS. Itself Gupta has shown, that the potential offered it adequately describes internuclear interaction not only in a volume phase, but also in surface layer that it is possible to consider as acknowledgement of adequacy of the yielded potential for metal nanochastits. The latest and, apparently, most adequate variant of parametrization of the yielded potential has been offered in work [48]. The yielded parametrization has been approved by authors with reference to calculations of bond energy of metals and elastic constants. It has been shown, that on the average this parametrization result ins to smaller divergences with experimental data, than earlier parametrization offered by the same authors.

According to [48], a potential part of intrinsic energy (cohesive energy) _{systems Ecnahoditsja} as the sum of two contributions

I.e. it is represented in the form of the sum of contributions E^{1}_{r}и E^{1}_{r} answering to forces of pushing away and attractive forces, accordingly. Bottom index R occurs from a word “repulsion” - pushing away, and an index B - from a word “binding” - communication, than and the potential name speaks. Energy

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Pushing away and energy of an attraction for i th atom, in turn, are calculated on the equations:

Where - the parametres which values are presented in

To work [48], - distance between the proximate neighbours, i.e. radius

The first coordination sphere. One of advantages PSS, above, that circumstance that [48] authors are more narrow in work is not noted have presented the yielded potential in such form which can be used for theoretical calculations and atomisticheskogo modelling not only singl-component, but also binary metal systems. Accordingly, indexes α and β answer components α and β accordingly. At the same time, the same parities (6) and (7) are applicable to one-component systems to which, first of all and concern the parametrization, presented in work [48]: to transitive metals (d - and to f-metals), and also to some other metals (p-metals), including lead. Apparently from formulas (6) and (7), energy of pushing away is as the sum of twin interactions, and the attractive force finding any more does not correspond to model of twin interactions.

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