Self Diffusion Parameters from Non-empirical Pair Potentials
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Self Diffusion Parameters from Non-empirical Pair Potentials S.Dorfman, D.Fuks*, J.Pelleg* and S.Rashkeevt Department of Physics, Israel Institute of Technology - Technion, 32000 Haifa, Israel *Materials Engineering Department, Ben-Gurion University of the Negev, Beer Sheva, Israel t Theoretical Physics Department, Chalmers Institute of Technology, GCteborg, Sweden
Abstract A scheme for construction of the pair potential from non-empirical calculations of electronic structure of solids is suggested. As an example, parameters of Lennard-Jones potential are obtained for fcc Cs, based on LMTO calculations of energy parameters. Vacancy formation and migration energies for fcc Cs are calculated from this first-principles pair potential. In addition, the frequency of vibration and the jump probability of an atom are calculated and it is shown that they are direction dependent.
The quantitative theory of diffusion is connected with the design of interatomic pair potentials, 4(r), in metals. It gives the possibility to construct the profiles of potential barriers and to estimate thus the values of migration energies and jump probabilities in different directions. Diffusion in metals generally takes place by a series of jumps of individual atoms from site to site throughout the crystal. A number of mechanisms have been proposed for the elementary atomic jump [1]. The vacancy mechanism is the dominant mechanism for diffusion for most of the pure metals[2, 3, 4], and it is associated with the formation and the migration of vacancies. Here only simple vacancies will be considered. These vacancies represent holes on atomic sites in the lattice and the corresponding atoms have been removed to the surface of the crystal. In order to determine the activation energy of the diffusion process the evaluation of the energies of formation and migration is needed. Calculations of diffusion parameters for high-pressure phases are of great interest as there are difficulties in their experimental determination. In this paper we suggest a quantitative scheme for calculations of these parameters, and as a particular example we consider the high-pressure phase of fcc Cs, which has been already investigated experimentally. A review of calculation of diffusion parameters calculations with semiempirical and empirical pair potentials is given in Ref.[5]. The limitations of such a pair potential approach are obvious from the expression for the total energy, Ejot, of the monoatomic crystal
Mat. Res. Soc. Symp. Proc. Vol. 291. 01993 Materials Research Society
194
Etot = 1
:-
i;
; )
2i'j;i~j
where the double summation over i and j is provided for all sites of atoms r1 . This expression does not include three-, four- and higher- particle interactions and that is why it is restricted. On the other hand Etot can be derived using more or less accurate solid state calculations[6]. The results of these calculations strongly depend on the number of electrons included in the core and may differ by several orders of magnitude. For example, the total
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