An embedded atom analysis of Au and Pt substitutional atoms in Ni
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I. INTRODUCTION This research work was directed at obtaining an improved understanding of the changes in energy and atom position that result when one atom is substituted into another crystal lattice; in this particular work Au and Pt were substituted into a Ni lattice. An understanding of the changes that occur in a crystal when one atom in a crystal is replaced by a different atom is the foundation of alloy theory; but from a theoretical viewpoint this is a very difficult problem to analyze because when a different atom is introduced into the crystal with both a different atomic size and a different electronegativity, there are changes in atomic positions in the host, and there are changes in electron energy. The displacements of the host atoms from their equilibrium positions has been analyzed with theory of elasticity analyses such as the work of Eshelby1'2 and Friedel3; however, a number of simplifying assumptions are necessary to make these analyses. One of the objectives of this research was to test the validity of the theory of elasticitytype analyses. The changes that occur in local electron energy are very difficult to analyze because the local electron energy is affected by both the change in electronegativity introduced by the solute atom and by the displacement of the host atoms resulting from the size difference. The displacement of the atoms from the lattice positions makes it difficult to utilize Bloch waves to analyze the perturbation to the electronic structure caused by the solute atom because of the requirement of a periodic lattice. Pairpotential simulations are also not suitable for the study of this problem in metals because, with a pair potential, it is necessary to add a volume-dependent term to obtain proper elastic response for metals, and the form of the a)
Present address: Universitat Stuttgart, Stuttgart, West Germany.
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http://journals.cambridge.org
J. Mater. Res., Vol. 4, No. 3, May/Jun 1989
Downloaded: 17 Mar 2015
volume-dependent term for metals such as Au, Ni, and Pt and their alloys is not well defined. The pair-potential approach is most suited to inert gas atoms and other molecules that interact primarily with van der Waals attraction and core-core repulsion. The embedded atom model (EAM) introduced by Daw and Baskes4'5 allows modeling of the displacement field around a metal atom substituted into another host metal, and it allows for an elementary treatment of the change in local energy caused by a change in local electron density. In the embedded atom model the total cohesive energy of the crystal is a sum of the energies obtained when each atom of the crystal is embedded into its local site where each local atom site (t) has a unique local electron density p r The total cohesive energy of the crystal is (1) where E(p) is the many-body embedding energy for the atom at site i, E(pL) is a function of the local electron density p t at the site where atom t is to be embedded, and $yis the pair potential. Foiles, Baskes, and Daw6 have published embedding energies E(p,) and
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