## Real-Space Descriptions of Structural Energies in Metals

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REAL-SPACE DESCRIPTIONS OF STRUCTURAL ENERGIES IN METALS

A. E. CARLSSON AND J. ZOU Department of Physics, Washington University, St. Louis, Missouri 63130-4899

ABSTRACT Two real-space methods for treating structural energetics of transition metals and compounds are described. The first uses a local description of the electronic density of states (DOS) in a tight-binding model to obtain an angular-force method containing up to four-body interaction terms. It is shown that this method yields bond-strengthening effects at surfaces which exceed those obtained by previous many-body potentials. Structural-energy calculations show that for W, several Frank-Kasper phases are only slightly higher in energy than the ground-state bcc structure; this near-degeneracy is driven by the energetic favorability of icosahedral sites. The second method uses a free-electron type approach to generate pair potentials for transition-metal solutes in Al. The calculated potentials have an oscillating form, with a much larger magnitude than those in Al. The potential is applied to complex Al-Mn phases, including the icosahedral quasicrystal. The results indicate that the oscillating pair potentials make a major contribution to stabilizing the complex phases. INTRODUCTION In evaluating real-space force methods for atomistic simulation of materials properties, structural energies are an important constraint for several reasons. First, it is desirable that the force method have the correct ground-state crystal structure. Second, correct magnitudes of structural energies are necessary for the evaluation of some types of physical phenomena, such as for example transformation toughening ahead of cracks. In this phenomenon, an applied stress causes a structural transformation of the material ahead of the crack. Third, structural-energy differences are closely related to some types of defect energies. For example, the D0 2 2 (Al 3Ti) structure in intermetallics can be thought of as a periodic array of antiphase boundaries (APBs) placed in a L1 2 (Cu 3 Au) structure material. Thus one expects the structural-energy difference to be closely related to the APB energy in this case. Finally, structural-energy differences provide a measure of the stability of various local bonding configurations, which will affect calculations of defect properties. We shall see below that the icosahedral arrangement is a particularly stable arrangement for elemental Group VI transition metals, and that transition-metal solutes in Al have a discrete set of preferred bond lengths. The current methods of choice' for simulations of extended defects are "glue" models 2 3 of the embedded-atom (EAM) or "'t 2 " types. The EAM method is based on a background charge density which is a sum of radial functions; li 2 -methods are based on the second moment or mean-square width of the electronic DOS,

112 (i)=

f

E2 pi(E)dE

(1)

Here, I92 is also a sum of radial terms involving the squares of the electronic interatomic couplings. In calculations using such glue models it is generall

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