Reconstruction of Twist Grain Boundaries in Gold
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RECONSTRUCTION OF TWIST GRAIN BOUNDARIES IN GOLD
S. R. PHILLPOT, Materials Science Division, Argonne National Laboratory, Argonne, IL 60439
ABSTRACT The reconstruction of high-angle twist grain boundaries on the four densest atomic planes in gold are investigated using the recently developed method of grand-canonical simulated quenching. It is found that the grain boundaries on the two densest planes, (111) and (100), do not reconstruct, while those on the (110) and (113) planes do.
INTRODUCTION Simulations of grain boundaries (GBs) are usually based on structures derived from the coincident-site lattice (CSL) construct. Often additional degrees of freedom associated with a volume expansion in the direction of the GB normal and a translation of the two halves of the bicrystal parallel to the grain boundary are included. 1,2 However, grain-boundary reconstruction in which atoms are added to, or removed from, the CSL structure is not usually taken into account. Here we describe the results of simulations of twist grain boundaries on the four densest atomic planes of gold in which the number of atoms in the interfacial region is not fixed to that of the CSL structure. The recently developed method of grand-canonical simulated quenching (GCSQ)3 is used in conjunction with an embedded-atom-method (EAM) potential 4 . Two questions will be addressed. First, do these grain boundaries reconstruct? Second, can the nature of the reconstruction be understood from an analysis of the unreconstructed GB?
GCSQ FOR EMBEDDED-ATOM-METHOD POTENTIALS Before addressing these questions, we show how the previously derived GCSQ formalism can be extended for use with EAM potentials. For a single component system, the grand-canonical heat function, L, is: L-E- gN
3
(1)
where E is the internal energy and ýi is the chemical potential of the N atoms in the system. The aim of a zero-temperature grand-canonical ensemble simulation is to minimize L by allowing the addition and removal of interstitials and vacancies in addition to structural relaxation. GCSQ overcomes the initially high energy barrier to the creation of a vacancy or an interstitial through two postulates: (i) A solid of mobile atoms is considered as being formed from M mobile sites, each of which is characterized by the number of atoms occupying the site, xi, its position, ri, and its momentum, Pi. (ii) The site occupancy, xi, may take on any fractional value in the range 0 and I inclusive and may vary during the course of the simulation. Mat. Res. Soc. Symp. Proc. Vol. 291. ©1993 Materials Research Society
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That the above two premises lead to physically meaningful structures will become apparent in the following discussion. In analogy with the previous work involving pair potentials,3 Eq. 1 may be rewritten for embedded-atom-method potentials as: L= Epair+Em-glaTxi i=1
(2)
where Epair is the part of the interaction energy arising from pair interactions and Em is the part of the interaction energy arising from the embedding term4 . To impose the constraint that the si
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