Simple Flexible Boundary if Conditions for the Atomistic Simulation of Dislocation Core Structure and Motion
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SIMPLE FLEXIBLE BOUNDARY CONDITIONS FOR THE ATOMISTIC SIMULATION OF DISLOCATION CORE STRUCTURE AND NOTION ROBERTO PASIANOT*, EDUARDO J. SAVINO*, ZHAO-YANG XIE**, AND DIANA FARKAS** *C.N.E.A., Av.Libertador 8250, Buenos Aires 1429, **Department of Materials Science and Engineering, VPI & SU, Blacksburg, VA 24061, USA.
Argentina.
ABSTRACT Flexible boundary codes for the atomistic simulation of dislocations and other defects have been developed in the past mainly by Sinclair (1), Gehlen et al.[2], and Sinclair et al.[3). These codes permitted the use of smaller atomic arrays than rigid boundary codes, gave descriptions of core non-linear effects and allowed fair assessments of the Peierls stress for dislocation motion. Green functions (continuum or discrete) or surface traction forces were used to relax the boundary atoms. A much simpler approach is followed here. Core and mobility effects at the boundary are accounted for by a dipole tensor centered at the dislocation line, whose components constitute six more parameters of the minimization process. Results are presented for (100) dislocations in NiAl. It is shown that, within the limitations of the technique, reliable values of the Peierls stress are obtained. INTRODUCTION Boundary conditions play an essential role in the atomistic simulation of dislocation core structure and motion. Two types of boundary conditions have been devised in the literature: fixed and flexible. In the first class, atoms far away from the dislocation core and surrounding it (the boundary atoms) are held fixed at the atomic positions given by elasticity theory, while the core atoms move independently such as to minimize the potential energy of the class, the geometrical simulation block. For the second description is the same but particular recipes are applied to relax mismatch forces between core atoms and boundary atoms. Fixed codes generally require bigger atomic arrays (and consequently more computing time) than flexible codes. This is specially true for studies of dislocation motion under stress; a small simulation block for a fixed code may hinder motion or give a roughly overestimated value for the Peierls stress. Besides this, flexible codes are better suited to describe core non-linear effects such as volume expansion and dislocation climb. Several elaborate flexible codes have been developed. Here, we Gehlen et al. (2], and quote only the work of Sinclair (1], Sinclair et al. (3]. Sinclair, in an elegant investigation (1], considered the general result for the elastic field in a hollow cylindrical region of continuous and anisotropic matter. According to Eshelby et al. [4], this field is given by 6
U(.a) - a-1 ' A.f. (z.)
Mat. Res. Soc. Symp. Proc. Vol. 291. 01993 Materials Research Society
86
where
C5 nz2 D. ln(za)+• f. (Z.)"- ±2ni n
(2)
Za X1 +PaX2
(3)
and
The Aa are complex vectors depending on the elastic constants and the cylinder axis orientation, pa are the roots of the so called "sextic equation", xi and x 2 are the cartesian coordinates of the point considere
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