Investigation of Relationships between Dislocations and Crystal Surface Ledges
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401 Mat. Res. Soc. Symp. Proc. Vol. 399 01996 Materials Research Society
(a)
(b)
Figure 1. Mechanical Models of Simulation Systems A 2-atom layer of viscous damping is also used to make our model behave more like a larger system. The reason for such damping is that due to our model's small scale, stress and deformation waves will be present and reflect off the fixed boundaries. This characteristic is not present in a real, large-area thin film. Ideally, some sort of nonreflective boundary conditions would greatly enhance the accuracy of this MD model. This area is currently under investigation by the senior author of this paper. The finite size of these simulation models required an energy minimization program be used in order to determine the dimensionless equilibrium lattice spacing under zero strain. A value of 0.993*do was determined, where do (= 21/6) is the dimensionless spacing for the LJ pair-potential. These models were subject to constant strain and relaxation was simulated by the MD program. This strain was varied between 5 and 10 % in order to determine critical values at which dislocation formation occurs. The initial configuration for the lattices was computed using elasticity theory along with estimations of the moduli as a function of the applied strain [2], [3]. The program developed by the junior author was based partly on the program MDNATO, developed by Farid Abraham at IBM research center in Almaden, CA [4] and partly on the Molecular Dynamics for Soft Spheres (MDSS) code from J.M. Haile's book [5] on MD Simulations. Both programs use reduced (dimensionless) quantities and have a time scale on the order of 10-14 to 10-12 sec. Results and Discussion Double-Ledge Models Several MD simulations were performed in order to determine the critical strain necessary for dislocation formation in the three different models (51, 26 and 15 layers) with various sized surface gaps (1 atom, 3 atoms, etc.) Table I lists these levels of strain. 51 layers of atoms When the top layer has a one-atom spacer or gap, the critical strain collapses this gap and forms an edge dislocation on the second layer with Burger's vector parallel to the surface (see Figure 2). In the simulation figures shown below, atoms which jump between
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layers are denoted by open circles while atoms which only move laterally within a layer are denoted by filled circles.
Table I. Critical Strain Needed to Form a Dislocation in U-Material with a Double Ledge Model Size 51 layers
Gap Size (# of atoms) I
26 layers
5 1
15 layers
3 5 1
Critical Strain (%) -6.4 -6.2 -6.4 -6.6 -7.0 -7.0 -6.6 -6.9 -6.9 -- 7.0 -7.0
3 5 7
(a) Initial State
(b) Final State
)00000000 000096999 1000000000000000009 ,0000000000*00000*00
'S0e0e00005 @0055000 *@00000@@*.00000004 •0000000000000
00
D1O0000..@e@00000001 000a00000000000 a
Figure 2. Initial and Final States of One-Atom Spacer For a surface gap of three-atoms, three atoms are squeezed up from the second and third layers and all the other atoms relieve the strain by making whole layers with no
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