Modeling Collision Cascade Structure of SiO 2 , Si 3 N 4 and SiC using Local Topological Approaches
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1 Introduction Amorphizability is governed topologically by available structural freedom f, which represents the difference between available degrees of freedom for and constraints on each atom [1]. Values for SiO 2 , Si 3 N4 and SiC are, in order, 0, -1.5 and -3, which indicates that such freedom should be marginally available in {4,2}-connected (4 tetrahedral vertices, each shared by two tetrahedra) Si0 2 , but much less available in {4,3}-connected Si 3N 4 and highly unavailable in {4,4}-connected SiC. Structural freedom criteria hence predict that Si0 2 should be relatively easy to amorphize by any means, Si 3N4 much less so, and SiC very difficult. Irradiation with energetic medium- to heavyweight ions results in collision cascades within which overall structural amorphization can be effected through direct impact amorphization or cascade overlap to achieve a critical defect density [2]. The cascade phenomenon represents an ideal platform for topological modeling of amorphization, since the violent cascade displacements are largely uncorrelated and represent atomic randomization followed by reassembly into chemically-preferred coordination polyhedra whose relative dispositions are then likely to be governed by the same sorts of local rules that also apply to longrange ordered crystalline assembly. While the conventional view is that epitaxial recrystallization will take place partially (or completely above a critical temperature) from the cascade boundary, we have explored first an alternative view in which topological disorder can propagate in the reassembly if sufficient local options are available; only when propagation of topological disorder is 39
Mat. Res. Soc. Symp. Proc. Vol. 504 © 1998 Materials Research Society
Alpha-Cristobalite 1 4 1 REGULAR y 24.7 0 1 z 90 0 0 z -90 0 3 z 90 0 2 z -90
Quartz
3A
3ý
4 1
REGULAR 0 1 0 0 0 3
z 60 z -60 z 60
0 2
z -60
3
Beta-Si3N4 1 4 2 REGULAR z 45 ; 0 1 y 60; 0 0 y -60; 01 y 60; 0 3 y 120;
02 0 2 0 0 0 3
y -60; ; y -120;
Alpha-SiC 1 43 REGULAR x -45 y -144.8 z 90 01 ; 02 ; ; 00 ; 02 00 ; 01 01z 180; 00 z180;
03 03 03 02
z180; z180; z180; zI180
Figure 1: Local rules for the assembly of ideal quartz (top left), a-cristobalite (top right), f3-Si 3N 4 (middle) and a-SiC (bottom). frustrated will propagation of long-range order from the periphery present the only option. Our second approach uses epitaxial recrystallization as the basic method for reconnection of the collision cascade. We analyze resulting structures for local clusters [3] compared to the crystalline precursor clusters as well as for underconnection and bond angle distribution.
2
Local-Rules based modeling
We simulate the generation of crystals using local rules. The viability of this approach has been demonstrated for the six known network silicas as well as a and 0 forms of Si 3 N 4 and SiC [4]. The approach (first described in [5]) is to use the local information of one tetrahedron (or more than one for some, more complicated structures) to iteratively "grow" arbitrarily large stru
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