Biomedical Engineering Reference
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together to form a SiC-Si 3 N 4 composite. Then the composite structure was
again equilibrated. A gap of 2 A ˚ was ensured between the SiC particles and
the corresponding Si 3 N 4 block's hole in order to prevent additional buildup
of internal stresses. However, changing the gap did not influence the
observed trends and results.
The composites were analyzed for crack propagation as well as for
mechanical deformation without an initial crack. The mechanical deforma-
tion methodology is based on earlier work by the authors [32, 39]. The initial
crack in the nanocomposites was defined by switching of interatomic
interactions along the plane shown in Fig. 5.8. After that, mechanical
deformation was applied and crack propagation visually followed and
analyzed. This methodology for analyzing crack propagation is based on
earlier published work [28, 58]. Important elements of the MD framework
are now described.
5.5.1 Interatomic potential for SiC-Si 3 N 4 material system
Classical MD simulations of Si 3 N 4 +SiC material systems require an
interatomic potential to describe Si-Si, Si-N, Si-C, N-N, C-C, and N-C
interactions. The potential should be fitted to the properties of Si 3 N 4 , SiC
and to an approximation to the interfacial transitions between these
components. The silicon nitride family consists of two members,
α
and
β
.
The higher symmetry
phase has a hexagonal lattice (space groups
C 6h , N176) with a primitive cell containing two Si 3 N 4 formula units
(a=7.606 A ˚
β
, c=2.909 A ˚
phase is trigonal (space
groups C 3v , N159) and has a primitive cell nearly twice as large (a=7.746 A ˚ ,
c=5.619 A ˚ ) with twice as many atoms. Both structures consist of a SiN 4
tetrahedron forming a 3D network with each N corner common to three
tetrahedra. Each NSi3 polyhedra has a pyramid-like form in the
). The lower symmetry
α
α
phase,
while the
phase can be regarded as being built of planar N2Si3 and nearly
planar N1Si3 triangles with each Si corner common to four triangles that are
oriented perpendicular to the direction (001) or along it. The interatomic
potentials for the Si 3 N 4 material system have been developed elsewhere [37,
59-61]. Fang et al. [62] carried out investigations of phonon spectrum and
thermal properties in cubic-Si 3 N 4 .
Of all the above approaches, the potential of Ching et al. [61] was chosen
to model
β
￿ ￿ ￿ ￿ ￿ ￿
-Si 3 N 4 because of its simplicity and ability to enable large-scale
MD simulations.
β
β
-Si 3 N 4 was chosen because of its relative abundance in
comparison to the
form. Different polytypes of SiC exist at ambient
pressure, which are differentiated by the stacking sequence of
α
the
tetrahedrally bonded Si-C bilayers [63]. Among these polytypes,
-SiC
(cubic-SiC) is of much interest for its electronic properties. In particular, in
recent years many theoretical and experimental studies have been carried
β
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