Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elasticity, Stability and Ideal Strength of $\beta $-SiC in
  plane-wave-based ab initio calculations   On the basis of the pseudopotential plane-wave(PP-PW) method and the
local-density-functional theory(LDFT), this paper studies energetics,
stress-strain relation, stability and ideal strength of $\beta $-SiC under
various loading modes, where uniform uniaxial extension and tension, biaxial
proportional extension are considered along directions [001] and [111]. The
lattice constant, elastic constants and moduli of equilibrium state are
calculated, and the results agree well with the experimental data. As the four
Si-C bonds along directions [111], [$\bar{1}$11], [11$\bar{1}$] and
[1$\bar{1}$1] are not the same under the loading along [111], internal
relaxation and the corresponding internal displacements must be considered. We
find that, at the beginning of loading, the effect of internal displacement
through shuffle and glide plane diminishes the difference among the four Si-C
bonds length, but will increase the difference at the subsequent loading, which
will result in a crack nucleated on \{111\} shuffle plane and a subsequently
cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa,
which agrees well with the recent experiment value, 53.4 GPa. However, with the
loading along [001], internal relaxation is not important for tetragonal
symmetry. Elastic constants during the uniaxial tension along [001] are
calculated. Based on the stability analysis with stiffness coefficients, we
find that the spinodal and Born instabilities are triggered almost at the same
strain, which agrees with the previous molecular dynamics simulation. During
biaxial proportional extension, stress and strength vary proportionally with
the biaxial loading ratio at the same longitudinal strain.

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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics