Elasticity, Stability and Ideal Strength of $\beta $-SiC in plane-wave-based ab initio calculations

TL;DR

This study uses ab initio calculations to analyze the elasticity, stability, and ideal strength of $eta$-SiC under various loading conditions, providing results consistent with experimental data and revealing fracture mechanisms.

Contribution

It presents a detailed first-principles investigation of $eta$-SiC's mechanical properties and fracture behavior under different stress modes, including internal relaxation effects.

Findings

Theoretical strength of $eta$-SiC is approximately 50.8 GPa, matching experimental values.

Internal relaxation influences bond differences and crack nucleation during loading.

Spinodal and Born instabilities occur nearly simultaneously at critical strains.

Abstract

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.