Heterogeneity governs diameter-dependent toughness and strength in SiC nanowires

Using a combination of density functional theory and molecular dynamics simulations, this paper reveals the atomistic origin of diameter-dependent extreme mechanical behavior of [111] 3C-SiC nanowires obtained from an energy-based framework. Our results suggest that heterogeneity in atomic stress and variations in diameter-dependent potential-energy density have a profound impact on extreme mechanical properties in the nanowires. The heterogeneity in stress evolves from the nonuniform bond lengths mediated by low coordinated surface atoms—and it penetrates the entire cross section in thinner nanowires and constitutes the atomistic basis for their large reduction in fracture strain, toughness, and strength. Although stress heterogeneity is substantially higher in ultrathin nanowires, its intensity drops and saturates rapidly in larger nanowires following a nonlinear dependence on diameter. The maximum stress heterogeneity in a cross section localizes crack nucleation at the core in ultrathin nanowires but near the surface in larger nanowires. Moreover results show that stiffness, toughness, strength, and fracture strain of the nanowires increase nonlinearly with increasing diameter and saturate at a lower value compared to bulk SiC. In addition to resolving wide discrepancies in the reported values of the first-order elastic modulus in SiC nanowires, the findings highlight heterogeneity as a critical factor for inducing diameter-dependent extreme mechanical behavior in brittle nanowires.

Figure 1

Comparison of the stress-strain curves obtained from simulating uniaxial deformation of bulk 3C-SiC along the [100] direction using DFT-generalized gradient approximation (DFT-GGA) and MD-SW. Results on stiffness $E$, ideal strength ${\sigma }_{max}$, and nucleation-toughness ${\mathrm{\Pi }}_c$ agree within 3.9%, 0.2%, and 1.5%, respectively. The simulation cell containing 96 atoms is displayed on the right.

Figure 2

(a) Twelve-atom unit cell of 3C-SiC with its two orthographic projections on the $\left\{\overline{1}10\right\}$ and $\left\{1\overline{1}2\right\}$ planes. The loading direction is the [111] direction (aligned along the unit vector ${\widehat{e}}_x$). (b) Cross-sectional view of a [111]-SiC nanowire of 0.98-nm diameter. Atoms are identified as Si and C.

Figure 3

Heterogeneity in bond lengths for (a) $d=0.98\mathrm{nm}$ and (b) $d=1.96\mathrm{nm}$ NWs at 15% macroscopic strain. The vertical lines $mm$ and $nn$ represent two cross-sectional planes at different locations along the loading direction highlighting nonuniformity in cross-sectional area and bond lengths. The atomic structures are rotated slightly with respect to the [111] direction to reveal heterogeneity in bond strain.

Figure 4

(a) Potential energy per atom as a function of macroscopic strain in bulk SiC for loading along the [100] direction. (b) Stress-strain curve obtained from DFT-given energy-strain data using $v_0$ is shown in black. It is compared with the DFT-given stress-strain data shown in red.

Figure 5

(a) Potential-energy density relative to the equilibrium as a function of macroscopic strain for 20 nanowires with diameters ranging from 0.32 to 6.53 nm in a log-log plot. (b) Stress-strain curves for the same set of nanowires derived from the energy-strain data. Colors from blue to red represent the diameter cases going from 0.32 to 6.53 nm.

Figure 6

Diameter-dependent (a) Young's modulus ($Y$), (a) ideal strength (${\sigma }_{max}$), (b) toughness (${\mathrm{\Pi }}_c$) and (c) fracture-strain (${\epsilon }_{\mathrm{f}}$) variation in [111] 3C-SiC nanowires. The horizontal dashed lines indicate the corresponding value of that property in bulk SiC along the [111] direction. The fitting parameters and bulk values are reported in Table 1.

Figure 7

Potential-energy density at the equilibrium as a function of nanowire diameter relative to the potential-energy density in bulk SiC.

Figure 8

(a) Heterogeneous atomic-stress ${\sigma }_{xx}^{\mathrm{atomic}}$ at 20% macroscopic strain in nanowires of (a) 0.32 nm, (b) 0.65 nm, (c) 0.98 nm, and (d) 1.30 nm. The stress range used for all the plots is 20–70 GPa. The color in the plot corresponds to the value of stress shown on the vertical axis.

Figure 9

Evolution of diameter-dependent heterogeneity in atomic-stress ${\sigma }_{xx}^{\mathrm{atomic}}$ in (a)–(c) for 0.32-nm NW and in (d)–(f) for 0.65-nm NW. The color in the plot corresponds to the value of stress shown on the vertical axis.

Figure 10

(a) Diameter-dependent maximum normal atomic-stress ${\sigma }_{xx}^{\mathrm{atomic}}$ and (b) diameter-dependent minimum normal atomic-stress ${\sigma }_{xx}^{\mathrm{atomic}}$ at 15% strain. (c) Comparison of the maximum and minimum stresses and observation of saturation in stress heterogeneity indicated by the vertical line. (d) Diameter-dependent maximum stress-heterogeneity ${\sigma }_{\mathrm{mHeterogeneity}}$. The stress extremum is calculated with an error bar of 0.1 GPa denoting the variation in values among the six corner sites where it is the maximum.

Figure 11

Stress-heterogeneity-induced nanocrack nucleation and its inward evolution in a 2.61-nm nanowire. The units of stress are gigapascals.