Transition between Hall-Petch and inverse Hall-Petch behavior in nanocrystalline silicon carbide

Despite much experimental and simulation effort, the existence of a Hall-Petch to inverse Hall-Petch transition in nanocrystalline ceramics remains elusive. By employing molecular dynamics simulations, we unambiguously reveal a transition from strengthening to softening in the shear deformation of nanocrystalline silicon carbide ceramics as a function of grain size. Results show a well-defined maximum in the shear strength for grain sizes in the range 6.2 to 7.7 nm. Further decrease in grain size leads to diminishing strength, consistent with an inverse Hall-Petch behavior. As grain size is reduced the increasing grain boundary (GB) regions lead to homogenization of shear stresses across the microstructure, allowing for lower local shear stress levels at higher macroscopically applied stresses. This delays shear localization within GB regions, preventing cavitation, nanocracking, and premature failure, and is responsible for the observed Hall-Petch behavior. In contrast, at grain sizes <6.2 nm, the rather compliant nature of the structurally disordered GB regions dominates the mechanical response, reducing the shear strength and triggering a transition into the inverse Hall-Petch behavior. A composite model delineating the transition between Hall-Petch and inverse Hall-Petch behavior is successful at describing the mechanical behavior of nanocrystalline silicon carbide as a function of grain size.

Figure 1

(a) Illustration of the nanocrystalline 3C-SiC structure with average grain size of 18.6 nm after relaxation. Grains are depicted in different colors. (b) Crystalline intragranular (pristine zinc blende structure) and disordered intergranular phases shown in blue and gray, respectively. (c) Grain size distribution of the sample shown in (a).

Figure 2

(a) Shear response of various nanocrystalline 3C-SiC systems with different grain sizes. (b) Shear strength ($\tau$) vs critical shear strain ($\gamma$).

Figure 3

Grain size dependence of SiC properties. Grain size ($d$) variation of (a) shear strength ($\tau$) and modulus ($G$). (b) Crystalline volume fraction ($V_g$) and density ($\rho$). (c) Total grain boundary (GB) energy ($E_{\mathrm{GB}}$). (d) Shear localization parameter ($\mathrm{\Psi }$).

Figure 4

(a) Shear response of the 3C-SiC crystalline and disordered phases at 300 K. The crystalline sample has the directions $\left[11\overline{2}\right]$, $\left[111\right]$, and $\left[\overline{1}10\right]$ aligned along the $x$, $y$, and $z$ axes and is sheared along the $xy$ plane. (b) Shear modulus ($G$) as a function of crystalline volume fraction ($V_g$) obtained by molecular dynamics (MD) and rule of mixture (RoM).

Figure 5

(a) Comparison of theoretical calculations and molecular dynamics (MD) results for the volume fraction of the grain interior (crystalline volume fraction). (b) Predictions of the theoretical composite model (CM) vs MD results. Fitted CM to MD results are based on $\delta =1.0\mathrm{nm}$, ${\tau }_0=2.5\mathrm{GPa}$, and $k=15.8\mathrm{GPa}\mathrm{n}{\mathrm{m}}^{1/2}$.

Figure 6

Diminishing the effect of grain boundary (GB) thickness on shear strength of nanocrystalline 3C-SiC at coarse grain range, i.e., ∼100 nm.

Figure 7

von Mises local atomic shear strain in the samples with $d=3.7\mathrm{nm}$ and $12.4\mathrm{nm}$ at different shear strains ($\gamma$). Atoms are colored by the von Mises local atomic shear strain proposed by Shimizu et al. [51]. Shear localization can be observed within grain boundaries (GBs) in both samples yet with higher extent and magnitudes in the coarser grain sample, triggering the heterogenous deformation.