Strength-toughness relation of single crystalline and nano-polycrystalline silicon specified by atomic-/nano-crystalline microstructures

• A non-LEFM model is proposed for shallow surface cracks comparable to microstructures of single crystal silicon (SCS) and nano-scale polycrystalline silicon (N-PCS). • The intrinsic relation between fracture toughness K IC and the tensile strength f t is established through the characteristic microstructure C ch (0.235 nm for SCS and 150 nm to 3 µm for N-PCS). • The asymptotic non-LEFM model is also confirmed by single crystal diamond and nano-scale polycrystalline diamond. • The closed-form intrinsic relation on strength, toughness and microstructure for brittle solids is comparable to the Hall-Petch relation for ductile metals. An asymptotic non-LEFM model is developed for shallow surface cracks comparable to material microstructures. The characteristic microstructure size ( C ch ) of single crystal silicon (SCS) is the atomic diameter (0.235 nm), and C ch of a nano-grained polycrystalline silicon (N-PCS) is its average grain size. N-PCS with C ch from 150 nm to 3 µm is considered in this study. The fracture toughness ( K IC ) of both SCS and N-PCS can be predicted from their intrinsic strengths and respective C ch . Predicted K IC values of 0.90–1.40 MPa m for SCS and 1.56–5.31 MPa m for N-PCS are confirmed by collected experimental data of 0.74–1.38 MPa m for SCS and 1.43–3.46 MPa m for N-PCS. The intrinsic relation between the K IC , intrinsic strength and characteristic microstructure is both practically useful and fundamentally significant. The macroscopic K IC and intrinsic strength, previously considered as two separate material properties, are now linked together by the atomic-/nano-scale microstructures. This fundamental relation on strength, toughness and microstructure for brittle solids, verified by SCS and N-PSC, is comparable to the classic “Hall-Petch relation” for ductile metals.