Prediction on the Theoretical Strength of Diamond, c-Bn, Cu and CeO ₂

Abstract

The theoretical (ideal) strength is the upper strength limit that any solid can withstand. Estimation of the theoretical strength of materials is vital for their applications. In material science field, the Griffith theory is the most widely used criterion for estimating the theoretical strength materials which sets an upper bound strength of ~ E/9. Besides, Frenkel and Orowan-Polanyi’s derivation from the force-displacement relationship using the sinusoidal correlation also gives a similar value of ~ E/10. Recently, with the improved quality of fabricated samples, people have reported the possibility of reaching or exceeding the theoretical strength. In this work, first-principles calculations based on density functional theory (DFT) is used to study the theoretical strength of four representative materials (diamond, c-BN, Cu, and CeO²) under uniaxial tensile loading along the low-index crystallographic directions. The results demonstrate that the theoretical strength of materials exhibit strong anisotropy. It is found that the ideal strength calculated by DFT is larger than the ideal strength predicted by Griffith theory or the approximate value of E/10, in all the four materials along some specific directions. This discrepancy is explained by the analysis of the fracture mechanism. In addition, based on the stability analysis of thermodynamical systems, the strength criterion based on the energy-strain relation was established which is verified by the DFT results.

Keywords: Theoretical Strength, Ideal Materials, Griffith Theory, DFT