Theoretical Strength and Cleavage of Diamond

Abstract

The theoretical strength of diamond has been calculated for the <100>, <110>, and <111> directions using a first principles approach and is found to be strongly dependent on crystallographic direction. This elastic anisotropy, found at large strains, and particularly the pronounced minimum in cohesion in the <111> direction, is believed to be the reason for the remarkable dominance of the 111 cleavage plane when diamond is fractured. The extra energy required to cleave a crystal on planes other than 111 is discussed with reference to simple surface energy calculations and also the introduction of bond-bending terms.

Carbon-based nanostructured composite films: Elastic, mechanical and optoelectronic properties derived from computer simulations

“…The NRL hamiltonian at low temperature was used in this study. This method has already been tested in the case of diamond and the findings compared well with previous ab initio results [34,35].…”

Large indentation strain-stiffening in nanotwinned cubic boron nitride

“…Interestingly, all the molecular dynamics (MD) studied nanostructured Cu samples show a maximum strength (2.5B3.7 GPa) that is lower than the ideal tensile strength (4.2 GPa) for single crystal Cu 16 , and the measured maximum strength (1.1 GPa) of nt-Cu 10,11 is lower than that predicted by MD simulations [12][13][14][15] . Similar results have been observed in covalent materials, such as strength enhancement by reducing grain size d down to 10 nm in cBN in the Hall-Petch regime 17,18 and strength reduction in nanostructured diamond with do4.5 nm (refs 4,5) whose peak tensile and shear strengths only reach less than half the values for single crystal diamond 19,20 , which is attributed to the weak interactions associated with the irregular bonds at the boundaries between nanocrystallites, a typical GB-dominated reverse Hall-Petch effect.…”

“…These calculations provide crucial insights into local bond breaking mechanism that determines incipient plasticity in a crystal 23 , and the obtained ideal indentation strength sets an upper bound on material strength, which can be reached in high quality samples 24 . This approach captures essential physics in indentation tests and is especially useful in a comparative study of different materials or structures, such as nt-cBN and cBN, and in identifying the atomistic mechanisms 9,19,20,[23][24][25][26][27][28][29][30] .…”

“…To simulate the indentation process with first-principles calculations, we consider a biaxial stress distribution beneath an (Vickers) indenter with a shear stress and a normal compressive stress (pressure) component (see Fig. 1a), which captures the main characteristic of the indentation process and is more realistic compared with the previous pure ideal shear strength calculations that neglect the effect of normal compressive pressures 9,19,20,[23][24][25][26][27] . The contact force between the indenter face and the specimen is decomposed into two components: F x parallel to the specimen surface and F z perpendicular to the surface.…”

Energy Landscape and Isotropic Tensile Strength of n-Alkane Glasses

“…11 More recently, at the microscopic-length scale, significant effort has been devoted toward predicting the tensile and shear strength of crystalline solids using sophisticated ab initio and quantum mechanical simulations. [12][13][14][15][16][17] Although much of this work, in addition to classical simulation studies, has provided important insight into failure mechanisms operating in ideal solids, [18][19][20][21][22][23][24][25][26] there still remains significant disagreement between computational predictions and experimental measurement. 13 Because glasses possess history-dependent structure and are hence not in equilibrium, they pose difficulties for theoretical and computational modeling not encountered with crystals.…”