Exceptional Ideal Strength of Carbon Clathrates

Abstract

We study by means of ab initio calculations the ideal tensile and shear strengths of the C-46 clathrate phase. While its bulk modulus and elastic constants are smaller than in diamond, its strength is found to be in all directions larger than the critical stresses associated with the diamond [111] planes of easy slip. This can be related to the frustration by the clathrate cage structure of the diamond to graphite instability under nonhydrostatic stress conditions [corrected] The criteria for designing strong materials are discussed.

Studies on high pressure-high temperature synthesis of carbon clathrates

“…2. For pure carbon clathrate C46 the Fermi level is located at the top of the valence band, in agreement with previous GW results [5]. The calculated lattice parameter 6.6725 Å is also in quite good agreement with earlier findings [4], however, it is a little bit lower (6.69÷6.72 Å) compared to results obtained using VASP and DMOL software.…”

“…Theoretical predictions point out that the carbon clathrates should show unusual combination of properties. Hypothetic carbon clathrate should be the one of hardest materials after diamond and lonsdaleite [2] and C46 should have a high bulk modulus, just 15% smaller than that of diamond, with an outstanding shear modulus, greater than that of diamond by at least 25% [2,5]. The results of numerical calculations indicates that high pressure-high temperature conditions are necessary to reach the thermodynamic stability range of the predicted new compounds.…”

Large indentation strain-stiffening in nanotwinned cubic boron nitride

“…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.…”

“…The present method is versatile in its ability to simulate various shear deformation modes that are useful for the analysis of the indentation strength of the crystal structure. When we set f ¼ 0 (thus s zz ¼ 0) in the calculation, it is equivalent to requiring that all the five stress components (except s zx ) become negligible during the structural relaxation, which is the relaxation procedure widely used in the calculations of pure ideal shear stresses that neglect the effects of the normal compressive pressure and geometry (indenter angles) of the indenter 9,19,20,[23][24][25][26][27] . We can also set both E zx and E zz fixed in the calculation procedure so that both stresses s zx and s zz are obtained independently for a given set of E zx and E zz .…”