Exceptional Ideal Strength of Carbon Clathrates

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 hydrostatic stress conditions. The criteria for designing strong materials are discussed.

Figure 1

Symbolic representation of (a) the C-46 clathrate, and (b),(c) the diamond phase. Different slip planes are indicated. In (a), a few ${\mathrm{C}}_{20}$ cages are indicated by white atoms.

Figure 2

Stress vs strain under (a) tensile load and (b) shear load, for several directions. The full lines correspond to the diamond phase (see text). In the case of C-46, the stress directions and slip planes are indicated next to their corresponding symbols. The arrow points to the structure shown in Fig. 3.

Figure 3

Representation in the $\{001\}$ plane of the C-46 clathrate under an $ϵ=0.2$ $⟨110⟩$ tensile strain, with the opening of the “lines” of hexagons. The formation of ${\mathrm{C}}_{20}$ layers is indicated by the two brackets. Black atoms are threefold coordinated. A $1.7\AA$ criterion is chosen for bond breaking.