Physical trends in amorphous carbon: A tight-binding molecular-dynamics study

Tight-binding molecular dynamics simulations reveal interesting physical trends in amorphous carbon networks. The variation of sp³ fraction, or mean coordination, is found to be linear over the whole possible range of densities. The density at the floppy transition is ~0.50.3em0exg0.3em0excm^-3, while the density of ``amorphous diamond'' is ~3.30.3em0exg0.3em0excm^-3. The bulk modulus vanishes at the floppy transition, having a critical coordination near 2.4, and its variation with the mean coordination has a scaling exponent of 1.5, confirming the constraint-counting model of Phillips and Thorpe. A hypothetical fully tetrahedral network has a bulk modulus of 3600.3em0exGPa, about 15% lower than diamond's. The bulk modulus is also found to vary with the average bond length d̄ as (d̄)3.5. The homopolar gap of ``amorphous diamond'' is ~11.50.3em0exeV, compared to ~140.3em0exeV for diamond.