Understanding of the Phase Transformation from Fullerite to Amorphous Carbon at the Microscopic Level

We study the shock-induced phase transformation from fullerite to a dense amorphous carbon phase by tight-binding molecular dynamics. For increasing hydrostatic pressures $P$, the ${\mathrm{C}}_{60}$ cages are found to polymerize at $P<10\mathrm{GPa}$, to break at $P\sim 40\mathrm{GPa}$, and to slowly collapse further at $P>40\mathrm{GPa}$. By contrast, in the presence of additional shear stresses, the cages are destroyed at much lower pressures ($P<30\mathrm{GPa}$). We explain this fact in terms of a continuum model, the snap-through instability of a spherical shell. Surprisingly, the relaxed high-density structures display no intermediate-range order.

Figure 1

Fullerite under increasing hydrostatic pressure, at 2000 K. (a) Evolution of bonding in the absence of shear stress, starting from an fcc crystal of fullerenes. Shown is the number of bonds per ${\mathrm{C}}_{60}$ molecule as a function of applied pressure. Intramolecular (red, upper curve) and intermolecular bonds (black, lower curve) are plotted separately. Insets show the shapes of a representative ${\mathrm{C}}_{60}$ molecule as the pressure increases, in steps of 14 GPa, and the results of a spherical shell continuum model at pressures 5, 20, 30, and 40 GPa. The instability occurs between the third and fourth configurations. (b) Comparison of density evolution of the compressed ${\mathrm{C}}_{60}$ crystal starting from the fcc (black curve) and from a tetragonally polymerized phase (red curve). Insets show the initial and intermediate configurations (at pressures 0 and 35 GPa, respectively) for the fcc (top row) and tetragonal (bottom row) phases.

Figure 2

Fullerite compressed in the presence of external shear. (a) Evolution of the number of bonds per ${\mathrm{C}}_{60}$ molecule [color coding as in Fig. 1a]. Insets: morphologies of a ${\mathrm{C}}_{60}$ molecule (top) as the pressure increases, in steps of 6 GPa, and from a continuum model (bottom). (b) Density as a function of pressure in the presence of external shear $S={\sigma }_{xy}$. Shown are four plots corresponding to four pathways in the $S-P$ plane as given in the inset: (i) black, (ii) red, (iii) blue, and (iv) green. Locations of the collapse transition are shown as points in the $S-P$ plane. Also shown is the critical line (red) as determined from a continuum model. Finally, morphologies of the $\mathrm{C}$-atom configurations in a unit cell for case (iii) are also shown.

Figure 3

Structures of fullerite relaxed from $P=35\mathrm{GPa}$, $T=2000\mathrm{K}$ to ambient conditions. (a),(b) Morphologies of the fcc unit cells resulting from compression with two different shear values: (a) no shear and (b) shear according to path (iv) in Fig. 2b. (c) Radial distribution function $G(r)$ averaged over 20 ps along a trajectory at ambient conditions: (i) sample after hydrostatic compression to $P=35\mathrm{GPa}$, (ii) same as (i) but with high shear, (iii) reference sample without any intermediate-range order (see text), (iv) after hydrostatic compression to $P=35\mathrm{GPa}$, (v) experimental $G(r)$ of shock-treated fullerite [15], (vi) same as (ii), but convolved with a peak-shape function $\sin (Qr)/(\pi r)$ with $Q=12.0\AA {\text{}}^{-1}$.