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Fig. 7.16. Temperature-pressure phase diagram for C60 crystals (dot-dash line). The triangle at 298 K indicates the approximate end of the transition. The onset of the transition (circles) and the maximum slope \dV/dp\ (squares) show a linear fit to the data points (solid lines) [7.5].

of the bulk modulus (3 (see Fig. 7.17) was found in both the fee and sc phases

where the coefficients /30 and /3' were found to be temperature dependent in the sc phase (j80 = 12.78 GPa at p = 0 and j6' = 17.9 at 152 K), but less temperature dependent in the fee phase (/30 = 6.77 GPa at p = 0 and P' = 21.5 at 336 K). Thus upon transforming from the fee to the sc phase, crystalline C60 becomes softer and the bulk modulus becomes less pressure dependent. This is in contrast to what is expected from the decrease in C60-C60 distance which occurs during this orientational phase transition, and would suggest increased intermolecular interaction in the sc phase. The decrease in /30 at the fcc-sc transition is explained by the alignment of the double bond of one C60 molecule near the center of the pentagon (or hexagon) of the neighboring C60 molecule (see Fig. 7.7), thereby minimizing p-orbital interactions. The smaller pressure dependence of (3 in the sc phase is attributed to the lower energy required to compress one orbital within a current ring in comparison to compressing orbitals on adjacent spheres [7.5]. As the pressure increases, the C60-C60 distance decreases, until eventually the intramolecular and intermolecular C-C distances become comparable. When these distances become comparable, a phase transition occurs to another nonconducting transparent phase, which has not yet been

Fig. 7.17. Pressure dependence of the bulk modulus for C60 crystals, calculated between consecutive experimental points at 298 K. The fitted lines show the linear behavior in the fee (low pressure) and sc (high pressure) crystalline phases, respectively [7-5].

Fig. 7.17. Pressure dependence of the bulk modulus for C60 crystals, calculated between consecutive experimental points at 298 K. The fitted lines show the linear behavior in the fee (low pressure) and sc (high pressure) crystalline phases, respectively [7-5].

clearly identified [7.124-127], Placement of this phase on the phase diagram for carbon (Fig. 2.1) suggests that pressures of ~20 GPa may transform C60 into diamond [7.125].

However, if both the pressure and temperature are simultaneously increased, then two metastable forms of solid C60 can be stabilized by quenching from high temperature [7.128]. One phase, denoted by fcc(pC60) where "p" refers to a pressure-induced phase, is prepared at 5 GPa using quasi-hydrostatic pressure from an anvil pressure apparatus and 300 < T < 400° C [7.128], This phase has been described as a pressure-induced fee structure with a lattice constant of 13.6 A [about 4% smaller than that for the conventional fee structure (see §7.1.1)]. A second pressure-induced rhombo-hedral R3m phase, denoted by rh(pC60), is also stabilized at a pressure of 5 GPa but in a higher temperature range, 500 < T < 800° C. This second structure can be indexed by a rhombohedral unit cell with a0 = 9.77 A and a = 56.3° or, equivalently, by a hexagonal unit cell with lattice parameters a0 — 9.22 A and c0 = 24.6 A and containing three C60 molecules at (0,0,0), (5, |), and (|, |). The R3m structure describes an fee unit cell elongated along the (111) direction [7.128]. Values for the lattice constants for the various high-pressure phases are summarized in Table 7.13, in comparison with those for the fee phase that is stable at ambient pressure.

For the two pressure-induced phases, the Bragg x-ray diffraction peaks are very broad, indicative of short-range crystalline order (~40 A). The phase transition to fcc(pC60) reduces the nearest-neighbor Qq-C^ distance from 10.02 A to 9.62 A, while in the rh(pC60) phase, the C60-C60 distance for the six nearest-neighbors normal to the rhombohedral axis is 9.22 A, and along the rhombohedral axis the C6o—C60 distance is 9.76 A. Table 7.13 also shows that the volume per molecule decreases from 711 A3 for the ambient fee phase to 629 A3 for the fcc(pC60) phase, and finally to 603 A3 for the rh(pC60) phase [7.128],

Table 7.13

Lattice constants of various high-pressure phases of Cm in comparison to those for the ambient phase [7.128].

Table 7.13

Lattice constants of various high-pressure phases of Cm in comparison to those for the ambient phase [7.128].

Phase

Cubic cell

Hexagonal cell

Vol/Qo

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