Omo

structure. However, as also pointed out in §7.1.2, the point group Tk has no fourfold axes, so that there are two ways to align the twofold axes of the C60 anions, and these two orientations are shown more explicitly in Fig. 8.8. Keeping the same orientation for the z-axis, we see that the x- and _y-axes can have two different orientations: either (a) or (b, c) as shown in Fig. 8.8, where (b, c) are equivalent. To arrive at orientation (b, c) from orientation (a) in Fig. 8.8, we can rotate the C60 anion by tt/2 about the z-axis to obtain (b), or by ~ 44.5° about the [111] direction to obtain (c). The shaded pentagon in Fig. 8.8 helps to follow the rotations in going from (a) to (b) or from (a) to Jc). Although the symmetry of the structure in Fig. 8.7 is lower than Fm3m, the literature often uses the Fm3m space group designation for the K3C60 and Rb3C60 structures, based on the argument that both orientations (a) and (b, c) occur with equal probability.

Because of the equivalence, the equal probability, and the random occurrence of each of the two standard orientations (usually called A and B) for the twofold axes in crystalline K3C60 and Rb3C60, we say that these M3C60 compounds exhibit merohedral disorder [8.124], in analogy with the merohedral disorder of C60 (see §7.1.4). Because of the merohedral disorder, the transfer integral for charge transfer between the Cg0 anions has a random component, which can significantly increase the carrier scattering in the intermolecular hopping process. This merohedral disorder leads to relatively high values for the residual resistivity of the K3C60 and Rb3C60 compounds at low temperature. Explicit calculations of this residual temperature-independent contribution to the low-temperature re-

Fig. 8.8. Two "standard" orientations for the Qo anions (a) and (b, c) in M3C60 (M = K or Rb), with respect to a fixed set of crystallographic axes. The plane of each drawing is normal to the [111] direction. The transformation from (a) to (b) involves a 90° rotation about the [001] direction. The transformation from (a) to (c) involves a ~44.5° rotation about the [111] direction. One of the pentagons is shaded to illustrate these rotations. Orientations shown in (b) and (c) are equivalent [8.127].

sistivity, due to the merohedral disorder mechanism [8.125], yield good agreement with experimental values of the residual resistivity for K3C60 and Rb3C60 (see §14.1.2). In diffraction experiments, diffraction patterns consistent with a fourfold axis have been reported [8.107] due to the rapid molecular reorientations and the merohedral disorder. Neutron diffraction experiments show that merohedral disorder persists down to very low temperatures (12 K) [8.126],

Using A and B to denote the two equivalent "standard" orientations of the C60 molecules in the K3C60 and Rb3C60 structures (Figs. 8.7 and 8.8), it has been proposed [8.128-130] that some correlations should exist between the molecular orientations of the C60 anions on nearest-neighbor sites, but that no long-range orientational correlation should be present. Some experimental evidence for such short-range correlations has been reported, based on detailed analysis of neutron diffraction profiles and the pair distribution function of Rb3C60 looking for deviations from strict merohedral disorder, for which there are no nearest-neighbor correlations between molecules in the standard orientations A and B (see Fig. 7.6). The two standard orientations differ by a ir/2 rotation about the (001) axis [8.131],

In connection with the merohedral disorder, Stephens pointed out that the site ordering of the dopants would introduce three inequiva-lent sites for the hexagon rings of the Cg0 anions (see Fig. 7.2) [8.107]. These three inequivalent sites have been experimentally corroborated in Rb3C60, based on 87Rb-NMR studies of the chemical effect [8.132], and in K3C60 based on NMR studies of the jump rotation of the 13C

nuclei [8.133]. It is concluded from these experiments that the repulsive alkali metal-C60 interaction is important in K3C60 and Rb3C60 and plays a major role in determining the orientation of the molecule in the crystal lattice.

8.5.2. MjQo, A/4C60, and M6C60 Structures (M = K, Rb, Cs)

Three other stable phases are observed for M^C60 (namely, MC60, M4C60 and M6C60 for M = K, Rb, and Cs), and each has a different range of stability and crystalline structure (see Fig. 8.1), in accordance with the phase diagram of Fig. 8.5. The crystal structures of these phases are discussed below.

The MC60 alkali metal phase is stable at elevated temperatures only for a limited temperature range (410-460 K). This phase has been observed with M = Na, K, Rb, and Cs, where the M ion is in an octahedral site, thereby forming a rock-salt (NaCl) crystal structure [8.105,108,123,134-136], The reported lattice constants for Kli4C60, Rb0 9C60, CsC60 are 14.07 A, 14.08 A, and 14.12 A, respectively, somewhat smaller than that for undoped C60 (14.16 A) [8.105]. When cooled below ~100°C, the rock-salt structure becomes distorted to a pseudo-body-centered orthorhombic phase, with lattice constants for Rb,C60 a = 9.138 A, b = 10.107 A, and c = 14.233 A. The distance between the C60 molecules is very short along the a direction, as shown in Fig. 8.9, and a polymeric cross-linking between the C60 molecules has been reported for both KtC60 and RbjC«, [8.137], The differences in

Fig. 8.9. Atomic structure of the polymeric Rl^C«, phase determined from x-ray diffraction patterns [8.137], Solid (broken) lines show fullerenes and cations centered at x = 0 (x = 1/2) in the b-c plane at the top, and at y = 0 (y = 1/2) in the ac plane at the bottom. To the right is a projection of one chain perpendicular to the molecular mirror plane.

Fig. 8.9. Atomic structure of the polymeric Rl^C«, phase determined from x-ray diffraction patterns [8.137], Solid (broken) lines show fullerenes and cations centered at x = 0 (x = 1/2) in the b-c plane at the top, and at y = 0 (y = 1/2) in the ac plane at the bottom. To the right is a projection of one chain perpendicular to the molecular mirror plane.

bond lengths in the region of the cross-linkage relative to the ideal C60 molecule are shown in Fig. 8.9 in the lower right corner [8.137]. Presently, there is no concensus about whether the MjC60 phase is metallic or semiconducting. In the slow-cooled R^Qo phase, infrared transmission studies have been interpreted in terms of enhanced conduction along the a direction where C60 cages are coupled by [2+2] cycloaddition bonds [8.137]. One feature of practical importance regarding the polymerized phase shown in Fig. 8.9 is the observation that this doped RbjQo phase is stable in air, unlike all other reported alkali metal-doped C60 phases, which are highly reactive under ambient conditions. Regarding polymerization of MjQq, it is believed that slow cooling to room temperature (~25°C) results in a chain polymer which retains inversion symmetry, whereas rapid quenching to temperatures below room temperature gives rise to dimers and no inversion symmetry in the lattice [8.137-139], as evidenced by Raman and infrared spectra [8.140] (see §11.6.1). This orthorhombic crystal structure tends to be highly strained, has a very low heat of transformation, and transforms reversibly at 200°C to the rock-salt phase [8.137]. Presently available samples in the rock-salt phase show a high vacancy concentration at the metal dopant sites. The large volume available to the M ion in the rocksalt structure suggests that the C60 anions should have rotational freedom similar to that for undoped C60. A stable NaC60 phase has been reported [8.108], which shows a phase transition to a simple cubic structure below 320 K, similar to the undoped C60 crystal phases above and below T01.

The M^Qo phase [see Fig. 8.1(f)], which appears to be difficult to prepare, has a body-centered tetragonal (bet) structure with a space group IA/m mm [8.7,112]. Some values for the structural parameters for K4C6q and Rb4C60 are given in Table 8.4. For Rb4C60, the nearest-neighbor C60-C60 distance is 10.10 A, and the closest approach between a C60 anion and an alkali metal cation is 3.13 A, yielding a volume per unit cell of

Table 8.4

Unit cell dimensions and bond distances for K4CW and R^Qo in the IA/mmm structure."

Table 8.4

Unit cell dimensions and bond distances for K4CW and R^Qo in the IA/mmm structure."

Compound

a (A)

c(À)

O0~C-60 (A)

M-Qo (A)

V (A3)"

Reference

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