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"The radii of the cavities (or voids) available to tetrahedral and octahedral sites (see Fig. 8.1) are 1.12 A and 2.07 A, respectively.

"The radii of the cavities (or voids) available to tetrahedral and octahedral sites (see Fig. 8.1) are 1.12 A and 2.07 A, respectively.

phase for compositions x < 1 and into Kj C60 and K3C60 coexistence for 1 < x < 3. The diagram indicates that for T < 425 K and 0 < x < 3, phase separation into the phases C60 and K3C60 occurs [8.7,106]. The diagram also distinguishes between the two crystal structures for C60 below and above T01 = T, = 260 K. Between 3 < x < 4, phase separation into the fee K3C60 phase is shown coexisting with the body-centered tetragonal (bet) phase (stable at K4C60). Finally, for 4 < x < 6, the bet and bcc phases coexist with the bcc phase stable at M6C60. The stability regions for each of the phases are shown schematically in Fig. 8.5.

In alkali metal doping, charge transfer of one electron per dopant atom to the C60 molecule occurs, resulting in dopant ions at the tetrahedral and/or octahedral interstices of the cubic C60 host structure (see Fig. 8.1). Values for the ionic radii of various alkali metal ions which serve as donor dopants for C60 are given in Table 8.1, and the relation of these radii to the tetrahedral and octahedral voids or cavities is also given in the table. For the tetrahedral sites, the radius of the cavity available to an ion is 1.12 A (slightly smaller than the ionic radius, r;, of K+), while for an octahedral site, the cavity radius is 2.07 A (considerably larger than r{ for K+) [8.107]. The K+ ionic radius is 1.38 A in solid K3C60 [8.107], compared with r, = 1.33 A for the K+ ion in ionic salts, and compared with 1.03 A, which is half the thickness of the potassium layer in the stage 1 graphite intercalation compound C8K [8.78].

An important factor affecting the metal ion uptake in doping fullerene crystals is the size of the metal ion (see Table 8.1), which plays a major role in determining the lattice constant. In some cases the crystal structure of the doped fullerides is also dependent on the alkali metal species, as, for example, the NaxCfi0 compounds [8.108] (see §8.5.3). In particular, the ionic radius of the species occupying the tetrahedral (rather than octahedral)

sites most sensitively determines the lattice constant of the doped fulleride [8.109]. The shortest distance between a K+ ion at a tetrahedral site and the adjacent C60 anion is 2.66 A [8.107]. It is of interest to note that the Cs+ ion is too large to form a stable Cs3C60 compound with the fee structure unless pressure is applied [8.90]. If no pressure is applied, Cs3C60 crystallizes in a bcc structure, which is not superconducting (see §15.1).

Discussion of the doping of crystalline C60 with alkaline earth dopants is given in §8.6. Since the cavities in the C60 crystal structure are already large enough to accommodate alkali metal or alkaline earth metals, only a small lattice expansion occurs due to the intercalation of alkali metal species into fullerene crystals, in contrast to the behavior observed in graphite intercalation compounds (see §2.14) or in transition metal dichalcogenide intercalation compounds [8.110], where the lattice expansion is large (factors of 2 or 3 typically).

The effect of the addition of alkali metal dopants into the C6q lattice does expand the lattice somewhat, as can be seen in Tables 8.2 and 8.3. The larger the ionic radius, the larger is the lattice expansion, although in some cases, lattice contraction is seen because of the electrostatic attraction between the charged alkali metal cations and the C60 anions. Since the fee lattice is compact and close-packed, higher doping levels or larger dopant radii favor the more open bcc lattice. Table 8.2 lists lattice constants for mostly nonsuperconducting alkali metal-doped fullerides but includes the alkaline earth and rare earth superconductors (see §8.6). Listed separately in Table 8.3 are the lattice constants for the alkali metal M3C60-related compounds, most of which form superconductors.

8.5.1. M3C60 Alkali Metal Structures

Because of the discovery of relatively high Tc superconductivity in the MjQq (M = K, Rb) compounds, the M3C60 system has become the most widely studied of the doped C60 compounds, and therefore more is known about the M3C60 phase than the other phases shown in Fig. 8.5. For the composition M3C60, the metallic crystals for K3C60 and Rb3C60 have the basic fee structure shown in Fig. 8.1(d). Within this structure, the alkali metal ions can sit on either tetrahedral (|, \) sites, where the metal ion is surrounded by four neighboring C60 molecules, or octahedral (¿,0,0) sites, where the metal ion is coordinated to six nearest-neighbor C60 molecules. The tetrahedral sites are twice as numerous as the octahedral sites. Surrounding each Cg0 anion in M3C60 compounds are 14 dopant ions, 8 of which are in tetrahedral sites, and 6 are in octahedral sites. As shown in Fig. 8.1(d), alkali metal atoms can be placed only on tetrahedral (c) sites giving the stoichiometry M2C60, or only on octahedral (b) sites giving the

Table 8.2

Lattice constants for stable C^-related crystalline materials [8.7,8].°

Table 8.2

Lattice constants for stable C^-related crystalline materials [8.7,8].°

M.Qo

Phase

Lattice constants (Ä)

References

c6o

fee (Fm3m)

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