allows the intercalation of Na to high concentrations. For example, a stoi-chiometry as high as NanC60 has been reported, for which nine Na atoms are expected to go into an octahedral site, as shown in Fig. 8.11 [8.145].

The Na,C60 crystal structures also differ from those of the corresponding heavier alkali metal dopants with regard to the orientational alignment of the C60 anions. As mentioned above, the smaller size of the dopant species results in different relative magnitudes of the contributions to the orientational potential than for the case of the heavier alkali metals. For the Na^C60 compounds the repulsive interaction between the alkali cations and the C60 anions is very much smaller than for the larger cations, thereby reducing the tendency for the alkali metal ions to lie close to the large hollows of the C60 shell (at the hexagonal faces). For example, the repulsive interaction between Na cations and C60 anions [shown in Fig. 8.6(b)] almost cancels the attractive Coulomb interaction [shown in Fig. 8.6(c)], so that the orientational alignment potential VA(d) for the Na^Cgo compounds is almost the same as for C60 itself (see §7.1.3). X-ray and neutron diffraction experiments are in agreement with this prediction, so that the NaxC60 compounds tend to crystallize in the Pa3 structure at low temperature, with an orientational phase transition occurring at T01 in analogy with the crystal phases of C60 [8.123],

8.5.4. Structures for M2M\C60 and Related Compounds

The M2M'C60 compounds [8.91,109], where M = Li or Na is a small alkali metal ion and M' = Rb or Cs is a large ion, show an important site ordering effect, placing the smaller M ions in tetrahedral sites and the larger M' ions in octahedral sites. The orientational alignment is more sensitive to the dopant occupying the tetrahedral sites, because of their smaller cavity size. If the tetrahedral sites are occupied by dopants of small size (such as for Na2RbC60), then the repulsive interaction shown in Fig. 8.6(b) is less

Fig. 8.11. Schematic representation of a proposed x-ray-derived structure of Na,,^, [8.144]. For clarity, isolated Na atoms on tetrahedral sites are shown along only one of the body diagonals, and only the octahedral cluster of Na atoms centered at (¿,5,5) is shown. Note that the Cai molecules (shown on a reduced scale) are for simplicity orientationally ordered in this schematic diagram [8.145],

Fig. 8.11. Schematic representation of a proposed x-ray-derived structure of Na,,^, [8.144]. For clarity, isolated Na atoms on tetrahedral sites are shown along only one of the body diagonals, and only the octahedral cluster of Na atoms centered at (¿,5,5) is shown. Note that the Cai molecules (shown on a reduced scale) are for simplicity orientationally ordered in this schematic diagram [8.145], important, and for the case of Na ions the attractive and repulsive alkali metal-C60 anion interaction terms largely cancel and molecular alignment close to that for C60 itself results. Experimental evidence for such behavior in Na2RbC60 has been reported in neutron scattering studies [8.146]. This effect is also similar to the behavior described in §8.5.3 for the Na^C60 compounds [8.91,147,148], Examples of site selectivity for the smaller and larger ions have been reported for the compound Rb2CsC60 but not for RbCs2C60 [8.88,149], and for K2RbC60 but not for KRb2C60 [8.116,132], consistent with the above discussion. Of the various M2M'CgQ compounds that become superconducting at low temperature, the Na2RbC60 compound is the one having the best-established site selectivity (i.e., few Na ions occupy octahedral sites) [8.123]. In contrast, the Li2CsC60 compound has recently been reported [8.150] to show a large amount of orientational disorder.

One unusual effect is that alkali metal doping with the alloy dopants Na2Cs, Na2Rb, Na2K, and Li2Cs results in a crystal with a closer C60-C60 separation than is present in undoped C60 (see Table 8.2), presumably due to the attractive interaction between the metal ions and the fullerene molecules [8.141]. This interaction reduces the lattice constant of the M2M'C 50 fee phase relative to the value obtained for the M3C60 (M = K, Rb, Cs) fee binary phase.

8.5.5. Structure ofAmmoniated M3C60 Compounds The x-ray structural analysis of two ammoniated alkali metal fulleride compounds (NH3)4Na2CsC60 [8.119] and (NH3)K3C60 [8.120] has been reported. These compounds were initially prepared with the goal of increasing the lattice constant of the alkali metal M3_xMJtC60 compounds and thereby increasing their superconducting transition temperatures (see §15.1). Since no significant change in charge transfer is anticipated upon adding the (NH3) groups, it is appropriate to relate these compounds to the alkali metal-doped C60 compounds.

The structure of the (NH3)4Na2CsC6o compound has been identified with the Fm3 space group and a lattice constant of a — 14.473 A has been reported [8.119], with the Cs and half of the Na alkali metal dopants located on tetrahedral sites, and the remaining Na ions are located near the center of a tetrahedron of the (NH3) molecules on an octahedral site. The nearest-neighbor distances are N-Na(0)=2.5 A, N-N=2.89 A, N-Cs(T)=3.76 A, N-C=2.81 A, N-H=1.02 A, Cs(T)-C=3.37 A, and H-C=2.29 A [8.119], where (T) and (O), respectively, refer to tetrahedral and octahedral sites (see Table 8.3).

In contrast, the crystal structure of (NH3)K3C60 has been described by an orthorhombic distortion of an fee structure [8.120], with one K+ and one NH3 per distorted octahedral site, and with lattice constants a = 14.971 A, b = 14.895 A, c — 13.687 A. Some of the bond lengths for this compound are K-C(3) = 3.20 A, K-N=2.68 A, K-C(2)= 3.05 A, K-C(l)= 3.48 A, where C(i), i — 1,2,3, denote distinct carbon sites in the lattice (see Fig. 7.3). The departure of (NH3)K3C60 from a cubic crystal structure may be responsible for the absence of superconductivity in this compound [8.120], although it may be speculated that external pressure might restore the fee structure and perhaps also restore superconductivity.

8.6. Structure of Alkaline Earth-Doped C60

The structures of the alkaline earth-doped C60 compounds have been studied both experimentally and theoretically, because of their superconducting properties, as well as their interesting normal state properties. A variety of crystal structures and phases for M^Qq (M = Ca, Sr, Ba) have been observed. The divalence of these ions in the tetrahedral and octahedral sites leads to a partial filling of the broadened (LUMO+1) /^-derived electronic energy band of C60 and leads to semimetallic behavior in the Sr6C60 and Ba6C60 compounds [8.143] (see §12.7.4).

8.6.1. Car C60 Structure

The structure of the alkaline earth metal compound CaxC60 (for x < 5) follows the^ same space group Pa3 as C60 below Tm. No phase transition to the Fm3m structure is seen all the way up to 400° C. In the Pa3 structure, the Ca ions (nominally doubly charged) occupy both tetrahedral and octahedral sites. Because of the smaller size of the calcium ion (as also noted above for the Na+ ion [8.83]), the octahedral sites can accommodate multiple Ca ions, and it is believed that for Ca5C60 up to four Ca2+ cations are accommodated in a single octahedral site, despite the Coulomb repulsion between the Ca cations [8.1]. Since the charge transfer for the five Ca dopants/C60 is only about nine electrons (sufficient to fill all of the -derived band and approximately half of the r1?-derived band), the average charge transfer is somewhat less than two electrons per Ca dopant (see §12.7.4). Also for Ca5C60 the lattice constant a0 — 14.01 A is smaller than that for C50 prior to doping (see Table 8.2), again this must be associated with the attraction between the C60 anions and the charged Ca ions.

8.6.2. SrxC 60 and BaxCb0 Structures

The structures of strontium and barium intercalated fullerides SrxC60 and Ba^Qo are more complicated than that of Ca^C^,. The SrxC60 and Ba^C^, systems are the only fulleride systems, thus far reported, where fee and bcc phases compete in the same compositional range [8.93]. Near x — 3, a bcc A15 (Pm3n) phase coexists with an fee (Fm3) phase, with lattice constants 11.140 A and 14.144 A for the bcc and fee phases, respectively. Most of the Sr2+ ions in the fee phase are on tetrahedral sites, and the ions on the octahedral sites are displaced from the central position and are off-centered along the {111} axes [8.93]. In the bcc (Pm3n) phase for Sr3C60, the C60 anions are orientationally disordered. Studies as a function of x indicate that Sr,C60 starts to transform from an fee structure at small x to a bcc structure for x < 3. It is believed that the A15 phase is stabilized for the divalent alkaline earth cations because this structure allows the divalent cations to be located preferentially adjacent to the electron-deficient five-membered (pentagonal) rings [8.93],

Increasing the Sr dopant stoichiometry above x — 3 suppresses the fee and A15 bee structures and leads to the appearance of the bcc Im3 phase, with a0 = 10.975 A for Sr6C60. This Im3 phase is also found for Ba6C60 and certain M6C60 (M = K, Rb, Cs) alkali metal compounds (see §8.5.2). Figure 8.12 shows that the lattice constant for the Im3 structure increases with increasing size of the dopant species for both the alkali metal and alkaline earth systems. This figure also shows that the lattice constant depends on the amount of charge transfer, which is physically reasonable, because of the greater attractive Coulomb interaction between the doubly charged alkaline earth ions and the C60 anions, bringing these anions even closer together. The C60-C60 distance of 9.53A for Sr6C60 is the shortest C60-C60 distance thus far reported for unpolymerized C60 systems [8.93]. The structural and electronic properties of the Sr^Qp fullerides are intermediate between those of the Ca^C60 and BajtCfi0 intercalated fullerides [8.151], consistent with size considerations for the dopant ions.

The structure of BajCgy has also been investigated by x-ray powder diffraction techniques, yielding the A15 structure with a space group Pm3n, typical of several BCS superconductors (such as Nb3Sn) with Tc values above 10 K [8.111], The lattice constant for the bcc A15 Ba3C60 structure is 11.34 A with the Ba ions separated from the three nearest-neighbor inequivalent carbons by 2.98 A, 3.14 A, and 3.39 A, respectively. The nearest-neighbor carbon-carbon distance in this crystal structure is 1.47 A, as determined by a detailed x-ray analysis [8.111]. In the A15

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