Diamond muonium

Ceo and higher fullerenes are distinguished from other allotropes of carbon, diamond and graphite, in that they exist as discrete molecules. The spherical or ellipsoidal nature of the monotropes opens up the possibility of intriguing new areas of chemistry. Here we are only interested in the hydrogen (or muonium) adducts, although this study has important implications to the very vigorous and extensive research in fullerene chemistry. 

Two types of species have been detected in the /rSR spectrum of Ceo- One shows an unreacted or meta-stable muonium state which may well correspond to an internal state, muonium is trapped inside the cage Mu Ceo in the current notation [2]. This may be compared with normal muonium (Mu ) in diamond and many other elemental and compound semi-conductors, where the trapping site is in one of the cavities of tetrahedral symmetry. This state of CeoMu is not discussed here, but it does exhibit all the characteristics expected of the internal chemistry of Ceo-The anomalous muonium state. Mu, observed in semi-conductors and generally accepted to arise from muonium being trapped within one of the chemical bonds of the crystal, is unknown in molecules [5,6]. The constraints of the crystal lattice are necessary for the bond-centred state to be stable. 

The section on silicon is followed by a relatively brief discussion of muonium in other semiconductors. The /xLCR study of Mu in GaAs is noteworthy because again it permits a detailed model to be inferred. The important observation of the Mu— Mu transition in diamond and the unusual metastable centers in CuCl and CuBr also will be discussed. The main emphasis of this chapter will be on developments in the field since the extensive review by Patterson (1988), which covered the field up to December 1986. Other reviews on muonium in semicondutors that may be of... 

THE LARGE SPIN DENSITIES FOR NORMAL MUONIUM IN DIAMOND AND THE NEAREST-NEIGHBOR... 

The work on diamond is important both from an experimental and a theoretical viewpoint. Since the carbon atoms that make up diamond are simpler to deal with theoretically, some calculations on hydrogen and muonium in diamond are considered to be more reliable than similar calculations on higher-Z materials. Thus diamond can be used as a testbed for new ideas on simple defects such as muonium or hydrogen and the associated theoretical methods. For example, the first theoretical confirmation of the BC model of Mu and the metastablility of Mu was made for diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987). 

To put this in better perspective, although it is true that the hyperfine values for Mu in GaAs and GaP are closer than for any other pair of similar crystals (they differ by 30 MHz or 1.0% see Table II), there are several other cases in which A values are close but just not that close. For example, Table II shows that the hyperfine parameters for ZnS and ZnSe differ by 91 MHz or 2.6% and those for Mu" in CuCl and CuBr differ by 39 MHz or 3.1%. All of these could be explained if they corresponded to muonium in a tetrahedral interstitial surrounded by four cations to which they more strongly bond than to the anions, a suggestion similar to that of Souiri et al. (1987) and Cox (1987). Whether this could also be consistent with the closeness of the A values for Mu1 and Mu11 in CuCl and in CuBr, with the pLCR observation of appreciable anion bonding for Mu" in CuCl (see Section IV.4) and with the cluster of hyperfine parameters in SiC near the average of the diamond and silicon values (see Section IV.5), will probably require further experimentation and especially theoretical study to determine. 

In all group IV and group III-V crystals in which muonium has been seen, both normal and anomalous muonium occur, with the single exception of SiC. The tetrahedral location for interstitial muonium is metastable in diamond and very likely in unirradiated silicon just as it is in irradiated Si. However at present it is not possible to say whether Mu or Mu is the more stable in Ge, GaAs, and GaP. 

When relaxation is allowed, the global minimum shifts to the bond-center site (Claxton et al., 1986 Estle et al., 1987 Briddon et al., 1988). This is in agreement with the experimental observation that anomalous muonium is the most stable state for muons in diamond (Holzschuh et al., 1982). An expansion of the bond length by 42% is necessary. The bond center was found to be more stable than the interstitial muonium by s 1.9 eV. Displacements of the muon along directions perpendicular to the bond cost little energy (Estle et al., 1987). 

Hoshino et al. (1989) have recently carried out spin-density-functional calculations for anomalous muonium in diamond. They used a Green s function formalism and a minimal basis set of localized orbitals and found hyperfine parameters in good agreement with experiment. 

In diamond, Sahoo et al. (1983) investigated the hyperfine interaction using an unrestricted Hartree-Fock cluster method. The spin density of the muon was calculated as a function of its position in a potential well around the T site. Their value was within 10% of the experimental number. However, the energy profiles and spin densities calculated in this study were later shown to be cluster-size dependent (Estreicher et al., 1985). Estreicher et al., in their Hartree-Fock approach to the study of normal muonium in diamond (1986) and in Si (1987), found an enhancement of the spin density at the impurity over its vacuum value, in contradiction with experiment this overestimation was attributed to the neglect of correlation in the HF method. 

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