Muonium

Figure C2.16.6. The energy states of a metastable and bistable muonium in Si are illustrated in a configuration diagram. It plots the defect energy as a function of a coordinate which combines position and all the relaxations and distortions of the crystal. The specific example, discussed in the text, illustrates acceptor and donor levels, metastability, bistability and negative- U [50] behaviour.

This paper is concerned with the structures of the simplest possible adducts of the Ceo and C70 fullerenes, namely the monohydrides, CmH and C H. These open shell species or radicals may be considered as the product of the addition of one atom of hydrogen or one of its isotopes, among which we include specifically the light pseudoisotope of hydrogen known as muonium. Mu = pfe. Although Ceo//has been observed [1], the stimulus for these calculations arose from the experiments on muon implantation in solid [2,3] and C70 [4]. 

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. 

Previous calculations on CqoMu [11] have indicated that the distortion to the Ceo cage in the neighbourhood of the point of attachment is so localised that it can be well represented by allowing the positions of only six carbon atoms to relax. It is assmned here that the same will apply to muonium adducts of C70 and addition will take place according to process (1) at sites of unsaturation (Fig. 2a). 

Figure 3 The numbers at each site in the top half (above the dotted line connecting the extreme atoms to the left and right of the diagram) are the numbers of classical structures which can be constructed with hydrogen (muonium) attached to the position indicated and the unpaired electron at the indicated site. The corresponding numbers in the bottom half are the spin densities in atomic units from UHFAA calculations on the fully optimised geometry of CeoMu using an ST0-3G basis set within the ROHF method.

Apart from type 62, which is only slowly convergent to the optimised geometry, the other centres are well described by the ROHF method. Polyhedral views of the three type a structures are shown in Fig. 6. These all illustrate the change of hybridisation at the point of muonium attachment and at the adjacent carbon atom where the unpaired electron is effectively localised as expected from addition to an alkene. The bi and c defects (Fig. 7) are quite different. The expected hybridisation change to sp is clearly present for the atom bonded to muonium, but other significant distortions are not obvious. This is consistent with the prediction from resonance theory (Fig. 8) that the unpaired electron for these structures is delocalised over a large number of centres. 

Figure 8 Measure of delocalisation of each defect type predicted by resonance theory. The loops enclose centres which have numbers of classical structures larger than. 74 times the greatest number in the type. The cut-off point for type bi (or type 63) centres is particularly arbitrary since the delocalisation is spread around the equator. The small circles are the point of muonium attachment. The dotted circle is coincident with the equator of Cra-...

Ab-initio calculations on muonium adducts of fullerenes T.A. Claxton... 

Muonium, atom number zero , is composed of a positron and an electron. Calculate foe Rydberg constant for this species. 

In the final chapter of this volume, Van de Walle reviews the theoretical information that is available on isolated, interstitial hydrogen and muonium in crystalline semiconductors. Given the limited direct experimental information available on isolated, interstitial hydrogen and the vital contributions that muonium studies have made in confronting this deficit, it is clear that theory is a particularly essential tool for progress on this topic. Van de Walle first reviews the principal calculational techniques... 

Up to now, no direct measurements of diffusion coefficients have been reported for any system that show the low-temperature upturn just described, and it may well be that for most systems involving hydrogen such effects would occur only at ultra-low temperatures and minuscule diffusion rates. Also, the impurities and imperfections always present in real materials might well trap nearly all the diffusant atoms at the low temperatures at which coherent transport might be expected in ideal material. However, a recent measurement by Kiefl et al. (1989) of the (electronic) spin relaxation rate of muonium in potassium chloride over a range of temperatures gives spectacular support to the concept of coherent tunneling at low temperatures. (See Fig. 6 of Chapter 15 and the associated discussion.)... 

For the case of muonium, nonresonant spin precession in a magnetic field provides a copious source of information about its crystallographic sites and the associated unpaired electron distribution around them (see Chapter 15). Here, the concentration of muons is always too low for molecule formation, and migration to impurities and implantation defects can be kept small by the short muon lifetime and use of pure material and low temperature. 

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