3348 G. Brauer et al. /Applied Surface Science 252(2006)3342-3351 Table I estimated order of the positron diffusion length in Positron lifetimes(r)and affinities(A+)for graphite calculated using 3C-SiC should remain correct different computational methods and approaches(see text) to elec- tron-positron correlations LMTO 3.5. Positron lifetime ATSUR t(ps) In addition to the positron affinity, the positron lifetime is also calculated, and both the lmto and atomic superposition(ATSUP)[27, 28] methods are used for this purpose(see Table 1). The lifetime results obtained using these two methods differ non- (LMTO)method [24]. In the framework of this method, negligibly. This is probably due to LMTO limitations ne often needs to incorporate empty spheres(ES)into to describe properly the interstitial space. The ATSUP- the studied structure in order to describe properly the Bn results compare well with other calculated (electron and positron) charge distribution in the lifetimes presented in the literature [29,30), on the interstitial space [24. We tried several choices of the other hand, our ATSUP-GC value agrees well with ES sizes and positions and the results presented in 209 ps given [31] and obtained using a different Table I correspond to the most realistic case. Boronski- approach. Nieminen(BN) scheme [25] and gradient correction Positron lifetime measurements on the pyrolytic (GC)approach of Barbiellini et al. [26] were employed graphite and SiC/SiC composite samples were per- to treat electron-positron correlation effects. formed using a spectrometer of 160 ps time resolution The positron affinity of graphite is found to be (FWHM at" -Na window settings )which is described in positioned well below the one of 3C-Sic detail elsewhere [32]. The measured positron lifetime (A+=-557ev 5] independent of the various spectrum of graphite was decomposed into two potentials chosen in the particular calculations and components: [1=93+ 4 ps and t2= 242 t 4 ps with Iso independent of the position of the 3C-SiC Fermi corresponding intensities 11=23+ 1% and 12=77 level. This indicates that graphite precipitates (or 19. The components ti and t2 are attributed to regions)imbedded in a 3C-SiC host matrix would be delocalized and trapped positrons, respectively. When attractive to positrons. A formal application of Eq (4) the two state trapping model is considered, the and inserting numbers from Table I would give a corresponding bulk positron lifetime amounts to critical radius of the order re N0.1674-0 1876 nm. tb=177+ 1 ps, which corresponds reasonably well The lattice parameters of graphite can be found from to the calculated lifetimes given in Table 1, the LMTO- XRD(PDF 41-1487)thus giving the lattice constants N number being the closest one Measured positron 0. 24704 nm and c=0.67244 nm. Because carbon lifetimes presented in literature(see [29-31] and atoms may touch each other at the utmost within the references therein)range from 195 to 215 ps but were (0001) face, the atomic radiusof a carbon atom measured with time resolutions being worse than the should be less equal a/2, i.e. 0. 1235 nm. Taking this presently used. From the above two components, we number, another formal calculation gives the result also calculated the mean positron lifetime Tav= 208 hat a ' graphite precipitate'able to trap a positron t3 ps that falls into this range. This indicates that a inside a 3C-SiC matrix should contain at least three to lifetime of about 200 ps usually measured in graphite four carbon atoms. Certainly, such a consideration is corresponds to a mixture of delocalized and localized not applicable to the given composite sample because positrons. However, the nature of positron trapping sites the carbon is not evenly distributed inside the 3C-Sic is not fully certain, these could be monovacancies and/ matrix. From the production process described above, or small vacancy clusters on the basis of calculation it is more probable to have maybe continuous carbon iven in 311 threads after the sintering process. Anyway, the As for the SiC/SiC composite sample, we decided attractiveness of graphite overestimates the carbon to fix one of lifetime components to tav for graphite ratio m in Eqs.(1) and (2), i.e. the assumed linear as given above- because our sample contains graphite dependency does not really exist. Nevertheless, the regions'(as indicated by SPIs measurements) which(LMTO) method [24]. In the framework of this method, one often needs to incorporate empty spheres (ES) into the studied structure in order to describe properly the (electron and positron) charge distribution in the interstitial space [24]. We tried several choices of the ES sizes and positions and the results presented in Table 1 correspond to the most realistic case. Boronski– Nieminen (BN) scheme [25] and gradient correction (GC) approach of Barbiellini et al. [26] were employed to treat electron–positron correlation effects. The positron affinity of graphite is found to be positioned well below the one of 3C–SiC (A+ = 5.57 eV [5]) independent of the various potentials chosen in the particular calculations and also independent of the position of the 3C–SiC Fermi level. This indicates that graphite precipitates (or ‘regions’) imbedded in a 3C–SiC host matrix would be attractive to positrons. A formal application of Eq. (4) and inserting numbers from Table 1 would give a critical radius of the order rc 0.1674–0.1876 nm. The lattice parameters of graphite can be found from XRD (PDF 41-1487) thus giving the lattice constants a = 0.24704 nm and c = 0.67244 nm. Because carbon atoms may touch each other at the utmost within the (0 0 0 1) face, the ‘atomic radius’ of a carbon atom should be less equal a/2, i.e. 0.1235 nm. Taking this number, another formal calculation gives the result that a ‘graphite precipitate’ able to trap a positron inside a 3C–SiC matrix should contain at least three to four carbon atoms. Certainly, such a consideration is not applicable to the given composite sample because the carbon is not evenly distributed inside the 3C–SiC matrix. From the production process described above, it is more probable to have maybe continuous carbon threads after the sintering process. Anyway, the attractiveness of graphite overestimates the carbon ratio m in Eqs. (1) and (2), i.e. the assumed linear dependency does not really exist. Nevertheless, the estimated order of the positron diffusion length in 3C–SiC should remain correct. 3.5. Positron lifetime In addition to the positron affinity, the positron lifetime is also calculated, and both the LMTO and atomic superposition (ATSUP) [27,28] methods are used for this purpose (see Table 1). The lifetime results obtained using these two methods differ non￾negligibly. This is probably due to LMTO limitations to describe properly the interstitial space. The ATSUP￾BN results compare well with other calculated lifetimes presented in the literature [29,30], on the other hand, our ATSUP-GC value agrees well with 209 ps given [31] and obtained using a different approach. Positron lifetime measurements on the pyrolytic graphite and SiC/SiC composite samples were per￾formed using a spectrometer of 160 ps time resolution (FWHM at 22Na window settings) which is described in detail elsewhere [32]. The measured positron lifetime spectrum of graphite was decomposed into two components: t1 = 93 4 ps and t2 = 242 4 ps with corresponding intensities I1 = 23 1% and I2 = 77 1%. The components t1 and t2 are attributed to delocalized and trapped positrons, respectively. When the two state trapping model is considered, the corresponding bulk positron lifetime amounts to tb = 177 1 ps, which corresponds reasonably well to the calculated lifetimes given in Table 1, the LMTO￾BN number being the closest one. Measured positron lifetimes presented in literature (see [29–31] and references therein) range from 195 to 215 ps but were measured with time resolutions being worse than the presently used. From the above two components, we also calculated the mean positron lifetime tav = 208 3 ps that falls into this range. This indicates that a lifetime of about 200 ps usually measured in graphite corresponds to a mixture of delocalized and localized positrons. However, the nature of positron trapping sites is not fully certain, these could be monovacancies and/ or small vacancy clusters on the basis of calculations given in [31]. As for the SiC/SiC composite sample, we decided to fix one of lifetime components to tav for graphite – as given above – because our sample contains graphite ‘regions’ (as indicated by SPIS measurements) which 3348 G. Brauer et al. / Applied Surface Science 252 (2006) 3342–3351 Table 1 Positron lifetimes (t) and affinities (A+) for graphite calculated using different computational methods and approaches (see text) to elec￾tron–positron correlations Theory LMTO ATSUP t (ps) A+ (eV) t (ps) BN 174 9.0 185 GC 186 8.3 206