G. Brauer et al. / Applied Surface Science 252(2006)3342-335 3347 confirmed at atomic level by Pas because any possible than in the crystalline 6H-SiC Samp be at a lower remaining open volume fraction should 094 3.4. Positron affinity The positron affinity A+ as a bulk quantity is e sic y sIC defined by [20] A+=-++=-(中-+中+) A dislocation loop Here, p+ and - are the positron and electron work functions, and u- and A+ are the electron and positron chemical potentials, respectively. First-principles Fig. 4. Normalized lineshape parameters w/wb vs. S/S, plot for electronic structure and positron-state calculations different silicon carbide samples, defect states in 6H-SiC and for perfect and defected 3C-SiC and 6H-SiC were pyrolytic graphite. An untreated Si(1 00) sample served as already calculated by assuming that u_corresponds to reference(Sb. Wb)for normalization. the top of the valence band [5]. On the other hand when comparing positron affinities of two materials in contact(SiC and ere), one should be aware straight line is obtained in the Sw representation where the endpoints represent the two st of actual position of electron chemical potentials 17, 18]. If(SI, Wi) is taken to represent the 6H-SiC ( Fermi levels)of both materials (cf [21]). Neverthe less, we adopt here the same approach as in bulk, and(S2, W2) to represent the V2 defect, then a because the actual position of the Fermi level in the traight line connecting both states should contain the Sic composite is unknown. However, this simplifica (S, W) values of all defects having an open volume less tion does not influence conclusions given below than the v2 defect. Indeed, the (s, w value representing dislocation loops is found to be locate The positron affinity is a very useful materials property to judge whether positrons become trapped correctly regarding its wvalue but shifted slightly ins by precipitates. This concept implies an even towards the value of bulk pyrolytic graphite(see distribution of precipitates in a host matrix. Then, a Fig. 3). This could be an indication that in the positron will be trapped by a spherical precipitate if dilatation part of the dislocation loops observed in AI* the difference AA, between the positron affinity of the implanted 6H-Sic(see ref. [9] and references therein) host and the precipitate is positive and the radius of the the positron annihilates preferentially at carbon atoms From Al implantation into 4H-SiC [19], it wa precipitate exceeds a critical radius re given by [20] concluded that excess Si interstitials, being generated in a substitutional process upon annealing, form the (4) (△A4) dislocation loops For the composite, the bulk w value is negligibly different from the corresponding value The proportionality constant has the dimension for 6H-SiC, which is an indication that trapping at nm(ev), AA+ is given in eV and re is given in grain boundaries can be neglected. However, the nm. This 'positron affinity concept'was successfully noticeable shift in S towards the graphite value is a applied to consider, e. g. irradiation-induced precipi- direct confirmation of positron annihilation in graphite tates in reactor pressure vessel steels [22], and cluster- still contained in the composite ing of Ge [16 and B [23 in 6H-Sic due to ion The SPis results are another indication of the plantation and annealing perfectness of the composite in agreement with the Here, the positron affinity of graphite is of interest. findings from XRD described above, and furthermore The application of different calculational methods has a very nice confirmation of a perfectly sintered body been described already in detail elsewhere [5]. Here, we already found by TEM [13]. Now the TEM results are mention that we employ the linear-muffin-tin-orbitalstraight line is obtained in the S–W representation where the endpoints represent the two states itself [17,18]. If (S1, W1) is taken to represent the 6H–SiC bulk, and (S2, W2) to represent the V2 defect, then a straight line connecting both states should contain the (S, W) values of all defects having an open volume less than the V2 defect. Indeed, the (S, W) value representing dislocation loops is found to be located correctly regarding its W value but shifted slightly in S towards the value of bulk pyrolytic graphite (see Fig. 3). This could be an indication that in the dilatation part of the dislocation loops observed in Al+ implanted 6H–SiC (see ref. [9] and references therein) the positron annihilates preferentially at carbon atoms. From Al+ implantation into 4H–SiC [19], it was concluded that excess Si interstitials, being generated in a substitutional process upon annealing, form the dislocation loops. For the composite, the bulk W value is negligibly different from the corresponding value for 6H–SiC, which is an indication that trapping at grain boundaries can be neglected. However, the noticeable shift in S towards the graphite value is a direct confirmation of positron annihilation in graphite still contained in the composite. The SPIS results are another indication of the perfectness of the composite in agreement with the findings from XRD described above, and furthermore a very nice confirmation of a perfectly sintered body already found by TEM [13]. Now the TEM results are confirmed at atomic level by PAS because any possible remaining open volume fraction should be at a lower than in the crystalline 6H–SiC sample. 3.4. Positron affinity The positron affinity A+ as a bulk quantity is defined by [20]: Aþ ¼ m þ mþ ¼ ðF þ FþÞ: (3) Here, F+ and F are the positron and electron work functions, and m and m+ are the electron and positron chemical potentials, respectively. First-principles electronic structure and positron-state calculations for perfect and defected 3C–SiC and 6H–SiC were already calculated by assuming that m corresponds to the top of the valence band [5]. On the other hand, when comparing positron affinities of two materials in contact (SiC and graphite here), one should be aware of actual position of electron chemical potentials (Fermi levels) of both materials (cf. [21]). Neverthe￾less, we adopt here the same approach as in [5] because the actual position of the Fermi level in the SiC composite is unknown. However, this simplifica￾tion does not influence conclusions given below. The positron affinity is a very useful materials property to judge whether positrons become trapped by precipitates. This concept implies an even distribution of precipitates in a host matrix. Then, a positron will be trapped by a spherical precipitate if the difference DA+ between the positron affinity of the host and the precipitate is positive and the radius of the precipitate exceeds a critical radius rc given by [20]: rc ¼ 0:31 ðDAþÞ 1=2 (4) The proportionality constant has the dimension nm(eV)1/2, DA+ is given in eV and rc is given in nm. This ‘positron affinity concept’ was successfully applied to consider, e.g. irradiation-induced precipi￾tates in reactor pressure vessel steels [22], and cluster￾ing of Ge [16] and B [23] in 6H–SiC due to ion implantation and annealing. Here, the positron affinity of graphite is of interest. The application of different calculational methods has been described already in detail elsewhere [5]. Here, we mention that we employ the linear-muffin-tin-orbital G. Brauer et al. / Applied Surface Science 252 (2006) 3342–3351 3347 Fig. 4. Normalized lineshape parameters W/Wb vs. S/Sb plot for different silicon carbide samples, defect states in 6H–SiC and pyrolytic graphite. An untreated Si(1 0 0) sample served as a reference (Sb, Wb) for normalization