Mechanism of Formation of Filaments, Nanotubes, and whiskers carbon nucleus =1.767Jm2 a=0.718Jm metal-carbon particle Figure 2. Form of nucleus of graphite-like carbon(A)and silicon carbide(B) Table 1 represents the terms of Eq. (1)for the nucleation of graphite-like carbon and SiC Where Na is the Avogadro constant, AHi are the enthalpies of formation of corresponding single bonds(M-C, Si-C, C-C, Si-H, C-H), Q is a constant for curved edge of graphite-like nucleus following from the elas city theory, xo and x are the saturated and actual molar content of carbon and or silicon in metal particle, Ai represents the exchange energy of the binary i-j solution, oi is the corresponding specific surface energy, and w is the work of adhesion of metals to C(graphite)and Sic The maximum of AGs as a function of corresponds to the critical size of the nucleus d(AGs/dr=0, from which we easily deduce the equations of rcrit for graphite-like carbon deposits, Eq. (2) △HM-C-AHcc,Q)「RT·h rcrit A 45)w10+(Wwa-20v and for SiC whiskers, Eq (3) 2AHs;-c-AHcH-△Hsi-H h The details of getting these equation were published elsewhere(for carbon deposits see Refs. (1, 11)and for Sic (12) Eqs. (1)and(2)express the dependence of the critical radius on the different reaction parameters. The analysis of the influence of different reaction par- ameters on the critical radius of the carbon nucleus allows us to draw th following conclusions. The radius of critical nucleus decreases with increasing temperature(D), with increasing saturation coefficient of the metal-carbonTable 1 represents the terms of Eq. (1) for the nucleation of graphite-like carbon and SiC. Where NA is the Avogadro constant, DHij are the enthalpies of formation of corresponding single bonds (M –C, Si –C, C –C, Si –H, C –H), Q is a constant for curved edge of graphite-like nucleus following from the elas￾ticity theory, x0 and x are the saturated and actual molar content of carbon and/or silicon in metal particle, lij represents the exchange energy of the binary i–j solution, si is the corresponding specific surface energy, and Wad is the work of adhesion of metals to C (graphite) and SiC. The maximum of DGS as a function of r corresponds to the critical size of the nucleus d(DGS/dr ¼ 0, from which we easily deduce the equations of rcrit for graphite-like carbon deposits, Eq. (2): rcrit ¼ DHM
C
DHC
C 2NA rC
C þ Q 4:5h
RT h VM ln x x0 þ ðWad
2sgraphiteÞ 
1 ð2Þ and for SiC whiskers, Eq. (3): rcrit ¼2DHSi
C
DHC
H
DHSi
H 4rC
CNA h Vmolar
RT ln x x0
C x x0
Si þ X i=j lijxixj ( )þ ð2sSiC
WadÞ " #
1 : ð3Þ The details of getting these equation were published elsewhere (for carbon deposits see Refs. (1, 11) and for SiC (12). Eqs. (1) and (2) express the dependence of the critical radius on the different reaction parameters. The analysis of the influence of different reaction par￾ameters on the critical radius of the carbon nucleus allows us to draw the following conclusions. The radius of critical nucleus decreases with increasing temperature (T), with increasing saturation coefficient of the metal–carbon Figure 2. Form of nucleus of graphite-like carbon (A) and silicon carbide (B). Mechanism of Formation of Filaments, Nanotubes, and Whiskers 125