In this paper we have addressed thermodynamics of Fe-C nano catalysts with classical molecular dynamics and
quantum mechanical methods. We have introduced a novel approach, called “size-pressure approximation” which
allow an estimation of the effect of particle size on phase boundaries. We show that size-induced nucleation of
cementite Fe3C is responsible for the loss of C solubility in bcc Fe nano-catalysis. The implications of the phenomenon
on low temperature CVD growth of SWCNTs are addressed. Our theoretical modeling is corroborated by the increased
minimum synthesis temperature experimentally observed in SWCNT growth with CVD and very small iron catalysts.