Molecular dynamics simulations based on an empirical potential energy surface were used to study iron catalyzed nucleation and growth of single-walled carbon nanotubes (SWNTs). The simulations show that SWNTs grow from iron-carbide particles at temperatures between 800 and 1400 K, whereas graphene sheets encapsulate the particle at temperatures below 600 K and a three-dimensional soot-like structure is formed above 1600 K. Nucleation of these carbon (C) structures can be divided into three stages: (i) at short times the FeC particle is not saturated in C and all C atoms are dissolved in the particle; (ii) at intermediate times the FeC Cluster is highly supersaturated in C and carbon strings, polygons and small graphitic islands nucleate on the cluster surface; (iii) at longer times the FeC cluster is supersaturated in C and, depending on the temperature, the graphene sheet, SWNT, or soot-like structure is grown. At low temperatures the kinetic energy is not sufficient to overcome the attractive forces between the particle and the graphitic islands (that are formed in stage ii) and, because these islands cannot lift off the particle, a complete graphene sheet grows around the cluster. At temperatures above 800 K the kinetic energy is sufficiently high to overcome these attractive forces so that the graphitic island lifts off the particle to form a cap. Between 800 and 1400 K theses caps grow into SWNTs, and at temperatures larger than 1600 K the large number of defects in the,growing carbon structure produces a soot-like structure. The calculations also reveal that the growing SWNT maintains an open end on the cluster due to the strong bonding between the open nanotube end atoms and the C, cluster. The number of defects in the SWNT structure can be reduced by lowering the rate of carbon addition to the FeC cluster.