The growth process of single layer graphene with and without substrate is investigated using ab initio, finite temperature molecular dynamic calculations within density functional theory. An understanding of the epitaxial graphene growth mechanisms in the atomic level is provided by exploring the transient stages which occur at the growing edges of graphene. These stages are formation and collapse of large carbon rings together with the formation and healing of Stone-Wales like pentagon-heptagon defects. The activation barriers for the healing of these growth induced defects on various substrates are calculated using the climbing image nudge elastic band method and compared with that of the Stone-Wales defect. It is found that the healing of pentagon-heptagon defects occurring near the edge in the course of growth is much easier than that of Stone-Wales defect. The role of the substrate in the epitaxial growth and in the healing of defects are also investigated in detail, along with the effects of using carbon dimers as the building blocks of graphene growth.
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