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Understanding the fundamental mechanisms that control van der Waals epitaxy of two-dimensional layered materials is necessary in order to grow large, defect-free crystals. Two-dimensional materials, such as graphene and transition-metal dichalcogenides, are a relatively new class of materials that display unique electronic and optical properties and are promising candidates for continued improvement of microelectronics, improved sensors, and many other applications, some not yet conceived. However, the growth of single-crystal two-dimensional materials is often frustrated by the fact that different in-plane rotational variants nucleate and grow. Their nucleation is a consequence of the weak interaction between the film and substrate that is characteristic of van der Waals epitaxy. It is well known that the nucleation and growth behavior of graphene islands greatly varies with the growth substrate, which is surprising given the weak interaction between the film and substrate. A unique system is graphene on Ir(111) because graphene islands have properties that depend on their in-plane orientation relative to the Ir(111) lattice. Thus, graphene on Ir(111) is a model system to investigate the fundamental factors that control the van der Waals epitaxy of graphene.Experimentally, Ir(111) presents significant advantages for investigation by low-energy electron microscopy, including the quantification of surface adatom concentrations during growth. By using low-energy electron microscopy, the real-time evolution of graphene islands on Ir(111) were investigated during growth and annealing. First, island growth characteristics are compared under identical driving forces in order to isolate the orientation-induced differences. In the temperature range of 750-900 °C, islands rotated relative to the Ir(111) lattice are more faceted than islands aligned with the substrate (R0). Further, the growth velocity of rotated islands depends not only on the C adatom supersaturation but also on the geometry of the island edge. The growth of rotated islands is determined to be kink-nucleation-limited, whereas aligned islands are kink-advancement-limited. These different growth mechanisms are attributed to differences in the graphene edge binding strength to the substrate. By analyzing the growth rate as a function of the C adatom concentration, the size of the attachment species for R0 is determined to be a 4-atom carbon cluster.Next, the evolution of multi-domain graphene islands was monitored during annealing. Three distinct mechanisms were observed in which islands tend to align with the substrate: 1) the simultaneous growth of aligned domains and dissolution of rotated domains, i.e., "ripening", 2) domain boundary motion within islands, and 3) continuous lattice rotation of entire domains. By measuring the relative growth velocity of domains during ripening, the driving force for alignment is estimated to be on the order of 0.1 meV/C atom and increases with rotation angle. A simple model of the atomic-scale corrugation and resulting energy of the graphene sheet as a function of the rotation angle supports the experimental findings. It is proposed that the origin of the preferential alignment is caused by the varying degree to which carbon atoms can attain the preferred distance from the substrate: the graphene bending rigidity prevents the sheet from following the short wavelength corrugations inherent in highly rotated domains. The epitaxial properties observed here are common to graphene on many substrates; thus, it is concluded that the corrugation-induced energy is a significant factor in the resulting epitaxial relationship with the substrate during van der Waals epitaxy. This indicates that in order to control the rotational order in films of two-dimensional materials, growth should occur on substrates where corrugations are induced. Finally, these results show that annealing can still improve rotational order in graphene films on a variety of substrates.

Advances in synthesis are imperative if graphene is to fulfill its scientific and technological potential. Single crystal graphene of is currently available only in the small flakes generated by mechanical exfoliation. Layers of larger size may be grown either by the thermal decomposition of SiC or by chemical vapor deposition on metals. However, as they are currently implemented, these methods yield graphene films of inferior quality. Thus the requirement for wafer-scale, high-quality graphene films remains unmet. This dissertation addresses this issue by examining graphene growth on metal surfaces. Through a survey of the fundamental underlying processes, it provides guidance for improving the quality of the resulting graphene films.Graphene was grown on Cu(100), Cu(111), and Au(111) by physical vapor deposition of elemental C. The nucleation and growth behaviors of graphene were evaluated by low-energy electron microscopy. Graphene tends to nucleate heterogeneously at surface imperfections although it also does so homogeneously on Cu(111) and Au(111). Graphene growing on Cu(100) is governed by the attachment kinetics of C at the propagating crystal front. The resulting angularly dependent growth rate sculpts individual crystals into elongated lobes. In contrast, graphene growth on both Cu(111) and Au(111) is surface diffusion limited. This yields ramified, dendritic graphene islands.Graphene films grown on Cu(100) contain significant rotational disorder. This disorder is partially attributable to the symmetry mismatch between film and substrate. The common symmetry between graphene and Cu(111) contributes to a significant reduction in disorder in films grown on this surface. Most graphene domains occupy a ~6º arc of orientations. On Au(111) the vast majority of graphene domains are locked into alignment with the substrate surface. The extraordinary extent of their orientational homogeneity is such that the resulting graphene film is a quasi-single crystal. The findings presented illustrate how metal species and crystal symmetry influence the structural properties of monolayer graphene. The selection of an optimal substrate for graphene growth can significantly reduce crystalline disorder in the resulting film.