Grain boundaries (GBs) in graphene are stable strings of pentagon-heptagon dislocations. The GBs have been believed to favor an alignment of dislocations, but increasing number of experiments reveal diversely sinuous GB structures whose origins have long been elusive. Based on dislocation theory and first-principles calculations, an extensive analysis of the graphene GBs is conducted and it is revealed that the sinuous GB structures, albeit being longer than the straight forms, can be energetically optimal once the global GB line cannot bisect the tilt angle. The unusually favorable sinuous GBs can actually decompose into a series of well-defined bisector segments that effectively relieve the in-plane stress of edge dislocations, and the established atomic structures closely resemble recent experimental images of typical GBs. In contrast to previously used models, the sinuous GBs show improved mechanical properties and are distinguished by a sizable electronic transport gap, which may open potential applications of polycrystalline graphene in functional devices.

Buckling nanopatterns of monoatomic layer 2D materials on metal substrates attract significant attention due to their rich interface morphology affecting electronic applications. An experimental–theoretical study of a 2D boron–nitrogen–carbon (B _{x /2}N _{x /2}C_1−x ) alloy on a Ru(0001) surface is conducted and a profound relation between the composition x and the degree of buckling is discovered. Experimentally, real carbon–boron–nitrogen alloys on the Ru(0001) surface are demonstrated and various morphologies of pure and mixed compounds are shown. Density functional theory calculations are further carried out using the supercells of graphene, hexagonal boron nitride (h-BN), and random BNC on Ru(0001), as well as Monte Carlo simulations for elucidating the kinetics of their growth. The results show that unlike pure compounds (h-BN or C), the carbon–boron–nitrogen mix on Ru(0001) mostly exists in an uncorrugated form, thus greatly improving the interface contact. The likely cause of the diminished corrugation is a softening of bond angular interactions in the alloy relative to the pure phases.

Two-dimensional (2D) materials, such as graphene and boron nitride, have specific lattice structures independent of external conditions. In contrast, the structure of 2D boron sensitively depends on metal substrate, as we show herein using the cluster expansion method and a newly developed surface structure-search method, both based on first-principles calculations. The preferred 2D boron on weaker interacting Au is nonplanar with significant buckling and numerous polymorphs as in vacuum, whereas on more reactive Ag, Cu, and Ni, the polymorphic energy degeneracy is lifted and a particular planar structure is found to be most stable. We also show that a layer composed of icosahedral B₁₂ is unfavorable on Cu and Ni but unexpectedly becomes a possible minimum on Au and Ag. The substrate-dependent 2D boron choices originate from a competition between the strain energy of buckling and chemical energy of electronic hybridization between boron and metal.

Two-dimensional (2D) materials, such as graphene and boron nitride, have specific lattice structures independent of external conditions. In contrast, the structure of 2D boron sensitively depends on metal substrate, as we show herein using the cluster expansion method and a newly developed surface structure-search method, both based on first-principles calculations. The preferred 2D boron on weaker interacting Au is nonplanar with significant buckling and numerous polymorphs as in vacuum, whereas on more reactive Ag, Cu, and Ni, the polymorphic energy degeneracy is lifted and a particular planar structure is found to be most stable. We also show that a layer composed of icosahedral B₁₂ is unfavorable on Cu and Ni but unexpectedly becomes a possible minimum on Au and Ag. The substrate-dependent 2D boron choices originate from a competition between the strain energy of buckling and chemical energy of electronic hybridization between boron and metal.

Bi- and trilayer graphene have attracted intensive interest due to their rich electronic and optical properties, which are dependent on interlayer rotations. However, the synthesis of high-quality large-size bi- and trilayer graphene single crystals still remains a challenge. Here, the synthesis of 100 μm pyramid-like hexagonal bi- and trilayer graphene single-crystal domains on Cu foils using chemical vapor deposition is reported. The as-produced graphene domains show almost exclusively either 0° or 30° interlayer rotations. Raman spectroscopy, transmission electron microscopy, and Fourier-transformed infrared spectroscopy were used to demonstrate that bilayer graphene domains with 0° interlayer stacking angles were Bernal stacked. Based on first-principle calculations, it is proposed that rotations originate from the graphene nucleation at the Cu step, which explains the origin of the interlayer rotations and agrees well with the experimental observations.

Recent research progress in nanostructured carbon has built upon and yet advanced far from the studies of more conventional carbon forms such as diamond, graphite, and perhaps coals. To some extent, the great attention to nano-carbons has been ignited by the discovery of the structurally least obvious, counterintuitive, small strained fullerene cages. Carbon nanotubes, discovered soon thereafter, and recently, the great interest in graphene, ignited by its extraordinary physics, are all interconnected in a blend of cross-fertilizing fields. Here we review the theoretical and computational models development in our group at Rice University, towards understanding the key structures and behaviors in the immense diversity of carbon allotropes. Our particular emphasis is on the role of certain transcending concepts (like elastic instabilities, dislocations, edges, etc.) which serve so well across the scales and for chemically various compositions.