pressure, we refer to this 2D equivalent as the layer modulus (symbol γ ). This property has many analogies in other fields of study such as the "membrane stretching modulus" (also known as the "area-stretching elastic constant") used in the study of lipid bilayer membranes 21 and other soft materials. We use the EOS to extract fit parameters, including the layer modulus, for the monolayer systems of graphene (which we refer to as C) and boronitrene (also know as single-layer boron nitride, which we refer to as BN), and we also include results for Si, Ge, GeC, and SiC in the isostructural honeycomb structure for comparison. We consider four graphene allotropes to test the possibility of 2D phase transitions from graphene. We also consider bilayer, trilayer, and four-layered graphene (henceforth denoted as two-graphene, three-graphene, and four-graphene) to discover if the EOS can indicate any trends. In all cases, the elastic properties are calculated and the EOS is used to predict intrinsic strength.In Sec. II, we present the theoretical concepts and equation of state used to investigate the two-dimensional systems as well as the computational parameters. In Sec. III we apply our methods to various 2D systems, and we present and discuss our findings. Lastly, in Sec. IV, we give our conclusions and suggest possible future work.
Equation (10) for the two-dimensional bulk modulus γ of a general anisotropic medium should be replaced by [1] γ = c 11 c 22 − c 2 12 (c 11 + c 22 − 2c 12). Equation (10) was not used in our paper since all materials described were isotropic and since this expression is correct in the special case of isotropy. Thus, no results have been affected by this finding. We acknowledge Prof. D. Tomanek and Prof. A. Every for pointing out the error.
We perform ab-initio density functional theory calculations to investigate the energetics, electronic and magnetic properties of isolated stoichiometric and non-stoichiometric substitutional Si complexes in a hexagonal boron-nitride monolayer. The Si impurity atoms substituting the boron atom sites Si B giving non-stoichiometric complexes are found to be the most energetically favourable, and are half-metallic and order ferromagnetically in the neutral charge state. We find that the magnetic moments and magnetization energies increase monotonically when Si defects form a cluster. Partial density of states and standard Mulliken population analysis indicate that the half-metallic character and magnetic moments mainly arise from the Si 3p impurity states. The stoichiometric Si complexes are energetically unfavorable and non-magnetic.When charging the energetically favourable non-stoichiometric Si complexes, we find that the formation energies strongly depend on the impurity charge states and Fermi level position. We also find that the magnetic moments and orderings are tunable by charge state modulation q = -2, -1, 0, +1, +2. The induced half-metallic character is lost (retained) when charging isolated (clustered) Si defect(s). This underlines the potential of a Si doped hexagonal boron-nitride monolayer for novel spin-based applications.
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