The role of the 2D-to-3D transition in x-ray diffraction analysis of crystallite size

The diffraction behaviour of stacked layers of graphene and hexagonal boron nitride are studied computationally by direct calculation of the diffraction pattern using the Debye scattering equation. Analysis of the position and profile of the diffraction peaks show that while single-layer graphene is unambiguously a 2D material, ordered stacks of three or more layers diffract as bulk material. Following the Scherrer equation, we correlate the known crystallite size with the diffraction peak parameters and observe strong affine relationships which exist separately for single-layer, bi-layer and three or more layer (bulk) structures. We determine a series of expressions to calculate the crystallite size which do not suffer the well-known size-dependence or rely on assumptions about the shape. We present a detailed workflow showing how these expressions can be applied to experimental data. (paper)