Universal Scherrer equation for graphene fragments

Graphene fragments spanning a wide range of size and shape were studied computationally using the Debye scattering equation. The calculated diffraction patterns were analysed using the Scherrer equation to infer the fragment size, L-a. Comparison with the known fragment sizes reveals a strong affine relationship between L-a and the Scherrer quantity lambda/(Bcos theta). To preserve this relationship, we propose modifying the Scherrer equation to include an empirical additive constant. Our approach solves the well-known problem of size-dependence in the shape factor and yields a universal expression by defining L-a as the square-root of the fragment area. The relationship between observed diffraction peak positions and unit cell parameters is also discussed. (C) 2020 Elsevier Ltd. All rights reserved.