Universal Scherrer equation for graphene fragments

Abstract

© 2020 Elsevier Ltd

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, La. Comparison with the known fragment sizes reveals a strong affine relationship between La and the Scherrer quantity λ/(Bcosθ). 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 La as the square-root of the fragment area. The relationship between observed diffraction peak positions and unit cell parameters is also discussed.