Universal Scherrer equation for graphene fragments

By Daniel J. Lim, N. Marks, M. Rowles. Carbon, 2020

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Abstract 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 λ / ( B cos θ ) . 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.

Subfields: Computational Mechanics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/b36ec77a045929761bde6dce7b74f26d7f4bd390