where lm are combinations of l and m for spherical harmonic functions with integer l and m for the degree and order of the harmonic; Y lm (θ, ϕ) can be calculated from the coordinated O positions in polar coordinates (θ and ϕ) for the coordination system with the RE at the origin. The parameter q l can be made rotationally invariant by summing m for each RE coordination structure. The coefficients of the spherical harmonics were considered up to l = 6. This parameter correlates with the electric-field gradient of the central ion, and it is known as the quadrupolar coupling constant obtained by solid-state NMR experiments. Voronoi tessellation analysis was applied to each RE coordination structure to establish the local atomic arrangements in the amorphous materials. The Voronoi cells were made from Voronoi nodes (oxygen positions) for each RE coordination structure; the Voronoi cell volume (V vol ) and indices (V p ) represent the topology information of the Voronoi polyhedron.