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Halogenated argyrodites Li6PS5Br, Li6PS5Cl, and Li6PS5I exhibit large differences in the measured Li ionic conductivities. Crystallographic analysis has shown that these differences may be related to occupations of specific Wyckoff sites in different argyrodite types, but detailed understanding of the relationship between the atomic structure and operating diffusion mechanisms is still lacking. In this work, we employed ab initio molecular dynamics simulations to calculate the Li diffusivity for different argyrodite structure types. Our calculations show that the Li diffusivity does not depend implicitly on the type of halogen but is rather governed by the degree of structural disorder. Assuming disordered structures to arise naturally from the ordered structure type by thermally activated antisite defects, we are able to explain the degree of disorder found for the different types of halogens from the calculated defect formation energies. Comparing the calculated formation energies to the ionic radii of the halogen atoms, we find a strong correlation between the radii and energies required for introducing the antisite defects.