  Compounds crystallizing in the structure of NaZr$_2$(PO$_4$)$_3$ (NZP) are
considered as promising materials for solid state electrolytes in Li-ion
batteries. Using density functional theory (DFT), a systematic computational
screening of 18 NZP compounds, namely LiX$_2$(LO$_4$)$_3$ with X = Ti, V, Fe,
Zr, Nb, Ru, Hf, Ta, Os, and L = P, Mn is performed with respect to their
activation energies for vacancy-mediated Li migration. It is shown how the
different ionic radii of the cationic substitutions influence structural
characteristics such as the octahedron volumes around Li ions on the initial
and transition state sites, which affect the activation energies
(''composition-structure-property'' relationships). The prevalent assumption
that structural bottlenecks formed by triangularly arranged oxygen atoms at a
certain location along the migration path determine the energy barriers for Li
migration is not supported by the DFT results. Instead, the ionic neighborhood
of the migrating ion in the initial and in the transition state needs to be
taken into account to relate the structure to the activation energies. This
conclusion applies to Na containing NZP compounds as well.
