  Using a motif-network search scheme, we studied the tetrahedral structures of
the dilithium/disodium transition metal orthosilicates A2MSiO4 with A = Li or
Na and M = Mn, Fe or Co. In addition to finding all previously reported
structures, we discovered many other different tetrahedral-network-based
crystal structures which are highly degenerate in energy. These structures can
be classified into structures with 1D, 2D and 3D M-Si-O frameworks. A clear
trend of the structural preference in different systems was revealed and
possible indicators that affect the structure stabilities were introduced. For
the case of Na systems which have been much less investigated in the literature
relative to the Li systems, we predicted their ground state structures and
found evidence for the existence of new structural motifs.
