On the crystal energy and structure of A2TinO2n+1 (A=Li, Na, K) titanates by DFT calculations and neutron diffraction

First-principles quantum-mechanical calculations (CRYSTAL09 code, B3LYP functional) were performed on alkali titanates A2TinO2n+1 with layered structure (n=3,4,6). Monoclinic structural types with unshifted (P21/m) and with shifted (C2/m) layers were considered. Crystal energies and full structural details were obtained for all Li, Na, and K phases. Neutron diffraction data were collected on powder samples of P21/m-Li2Ti3O7 (a=9.3146(3), b=3.7522(1), c=7.5447(3) Å, β=97.611(4)°) and C2/m-K2Ti4O9 (a=18.2578(8), b=3.79160(9), c=12.0242(4) Å, β=106.459(4)°) and their structures were Rietveld-refined. Computed energies show the P21/m arrangement as favoured over the C2/m one for n=3, and the opposite holds for n=6. In the n=4 case the P21/m configuration is predicted to be more stable for Li and Na, and the C2/m one for K titanates. Analysis of Li–O and K–O crystal-chemical environments from experiment and theory shows that the alkali atom bonding is stabilized/destabilized in the different phases consistently with the energy trend. - Graphical abstract: Display Omitted - Highlights: • The P21/m structure-type is found to be more stable for A2Ti3O7 layer titanates. • The C2/m structure-type is found to be more stable for A2Ti6O13 layer titanates. • Tetratitanates are predicted to prefer the P21/m (Li and Na) or C2/m (K) structure. • Li–O and K–O bond distances follow a trend consistent with computed phase energies