First-principles simulations of extended phosphorus oxynitride structures in LiPON glasses

The thin film electrolyte LiPON, having the composition of Li$_{3+x}$PO$_{4-y}$N$_z$ with $x=3z-2y$, was developed at Oak Ridge National Lab in the 1990's for use in solid state batteries and related applications.\footnote{ N. J. Dudney, {\em{Interface}} {\bf{17}}:3, 44 (2008) and listed references.} In an effort to understand and to optimize properties of this electrolyte material, we expanded previous studies of isolated defects in crystalline Li$_3$PO$_4$\footnote{Y. A. Du and N. A. W. Holzwarth, {\em{Phys. Rev. B}} {\bf{78}}, 174301 (2008).} to focus on more complicated phosphate structures based on combinations of tetrahedral P$-$O bonds and bridging P$-$O$-$P bonds. For example, crystalline LiPO$_3$\footnote{E. V. Murashova and N. N. Chudinova, {\em{Cryst. Rept.}} {\bf{46}}, 942 (2001).} and P$_2$O$_5$\footnote{E. H. Arbib and co-workers, {\em{J. Solid State Chem.}} {\bf{127}}, 350 (1996).} are composed of phosphate structures with linear and branched chains, respectively. Both these and related structures derived from substituting O with N and adjusting mobile Li ion concentrations approximate components found in LiPON films.$^{\rm{2}}$ In the simulated structures, we find that N is energetically more stable at bridging bond sites than at tetrahedral sites by 2-3~eV and that the Li ion migration energies are 0.5$-$0.6~eV, similar to values measured in LiPON films.