First-principles study of surface properties ofLiFePO4: Surface energy, structure, Wulff shape, and surface redox potential

Using first-principles calculations within the generalized gradient approximation $(\mathrm{GGA})+U$ framework, we investigate several surface properties of olivine structure $\mathrm{Li}\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$. Calculated surface energies and surface redox potentials are found to be very anisotropic. Low-energy surfaces are in the [1 0 0], [0 1 0], [0 1 1], [1 0 1], and [2 0 1] orientations of the orthorhombic structure. We find that the coordination loss of Fe atoms on the surface is energetically more unfavorable than for Li, and generally a low-energy surface has fewer Fe-O bonds affected by the surface cut. Conversely, undercoordinated Li on the surface are somehow beneficial to reduce the energy of a surface except for the twofold coordinated Li. With the calculated surface energies, we provide the thermodynamic equilibrium shape of the $\mathrm{Li}\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$ crystal through a Wulff construction. The two low-energy surfaces (0 1 0) and (2 0 1) dominate in the Wulff shape and make up almost 85% of the surface area. Similar calculations for $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$ indicate a very low energy for the (0 1 0) surface of $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_{4}$. This result suggests that surface chemistry can induce a change in the aspect ratio of the Wulff shape. Surface redox potentials for the extraction and insertion of Li from various surfaces are also investigated in this work. The Li redox potential for the (0 1 0) surface is calculated to be $2.95\phantom{\rule{0.3em}{0ex}}\mathrm{V}$, which is significantly lower than the bulk value of $3.55\phantom{\rule{0.3em}{0ex}}\mathrm{V}$. For several other surfaces the Li extraction potential is above the bulk potential. We also develop a simple model that can be used to predict surface energies based on the change in the coordination of Fe and Li.