Comparison of the electronic structures of four crystalline phases of $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$

$\mathrm{Li}\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$ in the olivine structure is a promising cathode material for Li ion batteries. During normal battery operation, an olivine form of $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$ is produced. In addition to the olivine form, $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$ is known to form in a quartzlike structure, a high pressure $\mathrm{Cr}\mathrm{V}{\mathrm{O}}_4$-like structure, and a monoclinic structure. We report the results of a detailed density functional study of the electronic structures and total energies of these four crystalline structures of $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$. Partial density of states analysis of the four materials finds them all to be characterized by strong hybridization between the Fe and O contributions throughout their upper valence bands, consistent with recent x-ray spectroscopy studies of olivine $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$. Results obtained using the local density approximation for the exchange-correlation functional find the olivine structure to be more stable than the quartzlike structure by $0.1\mathrm{eV}$, which is in good agreement with recent calorimetry experiments.

Figure 1

Relative total energy versus the lattice constant of ${\mathrm{Li}}_2\mathrm{O}$ in the fluorite structure obtained with the PWSCF (Ref. 18) PAW (Ref. 14) and LAPW (Ref. 20) computer codes. The set of curves indicated with the lighter lines and filled symbols with smaller equilibrium lattice constant was obtained with the LDA (Ref. 10) exchange-correlation form, while the other set of curves was obtained with the GGA (Ref. 11) exchange-correlation form.

Figure 2

Relative total energy versus lattice of FeO assuming a ferromagnetic NaCl structure, using the same conventions, as shown in Fig. 1.

Figure 3

Relative total energy versus bond length of a hypothetical neutral molecule of $\mathrm{P}{\mathrm{O}}_4$ assumed to have exact tetrahedral symmetry, using the same conventions, as shown in Fig. 1.

Figure 4

(Color online) XCRYSDEN (Ref. 25) drawing of the olivine crystal structure. Fe, P, and O spheres are represented with spheres of decreasing size, with online colors red, yellow, and blue, respectively.

Figure 5

(Color online) Quartz crystal structure, using the same convention, as in Fig. 4.

Figure 6

(Color online) $\mathrm{Cr}\mathrm{V}{\mathrm{O}}_4$ crystal structure, using the same convention, as in Fig. 4.

Figure 7

(Color online) Monoclinic crystal structure, using the same convention, as in Fig. 4.

Figure 8

(Color online) Partial densities of states for $\mathrm{Fe}\mathrm{P}{\mathrm{O}}_4$ in the four different crystalline forms, comparing LDA (left) and GGA (right) results calculated using Eq. (2), plotting the majority and minority spin contributions upward and downward along the vertical axis, respectively. The zero of energy is taken to be the Fermi level.