Structure and electronic properties of cerium orthophosphate: Theory and experiment

Using a combination of density functional theory (DFT) calculations and experiments, we determine the structural and electronic properties of cerium orthophosphate (CePO${}_4$), a promising proton-conducting electrolyte for fuel cell applications. To better account for strongly-localized Ce 4f electrons, we use a DFT $+$ $U$ approach, where the exchange-correlation functional is augmented with an adjustable effective Hubbard-like parameter $U$. We find that the calculated structural properties are in good agreement with x-ray diffraction measurements, largely independent of the value of $U$ used. However, the electronic structure is much more sensitive to $U$, and values of $U$ $=$ 2.5–3 eV for Ce 4$f$ states provide excellent agreement between the calculated density of states and measured photoemission spectra near the valence-band edge, validating the efficacy of a DFT $+$ $U$-based approach for this system. With a judicious choice of $U$ determined from photoemission experiments, this work provides a natural starting point for future studies of charge transport and charged defect formation and migration in this important class of compounds.

Figure 1

The conventional CePO${}_4$ unit cell. The lattice vectors are a, b, and c, while the angle between a and c is $\beta$. The cerium cations are shown in blue, and the tetrahedra are made of orange oxygen atoms and yellow phosphorus atoms. An antiferromagnetic spin ordering of the cerium atoms is indicated with up and down arrows.

Figure 2

The valence and conduction bands for $U$ $=$ 0 and 3; the other values of $U$ follow this trend. The orange is the LDA functional and the blue is the GGA functional. The Fermi energy is set to 0 eV and the orbital assignments at the top of the plot are from the partial DOS (which is not shown).

Figure 3

The band structure for LDA $U$ $=$ 3 eV was calculated along lines between high symmetry points in the first Brillouin zone, which are given in the plot to the left-hand side. High symmetry points provided in reduced coordinates of the primative reciprocal lattice vectors are Γ (0,0,0), $A$ (−0.60,0,0.41), $B$ (0.40,0,0.41), $C$ (−0.40,0,0.59), $M$ (−0.5,0,0.5), $R$ (−0.5,0.5,0.5), $X$ (0.5,0,0.5), $Y$ (0,0.5,0), and $Z$ (0,0,0.5).

Figure 4

(a) The energy difference between the first two valence bands, measured peak to peak, is $2.5\pm 0.2$ eV. (b) The energy difference between these two bands as measured by DFT $+$ $U$ for $U$ $=$ 0–5 eV is plotted for LDA and GGA.

Figure 5

The valence-band photoemission spectra is plotted along with the calculated DOS with Gaussian smearing for the LDA $+$ $U$ (3 eV) plus spin-orbit (SO) coupling. The inset in the upper right-hand side compares the LDA $+$ $U$ and PBE0 near-valence-band edge spectra. The peaks are assigned via the calculated partial DOS, and are supported by known XPS binding energies.