Density functional theory study of La${}_2$Ce${}_2$O${}_7$: Disordered fluorite versus pyrochlore structure

The crystal structure of lanthanum cerium oxide (La${}_2$Ce${}_2$O${}_7$) is investigated using ab initio density functional theory calculations. The relative stability of fluorite- and pyrochlorelike structures is studied through comparison of their formation energies. These formation energies show the pyrochlore structure to be favored over the fluorite structure, apparently contradicting the conclusions based on experimental neutron and x-ray diffraction (XRD). By calculating and comparing XRD spectra for a set of differently ordered and random structures, we show that the pyrochlore structure is consistent with diffraction experiments. For these reasons, we suggest the pyrochlore structure as the ground-state crystal structure for La${}_2$Ce${}_2$O${}_7$.

Figure 1

(Color online) Ball and stick representations of (a) the fcc primitive $2\times 2\times 2$ ($p$222) and (b) the cubic ($c$111) CeO${}_2$ fluorite supercells. All the inequivalent Ce (big yellow spheres) and O (small red spheres) atom positions are indicated. The dashed tetrahedron on the cubic cell indicates the surrounding tetrahedron around the oxygen atom 8.

Figure 2

(Color online) Ball and stick representations of the different cation distributions, as constructed from Table  and Fig. 1 or taken from literature: (a) the LZO, (b) the $L$111, (c) the $c$111 $L$$1_0$, and (d) the SQS distribution (Ref. 25). Red, green and yellow spheres show the O, La and Ce positions, respectively.

Figure 3

(Color online) Comparison of calculated XRD images for the disordered fluorite (SQS, red curve at the front) and pyrochlore (LZO 4Ce, green curve in the middle) geometries to the experimental La${}_2$Ce${}_2$O${}_7$ spectrum (black curve at the back) (Ref. 52). The relaxed PBE geometries are used to calculate the XRD spectra. The nine peaks with the highest intensity are indicated with indices 1–9. All spectra are normalized with regard to the peaks with index 1. The inset shows a section of the spectra containing the pyrochlore (311), (331), and (511) peaks. The LZO 4Ce curve was shifted vertically by 1% for clarity.

Figure 4

(Color online) Comparison of the nine high-intensity peaks present in the spectra shown in Fig. 3. Scaling was done with regard to the third peak for each spectrum.

Figure 5

(Color online) Calculated XRD spectra of the $c$111 $L$$1_0$ 2Ce2La and $L$111 3Ce1La $A$ structures. Multiple peak splitting is clearly visible for the high-angle peaks.