Research ArticleBATTERIES

Visualizing redox orbitals and their potentials in advanced lithium-ion battery materials using high-resolution x-ray Compton scattering

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Science Advances  23 Aug 2017:
Vol. 3, no. 8, e1700971
DOI: 10.1126/sciadv.1700971


  • Fig. 1 Differences between the Compton profiles of LFP and FePO4, Embedded Image.

    Theoretical results based on three different models of the electronic structure of FePO4 are considered: rigid band model (gold line), rigid octahedron model (purple line), and relaxed octahedron model (green line). The electronic structure and the Compton profile for LFP, Embedded Image remains fixed for all three models, whereas the Compton profiles of FePO4, Embedded Image, are different. The inset shows a sketch of the DOS of LFP and FePO4. During the charge-discharge process, electrons are transferred from the highest occupied d states of LFP (yellow shaded area) to the lowest unoccupied d states of FePO4. Thus, in the rigid band model, FePO4 electronic structure is approximated similarly as LFP, but the Fermi level is adjusted below the highest occupied states as shown by the energy position of the arrow in the DOS of LFP. In the rigid octahedron model, FePO4 experiences the same FeO6 octahedral environment as LFP, whereas in the relaxed octahedron model, FePO4 structure is fully relaxed, which produces a distortion and a smaller volume in FeO6 octahedron. The experimental difference profile (red line) is seen to be well reproduced by the relaxed octahedron model. Pink shading gives the experimental error bars. Effect of the distortion of the FeO6 octahedron in FePO4 is highlighted by considering the distortion profile D(p), which is defined as the difference in Compton profiles between the relaxed (green line) and rigid octahedron (purple line) models.

  • Fig. 2 Kinetic energy ΔK and voltage as a function of Hubbard parameter U.

    The main figure gives the kinetic energy ΔK for several different values of U (red dots; dashed blue line is drawn to connect the dots), where ΔK is computed by taking the second moment of the difference Compton profile ΔJ. Inset shows the average Li insertion voltage as a function of U (gold dots; dashed blue line is drawn to connect the dots), where the voltage is calculated from the total energies of LFP, FePO4, and body-centered cubic lithium, as discussed in the text. The voltage calculated with U = 4.3 eV is 3.48V, which agrees well with the experimental value of 3.5 V.

  • Fig. 3 Momentum maps of the redox orbital.

    The difference of the 2D EMDs of LFP and FePO4 provides a visualization of the wave function of the redox orbital in momentum space for the three models considered in Fig. 1: (A) rigid band model; (B) rigid octahedron model; and (C) relaxed octahedron model. The white rectangular box marks the boundary of the first Brillouin zone. Py and Pz axes are parallel to the [010] and [001] directions, respectively. Amplitudes of the maps in (A) and (B) have been rescaled by factors of 3.3 and 1.7, respectively, to highlight the symmetry of the orbital without the masking effect of a decreasing amplitude due to the delocalization of the state.

  • Fig. 4 Distortion profiles D(p) for various olivine battery materials.

    Distortion profile, D(p), highlights the effect of distortion of the metal-oxygen octahedron. D(p) is defined as the difference in Compton profiles between the relaxed and rigid octahedron models, Embedded Image. Results for MPO4 (M = Mn, Fe, Co, and Ni) are shown. The amplitude of D(p) is seen to increase systematically in going from Ni to Co to Fe to Mn. The increasing amplitude of D(p) is also reflected in a corresponding loss in the redox potential (potential shift) due to distortion of the metal-oxygen octahedron. The inset shows the rigid and relaxed structures of FePO4. The metal-oxygen octahedron FeO6 in the rigid octahedron model is assumed to be the same as that in LFP. In the relaxed octahedron model, the FeO6 octahedron experiences a strong distortion during delithiation and produces a smaller average Fe–O interatomic distance (〈r〉 = 2.06 Å) than that of the rigid structure (〈r〉= 2.15 Å).

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