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Tomographic reconstruction of oxygen orbitals in lithium-rich battery materials


The electrification of heavy-duty transport and aviation will require new strategies to increase the energy density of electrode materials1,2. The use of anionic redox represents one possible approach to meeting this ambitious target. However, questions remain regarding the validity of the O2−/O oxygen redox paradigm, and alternative explanations for the origin of the anionic capacity have been proposed3, because the electronic orbitals associated with redox reactions cannot be measured by standard experiments. Here, using high-energy X-ray Compton measurements together with first-principles modelling, we show how the electronic orbital that lies at the heart of the reversible and stable anionic redox activity can be imaged and visualized, and its character and symmetry determined. We find that differential changes in the Compton profile with lithium-ion concentration are sensitive to the phase of the electronic wave function, and carry signatures of electrostatic and covalent bonding effects4. Our study not only provides a picture of the workings of a lithium-rich battery at the atomic scale, but also suggests pathways to improving existing battery materials and designing new ones.

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Fig. 1: Compton profile difference (CPD or ∆J) of LTMO for lithium concentrations of x = 0.8 minus x = 0.4.
Fig. 2: PDOS of Li0.4Ti0.4Mn0.4O2 for the majority-spin electrons near the Fermi level.
Fig. 3: Reconstructed 2D-EMD maps.

Data availability

The experimental data and theoretical simulations that support the findings of this study are available from the corresponding authors upon reasonable request.


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We thank M. Radin for providing feedback on the manuscript; A. Terasaka (Gunma University) for technical support with the Compton scattering experiment; and M. Nakayama (Nagoya Institute of Technology) for sharing insights into COOP analysis. K.S. was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI grants JP15K17873 and JP19K05519. Compton scattering experiments were performed with the approval of the Japan Synchrotron Radiation Research Institute (JASRI; proposals 2017A1122 and 2019B1668). The work at Northeastern University was supported by US Department of Energy (DOE), Office of Science, Basic Energy Sciences grant DE-FG02-07ER46352; and benefited from Northeastern University’s Advanced Scientific Computation Center (ASCC), and the allocation of time at the National Energy Research Scientific Computing Center (NERSC)’s supercomputing center through DOE grant DE-AC02-05CH11231. The work at Carnegie Mellon University was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US DOE through the Advanced Battery Materials Research (BMR) program under contract no. DE-EE0007810.

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Authors and Affiliations



H.H. performed all of the theoretical simulations and analysed the data. K.S., H.S., N.T and Y.S. performed the X-ray Compton scattering experiment and data analyses. N.Y., K.Y., Y.O. and Y.U. synthesized and characterized the materials. H.H. and B.B. wrote the manuscript. V.V. and A.B. contributed to the theory and oversaw the research and writing of the manuscript. All authors were involved in revising the manuscript.

Corresponding authors

Correspondence to Hasnain Hafiz, Arun Bansil or Venkatasubramanian Viswanathan.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks B. L. Ahuja, Stephen Dugdale and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Experimental valence Compton profiles of LixTi0.4Mn0.4O2 with different lithium concentrations.

Lithium concentrations ranged from x = 0 to x = 1.2.

Extended Data Fig. 2 Comparison of experimental CPDs in LTMO with theoretical models and fits.

CPDs are denoted as ∆J. The blue line shows the result of linear combination of atomic oxygen 2p orbitals; the cyan line represents the atomic lithium 2s orbitals; and the yellow line shows a model Coulomb repulsion profile for manganese 3d orbitals (see text). The experimental CPD is the difference in the Compton profiles for lithium concentrations of x = 0.8 minus x = 0.4. The model Coulomb repulsion profile was obtained analytically to take into account the effects of localization of the atomic manganese 3d orbitals using normalized Slater-type orbitals. The inset shows manganese 3d Compton profiles for two different effective values of Zeff. The fitting curve (red) and ∆J are both normalized to one. The experimental error bars were obtained from a statistical analysis of the curves in Extended Data Fig. 1 and have a total length of 2σ.

Extended Data Fig. 3 Spin-dependent PDOS associated with manganese eg, manganese t2g and oxygen p orbitals in LixTi0.4Mn0.4O2 for lithium concentrations of x = 0.4 and x = 0.8.

a, x = 0.4. b, x = 0.8. The vertical dashed lines mark the Fermi energy (EF). Up and down arrows indicate the contributions of spin-up and spin-down, respectively, to the PDOS.

Extended Data Fig. 4 COOP analysis between oxygen 2p and manganese 3d states for a lithium concentration of x = 0.4.

The vertical dashed line marks the Fermi energy (EF). COOP analysis indicates an antibonding character (green shaded area) for localized oxygen 2p states right above the Fermi level, as shown in the PDOS in Fig. 2 and Extended Data Fig. 3a. Here, localized oxygen 2p holes point in the direction of a lithium-atom vacancy along the direction of the Li–O–Li axis.

Extended Data Fig. 5 Fourier transform, B(r), of the CPD.

The reciprocal form factor B(r) was computed for the CPD (black solid line), the fitted curve (red line) and the Coulomb profile (yellow line) shown in Extended Data Fig. 2. The B(r) for experimental Coulomb profile (black dashed line) was obtained by subtracting the B(r) of atomic oxygen 2p (blue line) from the experimental B(r) (black solid line). Agreement between the fitted B(r) (red line) and the experimental B(r) (black solid line) was used to assess the goodness of fit of Extended Data Fig. 2.

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Hafiz, H., Suzuki, K., Barbiellini, B. et al. Tomographic reconstruction of oxygen orbitals in lithium-rich battery materials. Nature 594, 213–216 (2021).

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