The interplay between thermodynamics and kinetics in the solid-state synthesis of layered oxides


In the synthesis of inorganic materials, reactions often yield non-equilibrium kinetic byproducts instead of the thermodynamic equilibrium phase. Understanding the competition between thermodynamics and kinetics is a fundamental step towards the rational synthesis of target materials. Here, we use in situ synchrotron X-ray diffraction to investigate the multistage crystallization pathways of the important two-layer (P2) sodium oxides Na0.67MO2 (M = Co, Mn). We observe a series of fast non-equilibrium phase transformations through metastable three-layer O3, O3′ and P3 phases before formation of the equilibrium two-layer P2 polymorph. We present a theoretical framework to rationalize the observed phase progression, demonstrating that even though P2 is the equilibrium phase, compositionally unconstrained reactions between powder precursors favour the formation of non-equilibrium three-layered intermediates. These insights can guide the choice of precursors and parameters employed in the solid-state synthesis of ceramic materials, and constitutes a step forward in unravelling the complex interplay between thermodynamics and kinetics during materials synthesis.

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Fig. 1: Predicted thermodynamic stability and experimentally observed synthetic accessibility of NaxCoO2 polytypes.
Fig. 2: Solid-state synthesis of P2-Na0.7CoO2 monitored by in situ synchrotron XRD.
Fig. 3: P3 to P2 phase transition.
Fig. 4: Energy cascade and physical model for the solid-state reaction of CoO and Na2O2 to form P2-Na2/3CoO2.
Fig. 5: Reaction energies for the formation of the lowest-energy NaxCoO2 polytype as a function of x.
Fig. 6: Generalization to the NaxMnO2 system of in situ XRD during solid-state synthesis and reaction energy calculations.

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All relevant data within the article are available from the corresponding author on request. Source data for the figures are provided with the paper.


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Funding for this study was provided by the US Department of Energy, Office of Science, Basic Energy Sciences, under contract No. UGA-0-41029-16/ER392000 as a part of the Department of Energy Frontier Research Center for Next Generation of Materials Design: Incorporating Metastability, and supported by the Samsung Advanced Institute of Technology. This work used the 28-ID‐2 (XPD) beamline of the National Synchrotron Light Source II (NSLS-II), a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under contract No. DE‐SC0012704. Work conducted at the Cornell High Energy Synchrotron Source (CHESS) is supported by the National Science Foundation under award No. DMR-1332208. Work at the Advanced Photon Source (APS) at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract No. DE-AC02-06CH11357. The TEM characterizations were performed at the Molecular Foundry, Lawrence Berkeley National Laboratory (LBNL), supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract No. DE-AC02-05CH11231. We acknowledge W. Xu for the assistance at APS and A. Toumar for discussion and support with SCAN calculations.

Author information




W.S. and G.C. initiated and supervised the project. M.B. and J.W. designed the experiments. J.W. conducted synchrotron-based measurements with the help of T.S., M.Z., J.B., F.W. and H.K. M.B. and J.W. performed XRD data analysis and Rietveld refinement. R.J.C. and B.O. conducted DFT and reaction energy calculations and analysed the results with the help of D.K. R.J.C. constructed the finite-temperature phase diagram. P.X. carried out the solid-state nudged elastic band calculation. Y.Z. acquired the TEM and EDS data. Y.W. performed phonon frequency calculations. W.S. conceived and calculated the energy cascade with the help of J.W.. M.B., J.W., W.S. and G.C. wrote the manuscript.

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Correspondence to Wenhao Sun or Gerbrand Ceder.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–17, Notes 1–4 and Table 1.

Source data

Source Data Fig. 1

DFT calculations.

Source Data Fig. 2

XRD dataset, Rietveld refinement results.

Source Data Fig. 3

DSC dataset.

Source Data Fig. 4

DFT calculations, elemental distribution TEM.

Source Data Fig. 5

Reaction energy calculations.

Source Data Fig. 6

Reaction energy calculations.

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Bianchini, M., Wang, J., Clément, R.J. et al. The interplay between thermodynamics and kinetics in the solid-state synthesis of layered oxides. Nat. Mater. (2020).

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