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

Nature Materials volume 19, pages 1088–1095 (2020)Cite this article

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Abstract

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.

References

  1. Ong, S. P., Wang, L., Kang, B. & Ceder, G. Li-Fe-P-O-2 phase diagram from first principles calculations. Chem. Mater. 20, 1798–1807 (2008).

    CAS  Google Scholar 

  2. Andersson, J. O., Helander, T., Hoglund, L. H., Shi, P. F. & Sundman, B. THERMO-CALC & DICTRA, computational tools for materials science. Thermochemistry 26, 273–312 (2002).

    CAS  Google Scholar 

  3. Bianchini, M., Wang, J., Clément, R. & Ceder, G. A first-principles and experimental investigation of nickel solubility into the P2 NaxCoO2 sodium-ion cathode. Adv. Energy Mater. 8, 1801446 (2018).

    Google Scholar 

  4. Narayan, A. et al. Computational and experimental investigation for new transition metal selenides and sulfides: the importance of experimental verification for stability. Phys. Rev. B 94, 045105 (2016).

    Google Scholar 

  5. Sun, W. et al. The thermodynamic scale of inorganic crystalline metastability. Sci. Adv. 2, e1600225 (2016).

    Google Scholar 

  6. Aykol, M., Dwaraknath, S. S., Sun, W. & Persson, K. A. Thermodynamic limit for synthesis of metastable inorganic materials. Sci. Adv. 4, eaaq0148 (2018).

    Google Scholar 

  7. Gopalakrishnan, J. Chimie douce approaches to the synthesis of metastable oxide materials. Chem. Mater. 7, 1265–1275 (1995).

    CAS  Google Scholar 

  8. Stein, A., Keller, S. W. & Mallouk, T. E. Turning down the heat – design and mechanism in solid-state synthesis. Science 259, 1558–1564 (1993).

    CAS  Google Scholar 

  9. Chen, Y., Rangasamy, E., dela Cruz, C. R., Liang, C. & An, K. A study of suppressed formation of low-conductivity phases in doped Li7La3Zr2O12 garnets by in situ neutron diffraction. J. Mater. Chem. A 3, 22868–22876 (2015).

    CAS  Google Scholar 

  10. Wang, L. et al. Structure tracking aided design and synthesis of Li3V2(PO4)3 nanocrystals as high-power cathodes for lithium ion batteries. Chem. Mater. 27, 5712–5718 (2015).

    CAS  Google Scholar 

  11. Eriksson, R. et al. Formation of tavorite-type LiFeSO4F followed by in situ X-ray diffraction. J. Power Sources 298, 363–368 (2015).

    CAS  Google Scholar 

  12. Jensen, K. M. Ø., Tyrsted, C., Bremholm, M. & Iversen, B. B. In situ studies of solvothermal synthesis of energy materials. ChemSusChem 7, 1594–1611 (2014).

    CAS  Google Scholar 

  13. Shoemaker, D. P. et al. In situ studies of a platform for metastable inorganic crystal growth and materials discovery. Proc. Natl Acad. Sci. USA 111, 10922–10927 (2014).

    CAS  Google Scholar 

  14. Jiang, Z., Ramanathan, A. & Shoemaker, D. P. In situ identification of kinetic factors that expedite inorganic crystal formation and discovery. J. Mater. Chem. C. 5, 5709–5717 (2017).

    CAS  Google Scholar 

  15. Martinolich, A. J. & Neilson, J. R. Toward reaction-by-design: achieving kinetic control of solid state chemistry with metathesis. Chem. Mater. 29, 479–489 (2017).

    CAS  Google Scholar 

  16. Chen, B.-R. et al. Understanding crystallization pathways leading to manganese oxide polymorph formation. Nat. Commun. 9, 2553 (2018).

    Google Scholar 

  17. He, H. et al. Combined computational and experimental investigation of the La2CuO4–xSx (0 ≤ x ≤ 4) quaternary system. Proc. Natl Acad. Sci. USA 115, 7890–7895 (2018).

    CAS  Google Scholar 

  18. Kohlmann, H. Looking into the black box of solid-state synthesis. Eur. J. Inorg. Chem. 2019, 4174–4180 (2019).

    CAS  Google Scholar 

  19. Curtarolo, S. et al. The high-throughput highway to computational materials design. Nat. Mater. 12, 191–201 (2013).

    CAS  Google Scholar 

  20. Zunger, A. Inverse design in search of materials with target functionalities. Nat. Rev. Chem. 2, 0121 (2018).

    CAS  Google Scholar 

  21. Jain, A., Shin, Y. & Persson, K. A. Computational predictions of energy materials using density functional theory. Nat. Rev. Mater. 1, 15004 (2016).

    CAS  Google Scholar 

  22. Braconnier, J. J., Delmas, C., Fouassier, C. & Hagenmuller, P. Electrochemical behavior of the phases NaxCoO2. Mater. Res. Bull. 15, 1797–1804 (1980).

    CAS  Google Scholar 

  23. Lee, M. et al. Large enhancement of the thermopower in NaxCoO2 at high Na doping. Nat. Mater. 5, 537–540 (2006).

    CAS  Google Scholar 

  24. Takada, K. et al. Superconductivity in two-dimensional CoO2 layers. Nature 422, 53–55 (2003).

    CAS  Google Scholar 

  25. Delmas, C., Fouassier, C. & Hagenmuller, P. Structural classification and properties of the layered oxides. Phys. B+C. 99, 81–85 (1980).

    CAS  Google Scholar 

  26. Delmas, C., Fouassier, C. & Hagenmuller, P. Relative stability of octahedral and trigonal prismatic coordination in layered alkaline oxides AxMO2 (x less than or equal to 1). Mater. Res. Bull. 11, 1483–1488 (1976).

    CAS  Google Scholar 

  27. Parant, J. P., Olazcuaga, R., Devalette, M., Fouassier, C. & Hagenmuller, P. Sur quelques nouvelles phases de formule NaxMnO2 (x ⩽ 1). J. Solid State Chem. 3, 1–11 (1971).

    CAS  Google Scholar 

  28. Yabuuchi, N., Kubota, K., Dahbi, M. & Komaba, S. Research development on sodium-ion batteries. Chem. Rev. 114, 11636–11682 (2014).

    CAS  Google Scholar 

  29. Mo, Y., Ong, S. P. & Ceder, G. Insights into diffusion mechanisms in P2 layered oxide materials by first-principles calculations. Chem. Mater. 26, 5208–5214 (2014).

    CAS  Google Scholar 

  30. Guo, S. et al. Understanding sodium-ion diffusion in layered P2 and P3 oxides via experiments and first-principles calculations: a bridge between crystal structure and electrochemical performance. NPG Asia Mater. 8, e266 (2016).

    CAS  Google Scholar 

  31. Lei, Y. C., Li, X., Liu, L. & Ceder, G. Synthesis and stoichiometry of different layered sodium cobalt oxides. Chem. Mater. 26, 5288–5296 (2014).

    CAS  Google Scholar 

  32. Bianchini, M., Fauth, F., Hartmann, P., Brezesinky, T. & Janek, J. An in situ structural study on the synthesis and decomposition of LiNiO2. J. Mater. Chem. A 8, 1808–1820 (2020).

    CAS  Google Scholar 

  33. Delmas, C., Braconnier, J.-J., Fouassier, C. & Hagenmuller, P. Electrochemical intercalation of sodium in NaxCoO2 bronzes. Solid State Ion. 3, 165–169 (1981).

    Google Scholar 

  34. Avrami, M. Kinetics of phase change. I General theory. J. Chem. Phys. 7, 1103–1112 (1939).

    CAS  Google Scholar 

  35. Wang, L., Maxisch, T. & Ceder, G. A first-principles approach to studying the thermal stability of oxide cathode materials. Chem. Mater. 19, 543–552 (2007).

    CAS  Google Scholar 

  36. Richards, W. D., Miara, L. J., Wang, Y., Kim, J. C. & Ceder, G. Interface stability in solid-state batteries. Chem. Mater. 28, 266–273 (2016).

    CAS  Google Scholar 

  37. Takeda, Y., Akagi, J., Edagawa, A., Inagaki, M. & Naka, S. A preparation and polymorphic relations of sodium iron-oxide (NaFeO2). Mater. Res. Bull. 15, 1167–1172 (1980).

    CAS  Google Scholar 

  38. Fielden, R. & Obrovac, M. N. Investigation of the NaNixMn(1-x)O(2) (0 <= x <= 1) system for Na-ion battery cathode materials. J. Electrochem. Soc. 162, A453–A459 (2015).

    CAS  Google Scholar 

  39. Akimoto, J. et al. Single-crystal synthesis and structure refinement of Na0.44MnO2. Solid State Phenom. 170, 198–202 (2011).

    CAS  Google Scholar 

  40. Sun, W., Jayaraman, S., Chen, W., Persson, K. A. & Ceder, G. Nucleation of metastable aragonite CaCO3 in seawater. Proc. Natl Acad. Sci. USA 112, 3199–3204 (2015).

    CAS  Google Scholar 

  41. Sun, W., Kitchaev, D. A., Kramer, D. & Ceder, G. Non-equilibrium crystallization pathways of manganese oxides in aqueous solution. Nat. Commun. 10, 573 (2019).

    CAS  Google Scholar 

  42. Navrotsky, A. Nanoscale effects on thermodynamics and phase equilibria in oxide systems. ChemPhysChem 12, 2207–2215 (2011).

    CAS  Google Scholar 

  43. Ma, X. et al. Guiding synthesis of polymorphs of materials using nanometric phase diagrams. J. Am. Chem. Soc. 140, 17290–17296 (2018).

    CAS  Google Scholar 

  44. Sun, J., Ruzsinszky, A. & Perdew, J. P. Strongly constrained and appropriately normed semilocal density functional. Phys. Rev. Lett. 115, 036402 (2015).

    Google Scholar 

  45. Blangero, M. et al. High-temperature phase transition in the three-layered sodium cobaltite P’3-NaxCoO2 (x similar to 0.62). Phys. Rev. B 77, 18 (2008).

    Google Scholar 

  46. Stoyanova, R. et al. Stabilization of over-stoichiometric Mn4+ in layered Na2/3MnO2. J. Solid State Chem. 183, 1372–1379 (2010).

    CAS  Google Scholar 

  47. Kumakura, S., Tahara, Y., Kubota, K., Chihara, K. & Komaba, S. Sodium and manganese stoichiometry of P2-type Na2/3MnO2. Angew. Chem. Int. Ed. 55, 12760–12763 (2016).

    CAS  Google Scholar 

  48. Rodriguez-Carvajal, J. Recent advances in magnetic-structure determination by neutron powder diffraction. Phys. B 192, 55–69 (1993).

    CAS  Google Scholar 

  49. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).

    Google Scholar 

  50. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    CAS  Google Scholar 

  51. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Google Scholar 

  52. Kitchaev, D. A. et al. Energetics of MnO2 polymorphs in density functional theory. Phys. Rev. B 93, 045132 (2016).

  53. Yang, J. H., Kitchaev, D. A. & Ceder, G. Rationalizing accurate structure prediction in the meta-GGA SCAN functional. Phys. Rev. B 100, 035132 (2019).

    CAS  Google Scholar 

  54. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).

    CAS  Google Scholar 

  55. Linstrom, P. J. and Mallard, W. G. NIST Chemistry WebBook NIST Standard Reference Database Number 69 (NIST, 2018); https://doi.org/10.18434/T4D303

  56. Kaufman, J. L. & Van der Ven, A. NaxCoO2 phase stability and hierarchical orderings in the O3/P3 structure family. Phys. Rev. Mater. 3, 015402 (2019).

    CAS  Google Scholar 

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Acknowledgements

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.

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  1. These authors contributed equally: Matteo Bianchini, Jingyang Wang.

Authors and Affiliations

  1. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Matteo Bianchini, Jingyang Wang, Bin Ouyang, Penghao Xiao, Tan Shi, Yaqian Zhang, Haegyeom Kim, Wenhao Sun & Gerbrand Ceder

  2. Department of Materials Science and Engineering, University of California, Berkeley, CA, USA

    Matteo Bianchini, Jingyang Wang, Raphaële J. Clément, Bin Ouyang, Penghao Xiao, Tan Shi, Yaqian Zhang, Haegyeom Kim & Gerbrand Ceder

  3. Battery and Electrochemistry Laboratory, Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, Germany

    Matteo Bianchini

  4. Materials Department, University of California Santa Barbara, Santa Barbara, CA, USA

    Raphaële J. Clément & Daniil Kitchaev

  5. Samsung Research America, Burlington, MA, USA

    Yan Wang

  6. Brookhaven National Laboratory, Upton, NY, USA

    Mingjian Zhang, Jianming Bai & Feng Wang

  7. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, USA

    Wenhao Sun

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Contributions

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. 19, 1088–1095 (2020). https://doi.org/10.1038/s41563-020-0688-6

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