The magnesium secondary battery has drawn much attention as a post lithium-ion secondary battery at recent years because of the higher theoretical volumetric energy density. Similarly to the lithium-ion battery, inorganic oxides such as MgCo₂O₄ [1] and MgFeSiO₄ [2] can be regarded as one of the most promising candidates for a cathode material of the magnesium secondary battery. Due to a strong electrostatic interaction between Mg²⁺ and surrounding oxide anions, however, Mg²⁺ diffusion is deteriorated significantly in oxides and thus the battery performance is very low generally at room temperature. In order to overcome the problem, we have to carry out a systematic study on Mg²⁺ diffusion in solids and gain deeper understanding on Mg²⁺ dynamics.

      From such background, this work focuses on MgZr₄(PO₄)₆-based Mg-ion conductors [3], and investigated Mg²⁺ behaviors in the crystal by means of a combination of the density functional theory (DFT) and the reverse Monte Carlo (RMC) modelling using synchrotron X-ray total scatterings.

      We synthesized Mg_1-2x(Zr_1-xNb_x)₄(PO₄)₆ with a conventional solid-state reaction method using MgHPO₄·3H₂O, ZrO(NO₃)₂·2H₂O, Nb₂O₅ and NH₄H₂PO₄ as starting materials. In the sintering process, we performed the spark plasma sintering (SPS: LABOX-315, Sinter Land Inc.) in order to prepare dense ceramics of the samples for electrical conductivity measurements. For refinements of crystal structures (average structures) of the samples, synchrotron X-ray Bragg profiles were recorded at BL19B2 installed at SPring-8, Japan, and then analyzed by the Rietveld and maximum-entropy method (MEM) techniques. From the refined unit cells, we constructed super cells comprised of 276 atoms or above, and Mg-ion distributions were determined experimentally by the RMC simulations for polycrystalline materials [4, 5] using the Bragg profiles and X-ray structure factors S(Q) simultaneously. The S(Q) were measured with BL04B2 at SPring-8, Japan, and then degraded by convolutions considering the simulation box sizes.

      As a theoretical approach, we performed the DFT calculations and the DFT-based molecular dynamic (MD) simulations with the CP2K program which combines the localized Gaussian basis set and plane waves for a dual GPW basis set. As the exchange-correlation energy functional, the generalized gradient approximation of PBE was utilized. In the DFT-based MD simulation, the NVT ensemble was adopted, and the temperature was controlled with a CSVR thermostat. Initial cells for these calculations were constructed on the basis of the average structures or the atomic-configuration snapshots obtained by the RMC modelling.

      From preliminary laboratorial X-ray diffraction measurements, it is confirmed that Mg_1-2x(Zr_1-xNb_x)₄(PO₄)₆ can be synthesized successfully at least within the Nb-content range of x=0~0.25. The Rietveld analysis using synchrotron X-ray data reveals that the Nb-substituted samples have a monoclinic average structure with a space group of P2₁/n which is the same as MgZr₄(PO₄)₆. By using the refined unit cell, we constructed a super cell with 276 atoms and then performed DFT-base MD simulation to visualize Mg²⁺ diffusion. As a result, it is indicated that Mg²⁺ at an experimentally-determined crystallographic site with five-fold coordination migrates via another site. It is also found that a triangle formed by three oxide ions becomes a bottle neck for the migration. Such a diffusion pathway is supported by a bond-valence-sum (BVS) mapping using an atomic configuration relaxed energetically by the DFT.

Acknowledgment

      This work was financially supported in part by the ALCA-SPRING project.

References

[1] T. Ichitsubo, T. Adachi, S. Yagi, T. Doi, J. Mater. Chem., 21, 11764 (2011).

[2] Y. Orikasa, T. Masese, Y. Koyama, T. Mori, M. Hattori, K. Yamamoto, T. Okado, Z.-D. Huang, T. Minato, C. Tassel, J. Kim, Y. Kobayashi, T. Abe, H. Kageyama, Y. Uchimoto, Sci. Rep., 4, 5622 (2014).

[3] N. Imanaka, Y. Okazaki, G. Adachi, Electrochem. Solid-State Lett., 3, 327 (2000).

[4] M. G. Tucker, D. A. Keen, M. T. Dove, A. L. Goodwin, Q. Hui, J. Phys.: Condens. Matter, 19, 335218 (2007).

[5] N. Kitamura, J. Ceram. Soc. Japan, 123, 637 (2015).