_{2}O

_{4}[1] and MgFeSiO

_{4}[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 Mg

^{2+}and surrounding oxide anions, however, Mg

^{2+}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 Mg

^{2+}diffusion in solids and gain deeper understanding on Mg

^{2+}dynamics.

From such background, this work focuses on MgZr_{4}(PO_{4})_{6}-based Mg-ion conductors [3], and investigated Mg^{2+} 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-x}Nb_{x})_{4}(PO_{4})_{6} with a conventional solid-state reaction method using MgHPO_{4}·3H_{2}O, ZrO(NO_{3})_{2}·2H_{2}O, Nb_{2}O_{5} and NH_{4}H_{2}PO_{4} 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-x}Nb_{x})_{4}(PO_{4})_{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 *P*2_{1}/*n* which is the same as MgZr_{4}(PO_{4})_{6}. By using the refined unit cell, we constructed a super cell with 276 atoms and then performed DFT-base MD simulation to visualize Mg^{2+} diffusion. As a result, it is indicated that Mg^{2+} 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

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