Hidden chemical order in disordered Ba7Nb4MoO20 revealed by resonant X-ray diffraction and solid-state NMR

The chemical order and disorder of solids have a decisive influence on the material properties. There are numerous materials exhibiting chemical order/disorder of atoms with similar X-ray atomic scattering factors and similar neutron scattering lengths. It is difficult to investigate such order/disorder hidden in the data obtained from conventional diffraction methods. Herein, we quantitatively determined the Mo/Nb order in the high ion conductor Ba7Nb4MoO20 by a technique combining resonant X-ray diffraction, solid-state nuclear magnetic resonance (NMR) and first-principle calculations. NMR provided direct evidence that Mo atoms occupy only the M2 site near the intrinsically oxygen-deficient ion-conducting layer. Resonant X-ray diffraction determined the occupancy factors of Mo atoms at the M2 and other sites to be 0.50 and 0.00, respectively. These findings provide a basis for the development of ion conductors. This combined technique would open a new avenue for in-depth investigation of the hidden chemical order/disorder in materials.


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Supplementary Figure 11. TG-MS (thermogravimetric-mass spectroscopic) data of Ba7Nb4MoO20·0.15 H2O measured on heating at a rate of 20 K min -1 under dry He flow. Blue, red and orange lines denote the intensities of H2O (m/z = 18), O2 (m/z = 32) and CO2 (m/z = 44) molecules. The blue and orange dashed lines are a guide to the eye, which shows possible baselines of MS intensities. Upon heating, the weight of the sample decreases between room temperature and 670 ºC. MS measurements confirmed that the released gas between 294 and 673 K is mainly H2O molecules. The water content x in the bulk crystal Ba7Nb4MoO20+xH2x (= Ba7Nb4MoO20·x H2O) was estimated as follows. Assuming that there is no water (x = 0) at 1073 K and that weight loss is due to only dehydration, we obtain the water content x = 0.25 at room temperature. Since the CO2 desorption is observed at around and above 673 K, we can assume that there is no water (x = 0) at 673 K. In this case, assuming that the weight loss from 373 to 673 K is ascribed to only water desorption from the bulk, we obtain bulk water content x = 0.13. Therefore, the bulk water content is ranges from x = 0.13 to 0.25, which is consistent with the calculated water content x = 0.151(5) using the refined occupancy factors at 30 K.
p. 13 The energy barriers for proton migration Eb/H were also estimated using the bond-valence method.
The Eb/H along the c axis in Mo-ordered Ba7Nb4MoO20·0.15 H2O was slightly higher than that in virtual Mo-disordered Ba7Nb4MoO20·0.15 H2O (Supplementary Table 14). Figure 14. The bottlenecks for oxide-ion migration along c axis in the cases of a all Mo atoms in the M2 sites (ordered Ba7Nb4MoO20) and b occupationally disordered Ba7Nb4MoO20. The bottleneck (critical radius) for oxide-ion migration along the c axis in the ordered Ba7Nb4MoO20 0.9017(5) Å is smaller than that in the disordered Ba7Nb4MoO20 0.9052 (5)  24.06 7 a ICSD code of the crystal structure data used as the initial structure before the geometry optimizations. p. 20

Supplementary
Supplementary Table 4. 93 Nb NMR parameters and probable assignment of the signals to the sites of Ba7Nb4MoO20・0.15 H2O.  [36][37][38]. Because it is difficult to determine C Q and η for each peak with unclear shape probably due to the structural disorder, 39 P Q value was calculated from the positions of the experimental resonances (δ F1 and δ F2 ) in the F1 and F2 dimensions of the 3QMAS spectrum (Fig. 3a).

DFT-calculated Experimental
e Experimental |P Q | was estimated by the following equation: where 0 4 is Larmor frequency and I (= 9/2) is the nuclear spin. 36,[40][41][42] p. 21 Supplementary Table 5. Wavelengths and resonant scattering factors used in the Rietveld analyses of the RXRD data.
Using the data from XANES spectrum (Supplementary Figure 8) Using theoretical values 43,44 Beamline Wavelength  U iso (Xn) Isotropic atomic displacement parameter of X atom at the Xn site. Linear constraints in the Rietveld analysis: Reliability factors: R wp = 6.732%, R p = 4.503%, R B = 3.874%, R F = 2.235%. Goodness of Fit GoF = 65.5773 a Atomic coordinates of Oi (i = 1-5) atoms were fixed to those from ND analysis at 300 K. b z coordinate of Nb4 atom was fixed to those from a preliminary analysis.
c Occupational parameters of O5 and H atom were fixed to those from ND analysis at 300 K (   p. 26 Supplementary Table 11 Total energies of (Ba7Nb4MoO20)2 (2×1×1 cell) with different arrangements of the Nb and Mo atoms (Supplementary Figure 6), which were obtained by DFT calculations. The total energies for the models where Mo atoms are located only at the M2 site are a little lower than those for other models, which suggests that the Mo chemical order at the M2 site is energetically favorable.

Model
Mo arrangement Relative energy (meV per atom) (1) Mo atoms in only M2 site +1.68 (2) Mo atoms in only M2 site +1.45 (3) Mo atoms in only M2 site 0.00 (4) Mo atoms in only M1 site +29.96 (5) Mo atoms in M1 and M2 sites +12.50 (6) Mo atoms in only M3 site +17.94 Eb/O in the ab plane is much lower than that along c axis, which indicates two-dimensional oxide-ion diffusion ( Supplementary Fig. 13 The occupancy factors of atom X at site s g(X; s) of Ba7Nb4MoO20·0.15 H2O were refined in preliminary Rietveld analyses using neutron diffraction (ND) data at 300 K and conventional synchrotron X-ray diffraction (SXRD) data at 297 K with 0.6994806(5) Å X-ray far from the Nb K edge as follows.