Mechanism of Sodium-Ion Diffusion in Alluaudite-Type Na5Sc(MoO4

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C: Energy Conversion and Storage; Energy and Charge Transport

Mechanism of Sodium-Ion Diffusion in Alluaudite-Type NaSc(MoO) From NMR Experiment and ab initio Calculations 5

4

4

Nadezhda I. Medvedeva, Anton L. Buzlukov, Alexander V. Skachkov, Aleksandra A. Savina, Vladimir A. Morozov, Yana V. Baklanova, Irina E. Animitsa, Elena G. Khaikina, Tatiana A. Denisova, and Sergey F. Solodovnikov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11654 • Publication Date (Web): 05 Feb 2019 Downloaded from http://pubs.acs.org on February 5, 2019

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The Journal of Physical Chemistry

Mechanism of Sodium-Ion Diffusion in AlluauditeType Na5Sc(MoO4)4 from NMR Experiment and Ab Initio Calculations Nadezhda I. Medvedeva1*, Anton L. Buzlukov2, Alexander V. Skachkov1, Aleksandra A. Savina3,4, Vladimir A. Morozov5, Yana V. Baklanova1, Irina E. Animitsa6, Elena G. Khaikina5, Tatiana A. Denisova1 and Sergey F. Solodovnikov7

1 Institute

of Solid State Chemistry, Russian Academy of Sciences, 620990 Ekaterinburg, Russia

2

Institute of Metal Physics, Russian Academy of Sciences, 620137 Ekaterinburg, Russia

3

Skolkovo Institute of Science and Technology, 121205 Moscow, Russia

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Baikal Institute of Nature Management, Russian Academy of Sciences, 670047, UlanUde, Russia

5

Department of Chemistry, Moscow State University, 119899, Moscow, Russia

6

7

Ural Federal University, 620002 Ekaterinburg, Russia

Nikolaev Institute of Inorganic Chemistry, Russian Academy of Sciences, 630090, Novosibirsk, Russia

ABSTRACT

The crystal structure, electronic properties and sodium diffusion mechanism in Na5Sc(MoO4)4 were investigated using the powder X-ray diffraction (PXRD), nuclear magnetic resonance (NMR) and electrical conductivity measurements, as well as ab

initio calculations. Na5Sc(MoO4)4 belongs to the family of alluaudite-type oxides NaxMy(AO4)3 (M = In, Sc, Mg, Cd, Zn, Mn, Fe, Co, Ni; A = Mo, W, P, As, S), which are now considered

as promising materials for sodium-ion batteries. Our results

demonstrate a considerable difference in the mechanism of Na+ ion transport in 2 ACS Paragon Plus Environment

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Na5Sc(MoO4)4 and in previously studied alluaudite oxides, where one-dimensional sodium diffusion was suggested to occur through channels along the c-axis. The Na+ motion in Na5Sc(MoO4)4 is found to be rather two-dimensional occurring along in the bcplane. We believe that filling of the M- sublattice plays a key role in the mechanism of Na+ ion diffusion in alluaudite compounds. In particular, in Na5Sc(MoO4)4 characterized by a low Sc-occupancy of the M- sublattice, the sodium ions located far from scandium are the first to be activated with increasing temperature; and the activation energy for their jumps, Ea ≤ 0.3 eV, has one of the lowest values among Na-conductive materials.

*Corresponding author: Nadezhda I. Medvedeva, e-mail [email protected]

Phone

+7(912)2126529



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1. INTRODUCTION

Recently, sodium-ion batteries (SIB) have attracted considerable interest as a promising alternative to expensive lithium-ion batteries (LIB), and much attention has been paid to sodium-based electrolytes, cathodes and anodes.1,2,3 Along with structures similar to LIB materials (layered AMO2 and olivine AMPO4), the phosphates and sulfates having the NASICON structure (Na3Zr2Si2PO12)1,2,4 and the structure of alluaudite (Na, Ca)(Fe, Mn, Mg)(PO4)32,5 are currently considered as the most promising materials. Among these polyanionic oxides, there are compounds characterized by high operating voltages, high ionic conductivity, improved capacity and good cyclability. The highest redox potential (3.8 V) and energy density (>540 W∙h∙kg−1) along with a good cyclability were

found

in

alluaudite

Na2+2xFe2−x(SO4)3.5

The

double

molybdate

Na2.67Mn1.67(MoO4)3, which also belongs to the alluaudite family Na42xM2+1+x(MoO4)3 (M = Mg, Mn, Co, Ni, Cu, Zn, Cd)6–8, was found recently to exhibit promising electrochemical properties.6 The ionic conductivity of these compounds (>10-3 S·cm–1 at 673–773 K, Еа = 0.5–0.6 eV)7,8 is comparable to that of Na2+2xFe2-x(SO4)39 and


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exceeds the corresponding values of isostructural orthophosphates Na2M3(PO4)3 (M3 = GaMn2, GaCd2, InMn2 and FeMnCd) having  ~ 10–5 S·cm–1 at 673 K and

Еа = 0.7–0.8 eV.10 Besides the above-mentioned compounds, alluaudite double molybdates of trivalent metals Na5R(MoO4)4 (R = Sc, In) and Na9R(MoO4)6 (R = Fe, Al, Sc)11–16 are also known as good sodium conductors. Most of the studies of alluaudite molybdates have been devoted to their synthesis, crystal structure refinement and electrophysical properties.6–8,11–15,17–21 Much less consideration has been given to sodium transport mechanisms. Only recently, a microscopic mechanism of Na-ion diffusion was studied for Na2+2xFe2–x(SO4)3, where the energy barriers were estimated for sodium-ion migration between different structural sites. From the results of ab initio calculations and

23Na

NMR experiments it was

concluded that sodium migration occurs through 1D channels formed by Na sites along the c-axis.2,5,10,22,23 However, it was assumed22 that such one-dimensional paths are highly vulnerable to blocking with structural defects, and the cross-linking of channels providing 2D ion transport may contribute to a higher level of migration. Based on the



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local structure models, it was suggested that this cross-linking can be achieved either through iron deficiency or the formation of Na/Fe anti-site defects.22 In this article we present the results of a detailed study of sodium diffusion mechanisms in the alluaudite molybdate Na5Sc(MoO4)4. Unlike Na2+2xFe2–x(SO4)3, it contains no paramagnetic ions that make the analysis of NMR spectra more reliable. Moreover, in contrast to Na2+2xFe2-x(SO4)3, where the M-sublattice is filled mainly by Fe2+, the crystal structure of Na5Sc(MoO4)4 implies that two thirds of these sites are occupied by Na+ ions.12 Thus, a considerable difference in the mechanisms and/or parameters of sodium diffusion can be expected. We used a combination of powder X-ray diffraction (PXRD), nuclear magnetic resonance (NMR) and electrical conductivity measurements along with ab initio calculations to study the crystal structure, sodium conductivity and the diffusion mechanism. The DFT calculations of the electric field gradient (EFG) tensors helped us to attribute the observed

23Na

NMR signals to the distinct Na sites. To make

conclusions on the sodium transport, we compared the temperature behavior of the 23Na

NMR spectra and migration energies for different pathways, which were estimated 6 ACS Paragon Plus Environment

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with the nudged elastic band (NEB) method. Such comprehensive approach is regarded to be a powerful way of studying the mechanisms of ion diffusion.16, 24–25 2. DETAILS OF EXPERIMENT AND CALCULATIONS 2.1. Materials and Sample Preparation The double molybdate Na5Sc(MoO4)4 was synthesized by annealing of the stoichiometric mixtures of Na2MoO4 and Sc2(MoO4)3 at 823–843 K for 80 h with intermittent grinding every 15 h and slow cooling in the furnace from the annealing temperature to room temperature. The PXRD patterns of the prepared compound do not contain any reflections of the parent or foreign phases, and all the diffraction peaks match well with monoclinic Na5Sc(MoO4)4.11,12 This molybdate was found to melt incongruently at 911 K. A stoichiometric mixture of Sc2O3 (purity ≥ 99.9%) and MoO3 (≥ 99.5%) was used for the synthesis of Sc2(MoO4)3 at 723–973 K for 80 h. Anhydrous Na2MoO4 was obtained by calcination of the corresponding crystalline dihydrate (≥ 99.5%) at 823–873 K. The PXRD patterns of the prepared Sc2(MoO4)3 and Na2MoO4 were verified using the ICDD PDF-2 Data Base (2016) and they do not contain any reflections of the initial phases. 7 ACS Paragon Plus Environment


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2.2. PXRD and DTA characterizations The PXRD patterns of Na5Sc(MoO4)4 were obtained with the use of a Huber G670 Guinier

diffractometer

(CoKα1

radiation,

λ

=

1.78892

Å,

curved

Ge(111)

monochromator, transmission geometry, image plate detector). The PXRD data were collected at RT over the 5°–100° 2θ range with a step of 0.005° (2θ) and a constant counting time of 10 s. The Rietveld refinements were performed with the JANA2006 software.26 The illustrations were produced with this package and the VESTA program.27 The thermoanalytical studies were carried out on a Setsys Evolution (Setaram) thermal analyzer in air in the temperature range 300–1050 K with a heating rate of 5°/min. 2.3. Ab initio calculations The density functional theory (DFT) calculations were performed using the projectoraugmented wave (PAW) method as implemented in the Vienna Ab Initio Simulation Package (VASP)28,29 and the Perdew–Burke-Ernzerhof (PBE)30 generalized-gradient approximation (GGA) for potentials. The Plane-wave cutoff energy was set to 400 eV for all the calculations with a convergence criterion for the total energy of 0.01 meV. For 8 ACS Paragon Plus Environment

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Brillouin-zone sampling, we used the Monkhorst-Pack scheme31 with a mesh of 2×2×4 irreducible k-points. For the calculation of the electric field gradient tensor within the PAW method, we employed the approach described in Ref. [32]. As calculations of the EFG tensor require a very high accuracy, we included the semi-core Na2p6 states (Na atom was described with a 1s22s2 core). Indeed, as we obtained previously16, the pseudopotentials with the semi-core Na2p6 states give a twofold increase in the magnitude of EFG at the Na sites and provide a better agreement with the quadrupole frequencies obtained from NMR experiment. The initial structural data for the ab initio calculations were taken from experiment. They were relaxed with respect to atomic positions using a conjugate gradient algorithm until the forces on all unconstrained atoms were less than 0.01 eV/Å. The lattice parameters were fixed at the experimental values. The ion diffusion barriers for sodium were calculated using the nudged elastic band (NEB) method. The alluaudite-type compounds possess a positional disorder for the metal 8f (Na/Sc) site. The Na and Sc atoms occupy a crystallographically equivalent position with the total occupancy of 1, while the Na/Sc ratio can vary within the electroneutrality 9 ACS Paragon Plus Environment


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requirement. Modeling of such structures with a good reliability is a major problem, since the DFT methods are suitable for structures, where every site is occupied by one atom. Huge supercells are required to take into account the partial occupancy and low concentration of defects. So, we used fully ordered unit cells with a different Na/Sc ratio, where each crystallographic site was occupied by one type of atoms. To simulate the electronic properties of molybdates depending on scandium concentrations, we considered several 80-atom cells, which differ in the scandium occupancy of the (Na/Sc) site. These three cells with the most symmetrical distribution of atoms were Na20(MoO4)12, Na16Sc4(MoO4)12 and Na12Sc8(MoO4)12, where the (Na/Sc) site was completely or half-filled by Na atoms and completely filled by Sc atoms, respectively. These cells have a non-compensated electrical charge, and for the EFG calculations we introduced the charge corrections to reach electroneutrality and also considered the electrically neutral cells with two Sc atoms, Na18Sc2(MoO4)12. These calculations made it possible to analyze the Sc effect on the EFG tensor and the Na-ion diffusion paths. 2.4. NMR measurements 10 ACS Paragon Plus Environment

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The

23Na

AGILENT

MAS (Magic Angle Spinning) NMR spectra were obtained by using VNMR

400WB

spectrometer

(9.4 T,

23Na

Larmor

frequency

ω0/2π = 105.82 MHz) with standard Agilent 4.0 mm MAS Probehead in the temperature range 300–445 K. The sample temperature was set by changing the bearing gas temperature. The spectra were obtained by Fourier transform of free induction decay and/or spin echo signals with the exciting pulse 2 μs. The spectra deconvolution was performed using the DMFit program.33 2.5. Conductivity measurements Electrical conductivity measurements were performed using AC impedance spectroscopy on an Elins Z-1000P frequency response analyzer (Chernogolovka, Moscow region, Russia) at 100 Hz to 1 MHz frequencies in the temperature range 390– 680 K in air. The electrodes were made by coating the opposite faces of a sample pellet with a silver–palladium paste and heated at 770 K for 30 min in air to provide a good electrical contact between the electrode and the sample pellet. The least squares refinement program ZView (Scribner Associates Inc., Southern Pines, NC) was



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employed to fit the acquired impedance data to an (R1Q1)(R2Q2) equivalent circuit, where R is resistance and Q is constant phase element. 3. RESULTS AND DISCUSSION 3.1. PXRD characterization and crystal structure refinement All reflections on the PXPD patterns of Na5Sc(MoO4)4 were indexed in the C2/c space group

with

the

unit

cell

parameters:

a = 12.88737(7) Å,

b = 13.89612(7) Å,

c = 7.24874(4) Å, β = 113.0269(5). The fractional coordinates of the Na5Sc(MoO4)4 structure were used as the initial parameters for refinement.12 The reliability factors Rall and Rp demonstrate a good agreement between the theoretical and experimental data. Figure 1 demonstrates a part of experimental, theoretical and difference PXRD patterns of Na5Sc(MoO4)4. Other numerical characteristics illustrating the quality of structure refinement are listed in Table 1. The fractional atomic coordinates, isotropic atomic displacement parameters, cation occupancies and the main selected interatomic distances are listed in Tables 2 and 3. The refinement of the Na5Sc(MoO4)4 structure revealed that the atomic coordinates are close to those determined from single crystal data.12 The MoO4 tetrahedra are 12 ACS Paragon Plus Environment

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significantly distorted and the Mo−O distances vary in the range of 1.675(6)–1.829(6) Å. The M (Na/Sc) cations are octahedrally coordinated with MO bond lengths 2.101(7)– 2.644(8) Å. The other Na+ cations occupy three sites (Na1–Na3) with different Oenvironments (Table 3).

Figure 1. The observed, calculated and difference powder PXRD patterns of Na5Sc(MoO4)4. Thick marks denote the peak positions of possible Bragg reflections.

Table 1. Details of the Na5Sc(MoO4)4 structure refinement

Sample composition

Na5Sc(MoO4)4

Formula weight

799.7

Cell setting

Monoclinic

Space group

C2/c

Lattice parameters:



a, Å

12.88737(7)

b, Å

13.89612(7)

c, Å

7.24874(4)

β, 

113.0269(5)

V, Å3

1194.703(12)

Density,

3.3343

 (mm–1)

47.182

Formula units, Z

3

Color

white

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Data collection Diffractometer

Huber Guinier camera G670 with an Image Plate detector

Temperature,

293

Radiation/ Wavelength (, Å)

CoKα1 radiation / λ = 1.78892 Å

Data collection mode

Reflection

Scan method

Step

2 range (o)

5–100

Step scan (2)

0.005

Number of points

19000

Refinement Refinement

Rietveld 14 ACS Paragon Plus Environment

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Background function

Legendre polynomials, 15 terms

Number of parameters

58

R and Rw (%) for Bragg reflections 5.37/6.37; 5.47/6.38 (Rall/Robs) RP and RwP; Rexp

4.02, 5.39, 3.54

Goodness of fit (ChiQ)

1.52

maximum/minimum residual density

0.94 / –1.03

The Na5Sc(MoO4)4 structure is typical of all alluaudite-type compounds. It is built up of MoO4 tetrahedra, MO6 and Na1O6 octahedra forming a 3D framework (Fig. 2a). Originally, P.B. Moore determined the general structural formula of the alluaudite as

X1X2M1M22(PO4)3 (S.G. C2/c, Z = 4).34 The crystallographic X positions in the Na5Sc(MoO4)4 structure are occupied by Na+ cations (Na2 and Na3) and the M1 (Na1) and M2 (M) positions accommodate Na+ and Sc3+. The MO6 and Na1O6 octahedra form kinked chains of edge sharing octahedra MO6–MO6–Na1O6 running in the [101] direction (Fig. 2b). The MO6, Na1O6 octahedra and MoO4 tetrahedra are combined in such a way that two separate large hexagonal-shape channels run along the c-direction of the structure. These channels accommodate the X1 and X2 positions of alluaudite15 ACS Paragon Plus Environment


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type structure34 occupied by sodium cations. Two layers (parallel to the bc plane) can be distinguished in the 3D alluaudite-type framework (Fig. 2c). Layer I is built up of MoO4 tetrahedra and MO6 octahedra, while layer II is formed by Na(1, 2, 3)O6 polyhedra and MoO4 tetrahedra (Fig. 2c). Sodium cations Na2 and Na3 are located only in layer II and interactions between Na2O8 and Na3O8 polyhedra are possible via the Na1O6 octahedra (Fig. 2d).

Figure 2 Representation of the alluaudite-type structure of Na5Sc(MoO4)4 along the [001] (a) and [010] (c) directions, the chain of MO6–MO6–Na1O6 octahedra (b) and the interaction of Na2O8 and Na3O8 polyhedra via Na1O6 octahedra (d).


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Table 2. Atomic coordinates and equivalent isotropic displacement parameters for Na5Sc(MoO4)4

Atom Mo1

Wyckoff position 4e

occupancy

x/a

y/b

z/c

Uiso*/Ueq

1

0

0.79271(11

0.25

0.0178(6)

0.12471(15

0.0124(4)

) Mo2

8f

1

0.22825(9

0.61057(8)

)

)

Na1

4e

1

0

0.2313(5)

0.25

0.036(3)

Na2

4a

1

0

0

0

0.075(3)

Na3

4e

0.5

0

0.4963(9)

0.25

0.016(4)

Na/Sc

8f

0.625/0.37

0.2937(3)

0.8453(2)

0.3796(5)

0.0204(14)

5 O1

8f

1

0.0516(5)

0.7229(5)

0.4588(9)

0.0072(18)

O2

8f

1

0.1159(5)

0.8682(4)

0.2483(9)

0.0072(18)

O3

8f

1

0.1987(6)

0.6733(5)

0.2995(10)

0.040(3)

O4

8f

1

0.1445(5)

0.5059(6)

0.1124(9)

0.026(2)

O5

8f

1

0.3715(5)

0.5862(5)

0.1978(8)

0.021(2)

O6

8f

1

0.1647(5)

0.6723(4)

-0.0885(9)

0.004(3)



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Table 3. Selected interatomic distances (Å) for Na5Sc(MoO4)4

Mo1–tetrahedron

Mo2–tetrahedron Mo2–O3

1.699(8)

Mo1–O1

1.699(6) × 2

Mo2–O4

1.792(7)

Mo1–O2

1.829(6) × 2

Mo2–O4

1.744(7)

1.764

Mo2–O6

1.675(6)

1.728

Na1- octahedron

Na2- polyhedron

Na2–O6

2.393(6) × 2

Na2–O1

2.530(5) × 2

Na2–O5

2.542(9) × 2

2.488

Na1–O5

2.477(5) × 2

Na1–O2

2.593(6) × 2

Na1–O5’

2.844(5) × 2

Na1–O2’

3.324(5) × 2

2.809

M(Na/Sc)-octahedron

Na3– polyhedron

Na3–O4

2.558(6) × 2

Na3–O4’

2.436(6) × 2

Na3–O6

3.069(1) × 2

Na3–O3

3.467(12) × 2

2.882

M–O1

2.101(7)

M–O2

2.134(6)

M–O3

2.304(9)

M–O4

2.363(8)

M–O6

2.384(8)

M–O3’

2.644(8) 18

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2.322

The Na2 and Na3 positions form two conductivity channels in the structure. Channel I (denoted hereafter as Na2 channel) has a shape of a hexagon, elongated along one axis, with dimensions equal to ~ 3 Å × 8 Å. The dimensions of channel II (Na3 channel) are ~ 4 Å × 5 Å. The channels consist of chains of Na2O8 and Na3O8 polyhedra with the mean Na–O distances equal to 2.638 Å and 2.688 Å, respectively. The adjacent polyhedra in Na2 and Na3 channels are linked together via a common plane (O2–O2– O5–O5) and an edge (O4–O4), respectively (Fig. 3).



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Figure 3 Polyhedral representation of channels Na2 (a) and Na3 (b) in Na5Sc(MoO4)4 structure.

3.2. Conductivity measurements The results of AC impedance measurements performed on Na5Sc(MoO4)4 at different temperatures in air using Ag-Pd electrodes (Na-ion blocking electrodes) are shown in Fig. 4. The Nyquist plot of Na5Sc(MoO4)4 sample may be divided into two semicircles, which are typical of ordinary solid electrolytes. Usually, the semicircle in the highfrequency range corresponds to the contribution from bulk resistance, whereas the lowfrequency one should be attributed to the contribution of grain-boundary resistance. The obtained values of capacities for the bulk contribution are between 10-11 F and 10-12 F, in agreement with the value reported by Irvine et al.35 The capacities attributed to the grain boundary contribution have usually higher values, ~10-9–10-10 F.


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Figure 4. Typical AC impedance plots for Na5Sc(MoO4)4 at different temperatures

Figure 5. The Arrhenius plot of total (gray square) and bulk (red circle) conductivity of Na5Sc(MoO4)4 measured in the temperature range 390–680 K.

The bulk and total conductivities as functions of 1/T in the temperature range from 390 to 680 K in air are shown in Fig. 5. The conductivity, σ, for Na5Sc(MoO4)4 is typical of 21 ACS Paragon Plus Environment


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sodium-ion conductors and increases monotonically with increasing temperature from ~ 10–5 to ~ 10–3 S·cm-1 without distinct breaks on the ln(σT) vs 103/T plots. The activation energies for ionic conductivity were determined by fitting the experimental data on σ to the Arrhenius equation: Тσ = A·exp(-Ea/kBT), where σ is the ionic conductivity, T is the absolute temperature, A is the pre-exponential constant, kB is the Boltzmann constant and Ea is the activation energy. The activation energy obtained for the total conductivity in Na5Sc(MoO4)4 (Ea ≈ 0.63 eV) is close to the values obtained earlier for this molybdate18 and for Na42xM2+1+x(MoO4)3 (M = Mg, Mn, Co, Ni, Cu, Zn, Cd, 0  x  0.5)7,8,18 and it is lower than those for some other molybdates with sodiumion conductivity, e.g. Na9R(MoO4)6 (R = Fe, Al)14,16 and Na25Cs8R5(MoO4)24 (R = Sc, In)21, where the energy values are approximately equal to 0.8 eV. For Na5Sc(MoO4)4, the bulk and total conductivities reach 2.5×10-4 S·cm-1 and 6.7×10-5 S·cm-1 at 570 K; and 1.9×10-3 S·cm-1 and 5.1×10-4 S·cm-1 at 677 K, respectively. The total conductivity is close to that for Na42xM2+1+x(MoO4)3 (M = Mg, Ni, Zn, Cd, x = 0.2)7, but is lower than for Na9Fe(MoO4)614 and Na25Cs8R5(MoO4)2421, where the grain-boundary contribution is minimal. In the case of Na5Sc(MoO4)4, the lower 22 ACS Paragon Plus Environment

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conductivity can be explained by a lower annealing temperature and a shorter sintering time of the sample pellets compared to other alluaudite molybdates. 3.3. Electric field gradients from ab initio calculations The quadrupole frequency is defined as νQ ≡ ωQ/2π = 3eQVZZ/[2I(2I−1)h], where Q is the nuclear quadrupole moment (0.104b for 23Na).

23Na)

and I is the nucleus spin (3/2 for

The largest principal axis component VZZ is obtained from diagonalization of the

EFG tensor, where the eigenvalues of VXX, VYY and VZZ are chosen as |VZZ| > |VYY| > |VXX| and η = (|VYY| – |VXX|)/|VZZ| is the asymmetry parameter. The disorder in the (Na/Sc) position can affect the EFG tensors for all Na atoms. To study this effect, we calculated νQ and η for different model structures by varying the Sc content in (Na/Sc) site. Our calculations for model structure Na20(MoO4)12 (Table 4) predict the lines with quadrupole frequencies 0.73, 1.52, 1.42 and 1.03 MHz (asymmetry parameters are 0.47, 0.76, 0.78 and 0.66) for the Na1, Na2, Na3 and (Na/Sc) sites, respectively. The quadrupole frequencies and asymmetry parameters are close for the Na2 and Na3 sites and it can be suggested that they would provide one NMR line with νQ ~ 1.47 MHz and 23 ACS Paragon Plus Environment


Page 24 of 63

η ~ 0.77. For Na16Sc4(MoO4)12 with four scandium atoms per unit cell, the averaged frequencies are 0.71, 1.57, 1.38 and 1.56 MHz (asymmetry parameters are 0.81, 0.75, 0.77 and 0.51) at the Na1, Na2, Na3 and (Na/Sc) sites, respectively. For Na12Sc8(MoO4)12, where all (Na/Sc) positions are occupied by scandium, we predict three lines with νQ equal to 0.84, 1.69 and 1.25 MHz, and η = 0.37, 0.97 and 0.94 at Na1, Na2 and Na3, respectively. All model structures discussed above have noncompensated electric charges. To keep electroneutrality, we performed additional calculations of EFG tensors by varying the number of electrons in cells. We used a uniform constant background charge density that is the most common approach for charge compensation in bulk calculations. Few electrons were added or removed depending

on

the

Na/Sc

ratio

in

Na20(MoO4)12,

Na16Sc4(MoO4)12

and

Na12Sc8(MoO4)12. Addition or removal of electrons to preserve the electroneutrality leads to an increase or a decrease in νQ, respectively (Table 4), but it does not change significantly average νQ and η. Finally, the EFG tensors were calculated also for the electrically neutral cells: (i) Na18Sc2(MoO4)12 with two distant Sc atoms and (ii) Na15Sc3(MoO4)12 with three Sc atoms and two sodium vacancies. In these cases, the 24 ACS Paragon Plus Environment

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resulting νQ values were obtained by averaging over different configurations of Sc atoms in cell. As seen, these calculations provide the results similar to those obtained for other cells. Table 4. Quadrupole frequencies νQ (MHz) and asymmetry parameters η (in parenthesis) for

23Na

calculated for different structure models. The results for charged

cells with compensating electrons are displayed in bold type.

Na20(MoO4)1 Na16Sc4(MoO4) Na12Sc8(MoO4) Na15Sc3(MoO4) Na18Sc2(MoO4) 2

12

12

12

12

0.80 (0.67)

0.76 (0.58)

1.45 (0.69)

1.40 (0.93)

1.39 (0.65)

1.43 (0.76)

Na1 site 0.73 (0.47)

0.71 (0.81)

0.84 (0.37)

0.84 (0.34)

0.68 (0.67)

0.67 (0.41) Na2 site

1.52 (0.76)

1.57 (0.75)

1.69 (0.97)

1.67 (0.72)

1.39 (0.81)

1.38 (0.97) Na3 site

1.42 (0.78)

1.38 (0.77)

1.25 (0.94)

1.48 (0.77)

1.26 (0.73)

1.18 (0.99) Na/Sc site



1.03 (0.66)

1.56 (0.51)

1.17 (0.73)

1.64 (0.40)

–

Thus, the ab initio calculations predict three

Page 26 of 63

1.54 (0.54)

23Na

1.29 (0.43)

NMR lines with νQ ~ 0.7, 1.4 and

1.3 MHz and η ~ 0.6, 0.7 and 0.5 corresponding to Na1, Na2 + Na3 and Na/Sc sites, respectively. Taking into account the site occupancies, the relative intensities for these NMR lines are expected to be about 0.27:0.40:0.33 for Na1, Na2 + Na3 and (Na/Sc), respectively. These results were used for the assignment of the experimental 23Na NMR lines to the distinct Na sites (Section 3.4). 3.4. 23Na MAS NMR Figure 6 shows the temperature behavior of the

23Na

MAS NMR spectra in the

temperature range 300–445 K for Na5Sc(MoO4)4. The spectra deconvolution can be performed in the framework of a model assuming the dominant role of the second-order quadrupole effects. Nuclei with a spin I > 1/2 have a non-spherical charge distribution. This leads to the appearance of a quadrupole moment that in its turn interacts with the EFG. In the case of strong magnetic fields, the influence of the quadrupole interaction is


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usually described as small corrections to the Zeeman energy in the framework of the perturbation theory. In the first order of the perturbation theory, the presence of a quadrupole interaction leads to a characteristic splitting of NMR spectrum and to the appearance (in case of

23Na

with I = 3/2) of three lines: one line corresponding to the

central transition, mI = –1/2 ↔ +1/2, and two satellite lines (mI = ±3/2 ↔ ±1/2). For a powder sample, the satellites are placed at ±1/2νQ(1–η) from the central line, where the quadrupole frequency, νQ, and the asymmetry parameter, η, are the components of the EFG tensor (see Section 3.3). At sufficiently high gradients, the second-order effects are also of importance that is manifested in the characteristic splitting of the central line. The second order splitting is proportional to the square quadrupole frequency and inversely proportional to the resonance frequency: ωQ(2) ~ ωQ2/ω0. 36,37



Figure 6. The temperature evolution of the

23Na

Page 28 of 63

NMR spectrum in Na5Sc(MoO4)4 in the

temperature range 300–445 K in the magnetic field 9.4 T. Experimental data are shown as black lines, the fitting results – as magenta lines. Blue, red and green lines correspond to spectral components related to Na1, Na2 + Na3 and (Na/Sc) sites, respectively.


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As shown in Section 3.3, the ab initio calculations predict the three

23Na

NMR

components for Na5Sc(MoO4)4. The results of our NMR experiments are consistent with these predictions. At room temperature, one of these components (the blue line in Fig. 6) is characterized by νQ ~ 0.6−0.7 MHz and η ~ 0.6. The second NMR signal is characterized by νQ ~ 1.5 MHz and η~ 0.9−1 (the red line in Fig. 6). For the third spectral component, the estimates of νQ and η yield the values of 1.5−1.6 MHz and 0.5, respectively (the green line in Fig. 6). The observed NMR signals are attributed to the Na1, Na2 + Na3 and (Na/Sc) positions, respectively. At room temperature, the relative intensities of lines are about 30:40:30 for Na1, Na2 + Na3 and (Na/Sc), respectively, that is close to the expected ratio (see Section 3.3). The temperature dependences of the linewidth for central transition, Δν, the quadrupole frequency, νQ and the relative intensities for different spectral NMR components are shown in Figure 7.



Figure 7. The temperature behavior of the

23Na

Page 30 of 63

NMR signal parameters: (a) central line

width, Δν, (b) quadrupole frequency νQ and (c) relative intensities of lines, corresponding to the Na1, Na2 + Na3 and (Na/Sc) positions, respectively. The solid lines are shown as eye-guides.

At temperatures above 350 K, a drastic decrease in Δν is observed for the signal corresponding to the Na2 + Na3 ions (Fig. 7, a). Most likely this effect indicates that at this temperature the corresponding ions start to participate in diffusion. Indeed, Δν is


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determined mainly by the dipolar internuclear interaction. For a pair of interacting nuclei, it depends on the distance between the nuclei and the orientation of this pair with respect to the external magnetic field.36,38 Atomic jumps lead to changes in both distances and orientations. As a result, with increasing temperature and ion jump frequency, τd-1, the dipolar interaction is averaged and a sharp reduction of Δν can be expected. The temperature dependence of Δν(T) allows us to estimate the parameters of ion motion. A dynamic narrowing should be expected at a temperature where the frequency of atomic jumps becomes comparable to the linewidth of a “rigid lattice” (i.e. in the absence of atomic motion).36,38 Taking into account Δν at room temperature (≈ 500 Hz), we can estimate the value of τd-1 ~ 5×103s-1 at T ~ 350 K. Moreover, the temperature behavior of Δν also makes it possible to estimate roughly the activation energy for diffusion, Ea. In particular, the simplest phenomenological approach39 suggests that Ea (meV) = 1.617T0(K), where T0 is the temperature of the motion line narrowing onset. Assuming T0 ~ 350 K, we get Ea = 0.5–0.6 eV, which is close to that estimated from σ(T1)

data (Section 3.2). Here, we should make some remarks concerning the accuracy of 31 ACS Paragon Plus Environment


Page 32 of 63

Ea estimates. The main source of errors in our case is the accuracy of the sample temperature measurements. For the MAS NMR experiments, the sample temperature is changed by the bearing gas that of course leads to significant differences in the real and measured temperatures. Moreover, the sample temperature depends on the MAS speed due to rotational friction. Thus, accurate measurements of T in the MAS mode require additional thermometry using "model" samples.40 Similar studies performed earlier, allow one to estimate the temperature gradients for our conditions (medium temperature and MAS speed range) within ± 20 degrees.41,42 Thus, for our purposes, the standard procedure (with the bearing gas temperature setting) seems to be sufficient, and we decided not to perform additional experiments on thermometry. The ab initio results obtained for related Na2+2xFe2-x(SO4)35,22 predict that the most probable mechanism of Na-ion diffusion is the 1D jumps occurring through the channels formed by Na3 sites along the c-axis. Meanwhile, the jumps Na3 ↔ Na1 ↔ Na2 are considered to be less energetically favorable and the Na1 ions are supposed to be mainly the “donors” for mobile Na2 or Na3 ions. The temperature dependence Δν(T) agrees well with these predictions. The temperature behavior of the relative intensities 32 ACS Paragon Plus Environment

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for the detected NMR signals also confirms this assumption. It is seen from Figs. 6 and 7, c that the intensities of the signals corresponding to Na1 and Na2 + Na3 change gradually with temperature. This effect is due to the redistribution of ions and partial filling of the Na2 + Na3 sublattice with Na1 ions (most likely vacant Na3 sites). As a result, at T > 380 K the relative intensity of the NMR signal corresponding to Na1 decreases almost twice and reaches ~ 16 ± 2 %. Note, however, that in contrast to Δν(T), the temperature behavior of νQ can hardly be described in the framework of the model proposed above. Indeed, at T > 350 K, in addition to decreasing Δν value, the quadrupole frequency also decreases for a signal corresponding to Na2 + Na3 ions (see Fig. 7, b). The decrease in νQ is clearly seen from Fig. 6 that is manifested in a drastic change of corresponding line shape with temperature. In the case of jumps through identical sites, such as those expected for Na2 ↔ Na2 and Na3 ↔ Na3, νQ should not vary (unlike Δν). A significant change in the quadrupole frequency can be expected only for atomic jumps between heterogeneous positions, characterized by different EFG’s.43,44 Thus, the νQ(T) dependence allows us to suppose that the jumps within Na2 (Na3) sites occur not directly, but through some 33 ACS Paragon Plus Environment


Page 34 of 63

intermediate position. The most probable candidate for such an intermediate point for translational diffusion is the Na1 site. This means that the sodium diffusion in Na5Sc(MoO4)4 is more likely to be two-dimensional; it occurs both through channels along the c axis (formed by Na2 and Na3 sites) and through cross-linking channels (by Na2 ↔ Na1 ↔ Na3 jumps). This result obtained from the “local” NMR techniques is not consistent with the predictions for Na2+2xFe2-x(SO4)35,11 and our expectations based on the “long-range” structure analysis, which assume 1D jumps through the Na3 and Na2 channels as the most probable mechanism of Na-ion diffusion. Nevertheless, it is supported by the results of ab-initio calculations also implying the realization of 2D diffusion in Na5Sc(MoO4)4 (see below). 3.5. Na-ion diffusion from ab initio calculations The migration of Na-ion was examined for three compositions providing conclusions on the Sc effect on the diffusion paths and barriers. Since the scandium occupancy of the (Na/Sc) site is ~1/3, it can be expected that the real situation corresponds to an intermediate state between the extreme compositions, when all (Na/Sc) sites are occupied completely by Na atoms or by Sc atoms. The pathways and saddle points of 34 ACS Paragon Plus Environment

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migration were calculated by the NEB method, which allows one to study the vacancy hopping mechanism, when Na-ion migrates from one lattice site to a neighboring vacancy. The migration energy curves obtained using the NEB calculations for Na16Sc4(MoO4)12 and Na12Sc8(MoO4)12 are shown in Fig. 8. The situation reminds that obtained previously for Na2+2xFe2-x(SO4)3.5,22 The most probable pathways for Na+ migration are along the c-axis between the Na3 and Na2 sites. These linear channels have equal paths (c/2), but different distances in the Na2–O and Na3–O polyhedra in the saddle points. As a result, the nearest oxygen atoms block the sodium migration in a different way.



Page 36 of 63

Figure 8. Energies of Na-ion migration calculated for two structure models with four and eight Sc atoms in cells.

For the Na2–Na2 path in Na16Sc4(MoO4)12, the diffusion barrier is 0.40 eV, and it only slightly increases to 0.43 eV in Na12Sc8(MoO4)12 (Fig. 8, a). For the Na3–Na3 pathway, vice versa, the diffusion barrier decrease monotonously with increasing scandium content and when all (Na/Sc) positions are filled with scandium atoms it


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sharply decreases from 0.58 to 0.17 eV (Fig. 8, a). The shortest Na–Na distance corresponds to the Na1–(Na/Sc) pathway; however, the migration barrier along this direction is high (> 1.4 eV) in all structure models due to short distances between the nearest oxygen atoms during Na+ ion migration. Sodium diffusion in the bc-plane is also possible through the jumps between the neighboring Na1 and (Na2,Na3) sites. For these directions, the migration energy curves demonstrate

a

drastic

dependence

on

scandium.

The

calculations

for

Na12Sc8(MoO4)12 predict similar formation energies of the Na1 and Na2 vacancies and, as a result, the starting and end points on the migration energy curve differ only slightly. The energy barrier for this pathway is 0.38–0.43 eV. The Na1–Na3 transport in Na12Sc8(MoO4)12 requires energies equal to 0.56 and 0.05 eV for forth and back jumps, respectively (Fig. 8, b). The same (0.54 and 0.05 eV) and much larger (0.88 and 0.58 eV) energies were obtained, respectively, for the Na1–Na3 and Na1–Na2 transport in Na2Fe2(SO4)3.5 The migration energies for Na12Sc8(MoO4)12 (Fig. 9, red curve) are similar to those calculated for Na2Fe2(SO4)3 at low concentrations of Na.5



Page 38 of 63

The situation drastically changes for the model structure without scandium, Na20(MoO4)12, Fig. 9 (black line). The difference between the formation energies of the Na1 and Na3 vacancies decreases and migration from Na1 to Na3 requires a much lower energy (0.27 eV) compared with that for Na12Sc8(MoO4)12. The energy barrier for migration along the Na2–Na2 path remains the same (0.38 eV), whereas it sharply increases from 0.2 eV to 0.6 eV for the Na3–Na3 channel, and decreases for migration from Na2 to Na1 (0.20 eV) (Fig. 9). As a result, for the scandium-free structure, the activation energies less than 0.4 eV were obtained for Na1 ↔ Na3, Na2 ↔ Na2 and Na2 → Na1, but not for Na3 ↔ Na3.


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Figure 9. (a) Migration energy of Na+ ion calculated for models with eight Sc atoms (red line) and no Sc atoms (black line) in 8f site; (b) structure fragment for sodium diffusion along different paths in alluaudite structure.

Thus, the results of the ab initio calculations and NMR experiments allow us to suggest that the (Na/M) filling is crucial for ion transport mechanisms in alluaudite compounds. The low Sc occupancy of the (Na/Sc) site in Na5Sc(MoO4)4 leads to a drastic difference in the Na+ diffusion mechanisms compared to the previously studied Na2+2xFe2-x(SO4)3 with the 8f-site full-filled by Fe3+.5,22 For Na5Sc(MoO4)4, the following scenario can be proposed. With increasing temperature, the Na1 ions in the scandiumfree regions are activated first. Owing to low value of Ea = 0.27 eV, the Na1 ions can pass to the neighboring vacant Na3 sites (note that the obtained value is one of the lowest for Na-conductive materials45). As the temperature increases further, the Na3 (Na2) ions also start to participate in diffusion processes. However, in contrast to Na2+2xFe2-x(SO4)3, where Ea for ion jumps within the Na3 channels is significantly lower than for the Na3 (Na2) ↔ Na1 jumps5,11, in Na5Sc(MoO4)4 such an "anisotropy" on the



Page 40 of 63

migration energy curves is no longer observed. Indeed, although the value of Ea for the Na3 ↔ Na3 jump in Na12Sc8(MoO4)12 seems to be minimal (Fig. 9), the Ea value (above the “middle-line”) for the Na3 → Na1 jump is even smaller, only 0.05 eV. Thus, the probability of a Na3 → Na1 → Na2 jump (with Ea ≈ 0.4 eV) appears to be comparable to the probability of Na3 (Na2) ↔ Na3 (Na2) jumps. Moreover, for Na16Sc4(MoO4)12 (Fig. 8), the situation becomes even more “isotropic” and the activation energies for diffusion along the c-axis (through Na2 and Na3 channels) and in the bc-plane (i.e. by Na2 (Na3) ↔ Na1 ↔ Na2 (Na3) jumps) are approximately equal, Ea ≈0.4 eV. This scenario implies the realization of 2D diffusion in Na5Sc(MoO4)4. 4. CONCLUSIONS The crystal structure, electronic properties and diffusion mechanisms in the double molybdate Na5Sc(MoO4)4 were studied using a combination of experimental methods (PXRD, solid-state NMR and conductivity measurements) and ab initio calculations. According to the PXPD data, the structure of Na5Sc(MoO4)4 is typical of all alluaudite compounds and has separate sodium channels in the c-direction. The detailed studies of the ion diffusion mechanisms revealed drastic differences compared to the 40 ACS Paragon Plus Environment

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predictions for related Na2+2xFe2-x(SO4)3, where 1D sodium-ion diffusion is expected through these channels. The ab initio calculations and NMR experiments demonstrated that the Na+ diffusion in Na5Sc(MoO4)4 has rather 2D character and the probabilities for ion jumps along the c-axis (through the Na2 and Na3 channels) and in the bc plane (Na2(Na3) ↔ Na1 ↔ Na2 (Na3)) are almost equal. Moreover, the Na1 ions located far from Sc are activated first with increasing temperature and the predicted Ea values for the Na1 → Na3 jumps are less than 0.3 eV. The occupancy of the mixed (Na/M) position plays a crucial role in the sodium-ion diffusion mechanisms in the alluaudite compounds. Two-dimensional conductivity without blocking of one-dimensional paths can possibly be achieved by searching of a proper metal M and its concentration. This shows new ways to designing of new promising sodium-ion materials with the alluaudite structure.

Acknowledgements

This work was supported by the RSF (Grant No. 18-12-00395).

Author Information 41 ACS Paragon Plus Environment


Page 42 of 63

Nadezhda I. Medvedeva and Tatiana A. Denisova are Chief Researchers at the Institute of Solid State Chemistry; Anton L. Buzlukov is a Senior Researcher at the Institute of Metal Physics; Yana V. Baklanova is a Senior Researcher at the Institute of Solid State Chemistry; Alexander V. Skachkov is a PhD student at the Institute of Solid State Chemistry; Aleksandra A. Savina is a Researcher at the Skolkovo Institute of Science & Technology and at the Baikal Institute of Nature Management,; Vladimir A. Morozov is a Leading Researcher at the Moscow State University; Irina E. Animitsa is a Professor at the Ural Federal University; Elena G. Khaikina is a Chief Researcher at the Baikal Institute of Nature Management, and Sergey F. Solodovnikov is a Leading Researcher at the Nikolaev Institute of Inorganic Chemistry. The principal areas of research in which the authors have worked are Computational Material Science (Nadezhda I. Medvedeva), NMR (Anton L. Buzlukov, Alexander V. Skachkov, and Tatiana A. Denisova), Crystal Structure Refinement (Vladimir A. Morozov, Sergey F. Solodovnikov), Conductivity Measurements (Yana V. Baklanova, Irina E. Animitsa) and Synthesis and Properties of Solids (Aleksandra A. Savina, Elena G. Khaikina).


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ORCID

Nadezhda I. Medvedeva: 0000-0002-1187-9431 Anton L. Buzlukov: 0000-0002-2728-0503 Alexander V. Skachkov: 0000-0003-4970-4159 Aleksandra A. Savina: 0000-0002-7108-8535 Vladimir A. Morozov: 0000-0002-0674-2449 Yana V. Baklanova: 0000-0003-0988-2735 Irina E. Animitsa: 0000-0002-0757-9241 Elena G. Khaikina: 0000-0003-2482-9297 Tatiana A. Denisova: 0000-0001-8606-5697 Sergey F. Solodovnikov: 0000-0001-8602-5388



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Savina A. A.; Solodovnikov S. F.; Belov D. A.; Basovich O. M.; Solodovnikova Z. A.; Pokholok K. V.; Stefanovich S. Yu.; Lazoryak B. I.; Khaikina E. G. Synthesis, crystal

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Page 54 of 63

TOC Graphic


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Fig. 1. Observed, calculated and difference powder PXRD patterns of Na5Sc(MoO4)4. Thick marks denote the peak positions of possible Bragg reflections.



Fig. 2 Presentation of the alluaudite-type structure of Na5Sc(MoO4)4 along the [001] (a) and [010] (c) directions, the chain of MO6–MO6–Na1O6 octahedra (b) and the interaction of Na2O8 and Na3O8 polyhedra via Na1O6 octahedra (d).


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Fig. 3 Polyhedral representation of Na2 channel (a) and Na3 channel (b) in Na5Sc(MoO4)4 structure. The figures depict the distances between two subsequent Na2 and Na3 cations.



Fig. 4. Typical AC impedance plots for Na5Sc(MoO4)4 at different temperatures 79x67mm (300 x 300 DPI)


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Fig. 5. Arrhenius plot of the total (gray square) and bulk (red circle) conductivity of Na5Sc(MoO4)4 measured in the temperature range 390–680 K. 79x56mm (300 x 300 DPI)



Fig.6. The temperature evolution of the 23Na NMR spectrum in Na5Sc(MoO4)4 over the temperature range 300–445 K in a magnetic field 9.4 T. Experimental data are shown as black lines, the fitting results as magenta lines. Blue, red and green lines correspond to spectral components related to Na1, Na2 + Na3 and (Na/Sc) sites, respectively. 79x113mm (300 x 300 DPI)


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Fig. 7. Temperature behavior of the 23Na NMR signal parameters: (a) central line width, Δν, (b) quadrupole frequency νQ and (c) the relative intensities of lines, corresponding to the positions Na1, Na2 + Na3 and (Na/Sc), respectively. Solid lines are shown as eyes guides. 80x108mm (300 x 300 DPI)



Fig. 8. Energies for Na-ion migration calculated for two structure models with four and eight Sc atoms in cells. 80x125mm (300 x 300 DPI)


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Fig. 9. Migration activation energy of Na+ ion calculated for Na12Sc8(MoO4)12 (red line) and Na20(MoO4)12 (black line). 80x61mm (300 x 300 DPI)


Mechanism of Sodium-Ion Diffusion in Alluaudite-Type Na5Sc(MoO4

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