Anton L.
Buzlukov
*a,
Irina Yu.
Arapova
a,
Yana V.
Baklanova
b,
Nadezhda I.
Medvedeva
b,
Tatiana A.
Denisova
b,
Aleksandra A.
Savina
cd,
Bogdan I.
Lazoryak
e,
Elena G.
Khaikina
d and
Michel
Bardet
f
aInstitute of Metal Physics, Ural Branch, Russian Academy of Science, S. Kovalevskaya St. 18, Ekaterinburg 620137, Russia. E-mail: buzlukov@imp.uran.ru; buzlukov@mail.ru; Fax: +7-343-3745244; Tel: +7-343-3783839
bInstitute of Solid State Chemistry, Ural Branch, Russian Academy of Science, Pervomayskaya St. 91, Ekaterinburg 620990, Russia
cSkolkovo Institute of Science and Technology, Moscow 121205, Russia
dBaikal Institute of Nature Management, Siberian Branch, Russian Academy of Sciences, Sakh’yanova St. 6, Ulan-Ude 670047, Buryat Republic, Russia
eDepartment of Chemistry, Lomonosov Moscow State University, Leninskie Gory 1, Moscow 119899, Russia
fUniv. Grenoble Alpes, CEA, IRIG-MEM, LRM, 38000, Grenoble, France
First published on 26th November 2019
The rechargeable Na-ion batteries attract much attention as an alternative to the widely used but expensive Li-ion batteries. The search for materials with high sodium diffusion is important for the development of solid state electrolytes. We present the results of experimental and ab initio studies of the Na-ion diffusion mechanism in Na9Sc(MoO4)6. The ion conductivity reaches the value of 3.6 × 10−2 S cm−1 at T ∼ 850 K. The 23Na and 45Sc NMR data reveal the coexistence of three different types of Na-ion motion in the temperature range from 300 to 750 K. They are activated at different temperatures and are characterized by substantially different dynamics parameters. These features are confirmed by ab initio calculations of activation barriers for sodium diffusion along various paths.
Besides practical promise, these compounds are also interesting for fundamental studies of ion dynamics. In particular, our recent researches revealed a non-uniform sodium motion in Na9Al(MoO4)6.37 At T < 490 K it occurs exclusively through ion jumps within the sublattice of sodium sites located far from polyhedral [Al(MoO4)6]9− clusters, forming the structure framework. The activation energy for this type of motion Ea ≈ 0.55 eV. The ions located in the vicinity of [Al(MoO4)6]9− clusters are activated only at T > 490 K with Ea ≈ 0.8 eV. Strong correlation effects in sodium motion are present at low temperatures. They are manifested in a slowdown of ion diffusion and an artificial increase of the Ea value estimated from conductivity data.
A comparison of the electrophysical properties for the NASICON-type compounds19,38,39 shows that the substitution of the transition element can lead to a drastic change of the ionic conductivity (up to several orders of magnitude). In this regard, it was interesting to study the Na diffusion mechanisms in the compound related to Na9Al(MoO4)6: having similar local structure, but another trivalent cation. As such a related compound, Na9Sc(MoO4)6 was chosen. The basic structural units in Na9R(MoO4)6 (R = Al, Sc) are the isolated polyhedral [R(MoO4)6]9− clusters composed of the central RO6 octahedron sharing vertices with six MoO4 tetrahedra to form an open framework, where the Na+ cations are bound to three vertices of the MoO4 tetrahedra (see Fig. 1).
Fig. 1 Crystal structures of Na9Al(MoO4)6 (a and c) and Na9Sc(MoO4)6 (b and d) reproduced with program VESTA40 on structural data from ref. 37 and 41, respectively. Figures a and b represent the [Al/Sc(MoO4)6]9− clusters forming the structure framework and adjacent NaO6 octahedra. Figures c and d represent the Na-sites located in the structure cavities between the [Al/Sc(MoO4)6]9− polyhedra. |
The Na9Sc(MoO4)6 is crystallized in a structure with trigonal R space group.41 Replacing scandium (rVI = 0.74 Å42) with aluminum (rVI = 0.53 Å42) induces the monoclinic distortions (C/2c s.g.) and the “splitting” of sodium sites.37 As a result, there are five nonequivalent structural positions of sodium in Na9Al(MoO4)6, where Na1 and Na2 are located in the vicinity of AlO6 octahedra, and the Na3, Na4 and Na5 positions are placed in the cavities between the [Al(MoO4)6]9− polyhedra. Meanwhile, only three types of sodium positions are present in Na9Sc(MoO4)6: the Na1 ions are located near the ScO6 octahedra, and Na2 and Na3 ones are in between the [Sc(MoO4)6]9− clusters (Fig. 1). It has to be noted however that these structural changes during the Al → Sc substitution can only be detected by a detailed analysis of electronic diffraction, while the powder X-ray diffraction patterns can also be satisfactory fitted in trigonal R and/or R3c space groups.37 So, despite the apparent differences in the crystal structures presented on Fig. 1 they are really quite similar.
Here we present the results of detailed studies of the sodium diffusion mechanisms in Na9Sc(MoO4)6 performed at the “atomic level” using the NMR methods and DFT calculations. Differences in the sodium dynamics in comparison with Na9Al(MoO4)6 are discussed.
The 23Na MAS NMR spectra were obtained with room temperature bearing gas by using standard Bruker MAS NMR probeheads with 1.3 mm (AVANCE DSX 200 NMR spectrometer, external magnetic field 4.7 T) and 3.2 mm rotors (AVANCE III 500WB spectrometer, 11.7 T), and standard Agilent 4.0 mm MAS Probehead (AGILENT VNMR 400WB spectrometer, 9.4 T).
As for the static regime, the 23Na MAS NMR spectra were acquired by Fourier transform of free induction decay and/or spin echo signals with exciting pulse equal to 2 μs. The spectra deconvolution was performed by using the DMFit program.43
The tensors of electric field gradient (EFG) at Na nuclei in different positions were calculated using the method of ref. 49. After diagonalization of the EFG tensor, the principal components Vxx, Vyy and Vzz are chosen as |Vzz| > |Vyy| > |Vxx|. The largest principal component Vzz determines the quadrupole frequency νQ ≡ ωQ/2π = 3eQVzz/2I(2I − 1)h and asymmetry parameter ηQ = (|Vyy| − |Vxx|)/|Vzz|. The values of νQ and η were used for an assignment of the experimental NMR lines to the specific sodium sites.
The nudged elastic band (NEB) method was employed to calculate the energy barriers for Na-ion migration. We considered the diffusion mechanism through migration of single vacancy between two neighbor positions of Na ion. For every path, the total energies were calculated for a few intermediate images. The relaxed maximal energy and coordinates during the sodium migration provided the activation barrier and diffusion pathway between the starting and end states, respectively.
The determination of unit cell parameters from PXRD patterns using Le Bail decomposition revealed that all reflections could be indexed in the R space group with a = 15.0047(1) Å, c = 19.1891(1) Å; values of structural R-factors: RP = 3.10% and RwP = 4.37% (Fig. 2). It verifies good phase purity of the powder prepared by solid state synthesis.
Fig. 2 The experimental, calculated, and difference powder X-ray diffraction patterns of Na9Sc(MoO4)6. |
Fig. 3 Temperature dependence of the conductivity measured for Na9Sc(MoO4)6 in the range 343–843 K. The inset shows the Nyquist plot at 573 K. |
As can be seen a decrease of the external magnetic field strength leads to a substantial broadening of NMR spectrum. Similar effects can be expected when the main factor determining the shape of NMR spectrum is quadrupole interaction. Nuclei with a spin I > 1/2 have a non-spherical charge distribution in the nucleus. This leads to the appearance of a quadrupole moment that interacts with the Electric Field Gradient (EFG) which in its turn is determined by the features of local environment.50 The influence of quadrupole interaction is usually described as small corrections to the Zeeman energy within the framework of the perturbation theory. In strong magnetic fields or for nuclei with low Q (such as the 7Li), only the first-order effects are usually observed which are manifested in a characteristic splitting of NMR spectrum and appearance (in the 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 peaks of satellites are shifted relative to the position of central line at a distance ±1/2νQ(1 − ηQ). In weaker magnetic fields or for nuclei with high Q an important role can be played also by the second-order effects those are manifested in the splitting of central line. The second order splitting is proportional to square quadrupole frequency and inversely proportional to the resonance frequency: ν(2)Q ∼ νQ2/ν0.50,51
Interestingly, three 23Na NMR spectra on Fig. 4: static and MAS spectra acquired at ν0 = 52.94 MHz and MAS spectrum measured at ν0 = 132.29 MHz (panel c, d and b, respectively) can be fitted simultaneously taking into account only the second-order quadrupole effects. This “Quad2nd” model assumes the presence of two spectral components with νQ = 1350 ± 50 and 620 ± 30 kHz; and ηQ = 0.30 ± 0.05 and 0.70 ± 0.05 for Line-1 (red line) and Line-2 (blue one), respectively. Nevertheless, the simulation of static spectrum recorded in 11.7 T yields the result far from ideal with the same fitting parameters (see panel a). It suggests that the situation is more complicated and besides quadrupolar interaction there are another factors affecting the 23Na NMR spectrum in Na9Sc(MoO4)6. This interaction is directly proportional to the magnetic field strength and substantially averaged even at low MAS speeds. The most probable candidate is a chemical shift anisotropy (CSA), reflecting the anisotropic shielding of Na nuclei by surrounding electrons. The parameters of the anisotropy, Δδ, and the asymmetry, ηCS, of chemical shift are determined by the corresponding tensor components: Δδ = δ33 − δiso, ηCS = |δ22 − δ11|/|δ33 − δiso|, where isotropic shift, δiso = (δ11 + δ22 + δ33)/3.52,53 The best fit is achieved with the values of Δδ equal approximately to 20 ppm and −5 ppm for lines 1 and 2, respectively. The parameter ηCS is found to be in the range of 0–0.3 for Line-1. For Line-2 it was difficult to estimate the ηCS value unambiguously since its influence on the line shape is rather weak. The “Quad2nd + CSA” model contains another set of parameters which affect the line shape: the Euler angles φ, χ and ψ (in DMFit43 notations) defining the orientation of principal axes of the EFG and CSA tensors. The best result is achieved at χ = 15 ± 5° for both lines (the changes of φ and ψ do not disturb visibly the line shape).
We assign the detected Line-1 and Line-2 to the 23Na nuclei in the Na1 sites and the Na2 + Na3 sites, respectively. The relative intensities for observed signals ((1)I = 0.30–0.35 and (2)I = 0.65–0.70) agree well with the occupancies of corresponding positions in the crystal structure.41 Moreover this assignment is consistent with the results of ab initio calculations. The calculated quadrupole frequencies νQ and asymmetry parameters ηQ at 23Na nuclei in Na9Sc(MoO4)6 are shown in Table 1.
Site | ν Q (kHz) | η Q |
---|---|---|
Na1 | 1798 | 0.36 |
Na2 | 661 | 0.61 |
Na3 | 745 | 0.77 |
As seen, the quadrupole frequencies and asymmetry parameters for Na2 and Na3 sites are very close to each other and we can expect the appearance of two NMR lines with νQ ∼ 1800 and 700 kHz; and ηQ ∼0.4 and 0.7 for Na9Sc(MoO4)6. The relative intensities of these two lines should be (1)I = 0.33, (2)I = 0.67 as follows from the occupancies of different Na sites.41
Fig. 5 23Na NMR spectra for Na9Sc(MoO4)6 acquired in static mode at resonance frequency ω0/2π = 132.29 MHz in temperature range 300–750 K. |
The temperature dependencies of NMR spectra parameters are qualitatively similar to those observed earlier for the related molybdate Na9Al(MoO4)637 and indicate the presence of rather fast Na diffusion in the Na9Sc(MoO4)6. It should be noted however that all “motional” effects in Sc-containing compound are observed at higher temperatures compared to those for Na9Al(MoO4)6 that implies the slower ion diffusion in Na9Sc(MoO4)6. At temperatures above 390 K, the Δν value for a signal corresponding to Na2 + Na3 ions (open blue circles in Fig. 6a) sharply decreases. Such a Δν(T) dependence is typical for the materials with fast ion diffusion.50,54 The Δν value is affected mainly by the internuclear dipolar interaction. For a pair of interacting nuclei, it depends on the distance between nuclei and the orientation of this pair with respect to the external magnetic field. Atomic jumps lead to changes in both the distances and the orientations. As a result, with increasing temperature and growing ion jump frequency, the dipolar interaction is averaged and a sharp decrease of Δν is expected. The weak decrease of Δν for Na1 ions (filled red circles in Fig. 6a) can be explained as follows: for mobile Na2/Na3 ions themselves, the dipolar interaction is fully averaged (excluding some non-averaged part due to inhomogeneity of the external magnetic field etc.). Meanwhile the ions jumps in the Na2/Na3 sublattice affect only weakly the line width of static nuclei in Na1 sites, because for them the Δν is determined mainly by the 23Na–45Sc interaction (indeed, the nearest neighbor for Na1 is the Sc at a distance r ≈ 3.36 Å). At T > 550 K, the Δν for Na2/Na3 ions increases again. Such a Δν(T) dependence is reminiscent of that predicted for “classical” chemical exchange between two non-equivalent sites: with temperature increasing the NMR signals corresponding to different sites broaden at first, then they are merged into one wide line, then a dynamic narrowing of the merged line is expected.50 The parameters of this “merged” line are shown as black squares in Fig. 6. Thus, the experimental data on Δν can be interpreted within the next scenario: at 400 < T < 550 K the Na+ ions motion occurs exclusively within the Na2/Na3 positions which form the continuous paths for long-range ion diffusion, while sodium in Na1 sites remains static (on the NMR frequency scale). At T > 550 K the Na1 ions also start to participate in the diffusion processes through the Na1 ↔ Na2/Na3 jumps. It has to be noted that the latter assumption is in agreement with structure considerations: the Na1 ↔ Na2/Na3 jump it is only one possibility for Na1 because direct jump Na1 ↔ Na1 seems to be quite improbable due to too long jump length (rNa1–Na1 ≈ 5.83 Å).
Temperature behavior of νQ for Na2/Na3 ions is consistent with the proposed picture of ion motion. As is expected,50,55,56 besides the averaging of dipole–dipole interaction the ion jumps in the Na2/Na3 sublattice induce the changes of the EFG tensor components, Vij, for the corresponding NMR signal, those are reflected in the changes of νQ and ηQ values at T > 390 K (see Fig. 6b and c). Meanwhile only monotonous changes of the EFG parameters for spectral component corresponding to Na1 ions are observed at 300 < T < 550 K. Nevertheless, there are some substantial deviations from “classical” behavior expected at two-site exchange. In particular, instead of characteristic coalescence of two spectral components,55,57–60 at T > 550 K (i.e., with the beginning of Na1 ions motion) the corresponding signal sharply decreases. As a result, this line completely disappears at T ≈ 600 K. The changes of line intensity can be explained by a natural assumption that Na1 ions are involved in the motional process gradually with increasing temperature, thus the decreasing signal corresponds to ions still retained in the Na1 sites (whose fraction decreases with temperature). Concerning the absence of spectra coalescence, we have to take into account that the chemical exchange Na1 ↔ Na2/Na3 can not occur directly, but only through intermediate tetrahedral position Naint. For these “two-steps” jumps, Na1 ↔ Naint + Naint ↔ Na2/Na3, the NMR spectrum transformation can significantly differ from that expected at direct Na1 ↔ Na2/Na3 hopping. It has to be noted that some approaches allowing to predict the NMR spectrum shape at two-site exchange have been developed recently (see for example ref. 61–65). However, even for the simplest cases, they require rather complicated numerical calculations. In our case they already can hardly be applied, moreover, if we take into account that the probabilities for the “first step” (Na1 ↔ Naint) jump and for the “second step” (Naint ↔ Na2/Na3) one can be rather different.
Another possible explanation for the disappearance of Line-1 could be the presence of some phase transition at 550–600 K resulting in that the local surrounding of sodium ions in Na1 sites becomes similar to that for Na2/Na3. To trace possible structure transformations we performed also the 45Sc NMR spectra measurements in the temperature range 300–750 K. In contrast to the Na sites (18f in R structure) the point symmetry of the Sc site (6c) contains a 3-fold axis. It applies the strict constraints on the EFG and CSA tensors: they must have axial symmetry (i.e., ηCS = ηQ = 0) and, in addition, their principal axes must be collinear to this 3-fold axis (i.e., φ = χ = ψ = 0°). However, with these constraints we could not find the νQ and Δδ values allowing to fit the experimental spectra. The better result can be achieved either with the parameters φ = χ = ψ = 0° and ηQ = 0, ηCS = 1, or with ηCS = ηQ = 0 and φ = ψ = 0°, χ = 90°. Although the point symmetry plays as it is considered a decisive role, the deviations in both the orientations of principal axes and the axiality of CSA and EFG tensors have been observed in some cases (see, for example, ref. 66 and 67). On the one hand, local symmetry can be distorted due to deviations of the bond lengths/angles from their ideal values. On another hand the electron shielding and especially EFG on the nucleus-probe can be strongly affected by the second and even third coordination spheres. The environment of Sc3+ ions in Na9Sc(MoO4)6 is characterized by the “isotropic” first coordination sphere (containing 3 × O2− ions at a distance r = 2.09 Å and 3 × O2− at r = 2.10 Å), and rather “anisotropic” second one with 3 × Mo6+ (r = 3.49 Å), 3 × Mo6+ (r = 3.66 Å), and 1 × Na1+ (r = 3.37 Å). Thus, as a tentative hypothesis we can infer that the observed features are determined by these peculiarities of local Sc surrounding. Nevertheless we leave a detailed discussion of this issue beyond the scope of present article. It is rather a question of “NMR crystallography” and other studies are required to clarify it.
The Fig. 7a represents the results of 45Sc NMR spectra simulation. For all spectra deconvolutions the parameters of φ = χ = ψ = 0°, ηQ = 0 and ηCSA = 1, the estimates of dipolar line width, Δν, quadrupole frequency, νQ, anisotropy of chemical shift, Δδ, and isotropic shift value, δiso, are presented in Fig. 7b–e.
As can be seen, the parameters of CSA and EFG on the 45Sc nuclei show only monotonous changes with temperature indicating the absence of any structure transformations in the entire temperature range 300–750 K (excepting, of course, uniform lattice expansion). Meantime, the Δν(T) dependence reveals two characteristic “steps” at T ≈ 365 and 585 K which are most likely induced by the averaging of 23Na–45Sc internuclear dipolar interaction due to the activation at these temperatures of Na2/Na3 and Na1 ions, respectively. Thus, the 45Sc NMR data confirm our conclusions on the mechanisms of sodium diffusion in the Na9Sc(MoO4)6 compound.
The features of local structure allow us to explain why the Na2 and Na3 ions are activated at substantially lower temperature while the Na1 ions remain static up to 550 K (although, considering the jump length as a main criterion we should get the opposite situation because the interatomic distances rNa1–Na3 ≈ 3.65 Å, rNa1–Na2 ≈ 3.69 Å are shorter than rNa2–Na2 ≈ 3.85 Å and rNa3–Na3 ≈ 4.07 Å). We have to take into account the fact that the probability of ion jump is determined not only by the jump length directly but also by other factors such as the type of adjacent cation (that defines the force of coulombic attraction) and the size of the “saddle point” (triangular oxygen window that has to be passed for ion release from a distinct site).38,68–70 In some cases even more tiny features such as the “geometry” of saddle point can play an important role and determine the mechanisms of ion diffusion.60 From this point of view the “immobility” of Na1 ions at T < 550 K seems to be quite natural. Indeed, the jump Na1 → Na3 which is the most expected from interatomic distance is restricted most likely due to a very small square of a triangle face: the corresponding O–O distances for this face are only 3.528, 3.257 and 2.921 Å. The jump Na1 → Na2 seems to be more probable from “geometrical” point of view: the corresponding O–O distances are equal to 3.257, 3.835 and 4.463 Å. However, the adjacent tetrahedral site for this jump is very close to highly charged Mo6+ ion (r < 2 Å).
Besides the clarifying of ion transport mechanisms, the temperature evolution of NMR spectrum allows us to estimate the parameters of ion diffusion, in particular, the characteristic ion jump frequency, τd−1. As it is expected,50 the motional narrowing occurs at a temperature where the characteristic frequency of ion jumps exceeds the “rigid lattice” (i.e., in the absence of ion motion) line width: τd−1 ∼ 2πΔνRL. Taking into account the value of ΔνRL ≈ 1.2 kHz (see Fig. 6a) we can estimate τd−1 ∼ 104 s−1 at T ≈ 400 K for Na-ions jumps within the Na2/Na3 sublattice. Similarly, for the “two-site exchange” it is expected71 that in the point of spectra coalescence the τd−1 ∼ |ωQ1(2)RL − ωQ2(2)RL|. Thus, for Na1 ↔ Na2/Na3 jumps we can estimate the τd−1 ∼ 104 s−1 at T ≈ 600 K. The analysis of Δν(T) allows also to estimate roughly the activation energy for ion motion, Ea. Several approaches have been developed for such an analysis (see for example, ref. 72–74). The simplest one, proposed by Waugh and Fedin74 suggests that:
Ea (meV) = 1.617T0 (K), | (1) |
Fig. 8 Semi-logarithmic Arrhenius plot of the 23Na spin–lattice relaxation rate for Na9Sc(MoO4)6. The filled and empty circles correspond to the slow (T1S−1) and fast (T1F−1) relaxation components, respectively. The green line corresponds to fit of experimental data on T1F−1 by eqn (5). Red and blue solid lines are the contributions from high- and low-temperature T1F−1 peaks (see text). The inset shows the values of τd−1 = 109 s−1 estimated from (T1−1)HTmax (red circle) and (T1−1)LTmax (blue circle), as well as τd−1 = 104 s−1 (black square and triangle) which are expected from the 23Na Δν(T) and νQ(T) data for Na2/Na3 and Na1 jumps, respectively. The red and blue solid lines correspond to (τHTd)−1 and (τLTd)−1 values obtained from eqn (5), black dashed line – the estimates of τd−1 for Na1 ↔ Na2/Na3 jumps from eqn (4) (see text). |
The main feature of the T1F−1 temperature dependence in Na9Sc(MoO4)6 is the maximum at Tmax ≈ 730 K. The appearance of a maximum on the T1−1(T) dependence is typical for materials with fast ion diffusion. The simplest model describing the dynamic contribution to T1−1 was proposed by Bloembergen, Purcell and Pound.79 Within the framework of BPP model, the T1−1(T) dependence is determined by the expression:
T1−1(T) ∝ C{J(1)(ω0) + 4J(2)(2ω0)}, | (2) |
(3) |
τd = τd0exp(Ea/kBT), | (4) |
Nevertheless, as can be seen from Fig. 8 the T1−1vs. T−1 dependence for Na9Sc(MoO4)6 significantly deviates from the expected asymptotic behavior due to the presence of an additional low-temperature maximum at Tmax ≈ 500 K. Similar dependences with two peaks of T1−1 were observed earlier for some lithium and proton-conducting materials and have been interpreted in the assumption of a coexistence of different types of atomic motion with highly differing jump frequencies and activation energies.80–82 For this case the experimental data on T1−1 can be fitted by the modified equation:
T1−1(T) ∝ C1{J(1)HT(ω0) + 4J(2)HT(2ω0)} + C2{J(1)LT(ω0) + 4J(2)LT(2ω0)}, | (5) |
(6) |
τHTd = τHTd0exp(EHTa/kBT), τLTd = τLTd0exp(ELTa/kBT). | (7) |
As can be seen, the high-temperature maximum of T1−1 at Tmax ≈ 730 K and the 23Na NMR line narrowing observed at T ≥ 390 K are induced by one motional process, namely by the long-range Na diffusion within the Na2/Na3 sublattice. The maximum of T1−1 induced by the Na1 ↔ Na2/Na3 jumps should be observed at Tmax ∼ 1300 K. The most interesting feature of the T1−1(T) data is the low-temperature spin–lattice relaxation maximum at Tmax ≈ 500 K. It must be obviously induced by some much faster motional process. The most probable candidate for this fast ion motion is the localized “back and forth” jumps Na3 ↔ Na2. Indeed, the crystal structure of Na9Sc(MoO4)6 implies the formation of adjacent Na3O6 and Na2O6 octahedra (see Fig. 1). These sites have the shortest interatomic distance, rNa2–Na3 = 3.027 Å. Moreover, these Na3O6 and Na2O6 octahedra share faces, not edges, so this jump can occur directly without any intermediate position. Furthermore, this pair of ions is distant from other available sites at rNa2–Na2 = 3.847 Å and/or rNa3–Na3 = 4.074 Å. So, it seems to be quite reasonable to suppose the realization of localized jumps within this Na3–Na2 pair in the temperature range where the heat energy is already enough for these short “back and forth” jumps but not yet enough for the long-range diffusion onset. These considerations are consistent with the results of ab initio calculations.
Path | R Na–Na | E a, eV |
---|---|---|
Na2–Na3 | 3.04 | 0.12 |
Na3–Na3 | 4.05 | 0.53 |
Na2–Na2 | 3.93 | 0.59 |
Na1–Na3 | 3.78 | 0.69 |
Na1–Na2 | 3.84 | 0.84 |
Fig. 9 Calculated diffusion paths of sodium jumps in Na9Sc(MoO4)6: Na1 ↔ Na2/Na3 (yellow circles), Na2 ↔ Na2 and Na3 ↔ Na3 (purple circles), Na2 ↔ Na3 (black circles). |
The mechanism of the long-range sodium diffusion is similar to that revealed in the related Na9Al(MoO4)6. With increasing temperature, Na-ions located far from the [R(MoO4)6]9− (R = Al, Sc) clusters are activated first, while ions located in the vicinity of the [R(MoO4)6]9− polyhedra start to participate in diffusion processes at significantly higher temperatures. Nevertheless, there are substantial differences in the Na dynamics: first, all motional effects are detected by NMR at lower (on ∼100 degrees) temperatures in Na9Al(MoO4)6 and estimates of Ea for different ion jumps yield lower values (on ∼0.2 eV).37 Second, in contrast to Na9Sc(MoO4)6, the localized sodium jumps in Na9Al(MoO4)6 are not observed in explicit form. Some deviations from the linear behavior of lnT1−1(T1) at T ∼ 360 K (see Fig. 10 in ref. 37) can be interpreted by the presence of additional low-temperature peak of T1−1. Nevertheless, these deviations are rather small, so it is difficult to conclude whether this is the real presence of an additional peak of relaxation rate or just the errors in the T1−1 measurements. Moreover, even if we assume the presence of local Na jumps in Na9Al(MoO4)6, the amplitude of the corresponding T1−1 maximum is very low reflecting low fraction of sodium participating in this localized motion. The features of sodium dynamics correlate with the features of crystal structures for Na9Sc(MoO4)6 and Na9Al(MoO4)6. Indeed, Na9Al(MoO4)6 also contains the pairs of adjacent octahedra with a common face: Na3O6–Na5O6. These sites are even closer to each other (rNa3–Na5 = 2.86 Å) than the corresponding sites in Na9Sc(MoO4)6. However, due to very large distortions of the Na3O6 and Na5O6 octahedra37 the O–O distances at the common face are rather short (4.16, 2.93, and 2.95 Å), so the probability of direct Na3 ↔ Na5 jump should be rather low. The intermediate tetrahedral site must be involved for this jump, which elongates the total path and increases the total value of Ea. Meanwhile, other distances in the sublattice of the Na3–Na5 positions (rNa4–Na4 = 3.29 Å, rNa3–Na4 = 3.56 Å, rNa4–Na5 = 3.88 Å) are significantly shorter than the corresponding values in Sc-containing compound: rNa2–Na2 = 3.847 Å, rNa3–Na3 = 4.074 Å. Thus, it becomes clear that there are no structural prerequisites for the realization of localized ion motion in Na9Al(MoO4)6, meanwhile the overall ion dynamics should be higher than that in Na9Sc(MoO4)6.
Note, that the correlation effects in sodium motion that were found in Na9Al(MoO4)637 were not observed in Na9Sc(MoO4)6. For Na9Al(MoO4)6 we assumed that the correlation effects slowing down the Na motion at T < 575 K are induced by the interaction between the neighboring mobile ions Na3–Na5 and the “static” Na1, Na2 ones.37 Due to similar interatomic distances, we expected to observe similar effects also in Na9Sc(MoO4)6. However, the characteristic features,37,57,83–86 such as the bending on the σ(T) dependence with a higher slope in the low-temperature region and a lower slope at higher temperatures and/or a large difference between the values of ENMRa and Econda was not found in Na9Sc(MoO4)6. Thus, the question on the origin of the correlation effects in sodium motion in Na9M3+(MoO4)6 (R = Al, Sc) remains open so far.
This journal is © the Owner Societies 2020 |