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Coexistence of Two Types of Lithium Motion in Monoclinic LiHfO: Li NMR and ab Initio Calculation Results 2

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Anton L. Buzlukov, Irina Yu. Arapova, Yana V. Baklanova, Nadezhda I. Medvedeva, Tatiana A. Denisova, and Stanislav V. Verkhovskii J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06029 • Publication Date (Web): 28 Sep 2016 Downloaded from http://pubs.acs.org on October 7, 2016

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The Journal of Physical Chemistry

Coexistence of Two Types of Lithium Motion in Monoclinic Li2HfO3: 6,7Li NMR and ab Initio Calculation Results Anton L. Buzlukov,*,† Irina Yu. Arapova,† Yana V. Baklanova,‡ Nadezhda I. Medvedeva,‡ Tatiana A. Denisova,‡ and Stanislav V. Verkhovskii† †

Institute of Metal Physics UB RAS, 18 S. Kovalevskaya Str., 620990 Ekaterinburg, Russia

‡

Institute of Solid State Chemistry UB RAS, 91 Pervomaiskaya Str., 620990 Ekaterinburg,

Russia

ABSTRACT This paper presents the results of lithium dynamics studies in monoclinic βLi2HfO3. The 6Li MAS and 7Li static NMR experiments and ab initio calculations have been performed to clarify the features of lithium motion in this layered Liconducting oxide. It was revealed that two types of lithium motion with significantly different characteristic jump frequencies coexist at 425 – 900 K. One of the processes, responsible for the long-range lithium diffusion, is characterized by the activation energy, Ea = 1.00 ± 0.05 eV, and the ions jump frequency, τd-1 ~ 104 s-1, at T ~ 750 K. The long-range lithium diffusion

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represents the successive ion jumps between the non-equivalent octahedral sites in Li/Hf- and Lilayers, occurring through the distinct type of tetrahedral interstitials (meanwhile two other types of tetrahedra are less involved in motion). Another type of ion dynamics is much more rapid localized motion of Li ions with Ea ~ 0.6 eV and τd-1 ~ 104 s-1 already at T ~ 400 K. The mechanisms of lithium motion in Li2HfO3 are closely related to the features of local crystal structure and to the presence of substitution point defects Hf → Li.

1. INTRODUCTION The low-temperature monoclinic modifications of the so-called lithium metalates (compounds with general chemical formula Li2MO3, where M = Ti, Zr and Hf) are considered as promising materials for some practical applications. They have the prospects for use as CO2 sorbents,1,2 for breeder blankets in fusion reactors,3–7 as the materials for lithium-ion energy sources.8,9 For all these applications the information on the mechanisms of ion transport is critical, especially that obtained on the atomic level by “local” experimental methods. On the other hand, these materials can be considered as the model systems for the lithium diffusion mechanisms studies for wide range of layered Li-conducting oxides. The monoclinic phases Li2MO3 are described in the C2/c space group. Their crystal structure represents the cubic close packing oxygen atoms network, which is orderly filled by the metal ions (M4+, Li+) residing the edge-sharing octahedral interstitial sites. An ordering of the cation sites results in the layered structure which particular pattern depends on the difference of the sixcoordinated ion radii rVI(M4+) and rVI(Li+) = 0.76 Å.10 There are three lithium positions in the layered Li2TiO3 (rVI(Ti4+) = 0.605 Å): two distinctly distorted octahedral sites, Li1 and Li2 form


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pure Li-layer, and the Li3 site is placed in adjacent LiTi2 layers stacking along c-axis.11,12 Whereas only two lithium sites, Li1 and Li2,13 exist in the monoclinic Li2ZrO3 (rVI(Zr4+) = 0.72 Å): the Li2(O)6 octahedrons form the Li-layers in the ac plane, which are separated each other in the b direction by mixed, LiZr2, bilayers with alternating Li1(O)6 and Zr(O)6 octahedrons.14 Despite quite different long-range ordering of the (Li, M) cations the edge-sharing connection of the LiO6 octahedrons is the joint structural feature of the monoclinic Li2MO3 metalates. As a result for all these compounds the pathway of the Li jump should include intermediate tetrahedral pores, which are face-shared with neighboring octahedra. The other structural feature is that the pure Li-layer is characterized by the shortest distances between adjacent Li positions, meanwhile the sites from nearby mixed Li/M layers are more distant. So, the lowest energy barrier can be expected for ion jumps inside pure Li-layer that implies in turn the 2D diffusion as the most probable mechanism. Nevertheless, recent NMR studies of Li2ZrO314,15, Li2TiO316,17 and Li2SnO318 show that the long-range lithium diffusion in these layered compounds occurs mainly by chemical exchange between the sites in the Li- and Li/M-layers with the activation energy, Ea ≈ 0.6 and ≈ 0.80 eV, for Li2ZrO3 and Li2TiO3, respectively.14,17 Moreover, as it was suggested by B. Ruprecht et al.17 in Li2TiO3 in addition to the long-range lithium diffusion the localized Li jumps with much lower Ea ≈ 0.47 eV occur inside the Li-layers (in ab-plane).


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Figure 1. (a) Crystal structure of monoclinic Li2HfO3. (b) The octahedral sites Hf(O)6, Li1(O)6 and Li2(O)6, the relevant Li(Hf) – O distances (in angstroms) are shown. In contrast to more widely studied Li2ZrO3 and Li2TiO3, the hafnium metalate, Li2HfO3, is less studied. The Li2HfO3 is considered as a structural analogue of Li2ZrO3.19-21 Figure 1a shows the crystal structure of Li2HfO3 in the [0 ±1/6 1/2] projection illuminating the octahedral Li2 sites (we used the VESTA22 software for structure representations). Despite the proximity of crystal structures for Li2HfO3 and Li2ZrO3 the ionic radius of the six-coordinated Hf4+ is slightly less of that for rVI(Zr4+) and is shifted towards rVI(Ti4+).10 Taking into account the more compressed mixed (Li, M) bilayer, it is worth to study the Li dynamics in Li2HfO3 with aim to trace the possible impact of the “size” factors on the Li motion. This paper presents the results of Nuclear Magnetic Resonance (NMR) study performed on 6,7Li nuclei. The variations with temperature of NMR spectra and spin-lattice relaxation rates yield the direct information on the mechanisms of ion diffusion. The NMR data were supplemented by the results of ab initio calculations: the parameters of NMR spectra and the formation energies for different structural defects were


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calculated. The joint analysis of NMR results and theoretical calculations allowed us to shed light on the mechanisms of lithium motion in monoclinic Li2HfO3.

2. EXPERIMENTAL For the Li2HfO3 synthesis a stoichiometric amount of Li2CO3 (99.9%) and fresh HfO2×4.5H2O was dissolved in a nitric acid solution HNO3 (2M) with continual stirring and heating at 150 °C. Citric acid (C6H8O7·2H2O) powder was added to the solution, which then was boiled down till the formation of a dry residual solid. Calcination of the precipitate was performed in several steps in the temperature range 300 – 700 °С with intermediate cooling and regrinding in an agate mortar at each stage. Particular details of the synthesis of Li2HfO3 by citrate combustion method is reported elsewhere.21 According to X-ray diffraction (XRD) data the Li2HfO3 crystal structure belongs to the monoclinic space group C2/c with the lattice parameters a = 5.4149(2) Å, b = 8.9795(3) Å, с = 5.3991(2) Å and β = 112.83(1)°. The chemical composition of the sample was determined by an emission spectral analysis using an Optima 4300 DV with inductively coupled plasma (Hf contents) and by atomic absorption spectroscopy in an acetylene-air flame using a Perkin-Elmer 503 spectrometer (Li content). The error of determination of each element did not exceed 5% relative to a chemical composition. Before NMR experiments the sample was heattreated at 800 °C for 2 h to remove any sorption


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Figure 2. X-ray powder diffraction patterns of Li2HfO3 obtained at RT, 500 °C and 700 °C.

products CO2 and H2O. Albeit the NMR data have showed completely reversible behavior of the ceramic sample in the heating and cooling runs, the XRD and chemical examinations were performed at room T to confirm independently that the phase and the lithium and hafnium content remain unchanged after long-time heating at T > 700 K. In situ XRD patterns were collected at 30, 500 and 700 °С on XRD 7000 Maxima diffractometer equipped with a hot chamber HA-1001 Shimadzu using Cu Kα1 irradiation in the 2θ range 15 – 55° with a step of 0.03°. The temperature changes were performed with heating rate 5 °C/min and annealing during 45 minutes at each temperature. The phase purities were checked by comparing their XRD patterns with those in the Powder diffraction file - PDF2 database (ICDD, USA, release 2010). No additional peaks from any intermediate phases are observed; all diffraction peaks match well with the monoclinic Li2HfO3 phase (see Figure 2). The 7Li NMR measurements were performed over the temperature range (300 – 900) K on an AVANCE III 500WB BRUKER spectrometer in magnetic field H0 = 11.74 Т (the Larmor frequency for 7Li, ω0/2π = 194.37 MHz). The commercial high-temperature wide-line probe


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(Bruker Biospin GmbH, Germany), including the Pt-wired rf coil, nonmagnetic heater and the type-E thermocouple, was used to heat a sample in static air atmosphere up to 950 K with residual temperature gradient along the rf coil less than 10 K/cm at the highest temperature. The polycrystalline sample of Li2HfO3 was tightly packed inside an open quartz ampoule throughout NMR measurement. The static spectra of 7Li (the nuclear spin 7I = 3/2; quadrupole moment 7Q = – 0.04 barn) including all 2I transitions were obtained by Fourier transform of both free induction decay (FID) and spin echo signals. The duration of the first exciting radio-frequency (rf) pulse was equal to 1.8 µs, corresponding to the nuclear magnetization flip angle, θ ~ π/3. The 16-fold phase (x, y) cycling23 was applied for the spin echo sequence (π/3)x – tdel – (2π/3)y at tdel = 85 µs. This cycling scheme allows to suppress the unwanted FID and the acoustic-ringing signals appearing after second pulse. The spectra deconvolution was performed with the DMFit program.24 The quadrupole frequency, νQ = (3eQ/2I(2I-1)h)VZZ, an asymmetry parameter, η = (VXX – VYY)/VZZ of the electric field gradient (EFG) tensor, {Vii}, and relative NMR intensities for the distinct Li sites were estimated. The static 7Li NMR spectra were supplemented by the 6Li (ω0/2π = 73.60 MHz; 6I = 1; 6Q = – 0.0006 barn) spectra measured under magic angle spinning (MAS) conditions. The 6Li MAS NMR spectra were obtained at room temperature using a 3.2 mm rotor at a MAS speed of 20 kHz. A 1M aqueous solution of LiCl (6δ = 0 ppm) was used as a reference. The parameters of ion dynamics were determined from temperature dependences of the 7Li spin-lattice relaxation rates, T1-1, and the spin-alignment echo (SAE) decay times, τSAE. These experiments were performed in the temperature range (300 – 900) K. The relaxation times, T1, were measured using an inversion - recovery technique, "(π) - tdel - (π/2) - acq" with the π-pulse duration of ~ 5 µs. For τSAE measurements the three-pulse sequence originated from the Jeener-


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Broekaert experiment25 was used, "(π/2) - tp - (π/4) - tm - (π/4) - acq". The preparation time, tp = 10 µs, was fixed whereas the mixing time, tm, was varied in the range 10 µs – 10 s. This method allows to measure the characteristic frequencies of atomic jumps, τd-1, in a slow diffusion regime, τd-1 < 104 s-1, and shows oneself to be working well for nuclei with I = 3/2.17, 26–31 The theoretical calculations were performed by using ab initio projector augmented-wave (PAW) method with Vienna Ab initio Simulation Package (VASP)32,33 and generalized gradient approximation (GGA) for the exchange-correlation potential.34 We used a plane wave cutoff energy of 500 eV and a convergence criterion for total energy less than 0.1 meV. Integration in the Brillouin zone was done according to the Γ-centered Monkhorst–Pack scheme with a mesh of 10×10×12 and 6×6×8 irreducible k-points for small (12 atoms) and large (48 atoms) cells. All structures were relaxed with respect to atomic positions via a conjugate gradient method until the atomic forces were less than 0.05 eV/Å. The EFG tensor is directly determined as a second derivative of potential at nucleus and its diagonalization provides the principal components {VXX; VYY; VZZ}. The calculated values of νQ and η are compared with experimental results in Table 1. Moreover, using a 48-atom supercell, we calculated the formation energies of various defects, Ef, such as vacancies in the Hf, Li1 and Li2 positions; anti-site defects Hf ↔ Li1(Li2); “extra” Li atom in the Hf site (LiHf‴); “extra” Hf atom in Li sublattices (HfLi1•••, HfLi2•••); the formation of Li vacancies near such HfLi••• ions (the calculated Ef values are listed in Table 2). Table 1. The calculated values of quadrupole frequency, νQ, and asymmetry parameter, η, for Li1(O)6 and Li2(O)6 octahedra in Li2HfO3 in comparison with the 7Li NMR results. Li2HfO3 Li1-

νQ

calculations

experiment

0.066

0.054


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site

Li2site

(MHz) η

0.036

0.014

νQ (MHz)

0.032

0.032

η

0.016

0.15

3. RESULTS AND DISCUSSION 3.1. Different types of Li sites and vacancies distribution in “rigid lattice” For T < 425 K the 7Li NMR spectra in Li2HfO3 are reminiscent of those were revealed recently for the related Li2ZrO3 compound.14,15 The spectra (see Figure 3a) are composed of two distinct powder NMR spectra typical for quadrupole nucleus with the spin I = 3/2 in the presence of a non-zero EFG. The measured spectrum is a superposition of two signals each of them, in turn, consists of a set of three NMR lines corresponding to the central transition (mI = -1/2 ↔ +1/2) and two overlapped satellites lines corresponding to mI = +1/2 ↔ +3/2 and -3/2 ↔ -1/2 transitions. The peaks of satellites are symmetrically shifted at a distance of ±1/2νQ(1 - η) relative to the central line.


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Figure 3. 7Li static NMR spectra acquired for Li2HfO3 at 300 K (a) and 500 K (b) by using spin echo pulse sequence (H0 = 11.74 T). The different NMR signals corresponding to lithium nuclei in Li1 (green) and Li2 (blue) sites are present. The sharp purple Line-3 corresponds to Li involving in local motion (see Sec. 3.3).

The values of quadrupole frequency, νQ, and asymmetry parameter, η, significantly differ for these two NMR signals. One of them (Line-1) is characterized by the values νQ ≈ 54 kHz and η ≈ 0.01; whereas for Line-2 these values are about 32 kHz, and 0.1, respectively. The widths of the central lines, ∆ν, are approximately the same for both signals (≈ 8 kHz). Taking into account the features of lithium local coordinations (see Figure 1b, which represents the octahedral coordinations Hf(O)6, Li1(O)6 and Li2(O)6 with the relevant characteristic distances Hf(Li) － O)


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we can unambiguously attribute the observed Line-1 and Line-2 to the octahedral positions Li1 and Li2, respectively. Indeed, the higher νQ values can be expected for more distorted Li1 sites.14,15 Such assignment is consistent with the results of numerical calculations of the EFG tensor parameters for distinct Li sites (see Table 1). The 6Li MAS NMR spectrum (Figure 4a) is reminiscent again of that is observed for Li2ZrO3 14,15

and consists of two lines with different widths and chemical shifts, δ. The tendency to a

decrease of δ value is usually attributed to an increase of Li – O ionicity that accompanies higher coordination number of lithium.35

Figure 4. 6Li MAS NMR spectra obtained in Li2HfO3 for (a) pristine sample, and (b) after annealing (900 K, 1hour) and subsequent quench in liquid N2 (H0 = 11.74 T). The different NMR


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signals corresponding to lithium nuclei in Li1 (green) and Li2 (blue) sites are present. The Line-3 corresponds to Li in tetra-sites (see Sec. 3.3).

As it was noted above, the octahedron (Li1)O6 is more distorted as is compared to the (Li2)O6 one. So, the coordination number of lithium ions in Li1 positions should be lower than that for Li2. Based on these considerations, we attributed the Line-1 (δ = 0.12 ppm, ∆ν ≈ 12.8 Hz) to the lithium ions in the Li1 sites, while the Line-2 (δ = –0.15 ppm, ∆ν ≈ 10.7 Hz) corresponds to the positions Li2. Thus, both 6Li and 7Li NMR data reveal for the “rigid lattice” (i.e. in the absence of ion motion) only two types of Li sites in Li2HfO3 in accordance with structural data. Moreover, for both 6Li and 7Li NMR the signal corresponding to Li1 is characterized by slightly higher relative intensity: the ratio Int(Line-2)/Int(Line-1) equals to 0.83(4) and 0.87(8) for 6Li and 7Li, respectively. It suggests that the sublattice of Li2 sites is less filled and contains a larger number of vacancies. These data coincide with the results of numerical calculations which predict slightly lower energy for vacancy formation in Li2 sublattice (4.6 eV) comparing with that for Li1: Ef = 4.7 eV (see Table 2).


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Figure 5. 7Li static NMR spectra acquired for Li2HfO3 at 300 ≤ T ≤ 900 K (spin echo pulse sequence, H0 = 11.74 T). For clarity the central line (a) and satellites (b) are shown separately.

Moreover, they are consistent with the calculations and NMR results reported recently for the related Li2ZrO3 compound.14

3.2. Long-range lithium diffusion 3.2.1. The 7Li NMR spectra temperature behavior


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Figure 5 presents the 7Li NMR spectra, measured in the temperature range 300 – 900 K (the central line and satellites are shown separately for clarity on Figure 5a and 5b, respectively). Figures 6a - c show the temperature dependences of the quadrupole frequency, νQ, the central line width, ∆ν, and the relative lines intensities, respectively. As can be seen from these data, the 7

Li NMR spectra are drastically changed with temperature increasing. First, some new line

appears at T ≥ 425 K (this line is present on Figure 3b which shows the deconvolution of 7Li NMR spectrum obtained at T = 500 K). This Line-3 is characterized by small value of ∆ν ≈ 1.3 kHz (which remains almost constant for the whole temperature range), and the absence of satellite lines. The reasons of this Line-3 appearance will be discussed in Sec 3.3. Second, at T > 750 K the line widths narrow sharply for both Line-1 and Line-2. Moreover, the distance between the satellites peaks, 1/2{νQ(Li1)[1 – η(Li1)] – νQ(Li2)[1 – η( Li2)]}, starts to decrease


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Figure 6. Temperature dependences of the 7Li static NMR spectra parameters: (a) quadrupole frequency, νQ; (b) central line width, ∆ν; and (c) the relative lines intensities are shown for Line1 (green solid circles), Line-2 (blue open squares), their merged line (black crosses) and Line-3 (purple diamonds).

rapidly at the same temperature range. As a result, Lines 1 and 2 are merged into one line at T ≥ 825 K (the parameters of this line are labeled on Figure 6 as “merged line”). The average values of and for this merged line are equal to 41.5(5) kHz and 0.02(2), respectively. The combination of both these dependences, ∆ν(T) and νQ(T), suggests the presence of a longrange lithium diffusion in Li2HfO3. In fact, among the factors affecting the central line width only homonuclear 7Li–7Li magnetic dipolar interaction has to be taken into account in our case.36 For 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 the changes in both the distances and the orientations. As a result, with temperature increasing and the growth of ion jump frequency the dipolar interaction is averaged and a sharp decrease of the ∆ν value is expected.36 As can be concluded form νQ(T) data, the main mechanism for the long-range lithium diffusion in Li2HfO3 is the chemical exchange Li1 ↔ Li2. Indeed, the peculiar merging of two NMR lines is direct evidence of that diffusive motion of lithium occurs mainly by means of inter-site jumps between non-equivalent Li1 and Li2 sites while a probability of the jumps between equivalent Li1 ↔ Li1 and/or Li2 ↔ Li2 sites remains negligible. These jumps should induce only the central and satellite lines (also due to magnetic fields averaging) narrowing, but the νQ values should remain almost unchangeable for Lines 1 and 2. The average = 41.5(5) kHz is slightly less than the arithmetic mean value for “rigid lattice”: [νQ(Li1)RT + νQ(Li2)RT]/2 =


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43 kHz. The average value of quadrupole frequency has to be defined (in the case of fast chemical exchange between the sites with almost equal filling) by the difference of the mean residence times at distinct positions: = [νQ(Li1)τd1 + νQ(Li2)τd2]/(τd1 + τd2). This result indicates that the thermally activated lithium diffusion is non-uniform even for the highest temperatures: Li ions spend slightly longer time in the Li2 sites between the subsequent jumps.

3.2.2. The parameters of long-range Li ions diffusion The experimental data on νQ(T) and ∆ν(T) make it possible to estimate the parameters of lithium diffusion. The Li jumps start to affect the NMR spectra parameters only when their jump rate reaches some characteristic value. It opens the possibilities for the ion jump frequency, τd-1, estimates. In particular, the beginning of the satellite lines "merger" should be observed at the temperatures, where the τd-1/2π value becomes comparable with the difference of quadrupole splittings for the "rigid lattice": ∆νQ = [νQ(Li1) – νQ(Li2)]RT. Analogously, the central line narrowing is expected when the characteristic ion jump frequency exceeds the 2π∆ν value for "rigid lattice".36 Thus, taking into account the “rigid lattice” values for ∆νQ ≈ 22 kHz and ∆ν ≈ 8 kHz, we can roughly estimate the value of τd-1 ~ 104 – 105 s-1 at T ~ 750 K. The temperature behavior of ∆ν allows also to estimate the activation energy value for long-range lithium diffusion, Ea. The different approaches for such type of analysis can be found, for an example, in the paper.37 The simplest phenomenological approach proposed by Waugh and Fedin suggests:38

(1)

Ea ( meV ) = 1.617T0 (K ),


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where T0 is the temperature of the beginning of “motional” line narrowing. With T0 ~ 700 – 750 K (see Figure 6b) the Eq. (1) yields the value of Ea ≈ 1.1 – 1.2 eV. It has to be noted however that only rough estimates can be done in the framework of this approach. For more accurate determination of Ea value we performed also the 7Li spin-lattice relaxation rates, T1-1, measurements.

Figure 7. Temperature dependences of the 7Li spin-lattice relaxation and SAE decay rates measured at 300 ≤ T ≤ 900 K. Both relaxation component T1S-1 (squares) and T1F-1 (circles) are shown. The up and down triangles represent the τSAE-1 values obtained in Eqs. (3) and (4), respectively. The estimates of Ea are shown as solid lines.

For the entire temperature range 300 – 900 K the recovery of nuclear magnetization, M, was characterized by non-exponential behavior after the inverting π-pulse. At least two relaxation components were required for the experimental data approximation: M(t) = M0(1 – c1exp(-t/T1S) – c2exp(-t/T1F)), where M0 is the equilibrium value of the nuclear magnetization, T1F and T1S - the fast and the slow component of the magnetization recovery, respectively; the values c1 and c2


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determine the weight of corresponding components: c1 + c2 = 1. Such biexponential behavior of M(t) is expected for nucleus with I = 3/2 in the case of pure quadrupole relaxation at uniform excitation of the central and satellite transitions.39,40 Nevertheless the weights of exponents deviate from the expected values: c1 = 0.8, c2 = 0.239,41 that can be induced by magnetic contribution to T1-1 which is hard to be accurately evaluated. This contribution was taken into account by adjusting the weight of each exponent to obtain the best fitting result (c1 was varied with temperature in the range 0.6 - 0.8). As can be seen from Figure 7 both components T1S-1 and T1F-1 display a drastic increase at T > 750 K. It is induced most likely by the diffusion of Li ions, which leads to a reinforcement of the spin-lattice relaxation mechanisms. The simplest model, appropriate for the analysis of motional contribution in T1-1 was developed by N. Bloembergen, E.M. Purcell and R.V. Pound.42 In the framework of BPP model the maximum of T1-1 is expected at the temperature where τd-1 ~ ω0. If the τd-1(T) dependence is submitted to the “classical” Arrhenius low: ~ exp(–Ea/kBT), the plot lnT1-1 vs T-1 is expected to be linear with the slopes Ea/kB and –Ea/kB at the fast- and slowdiffusion limits, respectively. The linear fit (solid lines) yields in both cases the activation energy value Ea = 1.00 ± 0.05 eV, coinciding with that is obtained from ∆ν(T) dependence. It has to be noted that this value may be slightly lower than the real energy barrier. For an example, in the presence of a significant distribution of ionic jumps frequencies the low-temperature slope of the lnT1-1(T-1) plot is less steep than the high-temperature one.43-45 So, it is necessary to have the data on T1-1 on the high-temperature slope for more accurate determination of Ea. The other striking feature of T1-1(T) dependence is some low upturn of T1S(F)-1 values at 550 < T < 700 K (which is clearly seen with respect to linear non-diffusive T1bgr-1 on Figure 7). It can be


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ascribed to the presence at these temperatures the maximum of T1S(F)-1 arising from the localized Li jumps (see Sec. 3.3. for more details). To scrutinize the parameters of ion diffusion in an independent way the spin-alignment echo (SAE) decay time, τSAE, was measured at temperature range (300 – 900) K. The spin-alignment echo appears at t = tm in the three-pulse sequence experiment (90°)φ1 – tp – (45°)φ2 – tm – (45°)φ3 – t – acq, based on the pioneer experiment by Jeener-Broekaert.25 By choosing the proper pulse phasing {φi}46–50 the spin-alignment echo amplitude can be expressed as the two-time correlation function:

S 2 (t p , t m ) ∝ sin [ωQ (t m = 0)t p ]sin [ωQ (t m )t p ] ,

(2)

where ωQ(tm = 0) and ωQ(tm ) are the quadrupole frequency of the 7Li nucleus at the mixing time tm = 0 and tm respectively. The jumps of Li ions between the sites with different EFG’s (and different ωQi) change in time the ωQ value of the corresponding 7Li nuclei. The correlation function S2(tm) represents the ensemble average probability to detect the 7Li spins, which keep unchanged the ωQ value during mixing time interval (0; tm). The SAE amplitude usually decays with time tm following to a stretched exponential function:

S 2 (t p , tm ) ∝ exp(−(tm / τ SAE )γ ),

(3)

where the τSAE-1 value in the ideal case (γ = 1) equals to the frequency of ion jumps, τd-1. Figure 8 shows some characteristic dependences S2(tm) measured at different temperatures. Solid lines on Figure 8 represent the results of the experimental data fits by Eq. (3).


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Figure 8. 7Li spin-alignment echo (SAE) amplitudes (S2) as a function of mixing time (tm), the preparation time (tp = 10 µs); experimental points are shown as symbols, solid and dashed lines represent the fits by Eqs. (3) and (4), respectively. Insert: filled and open circles represent the γ values, estimated in Eqs. (3) and (4), respectively.

The Arrhenius plot τSAE-1 vs T-1 is present on the insert of Fig. 7 (up triangles). The estimates of the γ value are shown on the insert of Figure 8 (filled circles). Another factor that can affect the SAE decay is the spin-lattice relaxation rate influence.26,29,31 Thus, although our S2(tm) dependences do not show the characteristic "two step" decay, we tried to take into account the possible impact of the T1-1 contribution (moreover, as it can be seen from Figure 7, the value of τSAE-1 and T1F-1 are really close to each other). In general case:31

−1

S 2 (t p , t m ) ∝ exp( − (t m / τ SAE ) γ ) exp( − (t m T1 ) β ).

(4)


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On Figure 8 the dashed lines show the results of the approximation of experimental data by Eq. (4) with the substituted values of T1F-1 for the corresponding temperatures. The estimates of the γ value are shown on the inset of Figure 8 as open circles. The β value tends to 1 for all temperatures, thus, the final processing has been performed with a fixed value β = 1. The Arrhenius plot τSAE-1 vs T-1 is present on the insert of Figure 7 (down triangles). As can be seen from the data on Figures 7 and 8, at temperatures below 700 K, the SAE decay is determined mainly by the influence of T1-1. Meanwhile, at higher temperatures the contribution associated with the ions diffusion becomes dominant. Nevertheless even for the highest temperatures the possible impact of T1-1 cannot be excluded. It results in lower (on one-two order of magnitude) values of τSAE-1 as compared with τd-1 expected from NMR spectra analysis (Sec. 3.2.2.). Thus, from the joint analysis of temperature dependences ∆ν(T), νQ(T), T1-1(T) and τSAE-1(T) we can reliably estimate the activation energy value for long-range lithium diffusion in Li2HfO3, Ea = 1 ± 0.05 eV, and the characteristic ion jump frequency τd-1 ~ 104 s-1 at T ~ 750 K.

3.2.3. The most probable pathways of Li diffusion and the factors affecting lithium mobility in Li2HfO3 The Li(O)6 octahedra are shared only by edges in the layered structure of LiMO2 oxides. The jumps of lithium between the octahedrons Li1(O)6 ↔ Li2(O)6 should occur through the intermediate tetrahedral sites.14,18,51–53 Figure 9a shows such sublattice of the tetrahedral interstitials existing in Li2HfO3. The tetrahedron volume and the type of cation in the nearest octahedron that shares a face with this tetra-site are considered as critical parameters affecting the lithium mobility in layered Li-conducting oxides.51,54 A growth of the unit cell volume is


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accompanied usually by decreasing of Ea.55,56 Following this way of reasoning a slowing down of the lithium mobility in

Figure 9. (a) Sublattice of tetrahedral interstitials in Li2HfO3, three different types of tetra-sites are present. (b) The most probable Li1 ↔ T2 ↔ Li2 (blue arrows), and less favored Li1 ↔T1 ↔ Li2 (red arrows) pathways for long-range lithium diffusion. The edge distances (in angstroms) for T1 and T2 tetra-sites are shown.

Li2HfO3 comparing with Li2ZrO3 can be explained by taking into account the smaller unit cell parameters and lower volumes of the corresponding tetra- and octa-sites. Such structural considerations18,55 account only for a size of the face that has to be passed by Li ion for migration (the “effective” radius of Li+ ion is about 0.64 Å55 which is intermediate value for octahedral, 0.76 Å, and tetrahedral, 0.59 Å, oxygen coordinations10).


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However this approach does not allow to explain our results in the full extent. It remains unclear why the alone mechanism providing lithium diffusion in Li2HfO3 is the Li1 ↔ Li2 site exchange meanwhile the jumps between equivalent positions Li2 ↔ Li2 do not observed. At first sight the Li2 sublattice contains higher amount of vacancies and the distance between Li2 neighbors is much shorter than that for the Li1 – Li2: 2.99 and 3.08 – 3.10 Å, respectively (hereinafter the interatomic distances are estimated from room temperature XRD data). Moreover, the Li2 neighbors are separated by tetra-sites T1 (the dark blue tetrahedra on Figure 9a) which have the largest volume (3.61 Å3). It can be assumed, that the Li diffusion mechanisms in Li2HfO3 are determined by more tiny structural features yielding specific shape of the triangular anionic bottleneck that has to be passed by Li ion for octahedron release. Let us consider again two different types of Li octa-sites: Li1(O)6 and Li2(O)6. As can be seen from Figure 1b, the Li1(O)6 octahedron is characterized by higher difference of Li – O bonds comparing with the Li2(O)6 one. So, the faces of Li1(O)6 octahedron also become highly distorted, and the probability for Li release can be rather different for different faces (by the other words it means the difference of barriers values for octa → tetra jumps for different types of tetrahedra even at their comparable volumes and surface squares). From these “local” considerations it becomes possible to explain an absence of the direct Li2 ↔ Li2 jumps. The Li2(O)6 octahedra are separated from each other by T1 tetrahedra which are rather “symmetric” in the sense of O – O distances: their faces have one short edge with rO–O distances of 3.00, 3.05 Å, one medium (3.23 Å) and one long edge with rO–O value equal to 3.24, 3.30 Å (see Figure 9b). At the same time the Li1 ↔ Li2 jumps can occur through all T1, T2 and T3 tetra-sites. The T3 sites (gray tetrahedra on Figure 9a) have the smallest volume (less than 3 Å3), so they can be excluded from further considerations. The most interesting is the T2 site


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(dark yellow tetrahedra on Fig. 9a). It is slightly less in volume (3.51 Å3) comparing to T1, but has the grain (shared with Li1(O)6 octahedron) bounded by edges equal to 2.89, 3.30 and 3.31 Å (Fig. 9b). It is interesting to note that the “asymmetry” of such grains only increases with temperature increase: the XRD at T = 500 °C (i.e. in the field of long-range lithium diffusion presence) yields the values 2.90, 3.34 and 3.36 Å for corresponding rO–O distances. Such oxygen configuration with two closely placed and one distant anion reduces most likely the energy barrier and induces the easier release of Li ions from Li1 sites. From this point of view slightly longer residence time for Li2 sites, τd2 (Sec. 3.2.1), seems to be rather expected. It has to be noted however that these considerations suggest the direct Li1 ↔ Li1 as the most preferred type of lithium jumps. Nevertheless, these jumps do not observed in our experiments. There are several reasons for the absence of such Li1 ↔ Li1 hops: it can be due to a lower vacancies concentration in Li1 sublattice (see Sec. 3.1), and/or due to larger distances between the neighboring sites: 2x3.09, 2x4.23 Å (for comparison, the corresponding values of Li1 – Li2 are 2x3.08 and 2x3.10 Å). Moreover, the Li1 ↔ Li1 jumps can be suppressed due to higher electrostatic repulsion: the distances to the nearest Hf4+ ions equal to ≈ 2.93 and 3.03 Å for Li1 and Li2, respectively. Thus, our “microscopic” considerations allow to suppose that: (i) the Li1(O)6 octahedra become “open” for Li release at first, and (ii) the most preferable pathway for the long-range lithium diffusion in Li2HfO3 is Li1 → T2 → Li2. Nevertheless the other more energy consuming jumps Li1 → T1 → Li2 are most likely also occur at higher temperatures. This assumption is supported by the behavior of τSAE-1 vs (T)-1 which deviates slightly from Arrhenius behavior at T > 800 K (Figure 7). The involving of additional pathway (Li1 → T1 → Li2) for lithium diffusion can lead, in principle, to some reduction of Ea and, as a result, to deviations from the Arrhenius


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line. These effects allow to explain also rather high γ values observed at T > 800 K (of about 0.8 - 1, see insert on Figure 8). Such high γ values are expected usually at the ion motion in highly ordered energy landscape with a small or absent distribution of activation energies and/or ion jump frequency. With increasing temperature and increasing lattice expansion the small difference in barriers values for the jumps Li1 → T2 → Li2 and Li1 → T1 → Li2 is reduced and the energy landscape becomes more uniform.

3.3. Localized lithium motion As it was mentioned in Sec. 3.2.1, in contrast to Li2ZrO3,14 a third spectral component appears on the 7Li NMR spectra in Li2HfO3 at T ≥ 425 K. This line is characterized by small value of central line width ∆ν ≈ 1.3 kHz remaining almost constant with temperature, and by the absence of satellite lines (for an illustration see Figure 3b representing the deconvolution of the 7Li NMR spectrum acquired at T = 500 K). The temperature dependences of the Line-3 parameters are shown on Figure 6a - c. The temperature dependence of the Line-3 relative intensity (Figure 6c) is non-monotonic: the value of Int(Line-3) increases monotonically at 425 ≤ T < 550 K; some “plateau” with Int(Line-3) ≈ 7% is observed in the range 550 < T < 750 K; further temperature increase is accompanied by the Int(Line-3) growth, and its value reaches about 30% at T = 900 K. The “first” increase of the Int(Line-3) is accompanied by a decrease (on approximately the same value) of the Int(Line-1), meanwhile the intensity of Line-2 remains almost unchangeable. The “second” growth of Int(Line-3) at T > 750 K is accompanied by reducing intensities of both Line-1 and Line-2. These effects are clearly seen from Figure 6c (and also from the comparison of the satellite lines intensities, corresponding to Line-1 and Line-2, see Figure 5b).


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The small value of ∆ν and its temperature dependence (its independence precisely speaking, see Figure 6b) allows to assume that this Line-3 is already dynamically narrowed when it appears at T = 425 K. The similar results (the coexistence of broad and sharp NMR lines with different ∆ν(T) dependences) were obtained earlier for the nanocomposites Li2O:Al2O3.57 The sharp line was assigned to the mobile Li ions in the interfaces between different phases Li2O and Al2O3. Thus, the simplest explanation of the Line-3 appearance is the formation of some new highly Li-conductive phase in Li2HfO3 at T ≥ 425 K. The new phase generation were proposed previously for the Li2TiO3:58,59 in particular, the formation of nuclei of the cubic γ-Li2TiO3 at T > 700 K. Nevertheless, this assumption contradicts to our high-temperature XRD results. As can be seen from Figure 2 no any new phase observed for the whole studied temperature range. Moreover, even assuming that this phase is “invisible” for some reasons in XRD (for an example, if it is formed on the grain boundaries and is characterized by a small volume), this scenario does not allow to explain our NMR results. The temperature dependence of Int(Line-3) should be more continuous in this case (i.e. without any plateau).57 Furthermore, taking into account the fact that any first-order transition takes some finite time, some temperature “hysteresis” should be observed. The spectrum shape and the Int(Line-3) value must be dependent form the way how the temperature of measurement was reached (from lower side to higher temperatures or otherwise; by continuous “step by step” changes or by fast temperature increase/decrease from the limits to middle part etc). However, no any similar effects were found. Thus, the observed Line-3 can be originated only from the intrinsic Li+ ions dynamics in Li2HfO3. All "motional" effects arising from long-range lithium diffusion occur only at T > 700 K. So, some other type of Li motion with lower Ea value must exist in Li2HfO3, and only some fraction


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of lithium ions (which depends from temperature) participates in this motion. The only one possible candidate can be proposed for such kind of motion: the localized Li jumps. The existence of localized motion was assumed earlier (based on the τSAE temperature behavior) for Li2TiO3.17 It was attributed to the localized jumps of Li ions between the octahedral sites in Lilayer (ab-plane in Li2TiO3). However, for such jumps (Li2 ↔ Li2 in our case) we should observe the sharp satellites with νQ ≈ 32 kHz already at T ≥ 425 K. Another candidate for local lithium jumps is the chemical exchange Li ↔ Hf. The presence of Li ions in Hf sites has been assumed previously on the basis of XRD data analysis (about 6 – 8 % of such anti-site defects).21 Despite the low energy of Li ↔ Hf defects formation (the values of Ef equal to 2.1 and 1.0 eV for Hf ↔ Li1 and Hf ↔ Li2, respectively, see Table 2) we have to reject this scenario. It requires not only lithium mobility, but also the Hf mobility on the NMR frequency scale, which seems to be rather unlikely taking into account the weight and charge of Hf4+.

Table 2. The formation energies (Еf) of various defects in Li2HfO3: the vacancies in the positions of Hf, Li1 and Li2; anti-site defects Hf ↔ Li1(Li2); “extra” Li atom in the Hf site (LiHf‴); additional HfLi••• atom in Li sublattices (HfLi1••• and HfLi2•••); the formation of Li vacancies near such “extra” HfLi••• ions. defect Еf (eV) VHf

15.2

defect

Еf (eV)

HfLi2•••

2.9

Hf ↔ Li1 LiHf‴

11.7

2.1 •••

(HfLi1 +Li1Hf‴)


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Hf ↔ Li2 VLi1ʹ

4.7

1.0 •••

(HfLi2 +Li2Hf‴)

VLiʹ VLi2ʹ

HfLi1

•••

4.6

3.2

relative to HfLi•••

VLi1ʹ + 2VLi2ʹ relative to HfLi•••

0.4–0.6 HfLi1••• 0.3–0.5 HfLi2••• 1.5 HfLi1••• 1.2 HfLi2•••

The most possible candidate for localized Li motion is the “back and forth” ion jumps from octa- to the adjacent tetra-sites. The Line-3 is clearly identified on our 7Li NMR spectra up to the highest temperatures. It implies that the local octa ↔ tetra jumps and the long-range diffusion are rather independent and they are not “merged” into one motional process. However, as it was already discussed the long-range lithium diffusion in layered oxides occurs also through the tetrahedral sites.14,18,51–53 Thus, besides the “regular” octa- and tetra-sites, there must be some specific positions in Li2HfO3 structure, where this localized motion is realized. As such specific positions the vacancies in Li1/Li2 sublattices can be proposed. The most important role play most likely the Li vacancies appearing in the vicinity of the “extra” Hf ions located in the Li sites, HfLi•••. Let us try to add one “extra” Hf4+ ion to the lithium sublattice (this scenario is shown on Figure 10, which represents the fragment of Li2HfO3 crystal structure). The Li2 position is more preferable for such HfLi••• substitution defect (this “extra” HfLi2••• ion is shown as gray sphere on Figure 10). In the sense of O–O distances and structural distortions the Li2(O)6 octahedron is closer to Hf(O)6 than the Li1(O)6 one, moreover, the distances to the nearest Hf ions are about 2.93 and 3.03 Å for Li1 and Li2, respectively. So, the results of numerical calculations (Table.


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2), showing slightly lower energy for the HfLi2 formation, seem to be rather expected. The appearance of such an additional Hf4+ ion in the Li2 site creates three vacancies in the lithium sublattice for the electroneutrality balance. Two Li2 sites and one Li1 from the neighboring Li/Hf-layer are the nearest to this HfLi2••• (they are shown on Figure 10 as yellow spheres and red sphere, respectively). According to numerical calculations, the energy cost for Li vacancy formation in the vicinity of such “extra” ion is only about 0.3 – 0.5 eV. Even for full “defect” cluster HfLi2••• + VLi1ʹ + 2VLi2ʹ generation, the Ef value remains less than that necessary for the formation of one separate vacancy in “regular” sites (about 4.1 eV for “cluster” vs 4.6 – 4.7 for VLi2ʹ and VLi1ʹ, see Table 2). On the one hand the formation of such “defect” cluster allows to explain some discrepancy with the results of ab initio calculations for the Li2TiO3 and Li2SnO3 oxides,60,61 predicting preferable localization of the Li vacancies in the LiTi(Sn)2 layer. On another hand it induces most likely local structural distortions and displacements of neighboring atoms from their equilibrium positions. The structural “relaxation” shows that in the vicinity of cluster the tetrahedra’s edges increase up to 3.37 – 3.39 Å. So, the activation energy for localized jumps can be significantly lower than that for the long-range lithium diffusion (as it was shown for the related Mn/Ni-containing layered oxide,52 in the presence of vacancies the “octa → tetra” transition can occur even spontaneously without any barrier overcoming). Assuming that the Line-3 appears as “dynamically narrowed” at T = 425 K we can estimate the T0loc value about 400 K. In this case the Eq. (1) yields the value Ealoc ≤ 0.6 eV for localized Li jumps. Taking into account that the “rigid lattice” value of ∆ν for Line-3 is the same as which is obtained for lines 1 and 2 we can expect the value of local jump frequency τd-1 ~ 104 s-1 already at T ≤ 400 K. These estimates of τd-1 and Ealoc ~ 0.6 eV yield the value of τd-1 ~ 109 s-1 at T ~ 650 K. Thus, the observed weak maximum on T1S(F)-1(T) dependence (Figure 7) indeed can be attributed to


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localized Li jumps (just to remind, the T1-1 maximum position is defined by the condition τd-1 ~ ω0). The more detailed analysis of T1S(F)-1(T) data is quite difficult to perform, since the fraction of ions involved in the localized motion in this temperature range is less than 10% and this motional contribution is barely visible on the non-difusive T1bgr. This scenario allows to explain also the absence of the satellite lines for Line-3. For fast “octa ↔ tetra” jumps the EFG will be significantly changed in both the magnitude and the direction of the main axis (our calculations yield the value of νQ ~ 200 kHz for Litetra). In this case, one can expect not the narrowing of the satellite lines (which is found for Li1 ↔ Li2 exchange), but rather their broadening and "disappearance".

Figure 10. Fragment of Li2HfO3 crystal structure representing the formation of “defect” cluster HfLi2••• + VLi1ʹ + 2VLi2ʹ. Different Li – Li bonds display the different Li sites involving in the localized motion at different temperatures.

The following picture can be proposed for the localized lithium motion in Li2HfO3. At T < 400 K all Li ions are “frozen” (on the NMR frequency scale). The temperature increase leads to the involving of some Li ions in the local jumps “octa ↔ tetra”. This induces (combining with the NMR linewidth decrease) the specific Line-3 appearance on 7Li NMR spectra at T ≥ 425 K. Two


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Li1 ions located near VLi2ʹ (their bonds are marked in red on Figure 10) will obviously be involved in such local jumps at first. These ions are located in Li1(O)6 octahedra which are more “preferable” for Li release (see Sec.3.2.3). Moreover, these ions are most distant from HfLi2••• (rLi-Hf > 5 Å), so the electrostatic repulsion that has to be surpassed for the jumps is minimal. This allows to explain both the fact that the Line-3 appearance is accompanied by a decrease of Line-1 intensity and the presence of a plateau on the plot Int(Line-3) vs T (Figure 6c). The value Int(Line-3) ≈ 7 % on the plateau is determined most likely by the amount of such ions: four per each HfLi2••• defect (Figure 10). At T > 750 K other lithium ions start to participate in localized motion: those are located in the Li1(O)6 octahedra in the vicinity of HfLi2••• ion, rLi-Hf ≈ 3 Å (gray bonds on Figure 10), and Li ions from Li2(O)6 octahedra (blue bonds). The “activation” of all available positions yields additionally 10 mobile Li ions per one HfLi2••• defect. Assuming the presence in Li2HfO3 of 1.5 − 2 at. % of such “extra” HfLi2••• ions, we obtain for the Int(Line-3) value about 6 − 8% on the plateau, and on about 2.5 times higher value at temperature increase. So, at the highest temperatures Int(Line-3) should be about 25 – 30%, which is close to that revealed in our experiments (Figure 6c). In this case, the chemical composition of the studied compound has to be close to Li1.92Hf1.02O3. This scenario allows also to explain why the long-range lithium diffusion and the localized Li jumps do not merge into one motional process. Indeed, the three lithium vacancies are “pinned” to the HfLi2••• + VLi1ʹ + 2VLi2ʹ cluster due to electroneutrality reasons. As a result, these clusters must be rather stable in time and temperatures. This retains the possibilities for local Li jumps regardless on the Li dynamics in the “regular” lattice. The following experiment has been performed to check our assumptions. The sample was annealed directly in the MAS rotor at T = 900 K during 1 hour and then it was quenched in liquid


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nitrogen. Immediately after this procedure the 6Li MAS NMR spectrum was recorded. If our assumptions are correct, we must observe some lithium ions to be “frozen” in the tetra-sites. Figure 4b presents the 6Li MAS NMR spectrum obtained after annealing and subsequent quench. As it is clear, the described procedure leads to some changes of NMR spectrum comparing with the pristine one (Figure 4a). Both Line-1 (δ = 0.13 ppm, ∆ν ≈ 12.5 Hz) and Line-2 (δ = -0.15 ppm, ∆ν ≈ 10.5 Hz) are observed, but their relative intensities are slightly changed: Int(Line2)/Int(Line-1) = 0.88 (3). Moreover, some new Line-3 is found (δ = 0.74 ppm, ∆ν ≈ 50 Hz, Int(Line-3) ≈ 8%). The increasing of Int(Line-2) seems to be expected: one would expect a more uniform distribution in Li1 and Li2 sublattices as compared with the “rigid lattice”. The Line-3 (its high ∆ν value allows to assume that this line can consist of several overlapped signals) can be originated from Li ions “frozen” in the tetrahedral sites. Indeed, taking into account their coordination number, the highest shifts can be expected for Litetra.35 From the comparison of our data for Li2HfO3 and the results obtained previously for Li2TiO317 and Li2ZrO314,15 we can conclude that the decrease of M4+ ion radius favor the presence of localized Li motion in these materials. In contrast to the Li2ZrO3, for Li2HfO3 and Li2TiO3 compounds a local lithium motion was observed in addition to the long-range lithium diffusion. The decrease of M4+ ion size leads to a reduction of Ealoc (~ 0.6 eV for Li2HfO3 according to our data, and 0.47 eV for Li2TiO317), and to an increase of the characteristic frequency of localized jumps. In fact, the typical narrow line similar to our Line-3 is clearly observed on the 7Li static NMR spectra in Li2TiO3 already at T = 320 K.16 The nature of this effect is unclear for the moment and the additional studies are required to clarify this question. We tentatively assigned these effects to the influence of “size” factors. It can be assumed that the substitution of the closest in sizes Zr4+ → Li+ induces only the small local structure distortions and there is only a


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small difference between the energy barriers for the ion jumps in "non-distorted" lattice and near such defects. So, there are no any prerequisites for the localized lithium motion realization. With decreasing ionic radius of M4+ the structural distortions become more substantial, which in turn leads to the appearance of localized Li+ jumps.

CONCLUSIONS The lithium diffusion mechanisms in the monoclinic β-Li2HfO3 were studied by means of 6,7Li NMR methods and ab initio calculations. The long-range Li diffusion is similar to that observed previously for the related Li2ZrO3 compound and occurs through thermally activated jumps between the non-equivalent octahedral structural positions in “pure” Li- and “mixed” Li/M-layer. The ion dynamics is significantly slower as compared with Li2ZrO3 and is characterized by the activation energy Ea = 1.00 ± 0.05 eV and the ions jumps frequency τd-1 ~ 104 s-1 at T ~ 750 K. The “atomic-scale” analysis allows to conclude that these jumps between Li- and Li/M-layers occur through only one distinct type of tetrahedral interstitials, meanwhile the other two types of tetra-sites are most likely not involved in the motional processes. Besides “traditional” structural factors (such as the volume of tetrahedral interstitials and corresponding bottleneck sizes) the mechanisms of Li diffusion in Li2HfO3 are determined by the local crystal structure peculiarities, in particular, by the features of triangle anionic bottleneck that has to be passed by Li ion for octahedron release. In addition to the long-range lithium diffusion the localized motion of Li ions is observed in Li2HfO3, (and it seems to be the first direct observation of such Li dynamics feature in the layered Li-conducting oxides). It originates most likely from the presence of substitution point defects Hf → Li2. The appearance of the extra Hf4+ ion in Li2 site leads to the ordering of Li


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vacancies in the neighboring sites and induces the formation of stable "defect" cluster HfLi2••• + VLi1ʹ + 2VLi2ʹ. It in turn causes the local structural distortions and creates the prerequisites for the realization of local ion jumps between adjacent filled octa- and empty tetra-sites. This localized motion is significantly faster than the long-range diffusion and is characterized by the parameters of Ea ~ 0.6 eV and τd-1 ~ 104 s-1 already at the T ~ 400 K.

AUTHOR INFORMATION

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6,7Li NMR and Ab Initio Calculation Results - American Chemical

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