Lithium ion dynamics in LiZr2(PO4)3 and Li1.4Ca0.2Zr1.8(PO4)3

Article abstract of DOI:10.1039/c9dt01786k

High ionic conductivity, electrochemical stability and small interfacial resistances against Li metal anodes are the main requirements to be fulfilled in powerful, next-generation all-solid-state batteries. Understanding ion transport in materials with sufficiently high chemical and electrochemical stability, such as rhombohedral LiZr₂(PO₄)₃, is important to further improve their properties with respect to translational Li ion dynamics. Here, we used broadband impedance spectroscopy to analyze the electrical responses of LiZr₂(PO₄)₃ and Ca-stabilized Li_1.4Ca_0.2Zr_1.8(PO₄)₃ that were prepared following a solid-state synthesis route. We investigated the influence of the starting materials, either ZrO₂ and Zr(CH₃COO)₄, on the final properties of the products and studied Li ion dynamics in the crystalline grains and across grain boundary (g.b.) regions. The Ca²⁺ content has only little effect on bulk properties (4.2 × 10^-5 S cm^-1 at 298 K, 0.41 eV), but, fortunately, the g.b. resistance decreased by 2 orders of magnitude. Whereas, ⁷Li spin-Alignment echo nuclear magnetic resonance (NMR) confirmed long-range ion transport as seen by conductivity spectroscopy, ⁷Li NMR spin-lattice relaxation revealed much smaller activation energies (0.18 eV) and points to rapid localized Li jump processes. The diffusion-induced rate peak, appearing at T = 282 K, shows Li⁺ exchange processes with rates of ca. 10⁹ s^-1 corresponding, formally, to ionic conductivities in the order of 10^-3 S cm^-1 to 10^-2 S cm^-1.

Full text of DOI:10.1039/c9dt01786k

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Lithium ion dynamics in LiZr2(PO4)3 and
Li1.4Ca0.2Zr1.8(PO4)3†
Cite this: DOI: 10.1039/c9dt01786k
Isabel Hanghofer,*a Bernhard Gadermaier, a Alexandra Wilkening,a
a,b
Daniel Rettenwander a and H. Martin R. Wilkening
*
High ionic conductivity, electrochemical stability and small interfacial resistances against Li metal anodes
are the main requirements to be fulfilled in powerful, next-generation all-solid-state batteries.
Understanding ion transport in materials with sufficiently high chemical and electrochemical stability,
such as rhombohedral LiZr2(PO4)3, is important to further improve their properties with respect to transla-
tional Li ion dynamics. Here, we used broadband impedance spectroscopy to analyze the electrical
responses of LiZr2(PO4)3 and Ca-stabilized Li1.4Ca0.2Zr1.8(PO4)3 that were prepared following a solid-state
synthesis route. We investigated the influence of the starting materials, either ZrO2 and Zr(CH3COO)4, on
the final properties of the products and studied Li ion dynamics in the crystalline grains and across grain
boundary (g.b.) regions. The Ca2+ content has only little effect on bulk properties (4.2 × 10−5 S cm−1 at
298 K, 0.41 eV), but, fortunately, the g.b. resistance decreased by 2 orders of magnitude. Whereas, 7Li
spin-alignment echo nuclear magnetic resonance (NMR) confirmed long-range ion transport as seen by
conductivity spectroscopy, 7Li NMR spin–lattice relaxation revealed much smaller activation energies
(0.18 eV) and points to rapid localized Li jump processes. The diffusion-induced rate peak, appearing at
T = 282 K, shows Li+ exchange processes with rates of ca. 109 s−1 corresponding, formally, to ionic
Received 29th April 2019,
Accepted 2nd June 2019
DOI: 10.1039/c9dt01786k
rsc.li/dalton
conductivities in the order of 10−3 S cm−1 to 10−2 S cm−1
.
ambient conditions. This property comes along with a wide
electrochemical stability window.12,13 LiTi2(PO4)3 is known as a
1. Introduction
In the years to come, all-solid-state Li or Na batteries1 are very good Li-ion conductor but it suffers from the fact that
expected to replace conventional systems2 that still rely on Ti(IV) can easily be reduced to Ti(III) when in contact with
flammable aprotic electrolytes. Ceramic cells may take advan- metallic Li.14
tage of highly flexible design possibilities if batteries with
In contrast to LiTi2(PO4)3-based ceramics, including those
dimensions in the mm range are considered.3,4 Moreover, in which Ti4+ is partly replaced by Al3+, LiZr2(PO4)3 (LZP)
ceramic batteries are going to withstand higher temperatures shows a much better stability against Li anodes. If in contact
than their analogous cells with liquid components.5
with a Li metallic anode LZP forms stable decomposing pro-
For their realization, ceramic electrolytes with sufficiently ducts, such as Li3P and layer-structured Li8ZrO6, that are able
high ionic conductivities are, however, needed.5–9 The overall to conduct Li ions when present as thin layers. Importantly,
performance of NaSICON-type (Na SuperIonic CONductor) this interphase also reveals sufficiently good wetting properties
conductors10,11 has attracted renewed interest to study the with respect to both Li metal and the electrolyte.15 LZP crystal-
influence of synthesis conditions and dopants on morphology lizes with different structures, ionic conductivities sensitively
and ion dynamics. Earlier reports have shown that LiM2(PO4)3 depend on both the overall morphology and the defect chem-
(M: Ge, Ti, Sn, Hf, Zr) exhibits good chemical stabilities under istry involved. The ionic conductivity can be improved by
incorporating different metals such as Y3+, Sc3+, Al3+, La3+ or
Ca2+; this strategy is usually accompanied by a stabilization of
the rhombohedral structure.13,16–22 LZP is typically prepared at
calcination temperatures of ca. 1173 K, the phase appearing
under these conditions is denoted as the α-phase of LZP,
which is subdivided in a orthorhombic form (α) and a mono-
clinic one (α′). At higher sintering temperatures, that is,
approximately at 1423 K, the highly conductive rhombohedral
aInstitute for Chemistry and Technology of Materials, Christian Doppler Laboratory
for Lithium Batteries, Graz University of Technology (NAWI Graz), Stremayrgasse 9,
A-8010 Graz, Austria. E-mail: isabel.hanghofer@tugraz.at
bALISTORE – European Research Institute, CNRS FR3104, Hub de l’Energie,
Rue Baudelocque, 80039 Amiens, France. E-mail: wilkening@tugraz.at
†Electronic supplementary information (ESI) available: Further X-ray powder
patterns, results from structure solution and Nyquist plots. See DOI: 10.1039/
c9dt01786k
ˉ
structure α-LiZr2(PO4)3 crystallizing with R3c symmetry is
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formed. α′-LiZr2(PO4)3, obtained at lower temperatures, is
a
step size of 0.02° (2
s
per step). Rietveld analysis
usually a mixture of monoclinic LZP and triclinic LZP; its ionic (X-PertHighScorePlus (PANanalytical)) was used to refine the
conductivity is reported to be in the order of 10−8 S cm−1 diffraction data.
whereas α-LiZr2(PO4)3 shows values around 10−5 S cm−1 15,22–25
.
2.3. Impedance spectroscopy
In this work, the structure variation of different educts on
the product formed is discussed. We analysed Li ion dynamics For the impedance measurements the sintered samples were
in LiZr2(PO4)3 and Li1+2xCaxZr2−x(PO4)3 (LCZP) by both broad- equipped with gold electrodes by a sputtering process. Gold
band impedance spectroscopy26,27 and 7Li nuclear magnetic electrodes with a layer thickness of 100 nm were applied on
resonance (NMR) spectroscopy, i.e., by recording diffusion- both sides with a sputter coater (LEICA EM SCD 050) to ensure
induced spin–lattice relaxation rates.28–30 The latter are sensi- a good electrical contact. To avoid any influence of moisture,
tive to both short-range and long-range ion transport through the samples were dried at 60 °C under vacuum prior to the
the crystal lattice of LZP. As we deal with powder samples with impedance measurements.
crystallite diameters in the µm range, NMR rates measured in
Impedance spectra were recorded with a Novocontrol
the laboratory frame of reference are solely sensitive to bulk Concept 80 broadband dielectric spectrometer equipped with
ion dynamics.
a BDS 1200 cell combined with an active ZGS cell
(Novocontrol). We measured complex impedances over a fre-
quency range of ten decades (10 mHz to 10 MHz). The temp-
erature in the sample holder was varied from 173 K to 473 K in
steps of 20 K; the temperature program was automatically con-
trolled by a QUATRO cryosystem (Novocontrol). During the
measurements a dry nitrogen atmosphere was build up
around the sample in the cryostat to avoid any contamination
with water and/or oxygen.
2. Experimental
2.1. Sample preparation
LiZr2(PO4)3 (LZP) was prepared via a classic solid-state reaction
by mixing stoichiometric amounts of Li2CO3 (Sigma Aldrich
≥99%), (NH4)2HPO4 (Sigma Aldrich ≥99.9%) with either ZrO2
(Sigma Aldrich ≥99%) or Zr(CH3COO)4 (= Zr(ac)4). The starting
compounds were mechanically milled for 2 hours by using a
high-energy planetary ball mill (Fritsch Pulverisette 7 Premium
line) at a rotation speed of 400 rpm. We used ZrO2 beakers
(45 mL), which were filled with 180 balls made of ZrO2 (5 mm
in diameter). The subsequent calcination process was carried
out in Al2O3 crucibles at 900 °C (heating rate 10 °C min−1) for
10 hours, where the decomposition of the hydrogen phosphate
starts and initiates the reaction with Li2CO3. The resulting
white powder was milled again for 2 hours at 400 rpm to guar-
antee a good contact between the particles. Finally, the
mixture was pressed with 0.4 tons into pellets with a diameter
of 5 mm. The pellets were filled into Al2O3 crucibles and
sintered at 1150 °C (heating rate 10 °C min−1) for 20 hours. To
incorporate Ca2+ into LZP we used CaCO3 (Alfa Aesar, >99%).
An excess of 10 wt% Li2CO3 should compensate the loss of
lithium during the high temperature heating process leading
to Li1.4Ca0.2Zr1.8(PO4)3 (LCZP). For the synthesis of LZP (and
LCZP) using Zr(CH3COO)4 we needed to prepare the acetate as
follows.31 20 mmol Zirconium oxochloride (Sigma-Aldrich
99.99%) was dissolved under reflux in 100 mL of a mixture of
MeCOOH (Sigma-Aldrich ≥99.5%) and Me(COO)2O (Sigma
Aldrich ≥99%) (1 : 9). After the mixture was allowed to cool to
room temperature, a white crystalline deposit appeared.
Finally, it was filtered and dried at 60 °C under vacuum.
2.4. Nuclear magnetic resonance measurements
For the time-domain NMR measurements, the powder
samples LiZr2(PO4)3 and Li1.4Ca0.2Zr1.8(PO4)3 were sealed in
Duran glass tubes (ca. 4 cm in length and 3 mm in diameter).
During the sealing procedure they were kept under dynamic
vacuum to safely protect them from any contact with humid
air. We used 7Li NMR line shape measurements, spin lattice
relaxation (SLR) experiments as well as 7Li spin alignment
echo (SAE) NMR to collect information about Li activation
energies and jump rates. Longitudinal NMR SLR rates (1/T1) as
well as spin-lock rates (1/T1ρ) were measured with a Bruker
Avance III spectrometer that is connected to a shimmed cryo-
magnet with a nominal magnetic field of 7 Tesla. This field
corresponds to a 7Li Larmor frequency of ω0/2π = 116 MHz.
For the measurements at temperatures ranging from 173 K to
583 K a ceramic temperature probe (Bruker Biospin) was used.
Depending on temperature and at a power level of 180 W the
π/2 pulse length ranged from 2.2 µs to 2.4 µs.
7Li NMR SLR rates (1/T1 = R1) in the laboratory frame were
acquired with the well-known saturation recovery pulse
sequence. This sequence uses a comb of closely spaced π/2
pulses to destroy any longitudinal magnetization Mz. The sub-
sequent recovery of Mz was detected as a function of waiting
time td with a π/2 reading pulse: 10 × π/2 − td − π/2 –
acquisition.32,33 To construct the magnetization transients
Mz(td), we plotted the area under the free induction decays vs.
2.2. X-ray powder diffraction
The sample obtained after the calcination process and the td. The transients Mz(td) were parameterized with stretched
finally sintered product were characterized by X-ray powder exponentials, Mz(td) ∝ 1 − exp(−(t/T1)γ), to extract the rates R1.
diffraction (XRPD). We used a Bruker D8 Advance diffract- Additionally, rotating frame 7Li NMR SLRρ rates 1/T1ρ (= R1ρ)
ometer operating with Bragg Brentano geometry and Cu Kα were measured by means of the spin lock technique: π/2-plock
–
radiation. Diffractograms were recorded in air atmosphere and acquisition.32 Here, we used a locking frequency ω1/2π of
at room temperature covering a 2θ range from 20° to 100° with 20 kHz. The duration of the spin-lock pulse tlock was varied
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from 10 µs to 460 ms. To ensure full longitudinal relaxation with the rhombohedral NaSICON structure37 (space group R3c,
between each scan the recycle delay was set to 5 × T1. The R1ρ Fig. 1);19 the corresponding XRPD pattern is shown in Fig. 2.
rates were obtained by analyzing the resulting transients This phase is isostructural with the sibling compound
Mρ(tlock) with stretched exponentials with the form Mρ(tlock) ∝ LiTi2(PO4)3.38 The increase in conductivity before and after sin-
exp(−(tlock/T1ρ)κ). The stretching exponent γ varied from 1 to tering, i.e., the difference in ionic transport properties of
ˉ
0.8, the exponent κ ranges from 1 to 0.6.
monoclinic and rhombohedral LZP is illustrated in Fig. S1b.†
Finally, mixing time (tm) dependent 7Li SAE NMR decay
The Zr2(PO4)3 framework of rhombohedral NaSICON-type
curves were recorded with the help of the Jeener–Broekaert34,35 LZP consists of two ZrO6 octahedra and three PO4 tetrahedra
three-pulse sequence: (90°)X-tp–(45°)Y-tm–45°-acq. We used a sharing O atoms. The octahedral and tetrahedral units are
constant preparation time tp of 25 µs to acquire two-time alternating with the cations to form infinite chains parallel to
sinus–sinus single-spin correlation functions. The mixing time the ternary axis of the structure. Each PO4 unit shares its
was varied from 30 µs up to several seconds. A suitable phase
cycle34,36 was employed to suppress unwanted coherences and
to eliminate, as best as possible, dipolar contributions
affecting the echo that appears after the reading pulse.36
Fourier transformation of the spin alignment echoes, starting
7
from the top of the signal, yields Li SAE NMR spectra useful
to highlight quadrupole intensities due to the interaction of
the quadrupole moment of the 7Li spin (spin-quantum
number I = 3/2) and a non-vanishing electric field gradient.
3. Results and characterization
3.1. Characterization via X-ray powder diffraction
The purity of the crystalline samples synthesized was exam-
ined by XRPD. As mentioned above, diffraction patterns were
collected at room temperature and under air atmosphere. The
Fig. 2 Rietveld refinement of LZP using ZrO2 as educt. The sample was
sintered at 1150 °C for 20 hours in a closed Al2O3-crucible. LZP crystal-
lizes with space group R3¯cH, see Table S1† for further information.
Selected reflections have been indexed with vertical bars. A very small
first XRPD pattern was recorded directly after the calcination
process, i.e., after removal of CO2, NH3 and H2O at 900 °C, the
pattern is depicted in Fig. S1.† After this calcination step
(10 hours), we see that LiZr2(PO4)3 crystallizes with monoclinic
amount (<4 wt%) of ZrO2 was detected. The inset shows the ab-plane of
structure (space group P121/c1, see Fig. S1 (ESI)†). Sintering
the rhombohedral NaSICON structure with the viewing direction along
the c-axis.
the samples yields a crystalline material that is in agreement
Fig. 1 Left: Rhombohedral crystal structure of LiZr2(PO4)3. The tetrahedra in purple represent PO4-units, octahedra in pink show ZrO6, while the
blue spheres denote the Li+ ions. Li+ is octahedrally coordinated by oxygen anions of the ZrO6 octahedra. Right: Section of the rhombohedral crystal
structure to show interstitial sites A2; the Li ions may use to jump between the regularly occupied sites A1. The A1–A1 distance is 6.3 Å, which is, pre-
sumably, much too large for a direct jump process.
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Fig. 3 (a) X-ray powder diffraction pattern of the crystalline LiZr2(PO4)3 and Li1+2xZr2−xCax(PO4)3 (x = 0.1 and 0.2). All samples were prepared by a
classical solid-state route with either ZrO2 as starting material (black) or Zr(CH3COO)4 (light grey). The vertical lines (in grey) at the bottom denote
the reflections of rhombohedral LZP, those of monoclinic ZrO2 are indicated by green dots. (b) XRPD pattern of Li1+2xZr2−xCax(PO4)3 prepared with
the help of ZrO2. The diffraction pattern reveal that the amount of the impurity phase ZrO2 decreases with increasing Ca2+-content.
oxygen with four ZrO6 octahedra of three Zr2(PO4)3 units to rhombohedral structure, as is illustrated in Fig. 3. The amount
form the NaSICON framework. A 3D network of conduction of unreacted ZrO2 continuously decreases with increasing Ca-
pathways is formed that is used by the ions to diffuse through content. This behavior is also found for LCZP prepared with
the crystal. In this case the Li ions (6b) are octahedrally co- the help of Zr(ac)4. Nonetheless, the amount of ZrO2 remains
ordinated by oxygen ions (36f ) at the intersection of three con- much higher (>15 wt%) than that in samples prepared from
duction channels (A1). The A1 sites are located between pairs ZrO2 directly. Dots in Fig. 3 denote reflections belonging to
of ZrO6 octahedra along the c-axis, while the (vacant) intersti- ZrO2. Worth noting, here we do not find any additional Bragg
□
tial sites ( ) A2 can be found between O3ZrO3A1O3Zr- reflections that belong to triclinic LZP in all diffractograms.
-O3ZrO3A1. Since the A1–A1 distance in LZP is rather larger, These have been seen in earlier reports.22,39–41 We recognize
□
we assume that interstitial sites, such as A2, are involved in Li+ that small variations in synthesis conditions, including heat
diffusion. Because of the large spatial separation of Li ions in treatment and cooling rates, might sensitively affect the phase
LZP, we expect rather low homonuclear dipole–dipole inter- purity of the final compounds.
actions resulting in narrow 7Li NMR lines even in the rigid
lattice regime, see below.
According to XRPD we decided to study, in detail, ion
dynamics of the following samples: LiZr2(PO4)3 prepared from
In Fig. 2 the result of our Rietveld analysis of the diffraction ZrO2 and Zr(ac)4 as well as Li1+2xZr2−xCax(PO4)3 (x = 0.1
pattern of LiZr2(PO4)3 synthesized by using ZrO2 as educt is and 0.2) prepared with the help of ZrO2. Similar to LiTi2(PO4)3
shown. Our structure solution indeed points to rhombohedral and other NaSICON-type materials α-LiZr2(PO4)3 shows low
ˉ
symmetry characterized by the space group R3cH (ICSD, no. relative densities, here ranging from 78% to 84%.
201935), as already found by the study of Petit et al.19 Via high-
temperature neutron diffraction (T ≥ 423 K), Catti et al.
3.2. Impedance spectroscopy
reported on two Li+ positions displaced from the A1 and A2 To study how Li+ ion transport is affected by x as well as to
sites (see Fig. S2†).24 Here, in addition to the main rhombo- investigate whether the starting materials influence the
hedral phase, a minor impurity of ZrO2 (<4 wt%) is seen (see dynamic parameters, we measured complex impedances over a
black bars). Rietveld analysis yields the following lattice pro- large temperature and frequency range.26,42 Exemplarily, in
perties a (= b) = 8.824 Å and c = 22.456 Å; V = 1514.24 Å3. By Fig. 4a conductivity isotherms of rhombohedral LiZr2(PO4)3
doping this sample with 5 wt% and 10 wt% Ca2+ the are shown. Isotherms are obtained by plotting the real part, σ′,
cell volume decreases (1512.64 Å3 (5 wt% Ca), 1506.22 Å3 of the complex conductivity σ of LiZr2(PO4)3 as a function of
(10 wt% Ca)) as expected; for further information we refer to frequency ν. They are composed of four regimes. (i) At low fre-
Table S1 in the ESI.†
quencies (and sufficiently high temperatures and, thus, high
The preparation route with Zr(CH3COO)4 as starting ionic mobility) electrode polarization (EP) appears owing to
material yields almost the same lattice parameters but the the piling-up of ions near the surface of the blocking Au elec-
amount of non-reacted material is much higher and reaches trodes applied. In many cases a stepwise decay of σ′ is seen (cf.
values as high as 25 wt%. The incorporation of aliovalent Ca2+ the two arrows in Fig. 4a). (ii) The polarization regime passes
ions, on the other hand, helps obtaining phase pure LZP with into so-called conductivity plateaus (P1) governing the iso-
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Fig. 4 (a) Conductivity isotherms of Ca-free LZP (synthesized from ZrO2) recorded at temperatures ranging from 173 K to 473 K; isotherms have
been recorded in steps of 20 K. We observed two plateaus P1 and P2 that correspond to the grain boundary (g.b., P1) and bulk response (P2). (b)
Arrhenius plot of the DC conductivities associated with P1 and P2. The solid and dashed line show line fits with an Arrhenius law yielding activation
energies ranging from 0.39 eV to 0.52 eV. Circles represent LZP synthesized from ZrO2 and rectangles show results of LZP that was synthesized
from Zr(ac)4. LZP prepared from ZrO2 shows the highest bulk ion conductivity that is characterized by 0.41 eV. (c) Real part of the complex permittiv-
ity as a function of frequency. P1 and P2 seen in (a) produce a two-step increase of ε’ characterized by permittivities and capacities being typical for
a bulk electrical response and a response including ion-blocking grain boundaries. The same characteristics are seen for LZP prepared from Zr(ac)4.
Both processes can be approximated with a power law of the form ε’(ν) = ε(∞) + Asν−p with p ≠ f(T) ≈ 0.75, wherein ε(∞) represents the permittivity
at very high frequencies.
therms at intermediate temperatures and low frequencies. If
In the Arrhenius plot of Fig. 4b, σDCT of the two plateaus P1
this plateau is identified with a bulk response, it reflects long- and P2 is plotted vs. the inverse temperature T. σDCT does
range ion transport and is given by the dc-conductivity σdc. By not change when several heating and cooling runs were
moving to higher frequency a shallow dispersive regime with a performed. The lines in Fig. 4b refer to fits according to
weak frequency dependence shows up. It directly merges into σDCT(P1, P2) ∝ exp(−Ea/(kBT)); kB denotes the Boltzmann’s
another plateau (iii, P2), which finally passes over in the high- constant and Ea the corresponding activation energy. For
frequency dispersive regime (iv) which can roughly be approxi- LiZr2(PO4)3 prepared from ZrO2 we obtain Ea(P2) of 0.41(1) eV
mated with Jonscher’s power law.
(in agreement with ref. 15 (0.40 eV) and ref. 25 (0.39 eV)),
In Fig. 4a the inflexion points of the plateaus P1 and P2 are whereas for LiZr2(PO4)3, when using Zr(ac)4 as starting
highlighted by filled circles; straight lines connect these material, Ea increases to 0.44(1) eV (see Fig. 4b). At room temp-
circles. The dispersive region belonging to plateau P2 is best erature, the ionic conductivities of P2 are 3.6(2) × 10−5 S cm−1
seen at 173 K, it can be approximated with Jonscher’s power and 3.4(2) × 10−6 S cm−1, respectively. For the sake of clarity,
law:43 σ′ = σdc + A0νn. Here A0 is the so-called dispersion para- in Table 1 all activation energies Ea are listed, the table
meter and n represents the power law exponent, which takes a also includes values referring to Li1+2xCaxZr2−x(PO4)3 (x = 0.1,
value of 0.73 at 173 K. To analyse our data in terms of dimen- x = 0.2) that has been prepared from ZrO2.
sionality effects, we also studied the frequency dependence of
Unfortunately, by using Nyquist diagrams (see Fig. S3†),
the real part of the complex permittivity; the corresponding which show complex plane plots of the imaginary part Z″ of
isotherms (ε′ vs. ν) are plotted in Fig. 4c; the plateaus P1 and the complex impedance, Z, vs. its real part Z′, the faster relax-
P2 produce a two-step increase of ε′ when coming from high ation process, corresponding to P2, cannot be resolved prop-
frequencies. As for σ′, also ε′(ν) can be approximated with expo-
nents around 0.75 for P2, see Fig. 4c. Such Jonscher exponents
are expected for 3D ionic conduction.44
Table 1 Comparison of activation energies Ea and prefactors σ0 of the
Arrhenius lines shown in Fig. 4b. The values refer to Ca-free and Ca-
containing LiZr2(PO4)3. Values in the brackets represent data determined
by blocking grain boundaries (P2). Results for Ca-bearing LZP are also
included
To determine which capacitances C govern the responses
P1 and P2, we used the equation for a parallel-plate capacitor
for an estimation C = ε0εr A/d. Here ε0 represents the electric
field constant (8.854 × 10−12 F m−1), A the area and d the thick-
ness of the sample. While the DC plateau (P2) at high frequen-
cies is characterized by C = 1.2(1) × 10−12 F, for the plateau at
lower ν we found C = 2.3(2) × 10−11 F. Therefore, the plateau
associated with C in the pF range represents the bulk
response, whereas P1 seen at lower frequencies is additionally
governed by grain boundary contributions (g.b.) for which
capacitances in the order of 10−11 F are typically expected.45
Starting
composition
Ea/eV
log10(σ0/S cm−1 K) material
LiZr2(PO4)3
LiZr2(PO4)3
Li1.2Ca0.1Zr1.9(PO4)3 0.43(1) (0.52(9))
Li1.4Ca0.2Zr1.8(PO4)3 0.41(2) (0.38(4))
0.44(2) (0.48(4))
4.97(1) (3.86(2))
Zr(ac)4
ZrO2
ZrO2
0.41(2) (0.37(4)a) 4.91(2) (1.49(7))
5.44(4) (4.14(7))
5.08(2) (3.49(1))
ZrO2
a At lower temperatures the activation energy increases to 0.43(4) eV.
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erly. Instead, we used the complex modulus M″(ν) rep- are separated by two orders of magnitude on the frequency
resentation46 to visualize the two processes, see Fig. 5a and 6 scale. This distance on the frequency scale is comparable with
(Fig. 6b includes data for Li1+2xCaxZr2−x(PO4)3 prepared the ratio of σDC,P2 : σDC,P1; thus, they refer, as is seen in Fig. 6
from ZrO2).
to the plateaus P1 and P2 governing σ′(ν). As expected the two
At sufficiently low temperatures two relaxation peaks M1 electrical relaxation frequencies mirror the ratio in conduc-
and M2 appear (see the orange arrows in Fig. 5a). These peaks tivities. The peak with the larger amplitude (M2) corresponds
Fig. 5 (a) Frequency dependence of the imaginary part of the electric modulus M’’, of LiZr2(PO4)3 prepared from Zr(ac)4. Spectra were recorded at
the temperatures indicated. The lines are to guide the eye. As suggested by σ’(ν), two distinct peaks are visible denoted as M1 and M2. The tempera-
−1
ture dependence of the corresponding relaxation rate τM is shown in (b). For comparison, the results of LiZr2(PO4)3 (prepared from ZrO2) and
Li1.4Zr1.8Ca0.2(PO4)3 (also prepared from ZrO2) are included as well. Error margins are at least 0.1 eV.
Fig. 6 (a) Frequency dependence of the imaginary part M’’ of the complex modulus, the real part, ε’, of the permittivity as well as the real part, σ’, of
the complex conductivity of LiZr2(PO4)3 (prepared from ZrO2). The isotherm was recorded at 213 K. The maxima in M’’ clearly refer to the plateaus
P1 and P2 seen in σ’(ν). For comparison, the change of ε’(ν) is shown, too. (b) Arrhenius plot of the ionic conductivities referring to the plateaus P1
and P2 (σDCT vs. 1000/T) of cation-mixed crystalline Li1+2xZr2−xCax(PO4)3. Solid lines and dashed lines represent fits according to an Arrhenius law
yielding the activation energies Ea as indicated. While solid lines refer to conductivities influenced by the grain boundary contributions, the dashed
lines represent bulk ion dynamics in Li1+2xZr2−xCax(PO4)3. For the sake of clarity, the bulk ion conductivities for the samples with x = 0.20 and x =
0.10 have been plotted using an offset of +2 and +1.5 on the logarithmic scale. These conductivities coincide with those of the Ca-free sample.
Activation energies with error margins are listed in Table 1.
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to P2 in σ′(ν), the one with the smaller amplitude (M1) see, in coming studies, whether Ca2+, here acting as a sintering
represents a relaxation process with a longer relaxation time aid, segregates in the g.b. regions; such segregation would
(cf. P1), see also Fig. 6. As an estimation, M″ is proportional to explain the finding that ion transport in the bulk regions is
the inverse capacitance, M″ ∝ 1/C.45,47 Thus, we expect peak only little affected by Ca2+ incorporation.
M2 to be characterized by a larger amplitude (3.4 pF) than M1
(30.1 pF). C1/C2 ≈ 10 is in good agreement with the amplitude with x = 0.2 is considered as an example (Fig. 6b), a slight kink
ratio seen in Fig. 5a and 6a. is seen for temperatures well above room temperature; the acti-
Careful inspection of σDCT(P1) reveals that, if the samples
In order to compare activation energies extracted from vation energy changes from 0.48 eV to 0.38 eV at higher T.
σDC(P1, P2) we determined characteristic electrical relaxation Presumably, Ca2+ in the grain boundaries influences the Li+
frequencies 1/τM using the modulus peaks of Fig. 5a. 1/τM arrangements in these regions. Li+ order/disorder phenomena
refers to frequencies at which the peaks appear. A comparison might lead to such changes.
of activation energies for selected compounds is shown in
Fig. 5b; errors are, at least, in the order of 0.01 eV.
3.3. Ion dynamics as seen by NMR measurements
As mentioned in the beginning, Ca2+ incorporation Fig. 7a gives an overview of the 7Li NMR SLR rate measure-
increases the ionic conductivity of LZP. Fig. 6b shows the ments performed using an Arrhenius representation plotting
change in σDCT(P1, P2) of Li1+2xCaxZr2−x(PO4)3 prepared from the R1(ρ) rates as a function of the inverse temperature. To
ZrO2 for x = 0, x = 0.1 and x = 0.2. Most importantly, while identify the thermally activated regions, we measured R1(ρ) of
σDCT(P2), which refers to bulk ion dynamics, is only slightly Li1.4Ca0.2Zr1.8(PO4)3 over a wide temperature range to detect
affected by x (Ea ranges from 0.41 eV to 0.43 eV, see Fig. 6b the maxima of diffusion-induced rate peaks.48 Here we
and Table 1 that also includes the prefactors), Ca2+ incorpor- focused
on
the
sample
with
the
composition
ation mainly reduces the g.b. resistance. We clearly see that Li1.4Ca0.2Zr1.8(PO4)3 as it shows the lowest bulk activation
σDCT(P1) is by two orders of magnitude larger than that of the energy and the lowest amount of residual ZrO2.
sample with x = 0, see Fig. 6b. Most likely, the sintering
Below 183 K the rates R1 reveal a non-diffusive background
process benefits from a Ca-rich composition, which helps regime. In this temperature range longitudinal relaxation is
reducing the blocking nature of surface regions of the induced by lattice vibrations or coupling of the Li spins with
Li1+2xCaxZr2−x(PO4)3 crystallites. For x = 0.2 we obtain σDC(P2) = paramagnetic impurities.48–50 At higher temperatures we
4.2 × 10−5 S cm−1 at 293 K. This value is only slightly lower expect the SLR rate to be increasingly induced by Li+ hopping
than that of Li et al.15 (3.8 × 10−5 S cm−1) when samples are processes. Such processes lead to magnetic and electric field
compared that have been prepared by conventional sintering. fluctuations that cause longitudinal relaxation.48 Indeed, the
If pellets were fired by spark plasma sintering, bulk values of rates increase with temperature and, in both cases R1 and R1ρ,
1.8 × 10−4 S cm−1 were reported.15 It would be interesting to characteristic
diffusion-induced
rate
peaks
appear.
Fig. 7 (a) Arrhenius plot of the 7Li NMR relaxation rates R1 and R1ρ of Li1.4Ca0.2Zr1.8(PO4)3 (prepared via the route using ZrO2) measured in the lab-
oratory frame of reference (116 MHz) and in the rotating frame of reference (20 kHz, nominal locking frequency). Dashed lines represent BPP-type
fits to determine activation energies, prefactors and asymmetry parameters β. Temperatures indicate Tmax of the rate peaks. The superposition of the
R1 rate peaks can be approximated with two symmetric peaks (β = 2). (b) Li+ jump rates as deduced from the diffusion-induced rate peaks R1 and R1ρ
.
For comparison, we also included jump rates that we estimated from frequency-dependent conductivity measurements and 7Li SAE NMR. See text
for further explanations and Table 2 for error margins of the activation energies shown.
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Importantly, we recognize that R1 passes through two maxima significantly lower than Ea obtained from σDC measurements
located at Tmax = 282 K and 492 K, respectively. In general, at describing bulk ion dynamics. The fact that Ea,i < Ea, DC shows
Tmax the motional correlation rate 1/τc is related to ω0 via the that the number of jump events seen by NMR does not include
relation τcω0 ≈ 1. The so-called motional correlation rate 1/τc is all types of jumps needed for long-range diffusion. Obviously,
identical, within a factor of two, with the Li+ jump rate 1/τ.48,50 the spin-fluctuations sensed by NMR are already sufficient to
For R1ρ, this maximum condition changes to τcω1 ≈ 0.5.51 As generate a full R1 peak. Thus, we conclude that the Li+ ions in
ω0 and ω1 differ by more than three orders of magnitude, we LCZP are highly mobile on a short-range length scale while
are able to characterize Li+ motional correlation rates in LCZP long-range ion transport is, however, characterized by much
with values in both the kHz and MHz range.52
larger activation energies than 0.2 eV. This situation resembles
Here, we approximated the superposition of the two R1 rate that of Li+ ion dynamics in argyrodite-type Li6PS5I, which has
peaks by a sum of two Lorentzian-shaped spectral density been studied recently by our group.42 Here, we assume that
functions J(ω0, T) ∝ τc/(1 + (ω0τc)β) according to the concept rapid forward–backward exchange processes between the sites
introduced by Bloembergen, Purcell and Pound (BPP) for 3D A1 and A2 might be responsible for the peaks seen in NMR
isotropic diffusion,53,54 see dashed line in Fig. 7a that follows spin–lattice relaxometry. A2 sites might be occupied in
the R1 rates. For each peak we used a single term to deconvo- samples with x > 0. Here, especially the peak appearing at
lute the temperature dependence of the overall R1 rates Tmax = 282 K for Li1.4Ca0.2Zr1.8(PO4)3 points to rapid (localized)
measured, cf. the dashed-dotted lines in Fig. 7a, which will be exchange processes with residence times in the order of
discussed below. The rate 1/τc usually obeys the Arrhenius several ns. According to ω0τc ≈ 1 we estimate that at Tmax the
relation 1/τc = 1/τc,0 exp(−Ea/(kBT)); 1/τc,0 represents the pre- jump rate should be in the order of 1/τ = 7.3 × 108 s−1 ≈ 109
exponential factor that is typically identified as the “attempt s−1. A very similar behavior has recently been seen also for
frequency” of the jump process.55
NaSICON-type Na3.4Sc0.4Zr1.6(SiO4)2PO4.
In general, J(ω0, T) is the Fourier transform of the under-
To complement our R1 measurements, we carried out spin-
lying motional correlation function G(t′).48 If G(t′) is or can be lock NMR SLR measurements at a locking frequency of 20
well approximated with a single exponential, β equals 2. kHz. As expected we detected a prominent spin-lock NMR
Values smaller than 2 are expected for correlated motion, peak R1ρ(1/T) at much lower temperature than 492 K. A single
which is, e.g., seen for cations exposed to an irregularly shaped peak appears at Tmax = 293 K. It turned out to be slightly asym-
potential landscape. In such a landscape short-ranged Li+ metric with an activation energy of Ea, high = 0.185(5) eV and
diffusion will be different to long-range ion transport. In par- Ea, low = 0.168(5) eV. At first glance we would say that the R1ρ
ticular, forth-and-back jumps or, more generally speaking, peak might correspond to the R1 peak seen at Tmax = 492 K.
localized motions will govern the rate R1 in the low-tempera- Keeping, however, both the locking frequency of only 20 kHz
ture regime, which is characterized by τcω0 ≫ 1. In this regime and the rather low activation energy of 0.185 eV in mind, the
we have J(ω0) ∝ τc−1ω0−β with (1 < β ≤ 2). β < 2 produces asym- R1ρ peak belonging to R1(1/T) with Tmax = 492 K would be
metric rate peaks which are often found for structurally expected to appear at much lower temperatures than ambient.
complex ion conductors with a non-uniformly shaped energy Even if we replace ω1 by an effective frequency ω1,
(>ω1),
eff
landscape. Ion dynamics in this regime are anticipated to be which takes local magnetic fields into account that increase
affected by correlation effects because of both structural dis- ω1, no satisfactory joint fit results that is characterized by the
order and strong Coulomb interactions of the moving ions.56 same Ea and the same τc,0 for the two peaks. Here, only unreli-
As the peak is asymmetric, the activation energy on this ably high ω1, eff values reaching the MHz range would result in
side of the peak, Ea, low, is lower than that of the high-tempera- a joint fit connecting the two peaks. Table 2 shows an overview
ture flank, Ea, high; the two values are linked to each other via of the results obtained from analyzing the three peaks indivi-
Ea, low = (β(ρ) − 1)Ea, high. In the regime τcω0 ≪ 1, that is, on the dually by BPP-type spectral density functions. It also includes
high-temperature side of the peak, many jump events are the amplitudes CNMR in R1(ρ) = CNMR J(ω0, T). We see that the
sensed during one Larmor precession and the probability is amplitudes of the two R1 rate peaks differ by approximately
high that also these jumps contribute to longitudinal relax- one order of magnitude. Most likely, stronger quadrupolar
ation which are characterized by higher activation energies. relaxation governs the peak appearing at higher T. The corres-
Usually, on this side of the rate peak R1(1/T) long-range Li ion ponding prefactor 1/τ0 is relatively low, while that of the peak
dynamics is sensed; in this limit we obtain J(ω0) ∝ τc.29
showing up at 282 K (1/τ0 = 5.9 × 1012 s−1) is consistent with
In the present case, approximating the rate peaks with a frequencies typically expected for phonons.
sum of two BPP-type spectral densities yields activation ener-
The above-mentioned jump rate derived from SLR NMR at
gies of Ea,1 = 0.210(5) eV and Ea,2 = 0.143(5) eV. As both rate Tmax (1/τ = 7.3 × 108 s−1) can be converted into diffusion coeffi-
peaks join up, information on β are difficult to obtain. Here, cients with the help of the Einstein–Smoluchowski equation
the fitting routine yields β = 2 for the two peaks resulting in according to DNMR = a2/(6τ), which is valid for 3D diffusion.29
symmetric peaks with Ea, low = Ea, high = Ea,i (i = 1, 2). Note that As an estimation, by inserting a = 6.3 Å, which is simply the
the peak at higher T (i = 2) is only partly visible which influ- shortest Li–Li distance, we obtain DNMR = a2/(6τ) = 4.8 × 10−11
ences the precise determination of Ea, high. We clearly recog- m2 s−1. Assuming the interstitial sites A2 participating in
nize that Ea,i as determined from R1 SLR NMR turned out to be exchange processes DNMR reduces to 1.8 × 10−11 m2 s−1. A dis-
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Table 2 Results of analyzing the 7Li NMR rate peaks R1 and R1ρ of Li1.4Ca0.2Zr1.8(PO4)3. The coupling constant CNMR, which is the amplitude of the
rate peak, J(ω0) = CNMRτc/(1 + (ω0τc)β, turned out to be in the range of 1010 and 1011 s−2. Values in the order of 10−13 s for τ0 correspond to (inverse)
phonon frequencies
Ea (= Ea, high
)
CNMR
β(ρ)
τ0
R1 (Tmax = 492 K)
R1 (Tmax = 282 K)
0.143(5) eV
0.210(5) eV
0.185(5) eV
1.8(1) × 1011 s−2
2.5(1) × 1010 s−2
1.5(1) × 109 s−2
2
1.93
2
4.1(2) × 10−11
1.7(2) × 10−13
s
s
R
1,ρ (Tmax = 293 K)
2.8(1) × 10−9
s
(0.168(5) eV)a
a The value in brackets refers to Ea, low of the R1ρ peak seen at 293 K.
tance of a = 6.3 Å is, of course, by far too long for a single lattice regime. With increasing temperature, the line undergoes
hopping process. In the structural model of Catti et al. the dis- a slight narrowing process because of Li diffusion that averages
tance reduced to 4.2 Å at 423 K.24
dipolar couplings. Finally, at even higher temperatures, i.e., in
In the Arrhenius plot of Fig. 7b we compare the rates 1/τ the extreme narrowing regime, its width is only governed by the
from NMR (1/τNMR) with those obtained after converting σDC inhomogeneity of the external magnetic field.
into jump rates by using the Nernst Einstein equation. As we
Interestingly, at 313 K two satellite lines emerge that belong
do not know the exact jump distance, we calculated 1/τσ for to a first-order quadrupole powder pattern arising from the
7
three different values of a. 1/τσ represents an average value interaction of the quadrupole moment of the Li nucleus (I =
mainly influenced by Li+ jumps necessary for long-range ion 3/2) with a non-vanishing electric field gradient (EFG) at the
transport. Most likely, the R1 peak appearing at 492 K is more nuclear site. The EFG is produced by the electric charge distri-
related to jump processes enabling the ions to move over bution in the direct neighborhood of the 7Li nucleus. This
longer distances. The large discrepancy between 1/τNMR(282 K) additional interaction alters the Zeeman levels and, thus, also
and 1/τσ once again visualizes that the R1(1/T) peak at low T the associated (angular) Zeeman frequency ω0 towards ω0
reflects localized jump processes. We do not find evidences ωQ.32,54 The singularities seen in Fig. 8a correspond to the 90°
that this peak originates from any phase transitions, as the satellite transitions of a powder pattern, which typically show
phase-pure Ca-bearing samples show rhombohedral structure. up at sufficiently high T; this feature belongs to the universal
For comparison, in Fig. 7b we also included 1/τσ rates esti- characteristics of crystalline materials studied by NMR.32,50,61
mated from conductivity values that characterize the influence Their distance on the frequency scale, if we simply assume an
of grain boundaries. Interestingly, 1/τNMR(293 K, R1ρ) = 2.5 × EFG with axial symmetry, corresponds to δ/2. δ is the quadru-
105 −1, which we estimated via the relation ω1τc ≈ 0.5, see pole coupling constant. A distance of 49 kHz leads to δ = 98
s
above, agrees with 1/τσ, g.b. In contrast to R1, which as far as kHz,58 which is in fair agreement with the value reported by
µm-sized crystallites are considered, is mainly affected by bulk Petit et al.20 Here, this value should, however, be interpreted as
processes, the corresponding spin-lock NMR rates R1ρ seems an average value, as we cannot exclude a small distribution of
to be (also partly) sensitive to ion dynamics also influenced by EFGs the ions are exposed to at very low temperatures. At very
interfacial processes. This behaviour is consistent with the fol- low T, the intensity of the singularities is too low to be detect-
lowing comparison. At frequencies in the kHz range (ω1/2π = able by single pulse experiments. Instead, echo experiments
20 kHz) and at T = 282 K the isotherms σ′(ν) are mainly influ- should be used that are able to avoid receiver dead time effects.
enced by the g.b. response rather than bulk ion dynamics.
In Fig. 8b (see inset) a spectrum is shown that is the Fourier
To shed more light on long-range ion dynamics, we used transform of a stimulated echo. Indeed, a sharp central line is
7Li NMR line shape measurements and 7Li SAE NMR located on top of a broad quadrupole foot. Hence, we conclude
experiments46,57–60 to further characterize ionic transport in that the Li ions are exposed to a distribution of EFGs.
LCZP. Via SAE NMR we should be able to get access to
Fluctuations in ωQ seen by the ions when jumping between
diffusion parameters that characterize ion transport over electrically inequivalent sites can be used to record sinus–
longer distances as the method is sensitive to exchange pro- sinus two-time correlation functions. In Fig. 8a the change of
7
cesses on the time scale that is comparable to that of DC con- the Li SAE amplitude S2 is shown vs. the logarithmic mixing
ductivity measurements.48 In Fig. 8a variable-temperature 7Li time tm. S2 depends on both the preparation time tp and tm.
NMR spectra of Li1.4Ca0.2Zr1.8(PO4)3 are shown. Remarkably, at Here, we measured the decay curve at fixed tp (= 20 µs) but vari-
temperatures as low as 213 K a relatively narrow NMR line is able mixing time. Stretched exponentials of the form S2 ∝ exp
detected whose width is only 1.4 kHz. Usually, we would expect (−(tm/τSAE)λ), with a stretching factor λ ranging from 0.21 to
a width in the order of several kHz due to 7Li–7Li dipolar inter- 0.37, are best suited to describe the dependence of S2(tp
=
actions. Here, the large Li–Li distance of 6.3 Å between the A1 const., tm) in this temperature regime. In general, stretching
sites, and between A1 sites and Li ions occupying interstitial factors deviating from λ = 1 indicate non-Debye-like motional
sites in samples with x > 0, leads to relatively weak dipole– process. For example, such deviations can arise from motions
dipole interactions producing a narrow line already in the rigid- in disordered matrices or in confined dimensions59,62 leading
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Fig. 8 (a) 7Li NMR spectra of Li1.4Ca0.2Zr1.8(PO4)3 recorded at the temperatures indicated. The NMR line transforms from a Gaussian shape at low
temperatures to a Lorentzian one at elevated T. Clearly visible and well-defined quadrupole powder patterns emerge at temperatures higher than
313 K. (b) 7Li SAE NMR decay curves of LCZP whose spectra are shown in (a). Decay curves follow stretched exponentials (0.2 < γ < 0.4) which are shown
as solid lines. Data have been recorded at a Larmor frequency of 116 MHz. See text for further details. Inset: Fourier transform of a spin-alignment echo,
starting from the top of the echo, which was recorded at a fixed tp of 20 µs and a short mixing time of tm = 100 µs. In addition to a “central line” a rather
broad quadrupole foot is visible illustrating the distribution of EFGs seen by the Li ions in the dynamic regime of the rigid lattice.
to motional correlation functions whose decay slows down with activation energies of 0.21 eV and 0.14 eV. The diffusion-
with increasing observation time. With increasing T the inflex- induced rate peak seen at 282 K points to a very high jump
ion point of the echo decay curves shifts towards shorter tm. At rate in the order of 109 s−1 at this temperature. On the other
the same time, the shape of S2 steadily becomes more hand, 7Li spin-alignment echo spectroscopy confirmed that
stretched until a value of λ = 0.21 is reached at T = 203 K. At long-range ion transport in the bulk regions of
sufficiently long mixing times the curves S2(tp = const., tm) Li1.4Zr1.8Ca0.2(PO4)3 needs to be characterized by an activation
always reach S2,∞ = 0, which either indicates a rather large energy of 0.41 eV as determined by variable-frequency conduc-
number of quadrupole frequencies involved or which points to tivity measurements.
the influence of dipolarly coupled spins, as is well-described
in literature.36 The rates 1/τSAE governing the stretched decay
functions are included in Fig. 7b. We recognize that they are in
fair agreement with those rates, 1/τσ, bulk, which were esti-
Conflicts of interest
mated from bulk ionic conductivities of Li1.4Ca0.2Zr1.8(PO4)3.
There are no conflicts to declare.
Acknowledgements
4. Conclusion
This project has received funding from the European Union’s
Horizon 2020 research and innovation programme under
grant agreement no. 769929. We thank the Deutsche
Forschungsgemeinschaft for further support (FOR1277,
WI3600(2-1;4-2). Further support by the K-project ‘safe battery’
(FFG) is highly appreciated.
We used a conventional solid-state reaction procedure to syn-
thesize NaSICON-type LiZr2(PO4)3 and investigated both its
ionic conductivity and Li+ diffusivity by broadband conduc-
tivity measurements and NMR spectroscopy. Ca2+ incorpor-
ation helps prepare Li1+2xZr2−xCax(PO4)3 crystallizing with
rhombohedral symmetry. While bulk ion dynamics is not
influenced by the Ca2+ content, the grain boundaries in LZCP
turn out to be less blocking for Li+ ions as compared to the
sample with x = 0. We observed an increase in the low-fre-
quency ionic conductivity by two orders of magnitude when
increasing x from x = 0 to x = 0.2. For Li1.4Ca0.2Zr1.8(PO4)3 7Li
NMR relaxometry revealed rapid localized Li+ jump processes
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