Li+ Ion Dynamics in Î²-Li3PS4 Observed by NMR: Local Hopping and

Article Cite This: J. Phys. Chem. C 2018, 122, 15954−15965

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Li+‑Ion Dynamics in β‑Li3PS4 Observed by NMR: Local Hopping and Long-Range Transport Heike Stöffler,† Tatiana Zinkevich,†,‡ Murat Yavuz,† Anatoliy Senyshyn,§ Jörn Kulisch,∥ Pascal Hartmann,∥ Torben Adermann,∥ Simon Randau,⊥ Felix H. Richter,⊥ Jürgen Janek,⊥,# Sylvio Indris,*,†,‡ and Helmut Ehrenberg†,‡

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†

Institute for Applied MaterialsEnergy Storage Systems (IAM-ESS), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany ‡ Helmholtz Institute Ulm, Helmholtzstraße 11, 89081 Ulm, Germany § Research Neutron Reactor ZWE FRM-II, Munich University of Technology, Lichtenbergstraße 1, 85747 Garching n. Munich, Germany ∥ BASF SE, 67056 Ludwigshafen am Rhein, Germany ⊥ Institute of Physical Chemistry, Justus-Liebig-University Giessen, Heinrich-Buff-Ring 17, 35392 Giessen, Germany # BELLABatteries and Electrochemistry Laboratory, Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany ABSTRACT: A detailed structural characterization is performed on β-Li3PS4 using 6Li and 31P magic-angle spinning NMR spectroscopy in combination with X-ray and neutron diffraction. High-temperature synchrotron X-ray diffraction was used to determine the phase stability and observe phase transitions. In addition, we investigated the Li+-ion dynamics by temperature-dependent 7Li NMR lineshape analysis, 7Li NMR relaxometry, and 7Li pulsed field-gradient (PFG) NMR measurements. A good agreement is obtained between the local hopping observed by T1 relaxation time measurements and the long-range transport investigated by PFG NMR with a Li+ diffusion coefficient of 9 × 10−14 m2/s at 298 K and an activation energy of 0.24 eV. From this, a Li+ conductivity of 1.0 × 10−4 S/cm is estimated, which corresponds well with impedance measurements on β-Li3PS4 pellets.

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well as bulk β-Li3PS4. In contrast, a higher lithium-ion conductivity in the order of 10−4 S/cm has been reported by Liu et al. for β-Li3PS4 with a nanoporous structure, prepared via a solvent-based synthesis.3 Overall, the conductivity reported for Li3PS4 shows a quite large spread with values between 3 × 10−7 and 10−4 S/cm and activation energies between 0.22 and 0.49 eV.3−8 This is probably due to the strong influence of the grain boundaries that can be at least partially suppressed by applying an external pressure during the conductivity measurement. The high sensitivity of these samples toward, e.g., moisture, can result in impurity phases at the grain boundaries. Furthermore, the presence of an amorphous fraction of the material that is hard to be detected by diffraction techniques can also have an influence on the overall conductivity. The amount of this amorphous contribution will depend on the synthesis technique.

INTRODUCTION All-solid-state batteries (ASSB) using inorganic solid electrolytes instead of flammable organic liquid electrolytes are a promising next generation battery technology with many advantages over conventional Li-ion batteries, such as safety and durability. Sulfide solid electrolytes with high ionic conductivity at room temperature (RT) and high ductility are considered as particularly suited for fabricating ASSBs because they do not require high-temperature sintering to realize good contact between the electrode and solid electrolyte. Thus, bulk-type ASSBs can be fabricated by simple cold pressing, which can prevent side reactions that might be induced at high temperatures. In addition, solution-based syntheses are increasingly available that allow processing routes close to conventional technologies.1,2 Among all sulfide-based solid electrolytes, Li3PS4 is likely to be one of the most suitable for use with lithium metal, showing negligible interfacial resistance when used in lithium batteries.3,4 Nevertheless, bulk γ-Li3PS4 exhibits a very low ionic conductivity (3 × 10−7 S/cm) at room temperature,3 as © 2018 American Chemical Society

Received: June 6, 2018 Revised: June 26, 2018 Published: June 26, 2018 15954

DOI: 10.1021/acs.jpcc.8b05431 J. Phys. Chem. C 2018, 122, 15954−15965

Article

The Journal of Physical Chemistry C

Figure 1. Orthorhombic crystal structure of β-Li3PS4 with Pnma space group. The Li, P, and S sites are depicted with gray, purple, and yellow spheres, respectively.

Figure 1 shows the crystal structure of β-Li3PS4 with Pnma symmetry.9 It is composed of isolated [PS4]3− tetrahedra that are connected with LiS6 octahedra via common edges. There are three different Li sites: a fully occupied tetrahedral site (8d), a partially occupied octahedral site (4b, 70%), and a partially occupied tetrahedral site (4c, 30%).10 The LiS6 octahedra are connected via common edges, thus forming a one-dimensional (1D) chain. Along this chain, the Li(1)S4 tetrahedra are connected via common corners, and between two Li(2)S6 octahedra and one Li(3)S4 tetrahedron, there is an interstitial tetrahedral site.9 In this article, we present results of investigations on the long-range and local structure of the solid electrolyte β-Li3PS4 by combining powder X-ray diffraction and neutron diffraction with magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy on 6Li and 31P probe nuclei. Hightemperature synchrotron X-ray diffraction studies at temperatures up to 973 K are used to examine the thermal stability, phase transitions, and melting temperature of β-Li3PS4. The short-range and long-range Li+-ion dynamics are investigated by temperature-dependent static 7Li NMR lineshape measurements, 7Li NMR spin−lattice relaxation experiments (T1 and T1ρ), and 7Li pulsed field-gradient (PFG) NMR.

reflections of a vertically focusing composite Ge monochromator, accordingly. The vertical position-sensitive multidetector (300 mm effective height) consisting of 80 3He tubes and covering an angular range of 160° 2θ was used for data collection. Measurements were performed in the Debye− Scherrer geometry. The powder sample was filled into a cylindrical thin-wall vanadium container of 10 mm diameter under argon and metal sealed using indium wire. Two diffraction patterns at different wavelengths were detected, and exposure time was set to 12 h per pattern. The data analysis was performed by the full profile Rietveld method using the FullProf12 program package. NPD data at two wavelengths and the X-ray diffraction (XRD) dataset were modeled simultaneously using the same structure model. To model the peak profile shape, the pseudo-Voigt function was chosen. Background contribution was determined using a linear interpolation between selected data points in nonoverlapping regions. Instrumental resolution functions were determined using Na2Ca3Al2F14 reference and LaB6 in neutron and X-ray experiments, respectively. The scale factor, zero angular shift, profile shape parameters, resolution (Caglioti) parameters, asymmetry and lattice parameters, as well as fractional coordinates of atoms and their displacement parameters were varied during the fitting. As site occupations did not show considerable deviations during fitting, they were fixed to their nominal values to suppress correlations with the displacement parameters. Crystal structures were drawn using VESTA.13 Scanning electron microscopy (SEM) images were recorded on a Zeiss Merlin microscope using 5 kV acceleration voltage. Nitrogen physisorption experiments were carried out on a Quantachrome Quadrasorb evo instrument. The used measurement parameters were pressure tolerance 0.05 Torr, equilibration time 60 s, and equilibrium timeout 120 s. The Brunauer−Emmett−Teller (BET) specific surface area was determined from five data points between a relative pressure (p/p0) of 0.1 and 0.25. 6 Li and 31P MAS NMR spectroscopy were performed with a Bruker Avance 500 MHz spectrometer at a field of 11.7 T, corresponding to resonance frequencies of 73.6 and 202.5 MHz, respectively. For these measurements, the sample was packed into a 2.5 mm zirconia MAS rotor in an argon-filled glovebox. The spinning speed was 20 kHz, and the spectra

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EXPERIMENTAL SECTION The solid electrolyte β-Li3PS4 was provided by BASF company. X-ray diffraction data were collected on a STOE Stadi P powder diffractometer using Mo Kα1 radiation with a wavelength of λ = 0.7093 Å. High-temperature synchrotron Xray diffraction studies were done with a 0.5 mm quartz glass capillary at the high-resolution powder diffraction beamline (P02.1) at PETRA III, DESY, using synchrotron radiation with a photon energy of 60 keV (λ = 0.20714 Å). The capillary with the sample was heated in a ceramic oven from room temperature up to 973 K with steps of ΔT = 50 K. The diffraction patterns were acquired using a PerkinElmer area detector with a sample-detector distance of 1610 mm. The exposure time for each diffraction pattern was 1 min. Neutron powder diffraction (NPD) studies were performed at the high-resolution powder diffractometer SPODI (research neutron reactor FRM-II, Garching n. Munich, Germany).11 Monochromatic neutrons (λ = 1.5482 and 2.5360 Å) were obtained at a 155° take-off angle using the 551 and 331 15955


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Figure 2. Results of simultaneous Rietveld analysis for NPD and XRD patterns collected at room temperature. Experimental data are shown by red points, the model is presented by black lines, and the difference is shown by blue lines. Calculated positions of Bragg reflections are shown by vertical green tick marks where upper and bottom lines of tick marks correspond to reflections from β-Li3PS4 and Li2S, respectively.

were acquired with a Hahn-echo pulse sequence.14 The chemical shifts of 6Li and 31P were referenced to 1 M LiCl (0 ppm) and H3PO4 (85%, 0 ppm), respectively. Temperaturedependent static 7Li NMR line shapes and spin−lattice relaxation (T1, T1ρ) measurements were performed using a Bruker 200 MHz spectrometer at a magnetic field of 4.7 T (77.8 MHz for 7Li), on samples sealed in 10 mm glass vials. The spectra were acquired in the temperature range from 223 to 573 K with a quadrupolar-echo sequence, an radio frequency pulse spacing of 30 μs, a π/2 pulse length between 2.5 and 3.5 μs, and a recycle delay of 20 s. Thirty-two scans were acquired for each spectrum. 7Li NMR T1 measurements were performed in the temperature range from 303 to 573 K

with a saturation-recovery pulse sequence.15,16 T1ρ measurements were performed in the temperature range 303−453 K with a spin-locking pulse sequence and a spin-locking field corresponding to a nutation frequency of 37.7 kHz. For the 7Li PFG NMR measurements, the sample was sealed in a 5 mm glass tube. The experiments were done on a Bruker Avance 300 MHz spectrometer operated at 116.6 MHz for 7Li. The spectrometer was equipped with a PFG NMR probe that provides pulsed field gradients up to 30 T/m. A stimulated echo pulse sequence with bipolar gradients17 was used to suppress the influence of eddy currents. Electrochemical impedance spectroscopy (EIS) of β-Li3PS4 (sample with pellet geometry, 60 mg, 425 μm thickness, 10 15956


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Table 1. Experimental Structural Parameters of β-Li3PS4 at Ambient Temperature, As Determined by Rietveld Analysis of Neutron and X-ray Powder Diffraction Dataa,b,c,d a = 12.993(2) Å, b = 8.0458(15) Å, c = 6.1377(11) Å, V = 641.6(2) Å3 atom

Wyck. site

x/a

y/b

z/c

uiso, Å2

SOF

u11, Å2

u22, Å2

u33, Å2

u12, Å2

u13, Å2

u23, Å2

Li1 Li2 Li3 P1 S1 S2 S4

8d 4b 4c 4c 8d 4c 4c

0.318(3) 0 0.442(9) 0.0876(5) 0.1550(3) 0.9409(3) 0.1007(5)

0.017(6) 0 1/4 1/4 0.0402(4) 1/4 1/4

0.139(7) 1/2 0.55(2) 0.1666(9) 0.267(1) 0.254(1) 0.801(3)

0.26(3) 0.12(2) 0.12(2) 0.045(8) 0.051(8) 0.028(8) 0.097(9)

1.000 0.66(4) 0.34(4) 1.000 1.000 1.000 1.000

0.031(8) 0.026(7) 0.024(7) 0.049(9)

0.090(9) 0.039(7) 0.028(8) 0.044(9)

0.015(8) 0.087(8) 0.031(8) 0.199(12)

0 0.016(3) 0 0

−0.004(4) 0.012(4) 0.004(5) −0.005(10)

0 0.048(4) 0 0

NPD, λ = 2.536 Å: Rp: 1.43%, Rwp: 1.89%, Rexp: 0.85%, χ2: 4.92. bNPD, λ = 1.548 Å: Rp: 1.14%, Rwp: 1.33%, Rexp: 0.71%, χ2: 3.51. cXRD, Mo Kα1: Rp: 1.79%, Rwp: 2.41%, Rexp: 1.11%, χ2: 4.67. dThe space group is Pnma (No. 62). The displacement parameters of P and S atoms were modeled anisotropically, whereas displacements of Li ions were considered in isotropic approximation. Numbers in parentheses give statistical deviations in the last significant digit. a

Figure 3. Experimentally determined 3D network of lithium (left column) and characteristic projections illustrating structural motifs and lithium transport in the a−c plane (red) and a plane parallel to b (blue). Middle column: differential bond valence isosurfaces in β-Li3PS4 (ΔV = 0.125 v.u., 0.1 Å resolution; color code: blue ΔV = 1, red ΔV = 0.125). Maximum-entropy method (MEM) reconstructed negative nuclear density (right column) maps in β-Li3PS4 (surface threshold −0.02 fm/Å3, cell grid 256 × 192 × 128).

Figure 2. The refinement reveals β-Li3PS4 as a main phase with symmetry Pnma18 and lattice constants a = 12.993(2) Å, b = 8.0458(15) Å, and c = 6.1377(11) Å. Weak traces of Li2S have been also noticed in both NPD and XRD datasets. In NPD, its amount was determined to be 4.3(1) wt %, whilst a slightly higher fraction of 6.1(2) wt % of Li2S was obtained by the lab XRD measurement. The best results for the Rietveld refinements were obtained by using the parameters listed in Table 1. Large displacement parameters for Li indicate strong lithium disorder, which hints at fast Li mobility but hampers the

mm diameter) was performed using an EC-Lab Electrochemistry VMP-300 Biologic in the frequency range of 7 MHz to 1 Hz, applying a 10 mV signal amplitude. The pellets were prepared with a pressure of 380 MPa, and the pressure during EIS was 50 MPa. Impedance plots were fitted using RelaxIS software.

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RESULTS AND DISCUSSION Neutron Diffraction. Neutron diffraction patterns for two different wavelengths and the X-ray diffraction pattern for βLi3PS4 with the simultaneous Rietveld refinement are shown in 15957


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knowledge about lithium positions was not utilized, i.e., only atomic coordinates of phosphorus and sulfur were used. The obtained differential bond valence isosurfaces corresponding to the probable lithium distribution in β-Li3PS4 are presented in Figure 3 (middle row). The positions of equilibrium sites for lithium determined by Rietveld refinement all fall into the regions with ΔV = 0. However, analysis of differential bond valences indicates a potential 3D character of lithium conductivity with an ill-defined pathway. Regions with low bond valence mismatch (e.g., at Li1−Li2−Li1 triplets) are separated by the regions with enhanced ΔV caused by the close location of sulfur anions. Lithium with natural isotope composition possesses negative scattering length (bLi = −1.9 fm) and is the only negative scatterer in Li3PS4. Experimental lithium diffusion pathways were examined as an example of negative nuclear density maps extracted from the measured structure factors by maximumentropy method (MEM). The method is based on the estimation of 3D scattering densities from a limited amount of information by maximizing information entropy under restraints, consistent with experimental observations. Compared to Fourier analysis, the MEM is often better suited for the determination of electron/nuclear density maps from the powder diffraction datasets having “limited” statistics; i.e., termination effects often occur to be less pronounced in MEM evaluation. Negative nuclear density maps for β-Li3PS4 reconstructed from experimental structure factors (Figure 2) using the program Dysnomia20 are plotted in Figure 3 (right column). In contrast to the bond valence approach, the performed MEM analysis of nuclear densities yields a quasi two-dimensional (2D) lithium diffusion in the a−c plane with no continuous pathway (negative nuclear density) in b direction. Distribution of negative nuclear densities between neighboring Li1−Li2− Li1 triplets reveals the presence of the neck located at general position (0.23, 1/2, 0.38), which defines the energy barrier for lithium diffusion in the a−c plane. Assuming the lithium motion in the single-atom potential to be independent and nuclear density map to have the feature of a probability field, the observed lithium motion can be analyzed in the framework of Boltzmann statistics. The oneparticle potential (OPP) was recalculated from negative nuclear densities, and it is shown in Figure 4. The established 2D diffusion pathway has obvious energy preferences in the lattice. The cross section through the potential energy profile along the Li(2)−Li(1)−Li(1)−Li(2)−Li(1)−Li(1)−Li(2) chain indicates an activation barrier of ca. 0.15 eV around the general position (0.23, 1/2, 0.38). It should be noted that values of the energy barriers have to be taken with care because of the limited applicability of the OPP approximation (nonclassical behavior) at room temperature.21 Scanning Electron Microscopy and BET Surface Area. SEM images of β-Li3PS4 are shown in Figure 5. Particles with a size between 1 and 30 μm are visible. During synthesis of β-Li3PS4, pores are formed inside the larger particles. A specific surface area of 24 m2/g was determined by the BET method from nitrogen physisorption (see Figure 6). MAS NMR Results. The 6Li and 31P MAS NMR spectra of β-Li3PS4 are presented in Figure 7. The 6Li spectrum reveals two peaks at 1.03 and 0.65 ppm, with an intensity ratio of about 2:1. As described above, the neutron diffraction results reveal a fast exchange between the Li1 and Li2 sites, whereas the Li3 site is not involved in the diffusion pathway. Therefore,

accurate localization of lithium. Nevertheless, all cation−anion coordination polyhedra in Li3PS4 have been found to be slightly distorted (Figure 2). The P1S4 tetrahedron is built by distances dP1−S2 = 1.981(8) Å, dP1−S1 = 1.999(5) Å, dP1−S1 = 1.999(5) Å, and dP1−S3 = 2.250(12) Å. The observed mean P− S distance ⟨dP1−S⟩ = 2.057(7) Å is consistent with ⟨dP1−S⟩ = 2.050 Å reported by Mercier et al.18 The Li1S4 tetrahedron is characterized by dLi1−S1 = 2.27(4) Å, dLi1−S1 = 2.36(4) Å, dLi1−S2 = 2.55(4) Å, and dLi1−S3 = 2.60(4) Å distances, with ⟨dLi1−S⟩ = 2.45(4) Å (according to ref 18, the Li···S distance is ≈2.46 Å). The Li2 site is sixfold coordinated by sulfur with lithium located between the opposite sulfur vertices so that three types of Li2−S distances define the Li2S6 octahedron: dLi2−S1 = 2.491(6) Å, dLi2−S2 = 2.629(5) Å, and dLi2−S3 = 3.029(7) Å distances and ⟨dLi2−S⟩ = 2.716(6) Å. The tetrahedron Li3S4 has four unique Li−S interatomic distances: dLi3−S2 = 1.9(1) Å, dLi3−S3 = 2.3(1) Å, dLi3−S1 = 2.97(7) Å, and dLi3−S1 = 2.97(7) Å distances, with ⟨dLi3−S⟩ = 2.52(9) Å. Defining the distortion criterion for the coordination |⟨d⟩ − d | 1 polyhedron as Δ = N ∑i ⟨d⟩ i , where N is the coordination

number, the following distortion coefficients Δ of P1S4, Li1S4, Li2S6, and Li3S4 polyhedra were calculated: 0.0468, 0.0532, 0.0767, and 0.1716, thus indicating the increase of the bondlength distortion in this sequence. Analysis of the shortest Li−Li distances (below 4.0 Å) does not reveal an obvious and simple diffusion pathway for lithium transport in Li3PS4. The shortest Li−Li distance occurs between the Li1 and Li2 sites and is d = 2.52(4) Å so that three atomic sites Li1−Li2−Li1 are forming lines, thus potentially enabling a direct lithium exchange within the Li1−Li2−Li1 triplet (Figure 3). The triplets are then interconnected into a three-dimensional (3D) network either via Li3 sites showing 3.50(9) and 3.5(1) Å distances for Li3− Li2 and Li3−Li1 sites or directly via Li1−Li1 exchange, accordingly. The pathways alternative to the above mentioned will involve Li−Li exchange on distances above 4 Å. The sulfur atoms are located very close to the Li−Li line, which will affect the diffusion pathways. The geometrical aspect of diffusion can be evaluated by the differential bond valence model, which became very popular due to its simplicity, robustness, and high predictive power. Along with Hirschfeld surface analysis, the differential bond valence method yields all possible diffusion pathways in the material, which are permitted from the geometrical point of view. It is assumed that the ion transport between equilibrium sites might follow a pathway, along which the valence mismatch ΔV = |V − Vnom| between bond valence V and nominal valence Vnom remains as small as possible. The total bond valence sum V of cation A can be expressed as V=

∑ SA− X X

(1)

where individual bond valences SA−X are calculated using RA−X bonds to adjacent anions X and R and b parameter sets are tabulated as SA − X = e R − RA−X / b

(2)

The 3D distribution of valence mismatch was calculated for Li3PS4 using R and b parameters tabulated by Adams.19 Calculations were performed by summing up bond valence contributions to sulfur anions up to a cutoff distance of 5.5 Å on a 3D grid 0.1 × 0.1 × 0.1 Å3 within the lattice. The prior 15958


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Figure 6. Nitrogen physisorption isotherm of β-Li3PS4 powder.

9.0688(1) Å, and c = 8.4705(4) Å. The second phase was found to be P4S4 (9 wt %).26 At 873 K, the intensities of the reflections decreased compared with the pattern at 823 K, which shows that the melting process already started at this temperature. Above 923 K, the sample is completely melted and no Bragg reflections are visible. The unit cell volume V was extracted from the refinement for each investigated temperature. Figure 10 shows the volume expansion with increasing temperature for β-Li3PS4 and αLi3PS4. In the whole temperature range, the estimated error for the volume is in the order of 0.1 Å3. Temperature-Dependent NMR. NMR spectroscopy is a versatile tool to investigate not only local structures around specific elements but also the dynamics of, e.g., Li ions in condensed matter. Combining different NMR techniques, such as temperature-dependent lineshape studies, NMR relaxometry, and field-gradient NMR, allows to investigate these dynamics over several orders of magnitudes for the time and length scales.16,17,27−31 The static 7Li NMR line shapes and their line width are shown in Figure 11 as a function of temperature in the temperature range from 303 to 573 K. As expected for 7Li (nuclear spin I = 3/2), different contributions are visible in the spectra. At 223 K, a broad contribution is visible in the range from −20 to +20 kHz, representing the socalled quadrupolar satellite contributions corresponding to the transitions |+3/2⟩ ↔ |+1/2⟩ and |−1/2⟩ ↔ |−3/2⟩. On top of this broad contribution, a narrower peak is visible with a width of about 3.5 kHz, representing the central line corresponding to the transition |+1/2⟩ ↔ |−1/2⟩. During heating to 573 K, both components show a clear narrowing. At temperatures

Figure 4. Two-dimensional (2D) section cut (010, d = 1/2 plane) of the lithium one-particle-potential (OPP) and its 1D section along lines connecting seven Li atoms in a chain Li(2)−Li(1)−o−Li(1)− Li(2)−Li(1)−o−Li(1)−Li(2), where o corresponds to the neck connecting Li(1)−Li(2)−Li(1) triplets at general position (0.23, 1/2, 0.38).

the peak at 1.03 ppm is assigned to the Li1/Li2 sites and the peak at 0.65 ppm is assigned to the Li3 site. The 31P spectrum is dominated by a narrow contribution at 86.5 ppm, which clearly reveals the presence of isolated [PS4]3− tetrahedra.22−24 A broader contribution with intensity between 90 and 80 ppm hints at the presence of a substantial amount of an amorphous phase, also containing isolated [PS4]3− tetrahedra. The area fraction of this broader contribution is 30%. X-ray Diffraction. The synchrotron X-ray diffraction patterns collected during the high-temperature experiment in the temperature range from 298 to 973 K are shown in Figure 8. The β-Li3PS4 structure is present for temperatures from 298 to 723 K. At 773 K, the β-Li3PS4 undergoes a phase transition to the high-temperature α-Li3PS4 phase, which is present until 873 K. Figure 9 shows the Rietveld refinement of the pattern at 823 K, where the presence of a second phase can be clearly identified. The refinement reveals 91 wt % α-Li3PS4 with space group Pbcn25 and lattice constants a = 8.6610(1) Å, b =

Figure 5. Scanning electron microscopy images of β-Li3PS4 powder. 15959


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Figure 7. (a) 6Li and (b) 31P MAS NMR spectrum of β-Li3PS4.

Figure 8. Synchrotron X-ray diffraction patterns of β-Li3PS4 for temperatures between 298 and 973 K.

T1ρ−1 as a function of inverse temperature are shown in Figure 12. For low temperatures, the relaxation rate T1−1 increases with temperature. At about 450 K, T1−1 shows a clear maximum and then decreases again for higher temperatures. The overall behavior of T1−1 can be well described according to the BPP theory33 by the expression

above 373 K, a characteristic quadrupolar lineshape is formed with a quadrupolar splitting of about 6.2 kHz. This lineshape is representing the temporally averaged local environment, as probed by the Li ions when moving quickly through the crystal structure (on the time scale of these experiments, i.e., some milliseconds). The line width of the central transition is shown in Figure 11b versus temperature. A clear motional narrowing is visible with an initial width of 3.5 kHz decreasing down to a plateau value of less than 500 Hz. The overall behavior shows that the motional narrowing already started at temperatures below 223 K, which reveals that the motion of the Li+ ions is very fast in this material. The temperature dependence is fitted with the expression by Hendrickson and Bray.32 From this, an activation energy for the motion of the Li+ ions can be roughly estimated to be 0.23 eV. It can be also seen that at high temperatures (above 350 K), a clear and very flat plateau is not reached. This could hint at the presence of a second contribution possibly from the amorphous fraction of the sample. The local hopping of the Li+ ions was also investigated with 7 Li NMR relaxometry. The 7Li NMR relaxation rates T1−1 and

T1−1 ∼ (

τ 4τ + ) 1 + ωL2τ 2 1 + 4ωL2τ 2

(3)

Here, ωL is the Larmor frequency at the given magnetic field and τ is the correlation time, i.e., the time during which the environment around the Li nucleus changes due to the movement of the Li+ ions. Apart from a factor of the order of unity, τ can be identified with the average residence time of the Li+ ions and its inverse is the average hopping rate of these ions. A similar expression is used for the spin−lattice relaxation rate T1ρ−1 in the rotating reference frame16 ij yz 6τ 10τ 4τ zz + + T1−ρ1 ∼ jjj z 2 2 2 2 2 2 j 1 + 4ω τ 1 + ωL τ 1 + 4ωL τ z{ 1 k

15960

(4)


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Figure 9. Rietveld refinement of the synchrotron X-ray diffraction pattern of α-Li3PS4 at 823 K.

activation energy is in good agreement with the rough estimation we got from the motional narrowing. From the average hopping rate τ−1 and the average jump length l (here taken to be the shortest Li−Li distance in the crystal structure ≈2 Å), we can roughly estimate the selfdiffusion coefficient of the Li+ ions via the Einstein− Smoluchowski equation34,35 D=f×

l2 6τ

(6)

f is the correlation factor, which we assume, for now, to be equal to one. This would correspond to a completely uncorrelated motion of the Li ions; i.e., the direction of a Li jump does not depend on the directions of the preceding jumps. We obtain a diffusion coefficient D = 2.4 × 10−13 m2/s at 298 K. From this, we can estimate the Li+ ion conductivity σLi via the Nernst−Einstein equation σLi =

Figure 10. Unit cell volume of β-Li3PS4 and α-Li3PS4 as a function of temperature.

the T1−1 +

(7) −3

Here, NLi = 2 × 10 m is the number density of the Li ions, q is their charge, and kB is the Boltzmann constant. With these values, a Li+-ion conductivity of 0.28 mS/cm is estimated. The long-range transport of the Li+ ions in β-Li3PS4 was investigated by PFG NMR.17,29,36 This method is sensitive to motions on timescales of about 1 s and thus to movement of the Li ions over several micrometers. Figure 13a shows exemplarily the echo damping at 303 K, i.e., the echo intensity as a function of the applied field gradient strength g. The damping can be well described by a Gaussian function in agreement with the expression given by Stejskal and Tanner37 28

Here, ω1 is the Larmor frequency in the spin-locking field (37.7 kHz). The temperature dependence of τ−1 can in general be described with an Arrhenius expression τ −1 = τ0−1 × e−EA / kBT

DNLiq2 kBT

(5)

T1ρ−1

Fitting eqs 3−5 to and data gives the average hopping rate of the Li ions and the activation energy these ions have to overcome for single jumps. T1−1 and T1ρ−1 have been fitted simultaneously with the same activation energy. We obtain an average hopping rate of (3.6 ± 1.0) × 107 s−1 (at 298 K) and an activation energy of (0.22 ± 0.01) eV. Since these values correspond to single Li+-ion jumps, they can be ascribed to the bulk conductivity and are not affected by grain boundary contributions. It should be noted that the behavior of T1−1(T−1) can be affected by the presence of the amorphous phase fraction and thus represents an averaged (weighted by the phase fractions) overall value for this material. The

+

I = I0 exp(−Dγ 2g 2δ 2(Δ − δ /3))

(8)

Here, I and I0 are the intensity in the presence and absence of gradient pulses, respectively, γ is the magnetogyric ratio, g is the gradient strength, Δ is the diffusion time, and δ is the gradient pulse duration. We used δ = 1.9−2.3 ms and Δ = 150−250 ms to obtain a suitable echo damping. Figure 13b displays the extracted diffusion coefficients for three different 15961


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Figure 11. (a) Static 7Li NMR lineshape for temperatures between 223 and 573 K and (b) line width of the central transition as a function of temperature. The inset shows a semilogarithmic plot.

negligible influence of the grain boundaries. The value of the diffusion coefficient is smaller by a factor of about 3 when compared with the value estimated from T1 and T1ρ relaxation measurements. Using an Arrhenius equation for the diffusion coefficient ij E yz D = D0 expjjj− A zzz j kBT z k {

(9)

the activation energy EA for the long-range transport of the Lithium ions was calculated to be (0.24 ± 0.01) eV. This value is in good agreement with the value determined by 7Li NMR relaxometry. The Li+ conductivity at 298 K estimated from the PFG NMR experiment, again via the Nernst−Einstein equation, is 1.0 × 10−4 S/cm. This value is close to that reported for impedance spectroscopy experiments on nanoporous β-Li3PS4 (σLi = 1.6 × 10−4 S/cm at RT)3 and also close to values from own impedance measurements, as described below. All in all, we consider one single motional process for the local and long-range transport of the Li+ ions with an activation barrier of 0.24 eV. The fact that the motion is somehow faster on short-length scales can be explained with a correlated motion of the Li+ ions, i.e., an enhanced probability of combined forward−backward jumps as it occurs for vacancy-mediated diffusion. This is consistent with the fact that two of the three Li sites in the crystal structure are only partially occupied. Furthermore, the neighboring pairs of Li1− Li1 sites that are both fully occupied represent a bottleneck for the long-range transport (cf. neutron diffraction results described above, Figure 4), whereas the local motion between the Li1−Li2−Li1 triple sites, as probed by the relaxation times, is faster. Therefore, the correlation factor f in eq 6 should be correspondingly smaller than 1. The long-range transport of the Li+ ions was also investigated by impedance spectroscopy on pelletized samples. From these measurements, we found an overall ionic conductivity of 1.09 × 10−4 S/cm at 25 °C (Figure 14a). This is close to the conductivity reported for nanoporous β-

Figure 12. 7Li NMR relaxation rates T1−1 and T1ρ−1 vs inverse temperature for β-Li3PS4. Dashed lines show fits according to eqs 3−5.

temperatures (303, 323, and 343 K) versus inverse temperature. The lithium-ion diffusion coefficients were determined to be D303K = (1.05 ± 0.03) × 10−13 m2/s, D323K = (1.82 ± 0.07) × 10−13 m2/s, and D343K = (3.10 ± 0.09) × 10−13 m2/s, demonstrating an increase of Li+-ion mobility with temperature. The diffusion coefficient at 298 K was extrapolated and is about (8.95 ± 0.15) × 10−14 m2/s. Since we used a diffusion time of about 200 ms, this corresponds to motion of the Li+ ions over length scales of about 0.3 μm. Therefore, this can be assigned to long-range transport of the Li+ ions but mainly still inside single Li3PS4 particles (cf. SEM results, Figure 5) with 15962


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Figure 13. (a) Echo damping vs gradient field strength g at 303 K. (b) The extracted diffusion coefficients for temperatures between 303 and 343 K.

Figure 14. (a) Impedance plot of β-Li3PS4 (sample with pellet geometry, 60 mg, 425 μm thickness, 10 mm diameter) at selected temperatures; (b) Arrhenius plot of the ionic conductivity, as obtained from the impedance measurements.

Li3PS4 (1.6 × 10−4 S/cm)3 and to that determined by temperature-dependent NMR relaxation times (2.8 × 10−4 S/ cm) and PFG NMR (1.0 × 10−4 S/cm) in this study. From temperature-dependent impedance analysis and the corresponding Arrhenius plot (Figure 14b), we determined an activation energy of 0.36 eV for the overall ionic conductivity of β-Li3PS4, which is 50% larger than the activation barrier calculated using the PFG NMR data (0.24 eV) in this study. The apparently higher value obtained from the impedance of the pelletized sample might be attributed to the stronger influence of the grain boundaries on the dc conductivity in comparison with the NMR techniques that are probing the motion of the Li+ ions on shorter timescales. Because the activation energy obtained from the impedance measurements is larger than that derived from the PFG NMR results, the good agreement we obtained for σdc at 25 °C from both measurements seems to be somehow coincidental. One difficulty for these samples is the presence of some amorphous material that might enhance the mobility of the Li ions on the timescales of the PFG NMR results whereas the impedance

measurements are probing even longer time/length scales. It might be possible to further suppress the influence of the grain boundaries by using stronger pressure during the impedance measurements. Combining different NMR and impedance measurements thus gives the possibility to investigate the dynamics of the Li ions on different time/length scales and thus to comprehensively study the energy landscape for the motion of the Li ions as it is generated by the different fully/ partially occupied Li sites. Additionally, the long-range transport can be influenced by the presence of a certain fraction of an amorphous phase, which will vary depending on the synthesis techniques, and also by the high sensitivity of these samples toward moisture, which might result in impurity phases at the grain boundaries. This also explains the big scattering in the data of the conductivity, as reported from impedance spectroscopy.

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CONCLUSIONS The structure of β-Li3PS4 was investigated on different length scales. The long-range crystal structure was probed by X-ray 15963


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(8) Tachez, M.; Malugani, J.-P.; Mercier, R.; Robert, G. Ionic Conductivity of and Phase Transition in Lithium Thiophosphate Li3PS4. Solid State Ionics 1984, 14, 181−185. (9) Homma, K.; Yonemura, M.; Kobayashi, T.; Nagao, M.; Hirayama, M.; Kanno, R. Crystal Structure and Phase Transitions of the Lithium Ionic Conductor Li3PS4. Solid State Ionics 2011, 182, 53−58. (10) Lim, M. S.; Jhi, S. H. First-Principles Study of Lithium-Ion Diffusion in β-Li3PS4 for Solid-State Electrolytes. Curr. Appl. Phys. 2018, 18, 541−545. (11) Hoelzel, M.; Senyshyn, A.; Juenke, N.; Boysen, H.; Schmahl, W.; Fuess, H. Nuclear Instruments and Methods in Physics Research A High-Resolution Neutron Powder Diffractometer SPODI at Research Reactor FRM II. Nucl. Instrum. Methods Phys. Res., Sect. A 2012, 667, 32−37. (12) Rodríguez-Carvajal, J. Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction. Phys. B 1993, 192, 55−69. (13) Momma, K.; Izumi, F. VESTA3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44, 1272−1276. (14) Duer, M. Introduction to Solid-State NMR Spectroscopy; Blackwell Publishing: Oxford, 2004. (15) Fukushima, E.; Roeder, S. B. W. Experimental Pulse NMR − A Nuts and Bolts Approach; Addison-Wesley: Reading, 1981. (16) Heitjans, P., Kärger, J., Eds.; Diffusion in Condensed Matter: Methods, Materials, Models; Springer: Berlin, 2005. (17) Price, W. S. Pulsed-Field Gradient Nuclear Magnetic Resonance as a Tool for Studying Translational Diffusion: Part 1. Basic Theory. Concepts Magn. Reson. 1997, 9, 299−336. (18) Mercier, R.; Malugani, J.-P.; Fahys, B.; Robert, G.; Douglade, J. Structure du Tetrathiophosphate de Lithium. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1982, 38, 1887−1890. (19) Adams, S. Research Papers Relationship between Bond Valence and Bond Soft- Ness of Alkali Halides and Chalcogenides. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 2001, 57, 278− 287. (20) Momma, K.; Ikeda, T.; Belik, A. A.; Izumi, F. Dysnomia, a Computer Program for Maximum-Entropy Method ( MEM ) Analysis and Its Performance in the MEM-Based Pattern Fitting. Powder Diffr. 2013, 28, 184−193. (21) Krivoglaz, M. A. X-ray and Neutron Diffraction in Nonideal Crystals; Springer: Berlin, 1996. (22) Eckert, H.; Zhang, Z.; Kennedy, J. H. Structural Transformation of Non-Oxide Chalcogenide Glasses. The Short-Range Order of Li2S-P2S5 Glasses Studied by Quantitative 31P and 6.7Li High-Resolution. Chem. Mater. 1990, 2, 273−279. (23) Gobet, M.; Greenbaum, S.; Sahu, G.; Liang, C. Structural Evolution and Li Dynamics in Nanophase Li3PS4 by Solid-State and Pulsed-Field Gradient NMR. Chem. Mater. 2014, 26, 3558−3564. (24) Dietrich, C.; Weber, D. A.; Sedlmaier, S. J.; Indris, S.; Culver, S. P.; Walter, D.; Janek, J.; Zeier, W. G. Lithium Ion Conductivity in Li2S−P2S5 Glasses − Building Units and Local Structure Evolution during the Crystallization of Superionic Conductors Li3PS4, Li7P3S11 and Li4P2S7. J. Mater. Chem. A 2017, 5, 18111−18119. (25) Homma, K.; Yonemura, M.; Nagao, M.; Hirayama, M.; Kanno, R. Crystal Structure of High-Temperature Phase of Lithium Ionic Conductor, Li3PS4. J. Phys. Soc. Jpn. 2010, 79, 90−93. (26) Minshall, P. C.; Sheldrick, G. M. Alpha-Tetraphosphorus Tetrasulphide. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1978, 34, 1326−1328. (27) Cahill, L. S.; Chapman, R. P.; Britten, J. F.; Goward, G. R. 7Li NMR and Two-Dimensional Exchange Study of Lithium Dynamics in Monoclinic Li3V2(PO4)3. J. Phys. Chem. B 2006, 110, 7171−7177. (28) Indris, S.; Heitjans, P.; Uecker, R.; Roling, B. Li Ion Dynamics in a LiAlO2 Single Crystal Studied by 7Li NMR Spectroscopy and Conductivity Measurements. J. Phys. Chem. C 2012, 116, 14243− 14247.

and neutron diffraction techniques, whereas the local environments around Li and P could be investigated by MAS NMR spectroscopy. The transition from β-Li3PS4 to α-Li3PS4 was investigated by temperature-dependent XRD. We were also able to investigate the Li-ion mobility in β-Li3PS4 on different timescales, from local hopping of Li+ ions in the nanosecond regime to the long-range transport occurring in the range of some seconds. We get a consistent picture with an activation energy of 0.24 eV, a room-temperature Li diffusion coefficient of 9 × 10−14 m2/s, and a corresponding Li conductivity, estimated by the Nernst−Einstein relation, of 1.0 × 10−4 S/cm, which was also confirmed by electrochemical impedance measurements. Furthermore, we could determine the exact diffusion pathway by combining X-ray and neutron diffraction. The diffusion turned out to be two-dimensional, involving two out of three available Li sites.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49-721-680-28502. ORCID

Jürgen Janek: 0000-0002-9221-4756 Sylvio Indris: 0000-0002-5100-113X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Financial support from the Federal Ministry of Education and Research (BMBF) within the FELIZIA project (03XP0026G, 03XP0026J) is gratefully acknowledged. This work has benefited from beamtime allocation at the neutron source FRM-II (SPODI experiment) and the synchrotron facility PETRA III (beamline P02.1), DESY. We also thank Felix Badaczewski and Prof. Bernd Smarsly for their help with nitrogen physisorption.

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Li+ Ion Dynamics in Î²-Li3PS4 Observed by NMR: Local Hopping and

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