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. 2024 Mar 4;9(10):12242–12253. doi: 10.1021/acsomega.3c09952

Synthesis and Comprehensive Analytical Study of β-Li3PS4 Stabilization by Ca- and Ba-Codoped Li3PS4

Fuki Baba †, Futoshi Utsuno ‡, Takahiro Ohkubo †,*
PMCID: PMC10938318  PMID: 38497009

Abstract

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Sulfide-based solid electrolytes with high Li+ conductivity, such as Li3PS4, are key materials for the realization of all-solid-state Li+ batteries. One approach to achieving high Li+ conductivity is to combine crystalline-phase stabilization at high temperatures with the introduction of defects at room temperature. In this work, this approach was verified by codoping Li3PS4 with two kinds of divalent cations. The resulting structural changes were comprehensively investigated both experimentally and computationally. The high-temperature β-Li3PS4 phase of Li3PS4 could be stabilized at room temperature by adjusting the amount of Ca or Ba doping. The synthesized samples doped with divalent cations were found to have conductivities about 2 orders of magnitude higher than that of the γ-Li3PS4 phase at room temperature. The resultant Li+ conductivity at room temperature was also higher than that expected from interpolation of results for nondoped β-Li3PS4. It is believed that the structural changes produced by the divalent cation doping contribute to this increase in conductivity. The stability of the β-Li3PS4 phase with divalent cation doping was also demonstrated using density-functional-theory calculations for models with equivalent compositions to the synthesized samples. The Li+ positions obtained by structural optimization calculations showed the presence of diverse and disordered Li sites in the Ca-doped lattice. Such structural changes can contribute to cascade processes involving Li+ collisions, referred to as the “billiard-ball” mechanism, which cannot occur in nondoped β-Li3PS4. This series of experiments involving the synthesis and analyses of β-Li3PS4 with divalent cation doping provides a way to enhance Li+ conductivity through structural modification and optimization.

1. Introduction

All-solid-state rechargeable Li+ batteries using solid-state electrolytes instead of organic liquid electrolytes have been widely studied in recent years with a view to their practical use.1−3 They are considered to be capable of achieving high energy density without the risk of the leakage of liquid electrolytes and ignition in harsh environments, such as when subjected to high temperatures or mechanical deformation.4−8

Current solid electrolytes for all-solid-state Li+ batteries can be roughly classified into oxide and sulfide compounds. Oxide-based solid electrolytes have excellent atmospheric stability. Typical crystalline compounds are NASICON,9,10 perovskite,11,12 LISICON,13,14 and garnet crystals.15 However, sulfide-based solid electrolytes are also promising candidates for practical use because of their superior Li+ conductivity and the fact that they form an electrode interface with better contact properties than oxide-based solid electrolytes.16,17 The argyrodite-type solid electrolyte Li7PS6, which is a material exhibiting high Li+ conductivity, has been found to exhibit a conductivity of 10–4 S cm–1 at room temperature.18 Furthermore, the conductivity of this material was improved to 10–2 S cm–1 by the substitution of halogen anions X (X = Cl and Br) for S2– at 4a and 4c sites in Li7PS6.19 Efficient conduction paths are formed by structural disorder due to this halogen substitution. This improvement of ionic conductivity based on atomic substitution is an important concept for designing electrolytes to improve their conductivity.20

Currently, two approaches have been proposed for the structural modification of crystalline materials to improve their ionic conductivities at room temperature. The first approach is to stabilize the high-temperature phase at room temperature, which has a relatively disordered structure involving open voids for ionic conduction. A typical crystalline compound for this concept is β-alumina solid electrolyte, in which the disordered structure can exhibit nonstoichiometric behavior and contain a large excess of mobile ions in the ionic conduction space.21 Stabilization of the high-temperature phase has generally been achieved by doping with impurities and creating multiphase composites such as glassy and crystalline states. These modifications can result in high entropy and lead to stabilization of the high-temperature phase at room temperature. Improvements in stabilizing high-temperature phases at room temperature have also been reported for sulfides. γ-Phase Li3PS4 (γ-Li3PS4; space group Pmn21) is a stable crystal in the Li2S–P2S5 system at room temperature. The phase transition from γ-Li3PS4 to the β phase (β-Li3PS4; space group Pnma) occurs at 573 K.22,23 Stabilized β-Li3PS4 including amorphous phases with nanoporous interference at room temperature has been obtained via liquid-phase synthesis.24 This compound was found to exhibit a dramatically high Li+ conductivity of about 10–4 S cm–125,26 when compared to that of γ-Li3PS4 at room temperature (10–6 S cm–1).

The second approach to improving the conductivity of these materials is the introduction of explicit vacancies for Li+ conduction by doping with multivalent cations instead of Li+.26−30 Substitution of Li+ for a divalent cation can produce a vacancy site for charge neutrality. An increase in conductivity based on this concept has been reported for Na+ solid-state electrolytes (Na3PS4), in which some Na+ are replaced by Ca2+.31

In this study, solid-state Ca- and Ba-doped Li3PS4 crystals were newly synthesized based on the concepts of the two approaches described above. The stabilization of the high-temperature β-Li3PS4 phases and the introduction of vacancies for Li+ conduction were studied to enhance the Li+ conductivity at room temperature. The changes in the crystalline lattice and the local structure of the PS units (PS3–4, P2S4–6, and P2S4–7) were comprehensively identified by powder X-ray diffraction (XRD) measurements and 31P nuclear magnetic resonance (NMR) spectroscopy. Theoretical verification of the synthesized Ca-doped Li3PS4 crystals was also performed by using ab initio calculations.

2. Experimental Section

2.1. Synthesis

Herein, Ca- and Ba-doped Li3PS4 are denoted as Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4, where x and y are 0, 0.0250, 0.0375, 0.0500, 0.1000, and 0.1500 and 0, 0.005, 0.015, 0.025, 0.035, and 0.045, respectively. The starting materials to synthesize Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4 were Li2S (Idemitsu Kosan Co., Ltd., >99.9%), P2S5 (Sigma-Aldrich, 99.8%), CaS (Kojundo Chemical Laboratory Co., Ltd., 99.9%), and BaS (Kojundo Chemical Laboratory Co., Ltd., 99.9%). These starting materials were weighed in the targeted stoichiometric ratios (total mass = 3.5 g) and mixed by using an agate mortar and pestle for 5 min. The mixed powder was transferred into a ZrO2 ball-milling pot (45 mL) with ZrO2 balls (ϕ = 5 mm, 56 g). These operations were performed in Ar-filled gloveboxes with a dew point below 80 °C (Glovebox Japan Inc.).

Mechanical milling using a Fritsch Pulverisette 7 Premium line was undertaken for 40 cycles, in which one cycle was composed of 60 min of milling (370 rpm) and 5 min of rest. The direction of rotation was also reversed for each cycle. After this mechanical milling treatment, the mixture was collected and pelletized using a hydraulic press and a stainless-steel mold in a glovebox. These pellets were transferred into a quartz tube in the glovebox. The quartz tube was connected to the vacuum line and sealed under vacuum at 0.1 Pa. The sealed pellets were heated to 823 K for 48 h and allowed to cool to room temperature naturally. The sample powder was collected by breaking the quartz tube in the glovebox for subsequent measurements.

2.2. Powder XRD

XRD measurements were performed using an M03XRF diffractometer (MAC Science Co., Ltd.) equipped with a Si monochromator with Cu Kα radiation (λ = 1.5418 Å) at 40 kV and 40 mA. The powder sample was mounted in a glass sample holder and sealed with Kapton polyimide film and NITOFLON tape to prevent any reaction with moisture and oxygen in the air. Diffraction data were collected within the range of 10–60° at room temperature. The Profex software package32 for Rietveld refinement was used to evaluate the lattice constants from the diffraction data. The XRD patterns obtained from the synthesized samples consist of unknown crystalline multiple phases, as described later. Additionally, the use of Kapton films results in broad background peaks. Consequently, determining all crystalline parameters such as atomic occupancy proves to be challenging. Therefore, Rietveld analysis in this study was employed solely to determine the lattice parameters for doped single β-Li3PS4 phases within the data range of 12–21°, where the peaks originating from the β phase are exclusively observed. In other words, the fitting range was restricted to data ranging from 12 to 21°, and the Ca/Li occupancy was fixed at the value expected from the composition.

2.3. Solid-State NMR Spectroscopy

31P magic-angle spinning (MAS) NMR spectroscopy using dry air was performed with a JEOL JNM-ECX400 spectrometer (9.4 T) with a 4 mm MAS probe. The 31P MAS NMR spectra were collected at a spinning frequency of 15 kHz with a π/2 excitation pulse of 3.11 μs. A total of 32 scans with a 60 s recycle delay were used to ensure good quantitative peak intensities. The chemical shifts of the 31P MAS NMR spectra were referenced to an 85% H3PO4 solution (0 ppm).

7Li MAS NMR spectroscopy was performed by using a JEOL JNM-ECZ-600R spectrometer (14.1 T) with a 3.2 mm MAS probe. The 7Li MAS NMR experiments were performed with a 20 kHz spinning speed and a 2.90 μs excitation pulse. The delay time between each of the eight scans was set to 60 s to ensure good quantitative peak intensities. A 1 M LiCl solution was used for the chemical shift reference (0 ppm).

For the solid-state 31P and 7Li NMR measurements, the samples were packed into ZrO2 sample tubes in a glovebox. No spectral changes were observed during the NMR measurements, meaning that the use of airtight sample tubes prevented reactions with oxygen and water in the air.

2.4. Impedance Spectroscopy

Electronic cells including the samples were fabricated in the glovebox. In each case, a powder sample in a poly(ether ether ketone) (PEEK) cylinder was pressed at 360 MPa by uniaxial compression using two stainless-steel rods. Cold pressing was performed three times by turning the PEEK cylinder over. Both sides of each pellet were coated with conductive carbon powder (MCP-15, Nippon Graphite) and pressed at 180 MPa. The cylindrical stainless-steel rods were used as electrodes. Each electronic cell was transferred into an airtight holder, and AC impedance measurements were performed using an impedance analyzer (Solartron, 1260) in the frequency range of 1 Hz to 1 MHz with a N2 flow. The temperature was controlled from room temperature to 353 K using heated N2 gas.

3. Ab Initio Calculations

First-principles density-functional-theory (DFT) calculations were performed using the Vienna ab initio simulation package33 within the projector augmented-wave method.34 The generalized gradient approximation using the Perdew–Burke–Ernzerhof revised functional (GGA-PBE) was applied to describe the electron exchange–correlation energy.35 The cutoff energy for the plane-wave basis was set to 258.7 eV as required by the pseudopotentials. The k-point sampling was distributed within the Brillouin zone in a 1 × 1 × 1 Monkhorst–Pack grid.36 The convergence criterion for the self-consistent field cycle was set as 1.0 × 10–8 eV in total energy. The DFT-D3 method was also used to correct for van der Waals interactions due to London dispersion forces.37 The structural optimization was performed until the maximum force in all atoms was less than 2.0 × 10–3 eV/Å.

The initial structures for ab initio calculations were obtained from a 2 × 4 × 4 supercell (512 atoms) of γ-Li3PS4 and a 2 × 2 × 4 supercell (512 atoms) of β-Li3PS4, which allowed representation of the compositions of the Ca-doped experimental samples in this study. There are three crystallographically equivalent Li sites in β-Li3PS4 (8d, 4b, and 4c).23 The occupancies of the 8d, 4b, and 4c sites in the reported crystalline data are 1.0, 0.7, and 0.3, respectively. Lepley et al. reported that a structure with 4b occupation of Li+ is the most stable for nondoped β-Li3PS4 crystals.38,39 In accordance with this result, only the 8d and 4b sites were considered for the substitution of Li+ for Ca. The distances between substitution sites were chosen to be as far apart as possible. The γ-Li3PS4 and β-Li3PS4 structures corresponding to Li3–2xCaxPS4 (x = 0, 0.0156, 0.0312, 0.0625, 0.0938, and 0.1250) were made by replacing two Li+ with one Ca2+ to maintain charge neutrality. The total number of atoms in Li3–2xCaxPS4 (x = 0, 0.0156, 0.0312, 0.0625, 0.0938, and 0.1250) was 512, 511, 510, 508, 506, and 504, respectively.

4. Results

4.1. X-ray Diffraction

Figure 1 shows the XRD patterns of Li3–2xCaxPS4 (x = 0, 0.0250, 0.0375, 0.0500, 0.1000, and 0.1500) along with the reference patterns of γ-Li3PS423 and β-Li3PS440 (first and second from the bottom). The XRD patterns of the reference compounds were calculated from the crystalline structure using the diffraction-pattern module in VESTA.41 The broad background peak ranging from 10 to 25° was observed for all samples, and this corresponds to the polyimide film used for sealing the samples.

Figure 1.

Figure 1

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XRD patterns for Li3–2xCaxPS4 (x = 0, 0.0250, 0.0375, 0.0500, 0.1000, and 0.1500) and referenced crystalline patterns of γ-Li3PS423 and β-Li3PS4.40 In the right-hand panel, selected peaks are shown enlarged to highlight their shift with compositional change.

The XRD pattern of Li3PS4 without Ca doping shown in Figure 1 (third from the bottom) matches the reference pattern of γ-Li3PS4 well. The main peaks of Li3–2xCaxPS4 (x = 0.0250, 0.0375, 0.0500, 0.1000, and 0.1500) were assigned to the β-Li3PS4 phase (high-temperature phase) at room temperature, meaning that the stabilization of the high-temperature phase at room temperature was achieved with Ca doping. Many diffraction peaks expected from β-Li3PS4 and γ-Li3PS4 crystals were overlapped, but the peaks split into two at around 31° for γ-Li3PS4, which is a unique peak not observed for β-Li3PS4. The samples with x = 0.0250 and 0.0375 showed weak peaks corresponding to γ-Li3PS4, indicating that γ-Li3PS4 and β-Li3PS4 are in a mixed phase. Quantification of γ-Li3PS4 and β-Li3PS4 will be discussed in 31P NMR experiments.

It has been reported that the phase transition of γ-Li3PS4 to β-Li3PS4 for Li3PS4 without Ca doping occurs above 573 K.23 Unassigned peaks marked with filled orange circles (Unknown1) were observed for Li3–2xCaxPS4 at 2θ = 20.3, 21.5, 28.1, 28.5, and 32.2°. It is noted that the peak patterns for CaS42 and Ca phosphorus sulfides (Ca2P2S6)43 cannot be assigned to Unknown1 as unreacted raw compounds. The relative intensities of the peaks from Unknown1 increased with an increase in Ca doping. The peaks at around 56.8° on the high-angle side were shifted to the lower-angle side when x was changed from 0 to 0.05, as shown in Figure 1 (right-hand panel). This behavior is associated with lattice expansion caused by increasing the amount of Ca doping. A slight low-angle shift was observed when x changed from 0.1 to 0.15. This may be due to the fact that excess Ca doping causes the shrunken lattice with increasing Coulombic interaction between Ca2+ and PS3–4 involving increasing vacancies. Two peak intensities at around 18° varied with the amount of doping. This corresponds to a change in the elemental composition caused by Ca doping. The main peak at around 18° in the doped sample was assigned to the β-Li3PS4 phase, as indicated by the 31P NMR result discussed later.

The lattice constants and volumes for Li3–2xCaxPS4 derived from the Rietveld refinement of experimental XRD patterns considering the β-Li3PS4 phase are shown in Figure 2 as functions of x. The fitting results of Rietveld refinement with experimental data, R-factors, and χ2 (goodness of fit) values for Li3–2xCaxPS4 are shown in Figure S1 of Supporting Information. The lattice volume of the β phase increased with increasing Ca doping up to x = 0.0500, as expected from the change in the peak positions at around 56.8°. In particular, the increase in the lattice constant b was significant compared to the changes in a and c. This change in the lattice constant corresponds to substitution of smaller Li+ (ionic radius 0.68 Å) with Ca2+ (0.99 Å); thus, Ca2+ doping can be successfully achieved by the solid-phase reaction. There may be a slight possibility of the substitution of P5+ and Ca2+. This substitution changes PS3–4, and it disrupts the crystal structure. The appearance of major β-Li3PS4 crystalline peaks proves that the substitution of P5+ for Ca2+ did not occur.

Figure 2.

Figure 2

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Lattice constants and unit-cell volume changes of Li3–2xCaxPS4. The filled blue and green circles show the values evaluated from Rietveld refinement and DFT calculations of β-Li3PS4, respectively.

The XRD patterns of Li2.9CayBa0.05–yPS4 (y = 0, 0.005, 0.015, 0.025, 0.035, and 0.045) are shown in Figure 3. Unassigned peaks marked with purple rhombuses (Unknown2) at 2θ = 10.5, 14.7, 20.9, 23.4, 31.7, 34.4, and 35.1° were also observed for all Li2.9CayBa0.05–yPS4 samples. Note that these peaks do not match those predicted for BaS44 or Ba2P2S6.45 The samples with y = 0 and 0.005 exhibit multiple splitting of diffraction peaks at around 31°, suggesting the existence of mixed γ-Li3PS4 and β-Li3PS4 phases.

Figure 3.

Figure 3

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XRD patterns for Li2.9CayBa0.05–yPS4 (y = 0, 0.005, 0.015, 0.025, 0.035, and 0.045) and referenced crystalline data for γ-Li3PS4 and β-Li3PS4. Selected peaks are shown enlarged in the right-hand panel to highlight the peak shift with compositional change.

A peak shift at around 56.8° toward the higher-angle side was found for samples with increasing y, as shown in Figure 3 (right-hand panel). This peak shift occurred continuously as y increased. This continuous shift was related to the lattice shrinkage with doping by Ca instead of Ba in β-Li3PS4. This result is simply explained by the ionic radius; the larger ionic radius of Ba2+ compared to that of Ca2+ contributes to the increased lattice expansion. Sulfide materials composed of P and S have anions in a variety of PS units. β-Li3PS4 and γ-Li3PS4 phases are composed of PS3–4 alone, but unknown peaks may originate from the conversion of PS3–4 to P2S4–6 or P2S4–7. Since such conversions of PS units are difficult to identify by diffraction patterns, the local structure of P was analyzed using 31P NMR.

The filled blue circles in Figure 4 show the lattice constants and volume changes for Li2.9CayBa0.05–yPS4 determined from the Rietveld refinement of the experimental data. As predicted by the observed peak at around 56.8°, the volume of codoped Li2.9CayBa0.05–yPS4 decreased with increasing Ca doping.

Figure 4.

Figure 4

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Lattice constants and unit-cell volumes of Li2.9CayBa0.05–yPS4 as functions of y, as derived from Rietveld refinement of β-Li3PS4.

4.2. AC Impedance Measurements

Nyquist plots obtained from impedance measurements and the conductivity for all samples with variable temperature are listed in Figure S2 and Table S1.

Figure 5a shows the logarithmic ionic conductivities, σ, of Li3–2xCaxPS4 (x = 0, 0.0250, 0.0375, 0.0500, 0.1000, and 0.1500) as functions of inverse temperature. The solid lines indicate the linear regression results to evaluate the activation energy Ea based on the Arrhenius law

4.2. 1

where σ, T, and R are the conductivity, temperature, and gas constant, respectively. The values of Ea were calculated from the slopes of the lines in Figure 5a. The values of σ at 300 K, σRT, and the derived activation energies are also displayed as functions of x in Li3–2xCaxPS4 (Figure 5b). All values of σRT and Ea are listed in Table S2 of the Supporting Information. The σRT value of γ-Li3PS4 without Ca doping was 4.84 × 10–7 S cm–1, which is in good agreement with a previous result for γ-Li3PS4 synthesized by solid-state reaction.22

Figure 5.

Figure 5

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(a) Arrhenius plots of ionic conductivities of Li3–2xCaxPS4. (b) σRT and Ea as functions of x in Li3–2xCaxPS4.

The σRT values were dramatically enhanced by 2 orders of magnitude with Ca doping. This behavior is attributed to the formation of the β-Li3PS4 phase, which has a higher conductivity than the γ-Li3PS4 phase at room temperature. The maximum σRT value was found for the sample with x = 0.0500; samples with doping above x = 0.0500 have lower σRT values. The Ea values of γ-Li3PS4 and β-Li3PS4 were slightly higher than those previously reported.23,24,40 This difference may be due to the synthesis conditions and the effects of the formation of unknown phases. The Ea value increased with increasing Ca doping, as shown in Figure 5b. The trends of σRT and Ea with x are explained by the formation of the unknown phases observed in Figure 1 and the effect of excess Ca doping. An increase of Ea with increasing Ca doping has also been found for solid-state Na+ electrolytes, denoted as Na3–2xCaxPS4.31 Although a variety of factors contribute to the conductivity of samples that are not single-phase, the vacancies likely created by Ca doping in monovalent solid-state electrolytes generate a conduction path with an increased activation barrier for monovalent cations.

Figure 6a,b shows Arrhenius plots of σ as functions of inverse temperature, and σRT and Ea as functions of y in Li2.9CayBa0.05–yPS4. These values are summarized in Table S3. Intermediate σRT values were found for γ-Li3PS4 and β-Li3PS4 samples with y = 0 and 0.005. This result is expected from the mixing of the γ-Li3PS4 and β-Li3PS4 phases. In fact, a characteristic peak at around 31° attributed to the γ-Li3PS4 phase can be observed in the XRD pattern in Figure 3. A convex change of σRT against y is found in Figure 6b, and the maximum σRT value was obtained for the sample with y = 0.025.

Figure 6.

Figure 6

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(a) Arrhenius plots of the σ value of Li2.9CayBa0.05–yPS4 as functions of inverse temperature. (b) Plots of σRT and Ea conductivity versus y.

The σRT values of Li2.9CayBa0.05–yPS4 were about 1.5–2.0 times larger than those of Li3–2xCaxPS4. The lattice expansion induced by Ba doping generated an efficient conduction path for Li+. However, the Ea value of Li2.9CayBa0.05–yPS4 tends to be larger than that of Li3–2xCaxPS4. The enlargement of the Li+ conduction path resulting from the lattice expansion generates new Li+ conduction paths; however, this does not contribute to the reduction of the migration barrier.

4.3. 31P Solid-State NMR

31P MAS NMR measurements were performed to evaluate the local 31P structure and quantify the PS units in the sample. Figure 7 shows the 31P MAS spectra of Li3–2xCaxPS4 along with peak assignments expected from previous 31P NMR studies of phosphate sulfide.40,46−49 There are no peaks originating from phosphate units in the lower-frequency side ranging from 50 to −100 ppm,50,51 indicating that there is no contamination of oxygen during synthesis. The peak assignments are indicated by filled rectangles of different colors, with spans showing their chemical shift ranges. The experimental 31P MAS NMR spectra were deconvolved based on six peaks corresponding to possible PS units. The main peaks observed ranged from 94 to 80 ppm, and these are magnified and displayed with the deconvolved results in Figure 7 (right-hand panel).

Figure 7.

Figure 7

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(a) 31PMASNMR spectra and (b) deconvolved 31PMASNMR spectra of Li3–2xCaxPS4 (x = 0, 0.0250, 0.0375, 0.0500, 0.1000, and 0.1500).

Although the crystalline structures of γ-Li3PS4 and β-Li3PS4 are composed of only PS3–4, the 31P chemical shift of PS3–4 for γ-Li3PS4 differs from that of β-Li3PS4.47 The 31P chemical shift of disordered PS3–4 units was also different from those of γ-Li3PS4 and β-Li3PS4. The 31P chemical shift ranges of PS3–4 in γ-Li3PS4, β-Li3PS4, and disordered units were 89 ± 2, 86 ± 2, and 85 ± 2 ppm, respectively.40,46,47,52 These known chemical shift ranges were imposed as the constraints for the spectral deconvolution, and they produced reasonable simulated spectra, as shown in Figure 7 (right-hand panel). The population of two PS3–4 in β-Li3PS4 and γ-Li3PS4 and disordered PS3–4 was obtained from the peak areas in the deconvolved spectra. Note that such quantitative information for the cophases cannot be accessed from the XRD patterns alone. The mixed phases with γ-Li3PS4 and β-Li3PS4 were expected from the diffraction patterns of the sample with lower Ca doping, which was consistent with results quantified in the 31P MAS NMR spectrum. Unknown peaks in the 31P MAS NMR spectrum of Li3–2xCaxPS4 with x = 0.1500 were observed on the higher-magnetic-field side, ranging from 86 to 80 ppm. The 31P chemical shift can be assigned to PS units near Ca2+. This trend has also been reported for phosphate glasses containing alkaline-earth cations.53−55 This local structure is related to the crystalline compounds observed in the XRD patterns of Figure 1.

Disordered PS3–4 was present in crystalline γ-Li3PS4 with x = 0, as shown in the peak filled with green at around 85 ppm. A small amount of P2S4–7 and a negligible amount of P2S4–6 in Li3–2xCaxPS4 were observed at around 96 and 110 ppm, as shown by the yellow and gray areas. Additional peaks colored pale pink on the higher-field side ranging from 80 to 86 ppm for Li2.9CayBa0.05–yPS4 were confirmed for all samples except for x = 0. Although these peaks are hard to distinguish from disordered PS3–4 due to line broadening, these were assigned to PS units in unknown phases based on the XRD results in Figure 1.

The populations as functions of x in Li3–2xCaxPS4 are displayed in Figure 8 along with the σRT results. All populations of the PS units and the chemical shifts derived from the spectral deconvolution are summarized in Table S4 of the Supporting Information The introduction of a small amount of Ca doping (x = 0.0250) clearly increased the amount of PS3–4 in the β-Li3PS4 phase, which is consistent with the XRD results in Figure 1. The maximum β-Li3PS4 content was found at x = 0.0500, which is consistent with a composition exhibiting the maximum σRT. Excess Ca doping above x = 0.1000 induces the formation of PS units in unknown phases and consequently leads to a decrease in σRT.

Figure 8.

Figure 8

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Populations of PS units and unknown phases and conductivities at room temperature in Li3–2xCaxPS4 (x = 0, 0.2500, 0.0375, 0.0500, 0.1000, and 0.1500) as functions of x.

Figure 9 shows the experimental and deconvolved 31P MAS NMR spectra of Li2.9CayBa0.05–yPS4 from the same procedure as that used to obtain the spectra of Li3–2xCaxPS4. The peak assignments are displayed by using different colors, as in Figure 7. The PS3–4 in both the β-Li3PS4 and γ-Li3PS4 phases are present in the samples doped only with Ba (y = 0). When Ca was additionally introduced into the sample, the PS3–4 of γ-Li3PS4 was not visible. These changes were consistent with the XRD results in Figure 3.

Figure 9.

Figure 9

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(a) 31P MAS NMR spectra of Li2.9CayBa0.05–yPS4 with the assignments of PS units displayed using different colors. (b) Deconvolved results of experimental and simulated 31P MAS NMR spectra for the main peak region.

Unknown peaks (unknown-Ca and unknown-Ba) in the 31P MAS spectra of Li2.9CayBa0.05–yPS4 with y = 0 were observed at around 64, 67, and 79 ppm. These peaks may be assigned to PS units related to the Ba2+ and Ca2+ positions. The populations of these unknown peaks slightly decreased with increasing Ca doping. The peak assigned to PS3–4 of γ-Li3PS4 was almost invisible for samples above y = 0.025.

Figure 10 shows the relationships between the PS-unit populations derived from the deconvolution of the 31P MAS NMR spectra and the σRT value of Li2.9CayBa0.05–yPS4 as a function of y. Table S5 summarizes the chemical shifts of 31P and the populations of PS units, including unknown crystalline phases for Li2.9CayBa0.05–yPS4. The population of β-Li3PS4 reached about 95% for the sample with y = 0.150. Consistency of σRT changes with the amount of the β-Li3PS4 phase was also found with Li3–2xCaxPS4.

Figure 10.

Figure 10

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Populations of PS units and unknown phases and conductivities at room temperature of Li2.9CayBa0.05–yPS4 (y = 0, 0.005, 0.015, 0.025, 0.035, and 0.045) as functions of y.

4.4. 7Li MAS NMR

Identification of Li species based on mobility was investigated using 7Li MAS NMR. The line widths of the peaks on the 7Li MAS spectra are related to the rotational correlation time (spin–spin relaxation time), meaning that mobile and immobile Li+ can be differentiated by narrow and broadened peaks.56,57Figure 11 shows the 7Li MAS NMR spectra of selected Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4 samples along with deconvolved results, showing three peaks. The number of peaks could not be determined definitively; however, deconvolution with two immobile and one mobile Li+ species represents the experimental spectra well. The chemical shifts and populations derived from the deconvolution are summarized in Table S6 of the Supporting Information.

Figure 11.

Figure 11

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Deconvolved 7Li MAS NMR spectra of Li3–2xCaxPS4 (x = 0, 0.0500, and 0.1500) and Li2.9CayBa0.05–yPS4 (y = 0.025 and 0.050). The reference sample was a 1 M LiCl solution.

A single broadened peak at around 1.5 ppm was observed for γ-Li3PS4 without doping, which corresponds to immobile Li+ species. The 7Li chemical shift of the immobile Li+ is close to the results of previous 7Li NMR studies of γ-Li3PS4.46 However, mobile Li+, with a narrow peak at around 1 ppm, appeared for Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4 instead of decreasing in immobile Li+. The appearance of these mobile Li+ when doping with Ca and Ba is consistent with increasing σRT.

The fast exchange of Li+ between 8d and 4b sites at the NMR time scale has been reported.56,57 This fast exchange is associated with the narrow peak and conduction path along the b axis in β-Li3PS440 revealed by bond-valence-sum analysis for X-ray and neutron diffraction data. The mobile Li+ can likely be assigned to exchange of Li+ between 8d and 4b within the NMR time scale.

The population of the broadened peak (immobile) in Li3–2xCaxPS4 with x = 0.1500 was relatively higher than that found in Li3–2xCaxPS4 with x = 0.0500. Since Li3–2xCaxPS4 with x = 0.1500 contains a more unknown crystalline phase than that with x = 0.0500, the immobile2 peak was assigned to Li+ in another unknown crystalline phase. The Li+ mobility in the unknown crystalline phase is not as high as expected from the results of the conductivity measurement.

The populations of Li+ species and σRT in selected γ-Li3PS4, Li3–2xCaxPS4, and Li2.9CayBa0.05–yPS4 samples are displayed in Figure 12 along with their σRT values. The populations of mobile Li+ were well-correlated with the σRT values for all samples. It is clear that the large amount of highly mobile Li+ detected by 7Li MAS NMR is key to achieving a superior Li+ conductivity. The amount of mobile Li does not reach 50%, even in the best Li+-conductive sample (Li2.9Ca0.025Ba0.025PS4). This result suggests the possibility of improving the Li+ conductivity by further modifying the β-Li3PS4 structure.

Figure 12.

Figure 12

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Populations of one mobile and two immobile Li+ species evaluated from 7Li MAS NMR spectra of selected Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4 samples. The σRT value for each sample is displayed as a reference.

4.5. DFT Calculations

The stability of β-Li3PS4 resulting from doping with Ca was theoretically investigated by using DFT calculations. The initial structures were made from crystalline β-Li3PS4 and γ-Li3PS4 with various x values in Li3–2xCaxPS4. The values of x were chosen to match the synthesized samples as closely as possible. To compare the system energies of the β-Li3PS4 and γ-Li3PS4 structures, we gave them both the same atomic composition. The compositions for DFT calculations were x = 0, 0.0156, 0.0312, 0.0625, 0.0938, and 0.1250, corresponding to 1, 2, 4, 6, and 8 substitutions of Li with Ca.

The stability of the β-Li3PS4 and γ-Li3PS4 structures was estimated by the difference in the enthalpy, H, obtained from the DFT calculations. The H values were evaluated for each system after structural optimization of the atomic positions and lattice constants.

The obtained lattice constants of Li3–2xCaxPS4 with β-Li3PS4 from the DFT calculations are displayed in Figure 2 along with the experimental results from Rietveld analysis. All lattice constants and volumes are also summarized in Table S7 of the Supporting Information. The lattice constants of Li3–2xCaxPS4 for the β-Li3PS4 lattice obtained from DFT were somewhat larger overall than those obtained from the experiments. This trend can be reasonably explained by overestimation of the bond lengths for the DFT calculations by the GGA-PBE exchange–correlation approximation;58,59 this overestimation of the bond lengths leads to a larger lattice. Although such errors are included in the DFT results, the trend in the lattice constant with different x values in Li3–2xCaxPS4 matches well with the experimental results. For instance, the lattice parameters b and c showed an increasing trend with increasing x. Therefore, the H values obtained from the structural optimization are considered to be a good representation of real samples.

The H values of β-Li3PS4 and γ-Li3PS4 structures with the same composition are indicated in Figure 13 as functions of x in Li3–2xCaxPS4. The differences in H (ΔH) for β-Li3PS4 and γ-Li3PS4 are displayed at the bottom of each bar in Figure 13. The ΔH value of Li3PS4 without Ca doping was 2.09 eV, meaning that γ-Li3PS4 is more stable than β-Li3PS4. It should be noted that the DFT calculations do not take into account thermal effects (under vacuum at 0 K). However, the lower H value of γ-Li3PS4 when compared to that of β-Li3PS4 rationalizes the preferential formation of γ-Li3PS4 at room temperature via the solid-state reaction route. For the composition with only a small amount of Ca doping (x = 0.0156), γ-Li3PS4 is still somewhat more stable. In systems with Ca doping above x = 0.0312, the stable phase transfers to the β-Li3PS4 lattice. This perspective on ΔH is consistent with the experimental formation of the β phase by doping with Ca.

Figure 13.

Figure 13

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Enthalpy H of Li3–2xCaxPS4 (x = 0, 0.0156, 0.0312, 0.0625, 0.0938, and 0.1250) for the β-Li3PS4 and γ-Li3PS4 lattices. The differences between the enthalpy ΔH are indicated in green text.

5. Discussion

Although a complete single phase could not be obtained via the solid-state reaction, β-Li3PS4, as the high-temperature phase, is stabilized by Ca or Ba doping at room temperature. The changes in the σRT values of the synthesized samples were consistent with the amount of the β-Li3PS4 phase, which was quantitatively evaluated by 31P MAS NMR. The ideal Li+ conductivity of the single-phase β-Li3PS4 at room temperature was derived from the extrapolation of data ranging from 473 to 573 K.22,24 The extrapolated value at room temperature is 8.9 × 10–7 S cm–1, which is approximately 2 orders of magnitude lower than that of the divalent doped β-Li3PS4 in this study. This gap suggests that Li+ conduction in divalent doped β-Li3PS4 is elevated by developing a path not present in the pure β-Li3PS4 phase. The volume expansion along the b axis is also related to the development of this conduction path and the change of the Li+ migration barrier.

The activation energy of the β-Li3PS4 phase with divalent doping was higher than that of β-Li3PS4 without doping. Therefore, the new conduction mechanism, which involves the generation of new conduction paths in divalent cation doping of β-Li3PS4, contributes to an increase in Li+ conductivity rather than a reduction in the Li+ migration barrier.

It is expected that the formation of Li+ vacancies caused by divalent doping in β-Li3PS4 reduces the frequency of ballistic Li–Li interactions. The “billiard-ball” mechanism of enhancing Li+ conduction has been proposed in recent experimental and theoretical studies of argyrodite-type lithium conductors.60 In this process, the kinetic energy required for Li+ migration can be relayed from one ion to another via cascade processes. The contribution of this effect is likely enhanced by the presence of vacancies. In a perfect β-Li3PS4 crystal without defects, the kinetic energy of Li+ migration is consumed by stationary vibrational motion, which cannot contribute to long-distance Li+ translational motion.

Ca and Ba codoping in β-Li3PS4 can expand the conduction path from that of β-Li3PS4, and this can be simply explained by the Ba2+ ions being larger than the Ca2+ ions. The Li+ conductivity of β-Li3PS4 with Ca and Ba doping (Li2.9Ca0.025Ba0.035PS4) is about twice that of the sample with only Ca doping (Li2.9Ca0.05PS4), as indicated in Tables S2 and S3, when comparing samples with the same amount of divalent doping. This result suggests that an appropriate extension of the conductive path can be controlled by codoping, and this can enhance the Li+ conductivity.

It has been reported that the formation of Li+ vacancies is needed to stabilize the high-temperature phase of oxide Li7La3Zr2O12.61,62 The application of the same idea to the sulfide has now also been demonstrated; thus, the stability of β-Li3PS4 involving vacancies has been theoretically revealed by DFT calculations. This phenomenon was associated with an increasing entropy by introducing divalent cations and involving vacancies. The structural disorder present in Ca-doped β-Li3PS4 was visually identified, as shown in the atomic images of Figure S3 of Supporting Information. The degree of disorder for β-Li3PS4 with Ca doping is higher than that for γ-Li3PS4.

Such disordering of Li+ sites is associated with a variety of conduction routes, which can promote Li+ conduction by means of the billiard-ball mechanism. These cascade processes can be facilitated by diverse Li+ sites in the conduction paths. The introduction of defects and path extension cause the generation of a variety of Li+ sites corresponding to an increase in entropy, which can work in conjunction with the enhancement of the billiard-ball mechanism. Changes in the Li+ dynamics with doping are necessary to understand the macroscopic conductivity. The details of the dynamic behavior of Li+ will be revealed by molecular dynamics simulation based on the structures modeled in this study.

6. Conclusions

The high-temperature β-Li3PS4 phase was successfully stabilized at room temperature by divalent cation doping by using a solid-phase reaction route. The generation of the β-Li3PS4 phase was examined by XRD and subsequent Rietveld analysis. The expansion of the lattice with divalent cation doping was demonstrated using 31P MAS NMR. The maximum Li+ conductivity obtained by divalent doping was more than 2 orders of magnitude higher than that of γ-Li3PS4 with the low-temperature phase. The Li+ conductivity is dependent on the amount of the β-Li3PS4 phase. Unknown phases with lower Li+ conductivity were induced with excess Ca doping, and these were tentatively assigned to PS units positioned near Ca2+.

The population of mobile Li+ was revealed by 7Li MAS NMR spectra. The increase in Li+ conductivity was consistent with the increased amount of mobile Li. The population of mobile Li+ was about 25%, meaning that a proportion of Li+ cannot work as conduction carriers. Converting such immobile Li+ to mobile Li+ is likely to enhance the Li+ conductivity further.

Crystalline structures of composition equivalent to that of the synthesized samples with Ca doping for the γ-Li3PS4 and β-Li3PS4 lattices were reproduced using DFT calculations. The stability of the β-Li3PS4 phase with suitable Ca doping at room temperature was theoretically demonstrated by considering the enthalpy. Defects produced by the substitution of Li+ with divalent cations induce disordering involving a variety of Li+ sites. The degree of disordering in β-Li3PS4 is significant compared to that in γ-Li3PS4. This result can be attributed to a variety of different Li+ conduction paths compared to that formed by ordered Li+ sites. It is expected that the modification of Li+ conduction paths induced by doping with divalent cations can enhance a billiard-ball mechanism involving cascade processes to improve long-range Li migration. As a result, the experimentally observed macroscopic conductivity is higher.

The introduction of defects by doping with divalent cations and controlling the conduction paths represent important concepts for the modification and optimization of existing crystals. Improving the performance of materials based on these concepts can contribute to the realization of solid-state batteries.

Acknowledgments

This work was supported by JSPS KAKENHI (grant nos. 21H02038 and 23H04096). The computation was carried out using the computer resource offered under the project (ID: hp220039) by the Research Institute for Information Technology, Kyushu University.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c09952.

  • Rietveld refinement of XRD patterns for Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4; conductivities at 300 K and activation energies of Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4; deconvolved results of 31P and 7Li MAS NMR spectra for Li3–2xCaxPS4 and Li2.9CayBa0.05–yPS4; and illustrations of optimized crystal structures for Li3–2xCaxPS4 obtained by DFT (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao3c09952_si_001.pdf (5.1MB, pdf)

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