Towards practical all-solid-state batteries: structural engineering innovations for sulfide-based solid electrolytes

Li-P-S glass ceramics

Inorganic glassy compounds comprising sulfides crystallize when heated to specific temperatures. These crystalline structures are classified as glass-ceramics^[88]. The most well-known glass-ceramics are Li₂P₂S₆(50Li₂S-50P₂S₅), Li₇P₃S₁₁ (70Li₂S-30P₂S₅), Li₃PS₄ (75Li₂S-25P₂S₅), Li₇PS₆ (87.5Li₂S-12.5P₂S₅), and Li₄P₂S₆(67Li₂S-33P₂S₅)^[27,89-94]. Similar to glass materials, the framework of these structures is highly dependent on the specific ratio of their precursors. The regular and repeating frameworks of the crystalline structure and the ionic conductivities of the crystallites are more strongly influenced by the arrangement of the polyanion building blocks than by those of the glasses^[55,95-98]. Because Li₃PS₄ and Li₇PS₆ have thio-LISICON and argyrodite crystal structures, respectively, they are discussed in a later section. This section focuses on the crystal structures of Li₂P₂S₆, Li₄P₂S₆, and Li₇P₃S₁₁.

Figure 4A and B shows the crystal structure of Li₂P₂S₆. The crystalline Li₂P₂S₆ structure was first identified by Eckert et al. using nuclear magnetic resonance (NMR) spectroscopy^[101]. Later, Dietrich et al. further elucidated the solvation of the crystal structure^[89], and both studies revealed edge-sharing PS₄ tetrahedral units (P₂S₆^2-) within a unit cell. Li₂P₂S₆ crystallized in the monoclinic space group C2/m (no. 12), and two edge-sharing PS₄ (P₂S₆^2-) were formed in an eclipsed arrangement along specific axes. The lithium ions were located within the basal-distorted octahedral sites, and formed chains with an edge-shared form [Figure 4C]. The low ionic conductivity (7.8 × 10^-11 S cm^-1 at room temperature) and high activation energy (0.48 eV) observed for the Li₂P₂S₆ can be explained by three main factors: (1) the absence of three-dimensional (3D) isotropic diffusion that prevented long-range lithium-ion transport, (2) the high activation energy barrier between different jumps along the chains, and (3) the fully occupied lithium-ion sites within a unit cell, which resulted in a limited number of available sites for hopping. To summarize, the main cause of the lower ionic conductivity in the Li₂P₂S₆-type crystal structure is the deficiency of charge carriers. Therefore, chemical tuning with aliovalent ions to control the charge-carrier concentration can enhance the lithium-ion conductivity of Li₂P₂S₆.

Figure 4. (A) Crystal structure of Li₂P₂S₆ and (B) reconstructed negative nuclear density map; (C) (left) Distorted LiS₆ octahedron and (right) edge-shared Li polyhedra along the b-axis in Li₂P₂S₆^[89]. Reproduced with permission^[89]. Copyright 2017, American Chemical Society; (D) Crystal structure of Li₄P₂S₆, projections along the a-, c-axis and perspective view emphasizing the P₂S₆^4- and LiS₆ units^[99]; (E) Diffusion pathways of Li₄P₂S₆ involving all three (upper) or two (middle) possible interstitial sites and vacancy-mediated diffusion (lower) between the lattice Li sites^[93]. Reproduced with permission^[93]. Copyright 2016, American Chemical Society; (F) Crystal structure of Li_4-2xZn_xP₂S₆, viewed along [100], [001] (g) Arrhenius plots of the ionic conductivities for the Li_4-2xZn_xP₂S₆ (0.25 ≤ x ≤ 1, nominal composition)^[100]. Reproduced with permission^[100]. Copyright 2023, Elsevier.

The crystal structure of Li₄P₂S₆ has been reported to have various symmetries; however, it is consistently described as a rigid framework composed of ethane-like P₂S₆^4- building units (P⁴⁺) featuring P-P bonds [Figure 4D]^{[92,93,102-104]}. The finalized crystal structure of Li₄P₂S₆ can be described by either P321 (no. 150) or P$$ \overline{3} $$m1 (no. 164) space groups, which are almost identical to each other because their symmetry operations are related by a group-subgroup relationship. The specific equivalent sites of P in a unit cell may become disordered because the crystallization of the material is not guided by covalent bonds beyond the P-S bonds, which causes a highly disordered nature of the resulting structure^[99]. The sulfur anions were packed in hexagonal hcp stacking, with the lithium ions occupying the octahedral sites, and formed a 3D honeycomb-like structure when viewed along the c-axis. Although the crystalline structure of Li₄P₂S₆ featured highly connected lithium-ion diffusion pathways, the material exhibited a poor ionic conductivity of 1.6 × 10^-10 S cm^-1 at room temperature, with an activation energy of 0.48 eV. Figure 4E shows the crystal structure and energy landscape diagrams of the lithium-ion diffusion pathways in Li₄P₂S₆, which were mediated through interstitial or vacant sites. The diffusion process faced a higher activation barrier because of the need to pass through two fully occupied LiS₆ octahedra, which are less likely to participate in diffusion. However, diffusion along the int3-int1 and int2-int2 pathways showed a negligible barrier. Therefore, lowering the int1-int2 or Li2-Li1 barrier energy can further facilitate lithium-ion mobility within the crystal structure. Lyoo et al. achieved a reduction in the overall activation energy and enhanced lithium-ion conductivity in the Li₄P₂S₆ crystal structure by introducing vacancies by substituting Zn²⁺ for Li⁺, the nominal composition of Li_4-2xZn_xP₂S₆ (0.25 ≤ x ≤ 1) [Figure 4F]^[100]. A four-order-of-magnitude increase in ionic conductivity (3.8 × 10^-6 S cm^-1 at room temperature) and lowered activation energy (0.30 eV) were observed at x = 0.75[Figure 4G]. These enhancements in diffusion properties were primarily attributed to the vacancies created by the Zn²⁺ ions occupying specific sites, which facilitated lithium-ion diffusion through two-dimensional (2D) ab planes through the lithium-ion-deficient, edge-sharing LiS₆ octahedra. However, exceeding x = 0.75 resulted in decreased ionic conductivity, which indicates that regulating the optimum defect concentration within the crystal structure of Li₄P₂S₆ is crucial.

Glass-ceramic Li₇P₃S₁₁ was first discovered by Mizuno et al. and it exhibited a high ionic conductivity of 3.2 × 10^-3 S cm^-1 at room temperature, along with a notably low activation energy of 0.19 eV^[105][Figure 5A and B]. The glassy compound 70Li₂S-30P₂S₅ demonstrated lower ionic conductivity (5.4 × 10^-5 S cm^-1 at room temperature) and higher activation energy (0.39 eV) than crystalline Li₇P₃S₁₁^[105], which demonstrates the importance of exploring suitable framework structures for lithium-ion conductors. Interestingly, crystalline Li₇P₃S₁₁ cannot be prepared directly through solid-state synthesis, and can only be obtained through crystallization from glass^[105]. The crystal structure of Li₇P₃S₁₁ is described in the triclinic space group P$$ \overline{1} $$ (no. 2), which is similar to the crystal structure of α-Ag₇P₃S₁₁^[109]. It features corner-sharing P₂S₇^4- ditetrahedral and isolated PS₄^3- units with lithium ions occupying the interstices within its structure^[90,110] [Figure 5C]. The framework closely resembles a bcc-like anion structure, which has been proposed to significantly reduce the activation energy within the diffusion channel surrounding the lithium ions^[55]. Furthermore, the flexible motion of the P₂S₇^4- ditetrahedral units, as revealed by combined synchrotron X-ray, time-of-flight neutron diffraction, and NMR analyses, facilitated lithium-ion diffusion by flattening the energy landscape and widening the diffusion pathways^{[107,111,112]} [Figure 5D]. Computational investigation supporting the 3D lithium-ion diffusion pathways with lithium-ion sites appeared to be disordered within the diffusion channels provided by the readily mobile P₂S₇^4- anion species. In addition to the computational results, Chang et al. found that lithium diffusivity was not significantly affected by the presence of excessive defects or lithium ions, which implies that compositional tuning strategies may not be effective in enhancing the ionic conductivity of Li₇P₃S₁₁^[108] [Figure 5E]. Overall, the framework consisting of P₂S₇^4- ditetrahedral units and isolated PS₄^3- units created a flattened energy landscape for lithium-ion diffusion, making it a desirable structure for lithium-ion conductors^[113].

Figure 5. (A) X-ray diffraction (XRD) patterns and (B) Arrhenius plots of ionic conductivities of the 70Li₂S-30P₂S₅ glasses with different synthetic conditions^[105]. Reproduced with permission^[105]. Copyright 2005, Wiley-VCH GmbH; (C) The crystal structure of Li₇P₃S₁₁^[106]; (D) Schematic illustration of lithium-ion conduction and local flip motion in Li₇P₃S₁₁^[107] Reproduced with permission^[107]. Copyright 2015, American Chemical Society; (E) (left) Pair distribution function, G(r), obtained from the AIMD calculation and (right) corresponding pair schematics with lithium-ion diffusion pathways^[108] Reproduced with permission^[108]. Copyright 2018, American Chemical Society. AIMD: Ab initio molecular dynamics.

Thio-LISICONs

The term “LISICON” was originally used to describe the oxide-based lithium-ion conductors^[114]. The resulting compounds by replacing the oxygen with sulfur in LISICON are referred to as thio-LISICON^[115]. Thio-LISICONs are generally represented by Li_xMS₄ (where M = Al, Si, P, Ga, Ge, Sn, or Sb). These compounds feature sulfide anions arranged in a hcp structure with minimal distortion and typically consist of isolated MS₄ tetrahedral frameworks with Li ions occupying the vacant sites within the framework. These lithium ions were coordinated within the LiS₄ or LiS₆ polyhedra^[43,115]. The ionic conductivity of thio-LISICONs ranges from 10^-7 to 10^-4 S cm^-1 at room temperature and is primarily influenced by variations in the crystal structure owing to different heat-treatment conditions or chemical tuning within the structure^{[26,27,41,69,116,117]}. Variations in the crystal structure were particularly evident in the different stacking arrangements of the isolated MS₄ tetrahedral networks. These arrangements create distinct lithium-ion diffusion pathways, which cause the varied ion-conducting behaviors of the structures^[118,119].

The most well-known polymorph is the Li₃PS₄ system, which exhibits three temperature-dependent phases: the high-temperature (HT) phase [Cmcm (no. 63) or P2₁/m (no. 11), α-Li₃PS₄], the intermediate-temperature phase [Pnma (no. 62), β-Li₃PS₄], and the low-temperature (LT) phase [Pmn2₁ (no. 31), γ-Li₃PS₄]. The ionic conductivities at room temperature for the three phases are as follows: 10^-7 S cm^-1 for γ-Li₃PS₄^[27,120], 10^-4 S cm^-1 for β-Li₃PS₄^[26], and 1 mS cm^-1 for α-Li₃PS₄^[69]. They primarily differed in the orientation of the PS₄^3- tetrahedra, as shown in Figure 6A and B. Owing to the low ionic conductivity of the γ-Li₃PS₄ phase, stabilizing the crystal structure of the β- or α-Li₃PS₄ phases is important to achieve a high-performance lithium-ion conductor. Liu et al. stabilized β- Li₃PS₄ by fabricating it with tetrahydrofuran (THF)^[26]. When THF was removed, pure nanoporous β- Li₃PS₄ was obtained, which exhibited a high ionic conductivity of 1.6 × 10^-4 S cm^-1 at room temperature and an activation energy of 0.36 eV. Furthermore, Kimura et al. stabilized the α-Li₃PS₄ at room temperature by rapidly heating the Li₃PS₄ glass and achieved a high ionic conductivity of 1.3 × 10^-3 S cm^-1 and an activation energy of 0.33 eV^[69]. Alternatively, chemical tuning can be used to stabilize the β-type crystal structure. Zhou et al. achieved this by introducing Si⁴⁺ ions instead of P⁵⁺ ions, which resulted in a high ionic conductivity of 1.22 mS cm^-1 at room temperature for a nominal composition of Li_3.25Si_0.25P_0.75S₄^[116].

Figure 6. (A) Three different polymorphs and (B) corresponding simulated XRD patterns of Li₃PS₄^[69]. Reproduced with permission^[69]. Copyright 2023, American Chemical Society; (C) Fraction of stacking type of anion-sublattice in β- (left) and α-Li₃PS₄ (right)^[121]. Reproduced with permission^[121]. Copyright 2018, American Chemical Society; (D) Three types of rotational motion of PS₄ (left: threefold rotation, middle: librational motion, right: occupancy-change-driven tilting)^[122]. Reproduced with permission^[122]. Copyright 2024, Proceedings of the National Academy of Sciences; (E) (left) Lithium occupancy factor and bottleneck area as a function of x in Li_4-xSi_1-xSb_xS₄ (0 ≤ x ≤ 0.25), and (right) 1D diffusion pathways of lithium-ion diffusion pathways with the corresponding LT-Li₄SiS₄ crystal structure; (F) (left) Arrhenius plots of ionic conductivities and (right) activation energy versus nominal composition for the Li_4-xSi_1-xSb_xS₄ substitution series (0 ≤ x ≤ 0.25)^[41]. Reproduced with permission^[41]. Copyright 2024, American Chemical Society.

Recent studies suggest that the key factor contributing to the difference in ionic conductivities among the three phases was the arrangement of sulfur anions in the substructures. The α-Li₃PS₄ phase exhibited bcc-like sublattices, which enabled facile 3D diffusion pathways, in contrast to the β- and γ-Li₃PS₄ phases [Figure 6C]^[118,121]. While the “paddlewheel effect” has been widely accepted in the literature as an explanation for the high lithium-ion diffusion within the crystal structure of β- and α-Li₃PS₄phases^[123,124]. Jun et al. have recently proposed that this effect does not actually exist or contribute to the high lithium-ion diffusion^[122]. Instead, they discovered that topologically isolated PS₄^3- units, with their tilting driven by changes in the lithium site occupancy, facilitated lithium-ion diffusion. This phenomenon has been termed the “soft-cradle effect” [Figure 6D]^[122].

On the other hand, the polymorph of Li₄SiS₄ exhibits a structure type similar to that of β- (LT phase) or α-Li₃PS₄ (HT phase), depending on the synthesis temperature. Unlike the Li₃PS₄ system, Li₄SiS₄ does not show a significant variation in the ionic conductivities between these different crystal structures (LT-Li₄SiS₄: 9.36 × 10^-7 S cm^-1; HT-Li₄SiS₄: 5.25 × 10^-7 S cm^-1 at room temperature). We demonstrated significantly enhanced lithium-ion mobility by introducing defects into the crystal structure of Li_4-xSi_1-xSb_xS₄(0 ≤ x ≤ 0.25). An improved ionic conductivity was observed at x = 0.15, with a value of 3.14 × 10^-5 S cm^-1 at room temperature. This enhanced conductivity was primarily attributed to the increased bottleneck area for lithium-ion diffusion and the formation of lithium vacancies [Figure 6E and F]^[41].

Li_xMS₃ (M = Si, Ge, Sn)

Li_xMS₃ includes glass ceramics such as Li₂P₂S₆ and Li₄P₂S₆^[89,93], and several materials containing tetravalent cations such as Li₂SiS₃, Li₂GeS₃, and Li₂SnS₃^{[25,46,71,73,125]}. Unlike Li_xMS₄, each element in the polyanion exhibits a distinct crystal structure with different space groups that are not related to one another. Based on the stoichiometric composition of Li_xMS₃, MS₄^y- tetrahedra in the structure should not be isolated. Instead, these tetrahedra were either corner-shared or formed edge-sharing M₂S₆^y- tetrahedra. Ahn et al. first reported the crystal structure of Li₂SiS₃ as an orthorhombic phase of Cmc2₁ (No. 36) in 1989^[46]. The structure comprised SiS₄^4- tetrahedra that were corner-shared with each other and formed infinite zigzag chains along the c-axis [Figure 7A]. Lithium ions occupied the tetrahedral interstices, where the LiS₄ tetrahedra were corner-shared in all directions within a unit cell. The low ionic conductivity observed for this crystal structure (2 × 10^-6 S cm^-1 at room temperature) was primarily attributed to the ordered arrangement of lithium ions within a unit cell^[25,46]. Huang et al. chemically modified Li₂SiS₃ by introducing small amounts of phosphorus (P)^[25]. They analyzed the resulting crystal structure, which featured an edge-shared dimer of the (Si/P)₂S₆ framework. This modification achieved a high ionic conductivity of 2.4 mS cm^-1 at room temperature. The key advancement in the ionic conductivity is the flattened energy landscape of the interstitial lithium ions created by the edge-shared (Si/P)₂S₆ framework, which introduces partially occupied lithium-ion sites within a unit cell [Figure 7B and C]^[25].

Figure 7. (A) Schematic crystal structure of orthorhombic-Li₂SiS₃^[46]. Reproduced with permission^[46]. Copyright 1989, Elsevier; (B) Crystal structure of tetragonal Li_1.82SiP_0.036S₃ viewed along the [010] and [001] directions, respectively; (C) Bond valence energy landscape calculations for lithium-ion diffusion pathways within Li_1.82SiP_0.036S₃ (left) and orthorhombic Li₂SiS₃ (right)^[25]. Reproduced with permission^[25]. Copyright 2022, American Chemical Society; (D) Crystal structure of Li₂GeS₃ and (E) corresponding lithium-ion diffusion pathways and energy diagram, as calculated by the bond valence energy landscape^[71] Reproduced with permission^[71]. Copyright 2023, American Chemical Society; (F) The crystal structure of Li₂SnS₃, which illustrates various projections to highlight the Sn-S framework^[73]. Reproduced with permission^[73]. Copyright 2015, American Chemical Society.

Recently, we determined that the crystal structure of Li₂GeS₃ exhibited a P6₁ (no. 169) space group. The structure featured infinitely shared corners of GeS₄ tetrahedra aligned along the c-axis of a unit cell, which formed a spiral GeS₄ framework. The lithium ions were located within the tetrahedral interstitial sites [Figure 7D]. Favorable lithium-ion connectivity was observed through one-dimensional (1D) pathways, which were interconnected to form 3D diffusion pathways within the crystal structure [Figure 7E]. However, the structure exhibited low ionic conductivity (1.63 × 10^-8 S cm^-1 at 303 K) and an activation energy of 0.37 eV, which may be because of the ordered arrangement of lithium ions within a unit cell, as no vacant sites were available for additional lithium-ion hopping. In this context, the aliovalent anion substitution series Li_2-xGeS_3-xCl_x (x = 0.15) was designed to introduce vacancies into the crystal structure. This resulted in a tenfold increase in the ionic conductivity (1.15 × 10^-7 S cm^-1 at 303 K), and confirmed the effectiveness of the structural engineering approach in enhancing lithium-ion transport properties^[71].

The crystal structure of Li₂SnS₃ was first reported by Kuhn et al., and was described as crystallizing in the monoclinic space group C2/c (no.15)^[125]. The structure exhibited a layered configuration characterized by a partial disorder in the Li/Sn sublattice. This disorder varied depending on the synthesis conditions. For example, melt-quenched Li₂SnS₃ exhibited significant Li/Sn disorder, which resulted in an average rhombohedral structure with higher symmetry and a smaller unit cell (R$$ \overline{3} $$m, no. 166). In contrast, a slower heating/cooling ramp rate generated a more ordered arrangement of Li and Sn in a unit cell. The relatively high ionic conductivity observed at room temperature for Li₂SnS₃ (1.5 × 10^-5 S cm^-1) primarily originated from the 2D diffusion pathways in the ab plane within a unit cell, which were formed by the alternatively stacked honeycomb-like [SnS₃]^2- layers [Figure 7F]. The ionic conductivity of this structure may be enhanced by introducing vacancies, which could promote the formation of 3D diffusion pathways or facilitate the concentrated migration of lithium ions within a unit cell. These modifications are expected to further improve the ionic conductivity.

Overall, the high ionic conductivities of thio-LISICON compounds depend on several factors. Key strategies include stabilizing the high-conductivity polymorphs, introducing vacancies to create sites for lithium-ion hopping, and leveraging diffusion mechanisms such as the soft-cradle effect to enhance lithium-ion mobility. These strategies emphasize the importance of controlling the charge-carrier concentrations in the development of high-performance ionic conductors. The effective management of these factors is crucial for advancing lithium-ion conductors in thio-LISICON systems.

Li₆PS₅X (X = Cl, Br, and I) argyrodite

The argyrodite structure was first identified in 1885 with the discovery of Ag₈GeS₆^[126]. This crystal structure was characterized by highly disordered silver ions within a unit cell. Additionally, Cu can be substituted for Ag in argyrodites, and both Ag- and Cu-containing argyrodites exhibited high ionic conductivity^[127-131]. The general composition of argyrodites is: A^m+_(12-n-x)/mBⁿ⁺Y^2-₆, where A = Li, Ag, Cu; B = Ge, Sn, P, As; Y = S, Se, Te; and 0 ≤ x ≤ 1, where m and n represent the valence states of the cations. Inspired by the similar ionic radii of Cu⁺ and Li⁺, Deiseroth et al. proposed “Li-argyrodites”, with a general structure of Li₇MS₆ or Li₆MS₅X (M = P, As, and X = Cl, Br, I)^[23,132]. This argyrodite structure exhibited polymorphic behavior. The HT phase had a consistent cubic symmetry of F$$ \overline{4} $$3m (no. 216), regardless of the composition, whereas the LT phase displayed either orthorhombic or monoclinic symmetries, depending on the specific composition^[131]. The LT polymorph of Li₇PS₆ typically exhibits a low ionic conductivity at room temperature, whereas a high ionic conductivity is only observed in the HT cubic phase^[132]. The well-known Li₆PS₅X (X = Cl, Br, I) exhibits the HT cubic phase, and each composition is characterized by varying the lattice parameters and ionic conductivity properties^[36,131,132].

Figure 8A shows the crystal structure of HT-argyrodite with Li₆PS₅X (X = Cl, Br, or I). In the tetrahedral close packing of the anions, there were 136 tetrahedral sites per unit cell (Z = 4). Among these, four tetrahedral sites were occupied by P. The remaining 132 tetrahedral sites were available to accommodate the 24 lithium ions and were classified into five types based on their orientation relative to the PS₄^3- tetrahedra [Figure 8B]. Typically, 24 lithium ions occupy type 5/5a or type 2 tetrahedral sites. Type 5a sites were arranged in a trigonal planar configuration at the shared face between two type 5 tetrahedra. These lithium ions were disordered across equivalent positions, which formed a cage-like network. The cages were located at the tetrahedral sites within a cubic close-packed unit cell and aligned in a mirror relationship along the (110) plane. The cages exhibited a zigzag stacking pattern relative to the isotropic axes of a unit cell. Interestingly, it was observed that the X^- and S^2- anions occupied distinct crystallographic sites within a unit cell, with X^- forming a close-packed cubic lattice. However, anion disorder between X^- and S^2- (1.84 Å) occurred when their ionic radii were similar. The degree of X^-/S^2- anion disorder depends on the ionic radius of X^-, with the strength of disorder following the trend: Cl^- (1.81 Å) > Br^- (1.96 Å) > I^- (2.2 Å)^[23,134]. The ionic conductivities of Li₆PS₅Cl, Li₆PS₅Br, and Li₆PS₅I are 1.4 × 10^-3 S cm^-1, 8.7 × 10^-3 S cm^-1, and 1.3 × 10^-7 S cm^-1, respectively, at room temperature^[36].

Figure 8. (A) (left) The crystal structure of Li₆PS₅I. (right) A face-shared S₃I₂ double tetrahedron with two distinct lithium-ion equivalent sites^[23]. Reproduced with permission^[23]. Copyright 2008, Wiley-VCH GmBH; (B) A simplified tetrahedron type in the argyrodite structure, where light gray represents PS₄ groups (type 0) and dark gray indicates lithium-containing tetrahedron types (types 1-5)^[131]. Reproduced with permission^[131]. Copyright 2010, Wiley-VCH GmBH; (C) (upper left) Lattice parameters of Li_6-xPS_5-xCl_1+x as a function of x. (upper right) Impedance plots at room temperature of Li₆PS₅Cl, Li_5.75PS_4.75Cl_1.25, Li_5.5PS_4.5Cl_1.5, and a sintered Li_5.5PS_4.5Cl_1.5. (lower left) Nyquist and Arrhenius plots for Li_5.5PS_4.5Cl_1.5. (lower right) Ionic conductivity and activation energy for Li_6-xPS_5-xCl_1+x (x = 0, 0.25, 0.375, 0.5)^[77]. Reproduced with permission^[77]. Copyright 2019, Wiley-VCH GmBH; (D) (upper left) Crystal structure of Li_6.7Si_0.7Sb_0.3S₅I. (lower left) Three distinct lithium ion diffusion pathways: the doublet jump (blue arrow), the intra-cage jump (red arrow), and the inter-cage jump (orange arrow). (upper right and lower left) The crystal structure of Li₆PS₅I is shown for comparison, with no additional lithium ions in the structure^[24]. Reproduced with permission^[24]. Copyright 2019, American Chemical Society; (E) (left) Two distinct lithium-ion cages, defined by their radius from isolated S^2- ions, are influenced by the Br^-/S^2-site disorder, and corresponding (right) lithium-ion diffusion pathways^[133]. Reproduced with permission^[133]. Copyright 2021, Wiley-VCH GmBH; (F) (left) The activation energy and Arrhenius prefactor as functions of X in Li₆PS₅X (X = Cl, Br, I). (right) The ionic conductivity as a function of X in Li₆PS₅X (X = Cl, Br, I)^[36]. Reproduced with permission^[36]. Copyright 2017, American Chemical Society.

The ionic conductivity of the argyrodite structure is widely recognized to depend on four key factors: (1) Li-ion concentration^{[24,77,79,135]}, (2) unit cell volume^[36,135,136], (3) degree of anion or cation site disorder^{[135,137-139]}, and (4) anion polarizability^[36,136]. The disordered state of lithium ions within the cages indicates that diffusion within the cage occurs at a faster rate than diffusion between cages. Therefore, these factors must be considered in relation to the specific crystal structure because the connectivity of Li cages significantly affects the lithium-ion transport properties^[140].

For instance, Li₆PS₅Cl exhibits a smaller unit cell volume than Br- or I-based argyrodites, which results in a shorter distance between the Li cages within a unit cell. This structure facilitates a high ionic conductivity of ~1 mS cm^-1 at room temperature, along with a low activation energy^[36,76,77]. The diffusion of lithium ions easily occurs between these Li cages, which facilitates control of the lithium-ion concentration or the induction of greater anion disorder, which is crucial for further enhancement of the ionic conductivity. Adeli et al. demonstrated that a Cl-rich argyrodite (with the nominal composition series Li_6-xPS_5-xCl_1+x, x ≤ 0.5) introduced more lithium-ion vacancies and greater anion disordering with Cl^-/S^2- within a unit cell of Li₆PS₅Cl, which resulted in an ionic conductivity of 9.4 mS cm^-1 at room temperature, which is nine times higher than that of the original Li₆PS₅Cl [Figure 8C]^[77]. Because the Li cages in the crystal structure already exhibited good connectivity, introducing vacancies and increasing the monovalent Cl- anion content enhanced the diffusivity and lowered the activation energy, thereby improving the ionic conductivity of the Cl-rich argyrodite.

In the case of Li₆PS₅I, different strategies should be applied to enhance ionic conductivity. Owing to the large volume of the unit cell, the distance between the Li cages was greater than that in Li₆PS₅Cl^[36]. Consequently, concerted migration could not occur along long-range diffusion between cages because of the deficiency of lithium ions within the cell. This resulted in a lower ionic conductivity and higher activation energy than those of Li₆PS₅Cl, despite their similar crystal structures^{[135,139,141]}. Therefore, the introduction of interstitial lithium ions is an effective approach for activating 3D lithium-ion diffusion between cages^[135,137]. Ohno et al. and Zhou et al. proposed a Li-rich substitution series of Li_6+xM_x(P/Sb)_1-xS₅I (M = Si, Ge, Sn), which demonstrated a high ionic conductivity of up to 24 mS cm^-1 at room temperature and a low activation energy [Figure 8D]^[24,139]. The enhanced ionic conductivity can be attributed to the more disordered arrangement of lithium ions, which occupied not only type 5 equivalent sites but also type 2 sites, further boosting the connectivity between the Li-ion cages and activating concerted migration within the unit cell.

Moreover, anion disorder can influence ionic conductivity by altering the local charge distribution, which subsequently affects the arrangement of lithium ions^[133,137]. Gautam et al. analyzed the crystal structure of Li₆PS₅Br by varying the degree of Br^-/S^2- disorder and adjusting the cooling rates of the samples. They found that higher cooling rates resulted in a higher degree of Br^-/S^2- disorder^[133]. As the Br^-/S^2- site disorder increased, the ionic conductivity also improved. This is because the increased disorder reduced the distance between the Li ions in the T2 sites that interconnect with the Li cages [Figure 8E]^[133]. Morgan proposed that long-range diffusion in X^-/S^2- disordered configurations is more favorable for lithium-ion conduction, owing to the inhomogeneous charge distribution within a unit cell. This inhomogeneity generated disorder in the lithium ions within the argyrodites, causing the energetically equivalent interstitial sites to become more uniform and facilitating easier diffusion^[137].

The polarization of the anions also affects ionic conduction. Similar to the design strategy of thio-LISICONs, more polarizable anions form weaker bonds with lithium ions, thereby lowering the activation energy barrier for lithium-ion conduction and leading to a higher ionic conductivity. Schlem et al. demonstrated this correlation in the argyrodite nominal substitution series Li₆PS_5-xSe_xI (0 ≤ x ≤ 5)^[136], where the incorporation of larger, more polarizable Se anions decreased the observable activation energy barrier for ionic migration, which resulted in an increase in the conductivity by approximately two orders of magnitude. The increase in the lattice volume and creation of wider diffusion pathways enhanced ionic conductivity without the disruptive effects of increased anion site disorder. This suggests that lattice softening is an effective strategy for improving the ionic conductivity of the argyrodite crystal structure^[136]. However, it should be noted that lattice softening also reduces the Arrhenius prefactor, particularly the attempt frequency (ν₀), as given in Equation (4). Kraft et al. systematically analyzed the influence of the lattice polarizability on the ionic conductivity of Li₆PS₅X (X = Cl, Br, I) [Figure 8F]^[36]. They proposed that increasing the lattice volume resulted in a longer jump distance and lowered the activation energy, which in turn reduced the attempt frequency, as defined by^[142]:

where M_Li refers to the mass of the lithium ions. Consequently, the optimal lattice softness in the argyrodite structure, such as that in Li₆PS₅Cl_0.5Br_0.5, results in a balanced value of the Arrhenius prefactor and activation energy, facilitating high ionic conductivity^[36].

As a result, structural engineering of argyrodites, such as controlling the lithium-ion concentration, lattice softness, and anion disorder, has proven to be an effective strategy for achieving high-performance lithium-ion conductors. By understanding lithium-ion diffusion within the unit cell and optimizing the chemical or structural properties, the conductivity can be significantly enhanced.

LGPS-type (Li₁₀GeP₂S₁₂) structures

The discovery of LGPS dates back to an investigation by Kanno et al. in 2001, which focused on the solid solution series in the Li₂S-GeS₂-P₂S₅ system^[143]. The solid solution in the Li_4-xGe_1-xP_xS₄ system (x = 0.75; Li_3.25Ge_0.25P_0.75S₄) exhibited notably high ionic conductivity (2.2 × 10^-3 S cm^-1 at room temperature), with XRD patterns that deviated from those of pristine Li₄GeS₄ (Pnma, no.62) or Li₃PS₄ (Pmn2₁, no.31)^[143]. The crystal structure of LGPS with the P4₂/nmc (no. 137) space group was first reported in 2011^[12]. It featured a 1D lithium-ion conduction pathway and exhibited exceptionally high bulk-ionic conductivity of over 10 mS cm^-1 at room temperature, comparable to that of organic liquid electrolytes used in LIB systems. The framework of the unit cell comprises two equivalent tetrahedral sites: a 4d site with a 1:1 partial occupancy of Ge and P and a 2d site exclusively occupied by P, which formed an isolated MS₄ (M = Ge, P) tetrahedra. Furthermore, single-crystal X-ray structural analysis revealed four equivalent lithium-ion sites: two LiS₄ sites that were edge-shared with each other (Li1 and Li3), which formed four channels along the c-axis; one LiS₆ octahedron (Li2); and a four-fold coordinated site located between the four channels along the c-axis (Li4)^[144]. The thermal ellipsoids of Li1 and Li3 were roughly aligned along the c-axis, which indicates diffusion channels in this direction. In contrast, the thermal ellipsoid of Li4 was aligned perpendicularly to the c-axis, suggesting that it formed 3D diffusion pathways connecting the channels along the c-axis. Notably, Li2 exhibited smaller thermal ellipsoids, indicating inactive diffusion pathways within the unit cell. The partially occupied Li ions within the unit cell further support the unusually high ionic conductivity of LGPS [Figure 9A].

Figure 9. (A) Crystal structure of the Li₁₀GeP₂S₁₂; (B) Single lithium-ion jumps within the hcp-like packing and bcc-like packing of anion frameworks^[145]. Reproduced with permission^[145]. Copyright 2020, Wiley-VCH GmBH; (C) The crystal structure of Li₁₀SnP₂S₁₂^[37]. Reproduced with permission^[37]. Copyright 2013, American Chemical Society; (D) (upper) Schematic of the hypothetical inductive effect in M-S Li bonding for M = Ge vs. M = Sn. (lower left) Changes in the S-Li distances and occupancies with changing force constant in Li₁₀Ge_1-xSn_xP₂S₁₂. (lower right) S-Li distance versus previously reported activation energies^[146]. Reproduced with permission^[146]. Copyright 2020, American Chemical Society; (E) Compositional complexity metric for LGPS-type and argyrodite-type versus crystal structure indicator, the volume ratio of anions to that of cations; (F) Arrhenius plots for the ionic conductivities of Li_9.54[Si_0.6Ge_0.4]_1.74P_1.44S_11.1Br_0.3O_0.6 and Li₁₀GeP₂S₁₂^[20]. Reproduced with permission^[20]. Copyright 2023, The American Association for the Advancement of Science.

The crystal structure of the LGPS-type material comprises an S^2- sublattice, which is packed more akin to a bcc structure, unlike the hcp-packed structure observed in thio-LISICONs. The ideal bcc framework provides a continuous, face-sharing tetrahedral pathway with lower activation energy than the hcp or fcc structures [Figure 9B]^[55]. Therefore, the unusually high ionic conductivity of the LGPS-type structure can be attributed to (1) the ideal bcc framework, where the flattened energy landscape throughout the lattice promotes disordered lithium-ion distribution within a unit cell, and (2) the connectivity of lithium-ion diffusion pathways, enabling 1D and 3D network diffusion.

Bron et al. identified the crystal structure of Li₁₀SnP₂S₁₂^[37], which had the same LGPS-type structure as that of LGPS [Figure 9C]. This new compound exhibited an ionic conductivity of approximately 4 mS cm^-1 at room temperature, slightly lower than that of LGPS. Culver et al. studied the inductive effect in a solid-solution system of Li₁₀Ge_1-xSn_xP₂S₁₂ to explain the reduction in the ionic conductivity despite the substitution of the more polarizable Sn for Ge^[146]. They found that substituting Ge with Sn weakened the {Ge, Sn}-S bonding interactions and increased the charge density associated with the S^2- ions. This strengthened the interaction with lithium ions, which resulted in a lower ionic conductivity than that of LGPS [Figure 9D].

The highest ionic conductivity among the LGPS-type compounds reported to date is that of Li_9.54[Si_0.6Ge_0.4]_1.74P_1.44S_11.1Br_0.3O_0.6, which exhibits a conductivity of 32 mS cm^-1 at room temperature^[20]. The design approach utilized high-entropy materials and high polarizability with a target LGPS-type structure. A higher compositional complexity of constituent cations and anions (excluding lithium ions) with greater polarizability, facilitated increased lithium-ion conduction. This principle is illustrated in Figure 9E. The highest reported ionic conductivity demonstrates that even at 263 K, the material maintains a high ionic conductivity of 9 mS cm^-1 at room temperature [Figure 9F].

Overall, the LGPS-type structure highlights the crucial role of the crystal architecture in achieving high ionic conductivity. The bcc-like framework in the LGPS-type materials facilitates continuous low-energy barrier pathways for Li-ion diffusion across both 1D and 3D networks. Further structural modifications, such as leveraging the inductive effect, enhancing lattice polarizability, or inducing high entropy within the crystal structure, can significantly enhance the ionic conductivity of the LGPS-type structures.