Introduction

Lithium metal halide solid-state electrolytes (SSEs), with the formula of LiaMXb, have represented one of the dominant families of superionic conductors (>10−4 S cm−1 at 25 °C) for all-solid-state lithium batteries1,2,3,4. The M stands for one or multiple metal elements that can dominate the structure and facilitate the migration of lithium ions. Except for the latest developed SmCl3-based chlorides3 (large-sized Sm3+ or La3+) and glassified LiTaCl62 SSEs, most LiaMXb halides are developed from LiX structure. Thus, these LiaMXb halides can be regarded as the distribution of cations (including lithium-ion and multivalent M cations) and vacancies in the anionic framework due to the much larger ionic radius of halogen anions5. The LiaMXb halides can initially be divided into two types based on the different anion frameworks, including the hexagonal-close-packed (hcp) and cubic-close-packed (ccp) type anionic sublattices (Fig. 1a, b). Both hcp and ccp are close-packed with a 74% atomic packing factor6,7. However, the ccp structure possesses higher structural symmetry than the hcp structure. The hcp structure is described by the D6h point group (24 symmetry elements), while the ccp structure is the Oh point group (48 symmetry elements).

Fig. 1: Cationic polarization factor and its application in designing metal halide SSEs.
figure 1

Schematic illustration of crystal representatives (a) ccp type (cubic-closed-packed anion sublattice) and (b) hcp type (hexagonal-closed-packed anion sublattice) metal halide SSEs. The illustration of (c) octahedral and (d) cubic coordination and the critical radius ratio. e Ionic radius rule and (f) cationic polarization factor of representative hcp-T, hcp-O, and ccp-M type LiaMXb halides11,12,15,16,17,18,21,22,23,24,25,26,27, considering the radii, Li content, metal cations, and halogen anions (see Supplementary text and Supplementary Fig. 1, Supplementary Tables 1–4 for details). g Schematic illustration of the evolution from basic LiCl structure to other structures and phase transition within these structures dominated by proposed τ (cationic polarization factor). ccp-M indicates the C2/m space group, hcp-T indicates the P3̅m1 space group, and hcp-O indicates the Pnma space group.

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When further considering the occupation of cations, the ccp stacked LiaMXb halides normally possess a monoclinic structure, which is labeled as ccp-M (space group C2/m). While there are two structure types for the hcp stacked halides, namely the trigonal (hcp-T, space group P3̅m1) and orthorhombic (hcp-O, space group Pnma) structures8. Here, the different occupancies of cations directly lead to the discrepancy in space-group symmetries between hcp-T and hcp-O typed LiaMXb halides. All three structure types are based on octahedral coordination. Halide lithium superionic conductors with these stackings show distinctly different Li+ ion migration properties. The ccp-M typed and hcp-O typed LiaMXb halides usually possess higher Li+ conductivity over 10−3 S cm−1 at 25 °C1,9,10,11,12,12. Normally, the structural transition among those different structures as well as the induced variation of ionic conductivities can occur through substitutions or adjusting the synthesis conditions12,13,14.

In the search for SSEs with high ionic conductivity, wide electrochemical stability window, and good compatibility with oxide cathodes, various hcp-T, hcp-O, and ccp-M typed LiaMXb halides have been synthesized and investigated. However, effective guidelines for designing and preparing optimal halide SSEs are lacking, which continues as a great challenge to accelerating superionic materials discovery. The basic descriptor is the radius ratio rule that relates to the structure and composition of solid-state compounds. For LiaMXb type halides based on octahedral sublattices, according to the law of ionic packing, they can be differentiated from other halides based on the radius ratio of cation to anion (k = r+/r−). Two critical values of 0.414 (octahedral factor) and 0.732 (cubic factor) are obtained from the geometric information as presented in Fig. 1c, d. The octahedral sublattice structure can be theoretically stable when 0.414 < k < 0.732. Thus, the two critical lines calculated from the radius ratio of multivalent cations and halide ions distinguish the LiaMXb type halides from others (Fig. 1e and Supplementary Table 1). We further propose another key k value of 0.647 (Supplementary Fig. 1 and Supplementary Table 2 for detailed calculation) that separates the cubic-close-packed (ccp-M) and hexagonal-close-packed (hcp-T and hcp-O) structures in these LiaMXb halides. This hints that the ionic radius of the cations/anions plays an important role in the stackings of the halide SSEs. Nevertheless, this method only accounts for the difference in cation/anion radii, which makes it impossible to predict the structure of halides with the same metal cations and anions (e.g. hcp-T typed Li3HoCl6 and hcp-O typed Li2.727Ho1.091Cl6)11, let alone give further guidance of structure regulation.

Results

Besides the basic crystal size requirements, another significant parameter that dominates the stability of solid-state compounds is the ionic potential of ions. The ionic potential (I) is defined as the ratio of cationic charge (z+) and cationic radius (r+), which reflects the polarizing power of cations. The ionic potential gives an indication of the strength of the electrostatic attraction of ions with opposite charges. Aiming at a guide for the crystal structure control of the halide SSEs, we propose the “cationic polarization factor” (τ) to predict the structure of LiaMXb halides based on the chemical composition, which has the form

$${{{{{\rm{\tau }}}}}}=\frac{\Sigma \Phi {{{{{\rm{cations}}}}}}}{\Sigma \Phi {{{{{\rm{X}}}}}}}=\frac{\Phi {{{{{\rm{Li}}}}}}+\Sigma \Phi {{{{{\rm{M}}}}}}}{\Sigma {{{{{\rm{\phi }}}}}}{{{{{\rm{X}}}}}}}$$
(1)

where ΦLi represents the molar content proportionally ionic potential of lithium ions, which is defined as ΦLi = nLi × ILi; Similarly, ΣΦM and ΣΦX represent the summation of the molar content proportionally ionic potential of different ions.

Then, we can apply the proposed cationic polarization factor to distinguish and design LiaMXb halide superionic conductors. The prediction of LiaMXb halides stability using the cationic polarization factor requires only the chemical composition. In addition to predicting if a LiaMXb material is stable as ccp-M, hcp-T, or hcp-O structure, the cationic polarization factor also provides an estimate of the phase transition among those different structures, which further induces different Li-conducting behavior (Fig. 1f, g). Thus, the forecast based on the cationic polarization factor can constitute a useful predictive tool for those still unexplored halides and for discovering new halides with superionic conductivity.

All the reported information to our best knowledge about the LiaMXb halides with octahedral sublattice was used to analyze the influence of τ. The radii used here were obtained based on Shannon crystal ionic radii which are closer to the physical size of ions in a solid15. The molar content proportionally ionic potential of lithium ions (ΦLi) were plotted as a function of the τ values to show the phase map of the reported LiaMXb halides as shown in Fig. 1f. There are two lines that separate the hcp-T, hcp-O, and ccp-M type halide SSEs, indicating that the τ is a promising descriptor of the crystallography structure of the LiaMXb halides. A lower τ implies stronger electronic cloud extension of the cations, thus leading to a stronger impact on the halogen anion framework when the cations stack into the anion framework. Finally, this will result in a degradation of the anion framework symmetry from ccp to hcp arrangement. On the other hand, a larger τ, achieved in the case of smaller M cations or larger anion framework, has less impact on the halogen anion framework, favoring the ccp structure (Fig. 1g).

Using the τ as a guide, we design specific stacking structures by controlling the compositions of the Li3MX6 halides. A notable starting point is Li3HoCl6, which possesses an hcp-T typed structure11,13. Increasing the τ suggests a possible route to adjust the structure to the ccp-M typed structure via partial substituting of Ho3+ by In3+ (Fig. 2a), where In3+ has a higher ionic potential. As presented, three target samples (including Li3Ho0.85In0.15Cl6, Li3Ho0.78In0.22Cl6, and Li3Ho0.6In0.4Cl6) were designed and synthesized to validate the trigger point of the structural transition. The Li3Ho0.85In0.15Cl6 sample with a small amount of In3+ substitution induces the transition from pure hcp-T structure to the co-existence of hcp-T and hcp-O structure (Fig. 2b). Further increase of the In3+ content indeed leads to the complete transition to the ccp-M structure. Such a structural transition can be predictable. With a larger τ, the weaker electron cloud extension of the cations is less likely to destroy the originally high symmetry of the ccp anion framework upon interstitial occupation of cations. Rietveld refinement of the X-ray diffraction (XRD) pattern of the Li3Ho0.6In0.4Cl6 sample in Fig. 2c confirmed its monoclinic structure. Meanwhile, the dramatic increase in ionic conductivity coincided with the formation of the ccp-M structure (Supplementary Fig. 2). Among the Li3Ho1-xInxCl6 samples, the highest ionic conductivity of 2.5 × 10−3 S cm−1 (25 °C) was achieved by Li3Ho0.6In0.4Cl6. The value is more than ten times higher than that of the pristine hcp-T type Li3HoCl6. The similar structure and ionic conductivity evolution can be further confirmed in the Li3Ho1-xScxCl6 and Li3Er1-xInxCl6 systems (Supplementary Figs. S3–7, Supplementary Tables 8, 9).

Fig. 2: Cationic polarization factor and structural design guide for halides through the M3+ regulation.
figure 2

a Analysis of the cationic polarization factor for Li3Ho1-xInxCl6 halides (see Supplementary Table 5 for details). b XRD patterns of the targeted Li3Ho1-xInxCl6 samples and the standard references. c Rietveld refinement of XRD pattern of ccp-M typed Li3Ho0.6In0.4Cl6 (see Supplementary Tables 6, 7 for details). d Schematic illustration of the corresponding structure of ccp-M typed Li3Ho0.6In0.4Cl6 sample. ccp-M indicates the C2/m space group, hcp-T indicates the P3̅m1 space group, and hcp-O indicates the Pnma space group.

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In the case of constant Li content and unchanged M3+ selection, the structure transition from hcp-T to ccp-M can also be realized by decreasing the ionic potential of X− with the substitution of a larger anion. Two representatives are hcp-T typed Li3YCl611,16 and ccp-M typed Li3YBr617. When Li+ and Y3+ cations stack into the anion framework, the larger size of the Br− anion will dilute the electronic cloud extension effect of cations, thus ensuring the high symmetry of the Br− anion framework in the ccp arrangement. However, the Cl− anion framework with a smaller anion size cannot balance the electronic cloud extension effect of cations, thus resulting in the decreased symmetry of the Cl− anion framework to the hcp arrangement. Taking hcp-T typed Li3YCl6 as a starting point, partial or total substitution of Cl− by Br− to form ccp-M typed Li3YCl3Br3 and Li3YBr6 has been proved to be effective17,18. As displayed in Fig. 3a, b, the target sample of Li3YCl5.6Br0.4 still remains the hcp-T structure, while further Br- substitution induces structural transitions to the hcp-O and finally the ccp-M phases at compositions of Li3YCl4.8Br1.2 and Li3YCl4.5Br1.5, respectively. Rietveld refinement of the XRD pattern reveals that the hcp-O structure of the Li3YCl4.8Br1.2 can be indexed by the orthorhombic pnma space group (Fig. 3c, d). Moreover, the phase change from the hcp-T typed Li3YCl6 to ccp-M typed Li3YCl4.5Br1.5 also leads to an increased ionic conductivity up to 2.16 × 10−3 S cm−1 compared to 7.1 × 10−5 S cm−1 of Li3YCl6 (Supplementary Fig. 8). The similar structure and ionic conductivity evolution can be further confirmed in the Li3ErCl6-xBrx, Li3YCl3Br317, and Li3YbCl3Br3 halides (Supplementary Fig. S9).

Fig. 3: Cationic polarization factor and its application in designing different-structured halides through the X− regulation.
figure 3

a Analysis of the cationic polarization factor of Li3YCl6-xBrx halides (see Supplementary Table 10 for details). b XRD patterns of the targeted Li3YCl6-xBrx samples and the standard references. c Rietveld refinement of XRD pattern of hcp-O typed Li3YCl4.8Br1.2 (see Supplementary Tables 11, 12 for details). d Schematic illustration of the corresponding structure of hcp-O typed Li3YCl4.8Br1.2 sample. ccp-M indicates the C2/m space group, hcp-T indicates the P3̅m1 space group, and hcp-O indicates the Pnma space group.

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We then use the cationic polarization factor to verify its feasibility in the influence on the cation stack within the same anion framework. In addition to the decreased structural symmetry from ccp to hcp anion framework due to the reduced cation polarization, further lowering the τ will boost the severe degradation of symmetry from hcp-O type (D4h point group, 16 symmetry elements) to hcp-T type (D3d point group, 12 symmetry elements) structure caused by the different cation stack within the hcp anion sublattice (Li3MX6 composition, line 1 in Fig. 4a). In addition, our previous work has proved that the structural symmetry of hcp-T type Li3MCl6 (M = Dy, Ho, Y, Er, Tm) can be increased to hcp-O by changing the component to Li2.727M1.091Cl6 though the decreased τ11. This is reasonable due to that more vacancies are generated, which can weaken the effect of the cation stack on the basic anion framework.

Fig. 4: Cationic polarization factor and its application in solving the critical points that separate hcp-T and hcp-O structured halides.
figure 4

a Definition of the critical points based on the proposed cationic polarization factor of Li3−3xDy1+xCl6, Li3−3xHo1+xCl6, Li3-3xY1+xCl6, and Li3-3xEr1+xCl6 halides (see Supplementary Table 13 for details). b XRD patterns of the targeted Li2.82Ho1.06Cl6, Li2.83Y1.057Cl6, and Li2.91Er1.03Cl6 samples and the standard references. Cationic polarization factor and its application in designing different-structured halides through both lithium content and M3+ regulation. c Definition of the two points based on the proposed cationic polarization factor of Li3-3x(Ho1-yIny)1+xCl6 halides along the line through hcp-T typed Li3HoCl6 to ccp-M typed Li2.727In1.091Cl6 (see Supplementary Table 14 for details). d XRD patterns of the targeted Li2.93Ho0.81In0.21Cl6 and Li2.85Ho0.525In0.525Cl6 samples and the standard references. ccp-M indicates the C2/m space group, hcp-T indicates the P3̅m1 space group, and hcp-O indicates the Pnma space group.

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By drawing the lines between Li3MCl6 and Li2.727M1.091Cl6 halides, several intersections with different Li3-3xM1+xCl6 compositions can be obtained. Based on these intersections, three target compositions of Li2.82Ho1.06Cl6, Li2.83Y1.057Cl6, and Li2.91Er1.03Cl6 were selected (Fig. 4a), which are close to the phase change line. The XRD patterns of these samples (Fig. 4b) demonstrate the hcp-O structure, proving the successful prediction of structural transition. The different amount of Li+ and M3+ cations that dominate the structural transition of Li3-3xM1+xCl6 halides is attributed to the various number of vacancies that are required to tolerate and balance the effect of the stacked cations within the anion sublattice. Compared to Li3ErCl6, the hcp-T type Li3HoCl6 with strong cation electronic cloud extension (small τ) needs a large number of vacancies to weaken the cation effect to achieve higher structural symmetry (change to hcp-O type). The impedance evaluation (Supplementary Fig. 10) confirms the prediction of higher RT ionic conductivities of the hcp-O structured Li2.83Y1.06Cl6 and Li2.727Y1.091Cl6 (5.7 × 10−4 S cm−1 and 6.9 × 10−4 S cm−1, respectively) than that of the hcp-T structured Li3YCl6 (7.1 × 10−5 S cm−1). The improved ionic conductivities should be due to the facile diffusion in the z-direction in the orthorhombic structure and such an increase in ionic conductivity from hcp-T to hcp-O type was also displayed in the Li2.727M1.091Cl6 (M = Dy, Ho, Y, Er, Tm) halides11.

The structural descriptor of the cationic polarization factor was further validated in the more complex cases with simultaneous change of cation concentrations and mixing of trivalent metal cations, identifying the borderline for structural transition among the three structures (hcp-T, hcp-O, and ccp-M). Along the line between hcp-T type Li3HoCl6 and ccp-M type Li2.727In1.091Cl6 halides, two targets of Li2.93Ho0.82In0.21Cl6 (Li2.93(Ho0.8In0.2)1.023Cl6) and Li2.85Ho0.525In0.525Cl6 (Li2.85(Ho0.5In0.5)1.05Cl6) are presented (Fig. 4c). By partial substitution of Ho3+ with In3+ and by the introduction of vacancies in the Li3HoCl6 base, the two target halide compositions presented the designed hcp-O and ccp-M structures as confirmed by their XRD patterns (Fig. 4d). The RT ionic conductivities along the line from Li3HoCl6 to Li2.727In1.091Cl6 also show the gradually increasing trend from hcp-T to hcp-O and the final ccp-M structure (Supplementary Table 4).

The calculation of cationic polarization factors is highly dependent on the cation and anion radii. For LiaMXb halides involved with M4+ cations, such as Li-M-Zr-Cl19, Li-M-Hf-Cl19, it can be seen that the structure based on the cationic polarization factor calculation should be ccp-M phase (Fig. 5a, Supplementary Table 15). However, the experimental results show that these Li-M-Zr(or Hf)-Cl halides possess hcp-O structure (except Li-In-Zr-Cl structure due to the stable Li2ZrCl6 is also ccp-M structured)20, which are different from the predicted.

Fig. 5: Cation radius difference effect.
figure 5

a Cationic polarization factor of the reported several Li-M-Zr-Cl halides (see Supplementary Table 15 for details). b Modified cationic polarization factor of the reported several Li-M-Zr-Cl halides (see Supplementary Table 15 for details) considering the cation radius difference. c The cationic polarization factor of LiaMXb halides that reported and developed in this study (see Supplementary Table 4 for details). d Topography of the RT ionic conductivities of LiaMXb halides. e Comparison of the RT ionic conductivities of the halide SSEs based on the proposed τ. ccp-M indicates the C2/m space group, hcp-T indicates the P3̅m1 space group, and hcp-O indicates the Pnma space group.

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The deviations are relatively interpretable. The radius difference of the cations should also be considered. The LiaMXb halides are developed from ccp-type LiX. Due to the larger radius of halogen anions, the structure of LiX can be seen as the distribution of small Li+ ions into the X− anion sublattice. When forming LiaMXb halides, M3+ cations are further added to the system. The highly symmetrical ccp structure can be maintained if there’s a minor difference in the cation radius. Thus, in the case of the same anion, Li3InCl6, and Li3ScCl6 with the smallest cation difference can keep the ccp structure (high symmetry). While Li3YbCl6 and Li3LuCl6 with moderate differences lead to decreased symmetry to hcp-O structure (moderate symmetry) and other Li3MCl6 halides (M = Y, Tb-Tm) with the largest difference result in a further decrease of symmetry to hcp-T structure (Supplementary Table 16). This further explains why Li3-xIn1-xZrxCl6 can achieve ccp structure while Li3-xYb1-xHfxCl6, Li3-xYb1-xZrxCl6, Li3-xY1-xZrxCl6, and Li3-xEr1-xZrxCl6 halides possess the hcp-O structure (Supplementary Table 17). Herein, the cationic polarization factor τ is modified for these Li3-xM1-x3+Mx4+X6 halides with a large cation radius difference.

$${{{{{\rm{\tau }}}}}}=\frac{6-x}{6}\,\frac{\Sigma \Phi {{{{{\rm{cations}}}}}}}{\Sigma \Phi {{{{{\rm{X}}}}}}}=\frac{6-x}{6}\frac{\Phi {{{{{\rm{Li}}}}}}+\Sigma \Phi {{{{{\rm{M}}}}}}}{\Sigma {{{{{\rm{\phi }}}}}}{{{{{\rm{X}}}}}}}$$
(2)

where the x is the molar content of tetravalent cations. After modeling modification, the optimized τ values of these Li3-xM1-x3+Mx4+X6 halides are shown in Fig. 5b. We have further added several typical examples involving Zr4+ and Hf4+ as shown in Supplementary Table 18 and Supplementary Fig. 11. It can be seen that most of these halides can still locate in the hcp-O region. Thus, the whole phase map was further presented in Fig. 5c, which also includes the typical clarified samples in this work. Furthermore, the topography of the RT ionic conductivities of LiaMXb halides (Fig. 5d, e) presents that most reported halides with conductivity over 10−3 S cm−1 are located in the ccp anion sublattice region. In contrast, halides with hcp structure possess relatively low conductivity.

Overall, most of the LiaMXb halides are derived from basic LiCl. When introducing different multivalent cations into the LiCl ccp structure, it can be regarded as putting charged balls with varied radii into this system. The proposed τ here describes the ability of the material to maintain the basic ccp skeleton, which involves three key factors. The first one is the size difference among the cations (Li+ and Mx+) and the increase of size difference will destroy the high symmetry from ccp to hcp-O and finally to the hcp-T structure with the lowest symmetry. The second one is the anion framework. Normally, a larger-sized anion framework can reduce the cation effect, such as the ccp-structured Li3YBr6 compared with hcp-structured Li3YCl621. The third one is introducing more vacancy to weaken the cation effect, such as the hcp-O structured Li3-3xM1+xCl6 compared with hcp-T structured Li3MCl611.

Note that some other halide-based SSEs with different structures, such as nine-coordinated LaCl3-based SSEs are reported lately3. The formation of this structure is the result that f electrons also participate in the bonding of more Cl−. Thus, a more covalent composition of the chemical bonds is involved, which is not the scope of the radius ratio and proposed τ here that mainly focuses on ionic bonds. Other glassy halides2 that recently reported are also not discussed here due to their glassy structure.

Discussion

In summary, we mapped the structural landscape of the existing and potential superionic Li+ conducting halide SSEs by proposing a proposed cationic polarization factor, τ. The main difference among the hcp-T, hcp-O, and ccp-M structures of halide SSEs is the polarization among the cationic and anionic sublattices. The τ can not only successfully classify the experimentally observed halide structures but also predict the structure of the unreported halide SSE compositions. Guided by the τ, more than 10 lithium halide SSEs with RT ionic conductivities over 10−3 S cm−1 have been identified and synthesized. Moreover, the τ can be used to predict the phase transition compositions of lithium halide SSEs with different cation concentrations and different mixtures of multivalent cations. Well-designed phase transition can effectively tune the Li+-conducting behavior of halide SSEs. In most cases, highly improved ionic conductivity can be achieved by tuning the base structure from hcp to ccp. The deficiency of the τ for some halide electrolytes with tetravalent cations arises mainly from the large cation radius difference, which leads to the decrease of symmetry and thus influences the structure. Due to the simplicity and accuracy of the proposed τ, we expect its use to accelerate the exploration and design of lithium halide superionic conductors.

From the viewpoint of crystal structures, the halide SSEs discussed in our work are mainly based on octahedral coordination similar to the studies of various tolerance factors proposed for perovskite materials. Moreover, the cationic polarization factor proposed here is based on the ion stacking in ionic crystals. For other classes of ion conductors (such as sulfides, and polyanionic oxides), most of these materials contain structural frameworks that involve covalent bonds, such as PS43−, PO43−, and SiO44−. The crystal structures of these ion conductors possess various coordination conditions (four-coordination for PS43−, eight-coordinated LaO813−, etc.), which are totally different from that of halide SSE discussed here. Thus, the cationic polarization factor is not suitable for these materials. Precisely because of the structural and chemical distinctions, the Li+ migration through these frameworks will lead to the different phenomena and diffusion mechanisms in halide SSEs. For ion conductors with specific crystal structures, it’s still possible to investigate the formability by similar rules. We also hope that this work will be helpful to the modification of the tolerance factor for perovskite materials by further considering ionic charges rather than just the ionic radii effect.

Methods

Sample synthesis

The resulting materials were prepared by a co-melt and recrystallization method. The starting materials include lithium chloride (LiCl, Alfa Aesar, 99.9%), lithium bromide (LiBr, Alfa Aesar, 99.9%), trivalent rare earth bromides (MBr3, Alfa Aesar, >99.9%), and metal chlorides (MCl3, MCl4, Alfa Aesar, > 99.9%). Raw materials with stoichiometric ratio were directly put and sealed in a quartz tube at ~10 Pa under vacuum. The quartz tube was heated for 4 h to reach 550–650 °C and kept at 650 °C for 12 h. Then the quartz tube was cooled down to 25 °C within 10–48 h.

Characterizations

Powder X-ray diffraction (XRD) patterns were characterized on a Bruker AXS D8 Advance (Cu Kα radiation, λ = 1.54178 Å). The samples were loaded into a homemade air-tight holder to avoid air exposure.

Conductivity measurements

All the alternating current (AC) impedance was measured using Bio-Logic VMP3 electrochemical working station with an amplitude of 10 mV at frequencies from 7 MHz to 1 Hz. The pressing and cell assembling operations were conducted in the Ar-filled glove box (O2 < 1 ppm, H2O < 1 ppm). The synthesized solid electrolyte powder was pressed into pellets (10 mm diameter, thickness around 10 mm) at ~380 MPa and attached with stainless steel rod electrodes. An external pressure of ~200 Mpa was added during the impedance tests.