journal of materials chemistry a - scholars at harvard · 2019-09-14 · dr xin li joined the...

Journal ofMaterials Chemistry A

REVIEW

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The effects of m

WDBaDcUofc

John A. Paulson School of Engineering an

Cambridge, Massachusetts 02138, USA. E-m

496 3075

Cite this: DOI: 10.1039/c9ta05248h

Received 18th May 2019Accepted 21st August 2019

DOI: 10.1039/c9ta05248h

rsc.li/materials-a

This journal is © The Royal Society of

echanical constriction on theoperation of sulfide based solid-state batteries

William Fitzhugh, Luhan Ye and Xin Li *

Recent years have seen an explosion in the amount of literature focused on sulfide solid electrolytes for use

in solid-state batteries. Successful battery performances based on sulfide solid electrolytes have been

reported, while the electrochemical bulk stability of sulfide electrolyte materials and their interfacial

stabilities with different high voltage cathode materials remain the current focus of research. Recent

studies have suggested that mechanical constriction can introduce energy barriers opposing bulk and

interfacial decompositions in sulfide solid-state batteries. These energy barriers have been shown to

have the effect of expanding the operating window for sulfide based solid-state batteries. Moreover, the

consideration of such mechanical constriction as a design principle introduces a largely neglected

degree-of-freedom for next-generation energy storage systems. That is, to design mechanically

constrained electrolytes for the purpose of expanding the operational voltage window of solid-state

batteries. This review will focus on both the studies leading to and detailing these new understandings as

well as exploring, retroactively, the impact of these understandings on this field's previously made

conclusions. In particular, the differences in the determined operating window between multiple

experimental methods will be evaluated against the mechanical nature of the methods themselves.

1. Introduction

Solid-state batteries offer paradigm shiing potential overconventional liquid-electrolyte based batteries.1–7 By imple-menting solid electrolytes, solid-state batteries can enable theadoption of higher-energy density electrode materials8–11 whilesimultaneously providing improved temperature robust-ness.12–14 Moreover, solid-state batteries eliminate the most

illiam Fitzhugh was born inallas, Texas and received his.S. from the Physics departmentt the University of Coloradoenver. Currently, he isompleting his PhD at Harvardniversity under the supervisionf Professor Xin Li. His researchocus is on the phase stability oferamic sulde solid electrolytes.

d Applied Sciences, Harvard University,

ail: [email protected]; Tel: +1 617

Chemistry 2019

dangerous component in current batteries, the ammableliquid-electrolyte. On the negative electrode side, solid electro-lytes can potentially enable the adoption of lithium metal byproviding a physical barrier that prevents lithium dendriteformation.15,16 Such lithium metal anodes represent the theo-retical optimum for negative electrodes with a capacity of 3860mA h g�1 and a voltage of 0 V. This, in contrast to graphite's 372mA h g�1 and 0.2 V,17,18 would represent a signicantimprovement in the anode material. With regards to the posi-tive electrode, solid electrolytes have demonstrated compati-bility with a multitude of high-energy density cathodesincluding both 1000 mA h g�1 high-capacity11 and 5 V high-

Luhan Ye received his B.S. fromthe University of ElectronicScience and Technology ofChina (UESTC), where his workfocused on the deposition of thinlms for lithium ion batteries.Currently, he is a PhD student atHarvard in Professor Xin Li'sgroup. His research interestsmainly focus on materialssynthesis and characterizationfor high-energy-density all-solid-state lithium ion batteries.

J. Mater. Chem. A

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Journal of Materials Chemistry A Review

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voltage9 materials. Solid electrolytes also maintain superiorperformance at low temperatures, where viscosity increases canplague liquid electrolytes, a key performance metric for manyapplications including electric vehicles for low-temperaturemarkets.

In evaluating the potential of solid electrolytes, two of themost important criteria are the lithium ion conductivity and theelectrochemical stability window. The stability window consti-tutes the range of voltages versus lithium metal in which thesolid electrolyte will not electrochemically decompose.Considering the two most studied families of solid electrolytes,oxides and suldes, there remains an inherent tradeoff betweenthese metrics. Oxides have a wider stability window thansuldes, but suffer from much lower ionic conductivities thanthose of the current organic liquids (10�4 to 10�3 vs. 10�2 Scm�1).19–23 On the other hand, sulde solid electrolytes havereached ionic conductivities up to 25 mS cm�1, exceeding mostliquids, but suffer from poor electrochemical stability.24–27 Withintrinsic stability windows of approximately 1.7–2.1 V versuslithium metal, sulde solid electrolytes are, theoretically,incompatible with most electrode materials.28,29 In addition, thecompatibility of the electrolytes with mass production proce-dures including brittleness and air stability30 of the electrolytesas well as the applicability of the low-cost cold pressing proce-dure also remain critical factors for solid-state batterydevelopment.

Historically, sulde solid electrolytes have progressed fromglassy to glassy-ceramic to ceramic, with each progressionresulting in a corresponding increase in ionic conductivity.Glassy suldes, which maintain the advantage of not havinggrain boundary resistances, were among the rst solid electro-lytes to be discovered. The ionic conductivities of these mate-rials typically range from 0.01–1 mS cm�1.31,32 The Li2S–P2S5–LiIglassy system, for example, achieved an impressive conductivityof 1.7 mS cm�1.54 The partial crystallization of glassy suldes toform glassy ceramics, or ceramic suldes embedded in a glassyframework, can signicantly boost the ionic conductivity. Insome cases, this partial crystallization can increase ionic

Dr Xin Li joined the School ofEngineering and Applied Sciencesat Harvard University in 2015,and is now an associate professorof materials science. Xin Li'sresearch group designs newenergy related materials throughadvanced characterizations andsimulations, with the currentfocus on solid state batteries andsodium ion batteries. Xin Lireceived his B.S. in Physics fromNanjing University in China in

2003, PhD in Materials Science and Engineering from PennsylvaniaState University in 2010, and performed postdoctoral research atCalTech (2010–2011) and MIT (2011–2015) before joiningHarvard.

J. Mater. Chem. A

conductivity by as much as two orders of magnitude. Glassyceramics frequently exhibit conductivities on the order of 1 mScm�1.34–36 Li10GeP2S12 (LGPS) was amongst the rst solid elec-trolytes to meet or exceed conventional liquid electrolytes witha conductivity of 12 mS cm�1 in 2011.37 Five years later, it wassurpassed by Li10SiP2S12 (LSPS) which reached an astonishinglyhigh conductivity of 25 mS cm�1.14

Despite a huge amount of interest in ceramic-sulde solidelectrolytes due to their exceptional conductivities, there havebeen contradictory reports with regards to their electrochemicalstability. Solid-state batteries based on ceramic suldes havebeen demonstrated with good cyclability up to around 4 V aswell as at large current rates (18C or approximately 3 minutesfor full charge/discharge).14 These results imply that ceramicsuldes are either stable up to around 4 V or, at the very least,kinetically stable. Some other experimental results have sug-gested that ceramic suldes are not, in-fact, stable in thisvoltage range. Oxidation of ceramic suldes above 2.5 V hasbeen reported by cyclic-voltammetry measurements.24 Ab initiocomputation agrees with later experiments, predicting thatLSPS and LGPS are only stable at room temperature in a narrowvoltage range of approximately 1.7–2.1 V.25,26 Moreover,computation predicts that at 4 V, the reaction energy of LSPS/LGPS oxidation is on the order of �1 eV per atom (approxi-mately �1500 kJ mol�1). To further complicate these contra-dictory reports, ceramic suldes have also demonstrateda propensity to react with common electrode materials.28,29

Despite being cycled to 4 V with LiCoO2 (LCO) for over 1000cycles, computational studies have suggested that ceramicsuldes will react with LCO with a reaction energy on the orderof �300 meV per atom, indicating the importance of thecathode coatingmaterial of LiNbO3 used for interfacial stability.

Recent studies have suggested a unifying theory to helpunderstand these disparate experimental and computationalresults.38 Ceramic suldes can undergo substantial volumeexpansion upon oxidation. This suggests that the decomposi-tion can be signicantly perturbed by the introduction ofmechanical constriction that resists such expansion. In experi-ments, mechanically constricted core–shell morphologies havemoved the onset of oxidation from circa 2.5 V to in excess of 5V.38,39 Theoretical considerations have shown that the pressureinducedmetastability can reach 4 V and the introduction of newkinetic limitations can further expand the functional voltagewindow. Additionally, such mechanical constraints also playa major role in the interfacial stability of ceramic suldes withcommon active materials. These new scientic understandingshave opened the door to design principles that can enable thedevelopment of practical solid-state batteries based on ceramicsuldes.

These mechanically induced stability mechanisms couldalso, in principle, be implemented with oxide solid electrolytesto obtain even larger stability windows. As will be discussed inSection 3, the mechanical stabilization mechanism is directlydependent on the electrolyte's bulk modulus. Suldes typicallyhave bulk moduli on the order of 25–30 GPa, whereas those ofoxides are on the order of 110–120 GPa.40 Thus it is possible thatthe mechanically induced stability is even more pronounced in

This journal is © The Royal Society of Chemistry 2019


Review Journal of Materials Chemistry A

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oxides than in suldes. However, such a mechanical constraintrequires the formation of a dense pellet, which could be chal-lenging for oxides with such stiffmoduli by low-cost procedureslike cold pressing, and instead requires high temperature sin-tering or thin lm techniques.

In this review, we focus on updating the audience on recentdevelopments that suggest that mechanical constriction can beused to improve the operating performance of sulde basedsolid-state batteries. Moreover, we highlight evidences thatmechanical constriction may have played a role in many priorstudies that, while not considering the constriction explicitly,adopted experimental methods in which it actually plays animportant role. The possibility that the non-standardizedconstriction between literature studies may be responsible forthe variability in reported stabilities is discussed.

In Section 2, we provide a brief overview of the historicalprogression of the sulde electrolyte eld along the pathway ofglassy, glass-ceramic, ceramic, and constrained ceramicsuldes. This progression is discussed in terms of the moti-vating factors of improved conductivity and the inherent coststo electrochemical stability. Comparing the results of priorsulde studies, we highlight that there have historically beenwidely varying reports of electrochemical stability amongstsimilar materials. Moreover, the magnitude of the variabilitysuggests the existence of an uncontrolled experimental degree-of-freedom. Section 3 provides an overview of recently devel-oped theoretical frameworks for understanding this constrain-ing degree-of-freedom. This understanding suggests that thevariability in historical reports may be due to using non-stan-dardized microstructures of electrolytes and methods forbattery testing with regard to the mechanical constraint of theelectrolytes. Section 4 details computational methods andresults that are relevant to mechanically constrained solid-statebatteries, including both bulk and interfacial calculations.Finally, concluding remarks constitute Section 5.

Fig. 1 (a) Conductivity versus composition for glassy sulfide solid-electrfrom Elsevier. (b) Temperature dependence (1000K/T) of conductivitiespermission from Elsevier.


2. Experimental history2.1 Background

Since inception, the sulde eld has been principally focusedon developing solid electrolytes with a comparable ionicconductivity to that of their commercial liquid counterparts.Recently, with materials such as LGPS/LSPS achieving theseconductivity goals, the amount of attention given to electro-chemical stability has increased dramatically. Below is a briefoverview detailing how experimental conditions relevant tomechanical constriction (e.g. pressurized cells and glassembedding matrices) originated from the pursuit of highconductivity and ultimately became common place within theeld. In accordance with these historical norms, mechanicallyrelevant developments are introduced here in terms of theeld's pursuit of conductivity. However, a detailed analysis onthe impact on ionic conductivity is outside the scope of thiswork. Such a detailed overview can be found in ref. 1, 3–7, 41and 42.

2.1.1 Glass suldes. Glass suldes rst reached promi-nence in the 1980's as one of the earliest high performance solidelectrolytes.3,41,43 The basic structure of glass sulde systemsconsists of Li2S plus glass formers such as GeS2,44 SiS2,31,45 orP2S5.46,47 While the conductivity of glass suldes is typically oneto three orders of magnitude less than that of the industrialstandards set by liquid electrolytes, they are amongst thehighest conductivity glasses. Fig. 1a depicts the relative scale ofconductivity for sulde glasses versus the next most promisingfamily, oxide glasses.47 Compared to crystalline solid electro-lytes at that time, these glassy phases enjoy the benets ofisotropic conduction, decreased grain boundary resistances,48

and high conductivity with a variety of compositions. An addi-tional advantage of glass suldes over other solid electrolytes isthe compatibility with multiple synthesis techniques, poten-tially easing the barriers to commercial adoption. Some of themost prevalent synthesis methods for glassy sulde electrolytes

olytes at room temperature. Reproduced from ref. 47 with permissionfor (100 � z)(0.6Li2S$0.4SiS2)$zLi4SiO4. Reproduced from ref. 51 with

J. Mater. Chem. A


Fig. 3 (a) Temperature dependency of the conductivity of 70Li2-S$30P2S5 samples prepared by mechanical milling or a solid-statereaction. LIPON, a typical oxide solid electrolyte, is also shown. (b) XRDpatterns of (a) the 70Li2S$30P2S5 glass, (b) the glass ceramic, and (c) thesample obtained by the solid-state reaction. Both images reproducedfrom ref. 34 with permission from John Wiley and Sons.


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have been quenching, twin-roller quenching, and mechano-chemical milling.31,44,49,50

Glass suldes experience characteristic ionic conductivitieson the order of 10�3 to 100 mS cm�1 and stability windows thatcan exceed 4 V. Successful pursuits to reach the higher range ofconductivities have included the doping of a small amount ofoxide51–53 or halide salts49,54 as well as the adoption of pressur-ization to improve contact and reduce the presence of voids.55

Fig. 1b, for example, shows the impact of oxide doping in thesystem (100 � z)(0.6Li2S$0.4SiS2)$zLi4SiO4. A small (5 mol%)doping is seen to approximately double the ionic conductivity ofthe glass. Pressing 80LiS2 + 20P2S5 glass pellets at pressures upto 360 MPa was shown to decrease the presence of voids andincrease the conductivity by nearly an order of magnitude.55 Theadoption of battery cells which remain pressurized duringelectrochemical cycling (illustrated in Fig. 2) has becomea common place.3,46,56 In a study on silicon anodes by Piperet al.,57 this pressurization of the cell has been considered as anindependent variable, and the impact on battery operationbeyond just conductivity has been reported. In many otherstudies, particularly those focused on increasing the conduc-tivity, however, pressurized cells have simply been listed as anexperimental detail rather than a systematic point of study.

2.1.2 Glass-ceramic suldes. An alternative approach toimprove the conductivity of glass suldes has been partialcrystallization to form the so-called glass-ceramic suldes.34,58–61

These phases consist of crystalline materials embedded ina matrix of glass suldes. Generally, partial crystallization isconsidered to reduce the bulk conductivity, as most crystallinephases are poor ionic conductors. However, in specic cases,the crystallized phase can be highly conductive, leading to bulkconductivities that surpass the values of the parent glass. Forexample, this phenomenon is depicted in Fig. 3a and b for thecomposition 70Li2S + 30P2S5 (mol%).34 In this case, the baseglass was synthesized via mechanochemical milling of crystal-lized Li2S and P2S5. The glass had a room temperature ionicconductivity of 5.4 � 10�2 mS cm�1. Crystallization was

Fig. 2 Typical solid-state battery cell design for applying and main-taining pressure. Reproduced from ref. 57 with permission from theElectrochemical Society.

J. Mater. Chem. A

performed by heating to 240 �C for 2 hours, resulting in a glassceramic with a drastically improved room temperature ionicconductivity of 3.2 mS cm�1. In contrast, the same precursorswere used for solid-state synthesis and resulted in an ionicconductivity of 2.6 � 10�5 mS cm�1. As shown in the XRDpattern of Fig. 3b, the crystallization step and solid-statesynthesis resulted in completely different crystal phases. Thesolid-state reaction produced the low conductivity phasesLi4P2S6 and Li3PS4. Recrystallization, however, resulted in anunknown crystalline phase with high conductivity (later deter-mined62 to be Li7P3S11).63

Later work showed that this high conductivity Li7P3S11 (LPS)phase could also be crystallized directly from the melt viaquenching, suggesting that it is the thermodynamically favoredphase at high temperatures.64 This is in contrast to the lowtemperature favored low conductivity phases Li4P2S6 andLi3PS4. Thus, it was concluded that while LPS is not a thermo-dynamically stable phase at room temperature, it can becomemetastable at room temperature when embedded in certainglassy matrices. However, the mechanism by which this meta-stability arises has been little studied.

2.1.3 Thio-LISICON. Amongst the rst crystalline lithiumsolid electrolytes families to be discovered was the oxide lithiumsuperionic conductor (LISICON) family.65 The LISICON family isbased on the framework Li16�2xDx (TO4)4 where D and Trepresent divalent and tetravalent cations, respectively. TheLISICON member Li14Zn(GeO4)4 was recorded as achievinga remarkable 100 mS cm�1 conductivity at elevated tempera-tures.65 The sulde equivalent, thio-LISICON family, was intro-duced based on a similarly structured Li4GeS4 framework.66,67

The introduction of lithium vacancies via phosphorus substi-tutions (VLi

1� � PGe1+) resulted in crystalline phases with

conductivities as high as 2.2 mS cm�1 at room temperature.66

Varying the vacancy concentration from x ¼ 0 to 1 in Li4�x-Ge1�xPxS4 resulted in a seemingly continuous shi in the XRDsignature as shown in Fig. 4a from that of Li4GeS4 to Li3PS4.Analysis of the lattice parameters (Fig. 4b), however, indicatedthat the cation ordering could be separated into three distinctranges. Thio-LISICON I are those for which x < 0.6, whereas



Fig. 4 (a) XRD patterns of Li4�xGe1�xPxS4. (b) Compositional dependence of the lattice parameters (a, b, and c) and angle b of Li4�xGe1�xPxS4determined by XRD analysis. (c) Compositional dependence of ionic conductivity. (d) CV of a Li/Li3.25Ge0.25P0.75S4/Au cell. All images reproducedfrom ref. 66 with permission from the Electrochemical Society.


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thio-LISICON II and III have 0.6 < x < 0.8 and x > 0.8,respectively.

The ionic conductivities of Li4�xGe1�xPxS4 are seen toincrease monotonically with x in regions I and II (Fig. 4c) beforesharply decreasing in region III. The maximum conductivityreached was 2.2 mS cm�1, which occurred in region II at x ¼0.75. The other region II compositions (x ¼ 0.65, 0.7) were theonly others to exceed the 1 mS cm�1 threshold. Cyclic voltam-metry (CV) was performed using a Li/Li3.25Ge0.25P0.75S4/Au cellto evaluate the electrochemical stability window. With theexception of lithium deposition and dissolution (Li+ + e� 4

Li(m)), negligible current was seen in the window of �0.5 to 5 V(Fig. 4d).

2.1.4 LGPS/LSPS. Li10GeP2S12 (LGPS) was rst demon-strated by Kamaya et al.37 to have a remarkably high roomtemperature conductivity of 12 mS cm�1, making it the rstroom temperature solid electrolyte to reach typical liquid elec-trolyte conductivities. Five years later, its silicon analog, Li10-SiP2S12 (LSPS), provided an even greater conductivity of 25 mScm�1.14 LGPS and LSPS are tetragonal crystals with highlyconductive channels running alongside the c-axis. Additionalchannels in the ab-plane allow three-dimensional conduction.The structure of LGPS consists of a framework of PS4 and LiS4tetrahedra, LiS6 octahedra and disordered68 (Ge0.5P0.5)S4


tetrahedra. As depicted in Fig. 5, the c-axis of LGPS consists ofone-dimensional chains of edge-sharing (Ge0.5P0.5)S4 tetrahedraand LiS6 octahedra. Those chains are in turn connected by PS4tetrahedrons. LGPS differs from thio-LISICONs in structure bythe ordering of (Ge/P)S4 tetrahedra.69

Understanding the mechanism by which LGPS and LSPSderive this remarkable conductivity has been the subject ofintense computational and experimental work. He et al.70

showed that LGPS experiences low lithium migration barrierswhen multiple lithium ions move in concert, rather than insingle ion steps. Additionally, both experiment and compu-tation have shown that the lithium ion conduction is largely,but not exclusively, along the c-axis channels.25,71 Theimportance of the ab-plane diffusion pathway is believed tobe that it enables transitions from one one-dimensionalchannel to another. In the event of a defect or a blockedchannel, these pathways would allow alternative diffusionroutes to circumvent the blockage.25,69,71 The presence of suchc-axis channel blocking events is extremely likely in thethermodynamic limit, hence the need for a three-dimen-sional mechanism is paramount. Recent work has conrmedthis anisotropic mechanism in single crystal LGPS.72 In short,LGPS and LSPS combine the high conductivity of one-

J. Mater. Chem. A


Fig. 5 The structure of LGPS. (a) The ion conduction framework. (b) One-dimensional chains formed by LiS6 octahedra and (Ge0.5P0.5)S4tetrahedra, which are connected by a common edge. (c) Conduction pathways of lithium ions. Zigzag conduction pathways along the c axis areindicated. Lithium ions in the LiS4 tetrahedron (16h and 8f sites) participate in ionic conduction. Reproduced from ref. 37 with permission fromSpringer Nature.


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dimensional diffusion pathways with the robustness of three-dimensional pathways.

2.2 Inconsistent stability reports

The initial reports on the stability of LGPS by Kamaya et al. weresurprisingly good.37 Not only could LGPS be synthesized (implyingchemical stability), but it also survived cycling in a battery cell withan indiummetal anode and LiNbO3-coated LiCoO2 (LCO) cathode.Such cycling clearly demonstrated that LGPS was sufficientlyelectrochemically stable for battery operation. Similarly, LSPS wasused to construct solid-state full cells with lithium titanate (LTO)anodes and LCO cathodes with good cyclability, indicating elec-trochemical stability.14 Additionally, these full cells could sustaincharge–discharge currents of 18C (charge/discharge in circa 3minutes). In this regard, LGPS/LSPS seemed to have joined thegrowing number of sulde solid electrolytes with operationalelectrochemical stability windows that reach above 4 V versuslithiummetal.66,73–75 However, other reports indicated that this wasnot the case and that battery cycling with LGPS/LSPS would quicklydecay.24,56 First principles calculations have supported the laterviewpoint, suggesting that the stability window for LGPS/LSPS islimited to roughly 1.7–2.1 V versus lithium metal.24–26,29

Fig. 6 illustrates these complicated reports of electro-chemical stability for LGPS and LSPS. Fig. 6a shows the initiallyreported cyclic voltammetry (CV) for LGPS by Kamaya et al. No

J. Mater. Chem. A

decomposition peaks were reported from below 0 V to 5 V,except for the lithium dissolution/deposition peaks. The batterywas constructed as Li/LGPS/Au in the CV test, where no carbonwas mixed with LGPS. Conversely, Han et al.24 drew a differingconclusion that LGPS reduces in the range 0–2.0 V (Fig. 6b) andoxidizes in the range 1–3.5 V (Fig. 6c) when combining carbonin the LGPS cathode. Adjusting for the weight of LGPS in thecathode (7.5 mg LGPS + 2.5 mg graphite), the oxidation currentis on the order of 0.001 A g�1. While this decomposition currentwas quite small, the CV supported the computationally deter-mined voltage range of 1.71–2.14 V. Fig. 6d–f from Wu & Fitz-hugh et al.38 show how core–shell LSPS can change thedecomposition current by orders of magnitude depending onthe nature of the surrounding shell of the core–shell particle.These measurements were made with carbon added and in theabsence of external pressure. The measured current ratesranged from a small 0.01 A g�1 at the 3.1 V onset of decompo-sition and around 0.1 A g�1 up to 5 V to a large 100 A g�1

catastrophic decomposition beyond 3.5 V depending on theshell. This order of magnitude change was attributed to thediffering mechanical stabilization provided by each shell as willbe discussed in depth in Section 3. The decomposition currentsof 0.01–0.1 A g�1 observed between 3 and 4 V for strong core–shell particles had no obvious detrimental effect on the solid-state battery performance, and the voltage window was reportedto be 0.7–3.1 V, with a quasi-stable performance up to 5 V.38



Fig. 6 Various CV results for ceramic sulfides. (a) A 0–5 V CV sweep of LGPS shows no noticeable decomposition at any voltage. Reproducedfrom ref. 37 with permission from Springer Nature. (b) Reduction experienced by LGPS in the 0–2.0 V range. Reproduced from ref. 24 withpermission from John Wiley and Sons. (c) Oxidation experienced by LGPS in the 1–3.5 V range. Reproduced from ref. 24 with permission fromJohn Wiley and Sons. (d–f) Orders of magnitude change in decomposition current experienced by core–shell LSPS as a function of synthesistemperature. Temperature ranges from 400 to 500 �C. Images reproduced from ref. 38 with permission from Springer Nature.


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LSPS with a voltage window of up to 4.1 V paired with LCO wasalso reported in an earlier solid state battery test,14 but withoutany discussion of the microstructural morphology or mechan-ical constriction effects.

These reports are compared in Table 1 to survey the dispa-rate ndings for LGPS and LSPS. Voltage windows listed inTable 1 are distinguished by computation (C), cyclic voltam-metry (CV), and battery cycling (B). For computational windows,the values given are the points where the hull energy exceeds thethermal energy (see Section 4). CV windows are where signi-cant redox currents begin whereas battery windows are thevoltage ranges in which the batteries were cycled. For reference,CV results for a characteristically stable glassy sulde (0.7Li2S +0.3P2S5) up to 5 V, an exceptionally stable glassy sulde(95(0.6Li2S + 0.4SiS2) + 5Li4SiO2) up to 10 V, and a characteristicglassy-ceramic sulde up to 4.3 V are also included. Computa-tional predictions of the electrochemical stability of glassysuldes are generally absent given the complexity in the atomicstructures.

Doping of LGPS, both isovalent (e.g. LSPS) and aliovalent, forimproved conductivity and/or stability has been the focus of majorresearch attention. The simplest doping scheme is the deviation ofLGPS away from Li10GeP2S12. For example, Du et al.68 computationally


investigated the stability of LixGeP2S12 and concluded that it will lith-iate [delithiate] at voltage below [above] approximately 1 V [3 V]. Thisnonzero capacity suggests that lithiation/delithiation might improvethe electrochemical window. However, the energy gain of this effect isonly on the order of 100 meV per atom, which would not be able toaccount for all of the voltage window widening reported previously.XRD of LGPS with composition Li10+dGe1+dP2�dS12 showed smoothshiing of the XRD peaks as d increased from 0 to 0.35.76 This impliesthat the material is, in fact, a solid solution with respect to (Ge/P)S4tetrahedra, as a stoichiometrically xed phase would require theadoption of impurity phase(s) as the precursor ratio shis.

Ong et al.26 performed a systematic rst-principles study onLi10�1MP2X12 where M ¼ Ge, Si, Sn, Al, P and X ¼ O, S, Se. Thechemical and electrochemical stabilities were studied usingconvex hull analysis77 and the conductivity was evaluated usingab initio molecular dynamics. This work concluded that sulfurcould not feasibly be replaced with oxygen or selenium. Oxygensubstituted structures were found to have large chemicalinstabilities (>90 meV per atom) and poor lithium ion conduc-tivity (circa 0.03 mS cm�1). Selenium substitution was predictedto increase conductivity (24 mS cm�1) but came at the cost ofnarrow electrochemical stability.

J. Mater. Chem. A


Table 1 Electrochemical windows of sulfide electrolyte systems asreported by experiment (cyclic voltammetry (CV) or battery (B)) orcomputational prediction (C). Reported battery windows are notexclusive (i.e. 2.5–4 V for a battery window does not mean thata voltage outside that range is unstable). Computational and CV resultsare exclusive as they represent the onset of electrochemical reductionor oxidation

Electrolytetype

Operatingwindowtype

Reported voltagewindow

Computationorexperiment Ref.

LGPS Wide 0–5 V (CV) Experiment 37Narrow 1.71–2.14 V (CV + C) Both 24Both Without constraint: 1.7–

2.1 V (C), with constraint:1.25–4.0 V (B + C)

Both 39

LSPS Wide 2.5–4.1 V (B) Experiment 14Narrow None Computation 26Both Without constraint: 1.7–

2.1 V (C), with constraint:0.7–3.1 V (B + C)

Both 38

Glassy0.7Li2S +0.3P2S5

Wide 0–5 V (CV) Experiment 78

Glassy95(0.6Li2S +0.4SiS2) +5Li4SiO2

Wide 0–10 V (CV) Experiment 79

Glassy-ceramic0.8Li2S +0.2P2S5

Wide 2.6–4.3 V (B) Experiment 47


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In short, there exists substantial variance in the reportedfeasible operating window for ceramic-sulde based solid-statebatteries. The possible operating windows range from as narrowas 1.7–2.1 V to as wide as 0–5 V and possibly even wider. Theseresults suggest that there exists an independent variable ofbattery design that can control this operating range, offering thewide stability needed for pragmatic battery development. Basedon computational studies26,68 regarding doping, it seemsunlikely that compositional differences between the afore-mentioned studies could potentially account for this variabilityin results. Moreover, the results of recent computational andexperimental studies suggest that unreported mechanicaldifferences in the experimental design may be able to accountfor these disparate ndings.

2.3 Mechanical constriction

2.3.1 Internal stresses. A unique, and oen neglected,aspect of solid-state batteries as compared to liquid counter-parts is the mechanical coupling of various components. Inconventional battery cells, the liquid electrolyte is free to owand, hence, shields particles from the strain of other particles inthe adjacent neighborhood. With the exception of lithiummetalcells,80,81 the effects of external stress are largely negligible inliquid batteries. In solid-state batteries, however, this is not thecase. Zhang et al.82 showed, using in situ pressure measure-ments, that solid-state batteries undergo “breathing” as

J. Mater. Chem. A

depicted in Fig. 7. On the le in Fig. 7 are the in situ results foran indium metal anode paired with LCO. As the indium metalalloys with lithium during cycling, very large periodic strains aremeasured. These strains rise and fall as the battery cell cycleslithium to and from the anode. The pressure accompanying thiscell breathing can be seen to uctuate by up to 1.25 MPa in eachcycle. This high strain anode is seen to have a poor cyclability. Incontrast, a low strain LTO anode is used for reference anddepicted on the right of Fig. 7. The adoption of LTO in place ofindium reduced the pressure uctuations during breathingfrom 1.25 MPa to approximately 0.08 MPa. This pressure uc-tuation decrease is seen to accompany an increase in the cell'scyclability.

Whitely et al.83 investigated the effects of applying pressureon a solid-state battery using a tin cathode and an indium–

lithium alloy anode. The electrolyte used was a glassy suldewith composition 77.5Li2S–22.5P2S5. Batteries were cycled atthree distinct pressures (0.05 MPa, 10 MPa, and 20 MPa). It wasreported that 0.05 MPa was the lowest pressure that could beused and ensure that the current collectors maintained a goodcontact. Both the cyclability and the discharge capacity of thebatteries were shown to improve as the applied pressure wasincreased. Similarly, Piper et al. showed57 that the introductionof pressurized cells can modify the working potential of elec-trode materials. In this case, a glassy-sulde based half-cell wasconstructed using a silicon anode material as the cathode andlithium metal as the anode. It was found that the introductionof an applied pressure (up to 230 MPa) would increase thechemical potential of the lithiated silicon. This is a directrealization of an isothermal Gibbs–Duhem relationship (Nidmi¼ Vdp).

Historically, pressurized battery cell congurations havebeen prolic in the solid-state battery eld and particularly so insulde systems. Unlike liquid cells, where electrolyte soaking ofthe active materials leads to conductive interfaces, solid-statedesigns must account for voids, grain boundaries, and intimatesolid–solid contact. Pressurized cells have been implemented tosolve many, or all, of these issues. For example, hot pressing80LiS2 + 20P2S5 glass pellets at pressures up to 360 MPa wasshown to decrease the presence of voids and increase theconductivity.55 Typically, sulde based solid-state batteries arefabricated via the pressing of powdered electrolytes into pellets,rather than by thin-lm techniques. Fig. 2 demonstratesa typical pressurized solid-state battery cell. Such systems typi-cally consist of a modied die/punch apparatus. An insulatingdie is used to inhibit internal short circuit andmetallic punchesare used as current collectors. The battery is assembled in thedie and then placed under an external pressure assembly.

As the eld has progressed from glassy to glass-ceramic toceramic sulde electrolytes, the use of pressurized cell designshas remained constant.84 In 2012, for example, one year aerdiscovery, the high rate discharge performance of LGPS wascompared with that of glass electrolytes in a similar assembly tothat in Fig. 2.85 The high conductivity of LGPS resulted ina much improved high rate capability. Koerver et al.86 per-formed a detailed analysis of the impact of pressurized cells onthe open-circuit voltage of solid state batteries (b-Li3PS4



Fig. 7 In situ pressure measurements for solid state batteries. (a and b) Cycling and pressure data for a high strain anode (In metal anode). (c andd) Cycling and pressure data for a low strain anode (LTO). Reproduced from ref. 82 with permission from the Royal Society of Chemistry.


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electrolyte), assuming that the pressure was homogenousthroughout the cell. The state-of-charge dependent reactionvolume was determined electrochemically via a linear regres-sion between the applied pressure to the cell and the shi in thecell's open circuit voltage (OCV). This contrasted with reactionvolumes determined by XRD. Ultimately, it was reported thatthe OCV shi is on the order of 1 mV MPa�1.

In short, internal stresses are a key factor in the design ofsolid-state batteries and are paramount to the progression ofthe eld. Unlike the tradition liquid cell counterparts, particlesin solid-state cells do not have the luxury of [largely] decoupledstrain. That is, strain in one particle is not shielded from strainin the neighborhood by conversion to hydrostatic pressure.Moreover, the increased presence of strain also leads to changesin the electrochemical behavior of the materials. The chemicalpotentials of the individual components are fundamentallycoupled to stress via the Gibbs–Duhem relationship. While thisprovides challenges to the development of solid-state batteries,it also affords opportunities for more electrochemical control ofthe devices. For example, Wu & Fitzhugh et al.38 showed thatmicrostructural modications that apply mechanical constric-tion could expand the onset of oxidation in LSPS full cells from2.1 V up to 5 V.

3. Theoretical considerations

The relationship between electrochemical lithiation/delithia-tion and the deformation/stress experienced by active materialparticles is well documented in the literature.87,88 Less studied,but intimately connected from a theoretical point of view, is theimpact of stress on the electrochemical stability window ofsolid-state electrolytes. As will be discussed below, the unique


nature of solid-state battery systems is such that the activematerials and electrolyte particles interact via both electro-chemical and mechanical mechanisms. Oen, this mechanicalinuence on the electrochemistry in solid-state batteries is seenas an obstacle to be overcome. In this section, prior studies arereviewed from an alternative point of view. It is suggested thatthis perceived weakness could, in-fact, be a great potentialadvantage for solid-state batteries. The electrochemical–mechanical coupling provides a mechanism which can be usedto control lithium batteries in new and unprecedented ways.Recent work that supports this point of view will be highlighted.

The coupling of strain to electrochemical lithiation/deli-thiation in battery components results from a variety of mech-anisms. The integration of these components and theirinteractions gives rise to cell level coupling. It is this totality thatmust be considered for optimal development of solid-statebatteries. In active materials, lithiation/delithiation occurs ineither intercalation, alloying, or conversion reactions. Each ofthem is accompanied by varying amounts of strain resultingfrom lattice vector distortions, defect formations or moredrastic phase transitions. Generally speaking, alloying andconversion are accompanied by much more signicant strainsthan intercalation. For solid electrolytes, decomposition is mostakin to conversion reactions, where the electrolyte decomposesto a series of other phases. For example, at high voltage LGPS isexpected to decompose to GeS2 + P2S5 + S + Li(m).24–26 Theseconversion decomposition reactions are not expected to bereversible. On the other hand, ab initio calculations have sug-gested that lithium excess/depleted LGPS is more stable at low/high voltages than stoichiometric LGPS, respectively.68 Thisimplies that such electrolytes do maintain certain intrinsiclithium capacity. This was conrmed by the construction of

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a pure-LGPS battery with LGPS serving as the cathode, electro-lyte and anodematerial in a limited voltage range.89 However, asdiscussed in the Experimental history section (Fig. 6), goingbeyond a certain voltage range was found to decompose LGPS,with the reported ranges varying between studies.24,37,38 Like theactive material analogs, electrolytes that decompose via phasetransitions are expected to experience far larger strains thanthose that are partially lithiated/delithiated.

This section is organized as follows. In subsection 3.1, anoverview of the thermodynamics of electrochemical–mechan-ical coupling is provided. Relevant thermodynamic theoryprovides a foundation to discuss exciting recent work inmechanical stabilization of LGPS/LSPS. The stresses experi-enced in a solid-state battery system as a result of suchmechanical stabilization are the subject of subsection 3.2.Subsection 3.3 discusses the impact of the decay morphology onvoltage window widening. The second order effects ofmechanical stabilization are introduced in subsection 3.4.Finally, the relationship between these thermodynamic theoriesand the experimentally observed lithium dendrite formation inceramic suldes constitutes subsection 3.5. This nal subsec-tion will also tie together the quantied theories of mechanicalstabilization and passivation layer theory for solid-state elec-trolytes. In each of these subsections, discussion will beincluded that evaluates various studies from the precedingExperimental history in light of the theoretical topic presented.

† The repeated indices of tensor elements imply summation (Einstein notation).

3.1 Mechanically induced metastability

The physical picture of mechanically induced metastability,introduced by Wu & Fitzhugh et al.,38 stems from the fact thatLGPS and LSPS tend to expand signicantly upon decomposi-tion. For example, the high voltage decomposition of LGPS waspredicted to be Li10GeP2S12 / 10Li(m) + P2S5 + GeS2 + 5S by abinitio calculations.24 In the absence of pressure, this decompo-sition is accompanied by over 30% volume expansion.Mechanically induced metastability arises from the applicationof a mechanical constraint such that this volume expansionnegates the electrochemical driving energy. For simplicity,isotropic models of the electrolyte are typically considered.38,39

Polycrystalline values are used for moduli by averaging Voigtand Reuss models.90 This approach has the added benet that itreects that, in practice, battery designers use polycrystallinepellets of pressed electrolytes rather than single crystals. Thegeneral physical picture of mechanically induced metastabilityresulting from this reaction strain is illustrated in Fig. 8. Inshort, mechanical constriction can improve the experiencedstability window by introducing an energy barrier that inhibitsstructural decay.

To quantify the metastability of the electrolyte, the problemis framed in terms of the decomposed fraction (xD) of thematerial.38,39 The Gibbs energy of partially decomposed LGPS isG(xD) ¼ (1� xD)GLGPS + xDGD, where GLGPS and GD are the Gibbsenergies of pristine and decomposed LGPS, respectively. Thetotal decomposition reaction energy is G(1)�G(0). Pristine LGPS(xD ¼ 0) is metastable whenever the inequality of eqn (3.1) issatised. In this case, an increase in the fraction of LGPS that is

J. Mater. Chem. A

decomposed will increase the system's Gibbs energy and henceis not probable (Fig. 8a). Note that this inequality is evaluatedonly at xD ¼ 0. This guarantees the metastability of the pristinestate, but it does not require the more stringent condition thatthe pristine LGPS is properly stable. This fact has importantimplications for the strain experienced in the particles and willbe discussed in depth in the following sections.�

vG

vxD

�xD¼0

. 0 (3.1)

The Gibbs energy given above, G(xD), represents a coarse-grained model for this system. That is, the volumetric Gibbsenergy of a small, but still macroscopic, subsystem of the pelletin question is given by the average volumetric Gibbs energywithin that subsystem. For example, if the material in thissubsystem is half pristine (xD ¼ 0) and half decomposed (xD ¼1), then the subsystem is, on average, xD ¼ 1/2 and has Gibbsenergy G(1/2) to be within surface effects. The volume expansiondiscussed above is termed the “reaction strain”38 and dened aseRXN ¼ V�1(xD ¼ 0)(V(xD ¼ 1) � V(xD ¼ 0)). The average volu-metric reaction strain within the subsystem is given by 3 ¼xD3RXN. Within the elastic limit, the average pressure within thesubsystem is given by an effective bulk modulus (Keff) to be p ¼Keff3 ¼ xDKeff3RXN. The elastic limit of the subsystem is justiedin the limit of xD / 0, where pressure and strain both trendtowards zero. Different decay morphology models can be usedto estimate Keff (Section 3.3) for a given mechanical constraint.Three morphologies are plotted in Fig. 8b and discussed in-depth in Section 3.3. Fortunately for stabilization attempts, theactual decay morphology appears to be that of inclusion decay,which has the highest value for the effective modulus.39

Following the notation of Eshelby,91 the coarse-grainedstress tensor (s) of the subsystem is expressed in terms ofdeviatoric stress/strain tensors (sd) and a generalized pressure�p ¼ �1

3trðsÞ ¼ �1

3sii

�.†39 Similarly, the strain tensor (3) is

divided into deviatoric (3d) and volumetric strain 3V ¼ V0�1(V �

V0), where V0 is the volume of the subsystem in its reference[undeformed] state. The deviatoric components are given by

sdij ¼ sij + pdij and 3dijh3ij � 133Vdij . By adopting this convention,

the work differential can be expressed as eqn (3.2) and the Gibbsdifferential as eqn (3.3).39

dW ¼ V0sdijd3

dij � pdV (3.2)

dG ¼ �SdT + midNi + Vdp � V03dijds

dij (3.3)

Combining eqn (3.1) with (3.3), neglecting the deviatoriccomponents which are expected to be smaller and applying thecoarse-grained pressure model, the metastability conditionbecomes:



Fig. 8 (a) Pictorial description of metastability in ceramic sulfides. Gibbs energy is plotted versus decomposed fraction (xD). For adequately steepGstrain(xD), the total Gibbs energy has a positive slope in the pristine case (xD¼ 0). (b) Pressure build up due to reaction strain in either a hydrostaticmodel of varying thickness or an inclusion model. The inclusion model was shown to be the infinite thickness limit of the core–shell model.Reproduced from ref. 39 with permission from John Wiley and Sons.


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V3RXNKeff . ��mi

vNi

vxD

�xD ¼ 0

¼ �DG0RXN (3.4)

where the right-hand side, dened as �DG0RXN, is the reaction

energy of the decomposition in an unconstrained system (i.e.�DG0

RXN ¼ G(1) � G(0) ¼ GD � GLGPS).38,39

The metastability condition of eqn (3.4) allows for calcu-lating the effects of the mechanical constraint on the voltagewindow, using Keff ¼ (bmaterial + bconstraint)

�1 where b representsthe compressibility of either the material or the constraint.38

Fig. 9a shows the voltage window widening of LGPS and LGPSdoped derivatives, as a function of a core–shell constraintmechanism (bconstraint ¼ bshell). The limit of isovolumetricconstraint corresponds to bconstraint / 0, whereas bconstraint /N represents no constraint. Such a constraint can be realizedthrough thin or thick core–shell structures, as in the case ofFig. 8b (Section 3.3). For nearly isovolumetric constraints, thevoltage window has widened from approximately 1.7–2.1 V to0�3.6 V (Fig. 9a). This calculation was performed following theperturbation method discussed in Section 4. For the core–shellstructure presented in ref. 38, the estimated bconstraint wasapproximately 0.03 GPa�1 with a predicted stability of 0.7–3.1 V.This prediction was in excellent agreement with cyclic voltam-metry (CV) measurements for the core–shell LSPS stability. Aswill be discussed in Section 4, the nearly isovolumetricconstraint in Fig. 9b was applied through minimizing�

vGvxD

�xD¼0

. This approach is quantitatively stricter than that

shown in Fig. 9a as all the possible decomposition reactionpathways were considered simultaneously. The predicted highvoltage stability in Fig. 9b is slightly wider to nearly 4 V at Keff ¼20 GPa.

An alternative derivation of this effect arises directly from theGibbs–Duhem relationship. For conventional battery cells thatdo not experience pressure or temperature changes, the Gibb–Duhem relationship reads Nid(mi + qif) � Vdp + SdT z Nid(mi +


qifi) ¼ 0 where mi and qif are the chemical and electrostaticpotentials of element i, respectively. This necessitates the rela-tionship between the cell voltage and the lithium chemicalpotential to be DmLi ¼ �qLiDf. That is to say that, for example,when the cathode is charged to 4 V above the anode, the cath-ode's chemical potential is �4 eV relative to the anode'schemical potential. In other words, the equilibrium lithiumelectrochemical potential (mLi + qLif) is constant throughout thebattery cell as any increase in the voltage is cancelled by a cor-responding decrease in the chemical potential. However, thecase of solid-state batteries can deviate from this model, as thepressures are no longer negligible. Instead, the equilibriumcondition becomes DmLi¼�qLiDf + rLi

�1Dp where rLi ¼ NLiV�1.

Hence, returning to the above example, the chemical potentialof a subsystem in the cathode does not need to be �4 eV belowthat of the anode when charged to 4 V as the pressure cancontribute signicantly. For LGPS/LSPS, rLi

�1 z 50 A3 perlithium leading to a pressure term on the order of 300 meV peratom per GPa of pressure generated via reaction strain (Fig. 8b).

As discussed in depth in Section 2, glassy-ceramic suldesolid electrolytes consist of metastable crystalline structuresembedded in a glassy matrix. For example, Li7P3S11 was foundto crystallize within a glassy matrix at high temperature.62 It wasconcluded that Li7P3S11 is only chemically stable at hightemperatures. Its existence within the glassy-ceramic impliesthat the glassy matrix provides an environment in whichLi7P3S11 is metastable at room temperature.41 In other words, inthe absence of the glassy matrix, Li7P3S11 cannot be stable atroom temperature as it will spontaneously decay. The mecha-nism by which the glassy environment stabilizes such phases, tothe author's knowledge, has not yet been understood. However,the above outlined theory offers a viable explanation for thisstabilization.

In ref. 38 and 39, core–shell microstructures are used towiden the electrochemical stability windows of LGPS and LSPS.Unlike Li7P3S11, LGPS and LSPS are chemically stable at room

J. Mater. Chem. A


Fig. 9 Comparison of metastable calculation procedures. (a) Chemical potential window versus lithiummetal for LGPS, and doped derivatives, inthe hydrostatic limit, calculated via the perturbationmethod. The effective compressibility is given by the LGPS bulkmodulus (KLGPS) and the shellcompressibility (bshell) via the relationship Keff

�1 ¼ KLGPS�1 + bshell. (b) Chemical potential window versus lithium metal for LGPS, and doped

derivatives, in the hydrostatic limit, calculated via the minimization of the Gibbs slope in the pristine case. Reproduced from ref. 39 withpermission from John Wiley and Sons.


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temperature and, hence, can be synthesized.14,37 However, LGPSand LSPS are not electrochemically stable outside the range ofapproximately 1.7–2.1 V versus lithium metal.24–26 The applica-tion of rigid amorphous shells can drastically improve thisstability window.38,39 This same mechanical stabilizationmechanism may be responsible for both the chemical meta-stability of Li7P3S11 and its wide electrochemical window whenembedded in a glassy matrix. In such a case, the glassy matrixwould not only provide improved conduction between theLi7P3S11 particles, but also provide the mechanical constrictionneeded for voltage and chemical stabilities. In short, the glassymatrix is analogous to the shell in ref. 38 and 39. By providingconstriction that resists decay, the glassy matrix and/or rigidshell inhibit the decay of the electrolyte material.

3.2 The stresses experienced

Mechanical work within a battery can be the result of eitherelastic deformation or an external load. In elastic deformation,stresses acting on the material deviate the lattice parametersaway from the equilibrium state. The energy of such deforma-

tions scales as12E32V0 where

12E32 is the elastic energy density

and V0 is the volume of the reference state. External loadsrepresent the work done to assemble a phase in the presence ofan external stress (s). The work done to assemble a referencestate with volume V0 in the presence of a pressure p is pV0.

Koerver et al.86 showed that the open circuit voltage (foc) ofa solid state full cell follows the anticipated relationship whenpressurized �

vfoc

vp

�T ;ni

¼ � 1

eDrVm (3.5)

where e is the charge of an electron and DrVm is the reactionvolume (i.e. the change in volume experienced as a result of

J. Mater. Chem. A

discharge). The relationship of eqn (3.5) arises from the externalload mechanism, rather than elastic deformation. The workneeded to assemble the charged materials of volume Vc in thepresence of an external pressure (pc) is pcVc. The same can besaid for the discharged materials, with work pdVd. Thus, thechange in work occurring from an external load is DW ¼ pdVd �pcVc. For the case of constantly maintained pressure (p ¼ pc ¼pd), the work is given by DW ¼ p(Vd � Vc) ¼ pDrVm. Due to therequirement that the discharge reaction does this work in orderto change the volume and proceed, the open circuit voltagereduces foc / foc � DW/e, which in turn yields eqn (3.5).Physically, eqn (3.5) represents the net effect of the free energycost of assembling a discharged phase plus the free energy gainof disassembling a charged phase. Note that the moduli of thephases have not been considered. Even in the event that themoduli trend towards innity, and thus 3 ¼ 0 and there is nodeformation energy, this open circuit voltage effect remains.However, changes in the elastic deformation can alsocontribute to changes in the open circuit voltage.

The stresses resulting from decomposition differ from thosein the above case in two principal ways. First, the decomposi-tion stresses are quite localized in solid-state batteries. Thepressure resulting in eqn (3.5), in contrast, is assumed to berelatively constant throughout the battery cell. When a ceramicsulde solid electrolyte decomposes, it tends to do so byforming inclusions.39 The nature of these inclusions is thatthere could be considerable stress within the inclusion and inthe nearby pristine material, but the stress quickly decreaseswith increasing distance from the inclusion. The second majordifference is that the stresses being discussed are not alwaysexperienced. That is, the stresses in question are the stressesthat would only occur in the event of a decomposition. Whetheror not those stresses are realized depends on whether thatreaction is thermodynamically favorable. For example, when




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eqn (3.1) or (3.4) is satised, no decomposition is predicted andhence the pressure p¼ Keff3RXN will not be experienced. When itis not satised, however, the decomposition will proceed andthe stress will occur.

It is important to note that the metastability of eqn (3.4) isdistinct from high-pressure stability. For high-pressurestability, both the reactants and products are evaluated at thesame pressure. In the example leading to eqn (3.5), the chargedand discharged phases were both evaluated at a pressure p ¼ pc¼ pd. Accordingly, the change in open circuit voltage repre-sented the change in the high-pressure stability of the chargedphase. In contrast, for mechanically induced stability (i.e. eqn(3.4)), the products and reactants are not evaluated at the samepressure. For example, in pristine LGPS, there is no decompo-sition induced stress. However, once decomposition does occurin a subsystem, the subsystem becomes pressurized. Hence, thedecomposed products exist at an elevated amount of stressrelative to the pristine LGPS. This increase in the amount ofstress following decomposition is the pressure given by Keff3RXN.In short, the thermodynamic comparison to bemade is betweenthe product (e.g. LGPS/LSPS) at [nearly] zero stress and thereactants at pressure Keff3RXN.

A natural question to arise in light of the mechanicallyinduced stability using a core–shell design is regarding thestrength of the shell. That is, can the shell adequately containthe generated pressures without fracturing? Or more generally,when do mechanical constraints fail to constrain rather thanstabilize the electrolyte? Eqn (3.4) is derived in the innitesimallimit. That is, a decay in which a subsystem goes from xD ¼ 0/0 + dxD is accompanied by an increase in the pressure p ¼ 0 /

0 + dp ¼ Keff3RXNdxD. If this decay is not thermodynamicallyfavorable (i.e. eqn (3.4) is satised), then no more pressure willbuild up. Hence, the only thermodynamic requirement on theconstraining system is with regards to the effective modulus.The strength of the system is not a thermodynamicallymandated quantity.

However, the strength of the constraint does havea substantial potential impact on the kinetics of decomposition.In Fig. 8a, the fracturing of the constraint is said to occur ata decomposed fraction xf. That is, the maximum stress that thesystem can handle without failure occurs at xf. For strongsystems (thick core–shell microstructure, inclusion decaymorphology, or densely packed pressurized battery cells) thisfailure point will be much higher than for weak systems (thincore–shell microstructures). The barrier posed by such a frac-ture limit is Gbarrier ¼ Gʹ(xf) � GLGPS. Metastability only requiresthat Gbarrier > 0, which is guaranteed by eqn (3.4). However, evenif the material is metastable, the decomposition rate will scaleas exp(�Gbarrier/kBT). Thus, a stronger constraint will havehigher xf, and by extension a higher barrier, and will decomposeat a slower rate. In short, the constraint should be strongenough to be able to withstand thermal uctuations of theelectrolyte at about xD ¼ 0.

This section has surveyed stresses experienced in solid-statebatteries as is relevant to the stability of solid electrolytes. Themechanical properties of the constraining system needed forpractical ceramic suldes were discussed in terms of both


thermodynamics and kinetics. Most importantly, the discus-sion focused on the absence of pressure in the metastable state.Whenever eqn (3.4) is satised, it is thermodynamically pre-dicted that there will be no pressure in the pristine electrolyte.When considering kinetics, there will likely be small thermaluctuations in the experienced pressure in the zero-pressurestate, but these uctuations should be innitesimal in anymacroscopic subsystem of the electrolyte. The constraintshould be rigid enough to satisfy eqn (3.4) and strong enough toreverse small thermal uctuations.

3.3 The impact of the decay morphology

The effective modulus (Keff) used in eqn (3) relates the averagepressure in a subsystem to the average reaction strain withinthat volume (p(xD) ¼ Keff3(xD) ¼ KeffxD3RXN). The precise value ofthe effective modulus depends both on the material propertiesof the subsystem and the mechanical nature of the neighbor-hood. This dependence of Keff on the neighborhood leads to thedependence on the morphology of the decay. That is, in order toknow Keff for a given conguration, the conguration of thedecayed products must be accounted for. Ref. 39 comparedexperimental stability results for core–shell LGPS with predic-tions from two decay morphology extrema (Fig. 8b). In the rstextrema, termed “hydrostatic” decay, the decomposed fractionwas taken to be constant everywhere within the LGPS particle.In the second, the decay morphology was assumed to be that ofspherical inclusions. That is, the decay fraction was 1 withina spherical region and 0 elsewhere. It was shown that thespherical inclusion model provided a larger value of Keff andbetter matched experimental results.

In the hydrostatic model, the local decomposed fraction wastaken to be equal everywhere within the core of the core–shellparticle (xD(~r) ¼ xD for arbitrary~r within the core). In this casethe effective bulk modulus of the system was the paralleladdition of the core's material modulus and the modulus of theshell (Keff

�1 ¼ KLGPS�1 + Kshell

�1). The modulus of the shellrepresents how much the shell will respond to pressure withinthe core and is a function of both the shell's material propertiesand the geometry. Keff was calculated for thin and thick core–shell structures where both the core and shell materials hada modulus of K ¼ 30 GPa and a Poisson ratio of n ¼ 0.2. It wasfound that when the thickness of the shell is approximatelyequal to the radius of the core (i.e. thick shell) the effectivemodulus was on the order of 13 GPa. When the thickness of theshell was only one tenth of the core radius, the effectivemodulus dropped to 4 GPa. These values correspond to theslopes in Fig. 8b.

However, experimentally, a thin core–shell was applied toLGPS using ultrasonication (thickness approximately 10% ofthe core radius). The value of Keff was found by comparing thevoltage window widening as determined by cyclic voltammetrywith eqn (3.4). The determined Keff was approximately 15 GPa –

well beyond the 4 GPa expected for hydrostatic decay.A spherical inclusion model was constructed which distin-

guished the average decomposed fraction �xD from the localdecomposed fraction xD(~r). In this model, it was assumed that

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the LGPS decomposed in local inclusion spheres such that xD(~r)¼ 1 within the sphere and remained pristine (xD(~r) ¼ 0) else-where. The radius of the spherical inclusion relative to thewhole particle was determined by �xD. In the limit of the pristinecase (lim �xD / 0), the predicted modulus was found to be 15GPa (Fig. 8b), in excellent agreement with the experimentalmetastability window. Moreover, the mechanics of this casepredicted that the shell thickness needs only to be comparableto the size of local spheres of inclusion decay, on the order of 20nm – again agreeing well with the experimentally synthesizedshell. The nature of LGPS to decay via inclusions was alsodemonstrated experimentally using electron microscopy. Forthose LGPS particles that were not constrained, TEM imagestaken aer cycling showed nucleated centers of sulfur richdecay products.

3.4 Second order effects: kinetics and interfaces

Beyond voltage window widening and improving interfacialcontacts in ceramic suldes, a mechanical constraint can alsohave signicant positive second order effects on solid-statebatteries. Sluggish decomposition kinetics have previously beenspeculated as a reason for successful lab-scale cycling of solid-state batteries based on sulde electrolytes beyond the intrinsicstability window. Generally, these slow kinetics are believed tocome from limited electrical conductivity as adding an elec-tronically conductive material can rapidly increase the decom-position rate.24,84,89 However, the pressurization induced byinclusion decomposition once eqn (3.4) is violated could lead toslowed kinetics due to reduced ionic conductivity in thesurrounding material. Thus, mechanically constrained suldeswould not only have a wider thermodynamic stability window,but could also have a kinetically slower decomposition once thestability window is exceeded. Additionally, interfaces with activematerials remain a major problem for sulde batteries. Eqn(3.4) applies equally as well to interfaces as it does to bulkmaterials, allowing for the possibility of improved prediction ofinterfacial stability.

In ref. 38, a core–shell microstructure was used to widen thevoltage window of LSPS from 1.7–2.1 to 0.7–3.1. Additionally,once above 3.1 V, LSPS with a more rigid shell was shown todecompose at an orders of magnitude slower rate than LSPSwithout such a shell. In fact, the decomposition rate was suffi-ciently slow that batteries based on LSPS could be cycled up to 5V with strong cyclability. For this reason, it was termed “quasi-stable” up until 5 V. It was suggested that pressurizationbetween 3.1 and 5 V could decrease conductivities which in turnslows down decomposition. This is in agreement with thepredictions of Ong et al.26 that conductivity drops quickly withlattice compression.

Multiple experimental studies have shown that LiNbO3

(LNO) can be used as a coating material for improved interfacialstability between ceramic suldes and LiCoO2 (LCO).14,37

However, pseudo-binary computational methods based on abinitio data predict that LNO-LSPS does not form a stable inter-face.92 This remains an open question and is suggested to besolved by combining pseudo-binary methods with constrained

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decay models. In a pseudo-binary method, the composition andenergy of a two-phase interface are linearly interpolated andevaluated for stability as a single material (see ComputationSection 4). We suggest that the same could be done fora pseudo-phase volume and modulus, which is then appliedwith eqn (3.4) to nd the metastability window. Given thenature of oxides being stiffer than suldes,40 it is anticipatedthat the pseudo-phase modulus for LSPS–LNO would be muchhigher than the typical 25–30 GPa experienced by ceramicsuldes,40 hence leading to even greater potential for voltagewindow widening.

3.5 Passivation layers and dendrite formation

Non-mechanical attempts to explain the variability in theoperational stability window have included the proposal ofa chemical passivation layer. It has been speculated that anelectronically insulating layer coating LSPS/LGPS could serve assuch a passivation layer by either (i) allowing deviation of thelithium metal potential within the electrolyte away from thevalue within the rest of the cell70 or (ii) sufficiently slowing downthe decomposition kinetics that require electron transport.24

More recent work39 has suggested that a critical advantage of anelectronically insulating layer may in fact be related tomechanical methods in that it retains lithium atoms within theparticle. This maximizes the reaction strain during high-voltageoxidation and leads to greater stabilities induced by eqn (3.4).

The proposed picture of potential retention of lithium atomsby an electrically insulating shell would also partially answercomplicated questions regarding dendrite formation in solidelectrolytes. Many experimental studies have showna surprising result that lithium metal dendrites form withcomparable ease in solid electrolytes as in liquid-electrolytes. Insome cases, it is suggested that the dendrites form even morereadily in solid electrolytes than in liquid ones.93–95 This iscounter intuitive as one major goal of developing solid elec-trolytes has been to inhibit dendrite formation by a rigid elec-trolyte, enabling the use of lithium metal as a commerciallyfeasible anode material.9 The picture of an electronically insu-lating shell for the retention of lithium atoms would suggestthat lithiummetal can form locally (i.e. within the electronicallyisolated electrolyte particle).39 Thus the ease of dendriteformation in solid electrolytes could be explainable not only bydendrite growth from the anode into the electrolyte, but alsothrough local internal formation. This mechanical picturewould also explain why dendrites are particularly likely to formin grain boundaries and voids,93,96,97 where the effectivecompressibility is lower than in the bulk.

The role of pressure during dendrite formation at theinterface between lithium metal and suldes has been studiedfor both amorphous and crystalline phases.98,99 The effect ofpressure on the stability of the interface between lithium metaland 75Li2S–25P2S5 was measured in terms of the critical currentdensity or the current density at which short circuit occurs.98 Itwas found that hot pressing the glassy sulde increased thiscritical current density. A recent study on pressurized interfacesbetween sulde Li6PS5Cl and lithium metal has suggested that




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lithium creep plays a central role in the formation ofdendrites.99 Voids in the interfacing lithiummetal are known toform when the lithium stripping current exceeds a threshold setby the system's ability to replenish the lithium.99–101 Such voidscan lead to signicantly increased local current densities,causing dendrite formation even when the total current densityis low. Using a pressurized, three-electrode cell, Kasemchainanet al. were able to distinguish the polarization that occursduring stripping versus plating under pressure. Signicantlymore polarization was seen during stripping than duringplating. Moreover, stripping showed a strong dependence onthe applied pressure leading to the conclusion that creep, notdiffusion, is the principal means by which lithium at theinterface is replenished.

4. Computational methods andresults

Computational studies regarding the impact of mechanicalconstriction on the important solid electrolyte gures of merit([electro-]chemical stability and ionic conductivity) haverequired advancement beyond conventional methods. Thechemical and electrochemical stabilities of bulk materials haverequired modication to account for the variable pressure thatexists in constrained systems following decay. Interfacial reac-tions with electrolyte materials, which are already complicatedby cumbersome interfaces, must also account for these samemechanisms. Additionally, the kinetics of solid electrolytesunder constraint could deviate from unconstrained values bothin terms of reaction kinetics (Section 3.4) and ion transportkinetics. This section provides a survey of relevant uncon-strained computational methods and discusses how thesemethods have been adapted for use in constrained electrolytesystems.

In unconstrained systems, calculations based on densityfunctional theory (DFT) collected data have greatly improvedunderstanding and design principles for crystalline solid elec-trolytes.5,26,77,92,102 This has been particularly important forceramic suldes as the seemingly contradictory experimentalresults have warranted a more detailed understanding ofcompeting effects.14,25,26,37,89 Comparing ground state energiesfor crystalline phases, determined via DFT, has proven to bea remarkably accurate method for evaluating chemical andelectrochemical stabilities.5,103 This has been true despite DFTphase energies only being accurate at absolute zero (and arealso typically calculated at zero pressure). Large-scale DFTrepositories, which catalog material phases and the DFTdetermined ground state energies, have enabled highly accel-erated evaluation of high throughput phase diagrams.92,104,105

Computational methods for evaluating lithium ion mobility invarious crystalline phases have also been very successful atcorrectly predicting experimental results.26,102,106 Nudged elasticband (NEB) methods have been used to determine the migra-tion barriers of particular migration pathways. Ab initio molec-ular dynamics (AIMD), which implements DFT determinedforce elds, has been able to predict bulk ionic conductivity


with remarkable precision. Recent developments in pseudo-phase methods have allowed the approximation of interfacialstability using only bulk energies, eliminating the need forcumbersome interface calculations.28,29,92

The calculation of the thermodynamic stability of a materialusing DFT phase data is done by minimizing the relevant freeenergy of a linear combination of all considered materials,subject to the constraint of a xed net composition.77 Of para-mount importance in performing these calculations is that thespan of included crystal phases must be a faithful representa-tion of the truly stable ground states.77,102 That is, exclusion ofa ground state material will quickly cause phase stability errors.Fortunately, large experimental databases of observed crystals,machine learning prediction of new but feasible stable struc-tures, and large-scale DFT material databases have negatedmuch of these concerns – providing computationalists witha robust framework of data with which to operate.107–109 Usingthe ground state energies, approximations can be made tocalculate both the chemical (canonical ensemble) and electro-chemical (grand canonical ensemble) stabilities of mate-rials.25,26,77,92,102 Vibrational entropy can be determined viaphonon calculations, potentially allowing for renement ofstability calculations that otherwise do not considerentropy.110,111 Furthermore, recent studies have adapted thesecomputational methods for determining the metastability ofphases under general constriction mechanisms.38,39

The interfacial reactions of ceramic suldes with commonelectrode materials have been a substantial barrier to solid statebattery development. Computational methods for under-standing such reactions either require the direct simulation ofthe interface, where two crystals are spliced together, or the useof pseudo-phase methods. Direct simulation of the interfaceaccounts for surface energies and allows the direct examinationof abundant interface phenomena, such as the space chargeeffect or grain boundary segregation, but requires the deter-mining of the energetically favorable interfacing planes – ofwhich there are many.112,113 Pseudo-phase methods were intro-duced to provide more convenient estimates of the interfacialenergy. Such pseudo-phase calculations have proved invaluablein high-throughput determination of coating materials that canallow the use of LSPS/LGPS with common cathode materialssuch as Li(NixMnyCoz)O2 (NMC) or LiCoO2 (LCO).92,114Moreover,these pseudo-phase methods allow for the separation of theinstability due to bulk vs. interfacial effects, which can becombined with mechanically constrained bulk calculations todetermine whether an interface will be unstable whenconstrained.92

4.1 Chemical and electrochemical stability

The chemical and/or electrochemical stability of a materialphase is determined by the energy difference between the phasein question and the lowest possible energy subject toconstraints.5,77,102 For chemical stability, the only constraint isthat of a xed composition. For example, the chemical stabilityof LCO is evaluated against the constraint that the productshave a total composition of Li + Co + 2O. Electrochemical

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stability calculations swap the constraint of lithium ionconservation for the constraint of a xed lithium chemicalpotential with all non-lithium atoms remaining conserved. Theenergy difference is termed the “energy above the hull” or the“hull energy” and represents the magnitude of the decay energyof a material. If the hull energy is zero, then there is nocombination of materials at that composition with lower energyand, hence, the material is stable. If the hull energy is positive,then there does exist a combination of materials that is lower inenergy. In this case, the material is in principle considered to beunstable thermodynamically and the magnitude of thedecomposition energy is given by the hull energy. The hullenergy will never be negative as being negative would imply thatthe predetermined hull energy is not the minimum energy.

4.1.1 Chemical stability. Following conventional methodsfor phase diagrams,77 the calculation of the chemical stability ofceramic suldes has been performed by neglecting pV and TSterms in the Gibbs energy and directly minimizing the DFTdetermined energy (G¼ UDFT � TS + pVz UDFT). For condensedsystems, these neglections are typically justied by small ener-getic scales for entropic or volumetric changes. Typically,a material is only reported as unstable when the hull energy islarge compared to thermal energy (kBT). This threshold, in part,adjusts the calculations for any neglected entropic changes thatmight have occurred. Precise cutoffs for when a hull suggestssufficient instability to be termed unstable varies betweenliterature studies, and are dependent on the kinetics that thereaction must drive, but generally are somewhere in the rangeof 25–100 meV per atom.5,26,38,92,114 On the other hand, if the hullenergy is comparable to kBT, the material may or may not bestable depending on entropic and mechanical contributions.LGPS and LSPS have both, for example, been calculated to havechemical hull energies on the order of 20–25 meV per atom.24,26

Considering the large lithium congurational entropycompared to the predicted decay products, Li3PS4 + Li4GeS4,Li4SiS4, it is not surprising that LGPS and LSPS are apparentlystable at room temperature. Li7P3S11 is expected to have a hullenergy comparable to thermal energy, with decay productsLi4P2S6 + Li3PS4 + S. Unlike the decay products of LGPS andLSPS, these decay products maintain lithium congurationalentropy. Thus, the entropic effects that beneted the chemicalstability of LGPS and LSPS are reduced in the case of Li7P3S11.This may explain why Li7P3S11 is typically seen inside of glass-ceramic structures, where the mechanical effect of the glasscould compensate for the reduced entropic terms. Accountingfor vibrational entropy terms predicts that Li7P3S11 becomesstable at 630K, conrming conclusions that it is a high-temperature phase.64,110

4.1.2 Electrochemical stability. The electrochemicalstability of materials is calculated by nding the convex hull forthe lithium grand canonical phase diagram, with free energygiven by FLi ¼ G � mLiNLi z UDFT � mLiNLi. The chemicalpotential of lithium is specied in terms of voltage versuslithium metal (mLi ¼ �ef) and the hull energy is taken at eachpotential of interest (Fhull(mLi)). No ceramic suldes have beencomputationally determined to intrinsically maintain evennearly stable hulls (Fhull z kBT) in a suitable voltage window for

J. Mater. Chem. A

battery operation.26 LGPS, for example, is expected to beginoxidation at lithium chemical potentials below �2.1 eV versuslithium metal and begin reduction at lithium potentials above�1.7 eV. Hence the voltage window is just 1.7–2.1 V, far short ofthe 4 V level needed for standard cathode materials.

4.1.3 High-pressure stability. The calculation of a mate-rial's stability, chemical or electrochemical, at xed pressurerequires that the pV term is retained.38 Minimizing the freeenergy FLi ¼ G � mLiNLi z UDFT + pV � mLiNLi for the Li–Ge–P–Sphase space resulted in the LGPS electrochemical window ofFig. 10. When there is no applied pressure, the expectedstability window was reported to be 1.75–2.2 V. This window iswidened considerably to a reduction threshold of 0.495 V andan oxidation threshold that exceeded 2.5 V when the appliedpressure was 20 GPa.

From a computational perspective, these isobaric calcula-tions are far simpler than calculations of the stability windowunder mechanical constraints. The ideal mechanical constraintis an isovolumetric constraint, which cannot be represented asan independent set of free energies. This is because the pres-sure is not xed, but instead is a function of the reactionstrain.38,39 That is to say the pristine LGPS under a mechanicalconstraint should be under little pressure, but upon decay, thedecomposed products will be under pressure Keff3RXN. Since thereaction strain is not known a priori, the pressure of thedecomposed phases is also not known and hence the electro-chemical stability cannot be calculated with such simple convexhull methods. To deal with these computational limitations,two approaches have been developed – perturbation and directminimization.

4.1.4 Constrained stability – perturbation method. As dis-cussed above, unlike high pressure phase diagrams that showstable phases at a constant pressure, where pV terms areexplicitly handled, in mechanically constrained systems theproducts and the reactants of decay exist at different pressures.The most direct method for addressing this is the perturbationmethod,38,39 which was depicted in Fig. 9a introduced in Section3.1. In this method, a convex hull is calculated for a solidelectrolyte at zero pressure and the decay products are used toobtain a reaction strain 3RXN with which eqn (3.4) can be eval-uated. bshell in Fig. 9a is a parameter that represents themechanical constraint of a core–shell microstructure. Whenbshell ¼ 0 the shell is taken to be perfectly rigid and the stabilitywindow is as wide as approximately 0–3.7 V. This perturbativeapproach has the advantages that it is computationally efficientand only considers reactions that are known to be problematic,i.e., only applies the bshell mechanical constriction to the reac-tions that are thermodynamically favored when unconstrained.The trade-off is that other reactions which could potentiallyhave small reaction strains are neglected.

4.1.5 Constrained stability – direct minimization. InFig. 9b introduced in Section 3.1, a more robust approach isused to minimize the derivative of the free energyvxDG ¼ P

imvxD Ni þ VvxD p with respect to all possible decay

products.39 This method has the advantages of considering allpossible reactions, and hence not overlooking low strain



Fig. 10 The electrochemical windows of LGPS at pressures of (a) 0 GPa, (b) 1 GPa, (c) 10 GPa, and (d) 20 GPa. Windows are given in terms ofchemical potential versus lithium metal, rather than voltage. The electrochemical window is seen to increase dramatically from 1.75–2.2 V to�0.5 to >2.5 V. Reproduced from ref. 38 with permission from Springer Nature.


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reactions that might otherwise be neglected, but is computa-tionally more expensive. Unlike the perturbation approach,a convex-hull method cannot be used as the products andreactants exist at different pressures. Other minimizationschemes (e.g. Lagrange minimization) must be used with anexplicit representation of pressure as a function of the decom-posed phases. That is to say the pressure changes based onwhich products are thermodynamically favorable. In the case ofFig. 9b, the pressure is given as p ¼ Keff3RXN, where 3RXN isa function of the lowest energy phases and the initial sulde.For rigid structures (Keff z 15–20 GPa) this shows high voltagestability up to between 3.5 and 4 V. When the minimum slope ofvxDG is zero, the material is thermodynamically stable withrespect to all products.

4.2 Interfacial stability

Ceramic suldes solid electrolytes are known to suffer frominstabilities at interfaces with most electrode materials used in


commercial batteries.8,28,70,92,115 Thus, the use of mechanicallyinduced metastability of the interface is a high priority. Likebulk material reactions, interfacial instabilities can be eitherchemical or electrochemical. The former consists of the ceramicsulde reacting with the contacting material, whereas the laterconsists of those two materials and the lithium ion reservoirreacting. While the bulk ionic conductivity of ceramic suldes isexceptional, these interfacial reactions can quickly build upinterfacial resistances that limit the rate capability.1,116–118

Amongst the most pursued ceramic sulde interfaces to bestabilized are those with either lithium metal or various high-voltage cathode materials.

The case of an interface with lithium metal is unique in thatthe voltage of the interface is denitively 0 V, regardless of thecathode's state of charge. Moreover, neglecting surface ener-gies, the chemical stability of the interface is also equivalent tothe material's electrochemical stability at 0 V. Hence, froma computational perspective, the only instability of concern is

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that of the 0 V electrochemical stability. Almost all sulde solidelectrolytes will fully reduce to constituent lithium binaries.24,92

It has been suggested that since virtually all materials fullyreduce to lithium binaries, the best approach to stabilizing theinterface with lithium would be to use a material with elec-tronically insulating lithium binaries.5,119 Ideally, if the resultinginterphase is electronically insulating, then the growth rate willbe limited by electronic kinetics and the battery can functionwith minimal impact. However, if the interphase is electroni-cally conductive, no such electronic barrier can exist. Forexample, LGPS is expect to decompose to Li2S + Li3P + Li15Ge4when in contact with lithium metal.24 Since the Li–Ge alloy iselectronically conductive, such decomposition on the interfaceis not self-kinetically-limiting and can continue to grow. Thistheory has been supported by the use of pretreating lithiummetal with LPS, which would form an interphase that does notcontain any Li–Ge alloy, to improve sulde half cell batteries.38

Additionally, the alternative solid electrolyte LiPON, whichlithiates to an electronically insulating interphase Li3P + Li3N +Li2O at 0 V, has been demonstrated in a solid-state half-cell withvery impressive cyclability (>10 000 cycles).9,120

The stability of the interface between ceramic suldes and anarbitrary cathode active material proves computationally morechallenging. While the interface between suldes and lithiummetal anodes is simply the grand canonical stability of thesulde at 0 V (to within surface factors), interfaces with cathodematerials require more advanced computational methods. Themost successful method for calculating these instabilities is thepseudo-phase (or “pseudo-binary”) method.28,29,92,121 Ratherthan directly simulating the interface by splicing two crystalstogether and performing DFT at the interface, each material isseparately simulated and a pseudo-phase is dened as a linearcombination of the two phases' composition and energy. Eqn(4.1) shows the pseudo-phase energy for an interface betweentwo materials (denoted as subscripts A and B).

Epseudo(x) ¼ (1 � x)EA + xEB (4.1)

Fig. 11 (a) Reaction energy determined via the pseudo-phase/pseudo-biReproduced from ref. 29 with permission from the Royal Society of Chmaterial and added instability when interfaced with LSPS. Reproduced fr

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The parameter x is any value between 0 and 1. The samevalue of x is used to linearly interpolate the composition. Witha pseudo-phase dened that represents the interface (i.e.a composition and an energy), the methods of Sections 4.1 canbe applied to evaluate the pseudo-phase stability. For example,the chemical hull energy of an LSPS–LCO pseudo-phase at x ¼0.5 represents the chemical instability of LSPS and LCO inreactions in which each phase constitutes 50% (mol) of thereactants. Electrochemical instability calculations can be per-formed similarly. In practice, the value of x that is used is theone that results in the least stable system (thermodynamicallyworst case). This value, dened as xm which maximizes therelevant free energy hull (Ghull(xm) ¼ max Ghull(x)), representshow much of each phase will be consumed if only the mostkinetically driven reaction occurs. In agreement with experi-mental ndings, ceramic suldes form unstable pseudo-phaseswith most cathode materials.28,29,121

Fig. 11a illustrates this process for the chemical stability ofinterfaces between LCO and various solid electrolytes, includingLGPS. The decomposition energy of the interface (dened to benegative of the hull energy) is plotted versus x from 0 to 1. Theminimum (i.e. most negative) decomposition energy for LGPS–LCO denes an xm value of 0.42.29 At this xm value, the interfaceis expected to decay to Co9S8, Li2S, Li2SO4, Li3PO4, and Li4GeO4

with a hull energy of 349 meV per atom.29 Of this hull energy,340 meV per atom was due to interfacial reactions betweenLGPS and LCO.29 Hence, only 9 meV per atom was due to theintrinsic instability of LGPS or LCO when separated. Theinstabilities at the interface between LPS and LCOwere found tobe even more severe.29

The high characteristic energies of the interfacial instabilitiesrelative to the material level instabilities necessitate the use ofstabilizing coating materials. Such coatings would serve asa barrier between the solid electrolyte and the cathodematerial toprevent both chemical and electrochemical reactions. Searchingfor such stabilizing coating materials has been the subject ofrecent high-throughput studies.92,114 One challenge that hasremained in evaluating the electrochemical stability of cathodeinterfaces with ceramic suldes is that because the ceramic

nary method for interfaces between LCO and various solid electrolytes.emistry. (b) Correlation between elemental composition in a coatingom ref. 29 with permission from John Wiley and Sons.




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suldes intrinsically have a nonzero hull energy in this region, sotoo will any pseudo-phases in which the ceramic suldes area component. This presents a challenge in that unstable mate-rials that have been stabilized via various mechanisms (kinetic,mechanical, etc.) will always result in predictions of unstableinterfaces. For example, LGPS can readily be stabilized viamechanical mechanisms at 3 V (ref. 38) but because the convexhull does not account for this, any interface with LGPS will bepredicted to be unstable at 3 V. That is, the interfacial hulls donot account for the stabilization that occurs within the LGPS.

Xiao et al.114 approached this problem by focusing on high-throughput screening for coating materials that formed chem-ically stable interfaces with LPS and common cathode materialsand were intrinsically electrochemically stable above 4 V.Following these searching criteria, it was found that polyanionicoxides, particularly phosphor oxides, were among the mostpromising. This process has the advantage of not requiringcoatings be applied to stabilize ceramic suldes; however, theelectrochemical stability of the interface was not considered.Alternatively, in ref. 92 a high-throughput search was explicitlyperformed including the electrochemical stability of the inter-face minus the intrinsic instability of the separate materials.Hence, the criterion was that the interface does not add morethan an additional 50 meV per atom of instability. Thisapproach has the advantage that it directly measures theinterfacial stability relative to what the stabilization mechanism(mechanical or kinetic) will have to apply in order to maintainsuitable material level stability. A total of over 2000 cathodecoating materials were predicted to be stable and are catalogedin the supplementary information of ref. 92.

Fig. 11b shows the results of calculating the interfacialchemical instability of LSPS with over 67 000 different crystalphases.92 The correlation between the elemental compositionand the interfacial instability is the basis for the heatmap ofFig. 11b. Those elements that are red have negative correlation,meaning that increasing their concentration in the coatingmaterial decreases the hull energy and improves the stability.These results indicate that those compounds with large anions,such as sulfur, selenium, and iodine, are most likely to formchemically stable interfaces. Similar plots revealed elementalcorrelation with electrochemical decomposition. Aeraccounting for all of the instability measures (material chemicalstability and interfacial chemical and electrochemical stability),the large anions (S, Se, and I) were found to have the bestperformance for high-voltage cathode coatings and nitrogen,phosphorous, and iodine were found to have the best perfor-mance for low-voltage anode coatings.

Interfacial stability calculations for mechanically con-strained systems have not yet been performed, but our vision isthat it represents a logical next step in determining the bestcathode coatings. Some materials, such as LNO, that have beenexperimentally successful but computationally are not pre-dicted to form stable interfaces, suggest that a greater under-standing is needed. Pseudo-phase methods could be readilyadapted for use with the mechanical constraint condition ofeqn (3.4).


4.3 Lithium ion mobility

While ionic conductivity is not the principal goal of mechan-ically stabilized battery cells, the calculation of lithiummobilityremains a key research direction for two reasons. First, core–shell morphologies have been a prominent means to inducemechanical metastability in ceramic suldes. Proper computa-tional methods for high-throughput screening of the best shellmaterials hence requires proper analysis of the lithiummobilitywithin the shell. If the shell is ionically resistive, then anymechanically induced stability of the core ceramic is pointlessas the bulk conductivity will suffer. Additionally, once thestability window has been exceeded, lithium ion mobility willplay an important role in kinetics of decomposition. That is,once a fraction of the ceramic sulde has decomposed, thegenerated local stress could inhibit ion transport in the neigh-boring pristine ceramic material. This has been theorized to bethemethod of quasi-stability up to and in excess of 5 V in ref. 38.

The impact of compression on conductivity was previouslyshown by Ong et al.26 in the simulated change in the conduc-tivity of LGPS based on lattice parameter constriction usingAIMD. For intrinsic LGPS, the ionic conductivity was estimatedto be 13 mS cm�1. Upon constriction by 1%, the conductivitydropped to 1.7 mS cm�1. Further increasing the constrictiondecreased the conductivity by orders of magnitude, resulting ina conductivity of 4.6� 10�8 mS cm�1 at 4% constriction. On theother hand, lattice parameter expansion increases the conduc-tivity to 75 mS cm�1 at 4% expansion. In line with the reactionstrain model discussed in Section 3.4, these results suggest thatmechanical constriction could provide a secondary kineticeffect that inhibits Li ion conductivity in the crystalline phaseclose to the decomposition. However, since stress decreasesquickly with increasing distance from the inclusion,39 such aneffect won't likely change the global Li-ion conductivity of theelectrolyte material when proper mechanical constriction isdesigned.

Lithium ion mobility is typically investigated using eitherNEB methods or AIMD. NEB calculations nd the minimumbarrier pathway between two prescribed ion congurations.102

For example, to obtain the migration barrier of a lithium ionfrom one site to another. Such NEB calculations are usefulwhenever the migration pathway is well known – either becausethe system has a high level of lithium ordering or to isolate oneparticular migration pathway from many.122,123 In contrast,AIMD solves for ion migration at elevated temperatures usingDFT determined force elds and applied thermostat func-tions.102,124,125 These AIMD results, the trajectories of mobileions at nite temperature, reveal the effects of all migrationpathways in parallel. The diffusivity of an ion can thus becalculated using the Einstein relationship of eqn (4.2).

D ¼ 1

2dDt

1

N

Xi

�|~riðtþ DtÞ � ri

!ðtÞ|2�

(4.2)

where the summation yields the mean-squared displacementduring the time step t / t + Dt, N is the number of ionsconsidered and d ¼ 3 is the dimensionality of the system.Combining the results of AIMD for diffusivity with the Nernst–

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Einstein equation recovers the conductivity of the system.Typically, due to computational costs, AIMD is performed withsmall time steps (Dt) at high temperatures and extrapolatedback to room temperature diffusivity. An Arrhenius relationshipD ¼ D0 exp(�Eab) is assumed for diffusivity where D0 and Ea arethe tted pre-exponential cofactor and activation energy,respectively, and b ¼ (kBT)

�1 is the inverse of thermal energy.For estimating ionic conductivity in ceramic suldes, AIMD

maintains a number of distinct advantages over NEB. The rstis ceramic suldes derive much of the high conductivity fromlithium congurational entropy.126 Hence, uncertainty in theionic congurations prior to and post migration is signicantand grows quickly as migration pathways progress from singleatom to multi-atom concerted migrations. Additionally, NEBonly reveals an energy barrier and not a pre-exponential cofactorfor determining diffusivity. Given the high conductivity natureof ceramic suldes, AIMD can be performed with smaller timesteps to reduce computational costs relative to higher imped-ance materials. Unlike NEB, AIMD can also be used to obtainstatistical data that illuminate the mechanisms of migration(occupation, attempt rate, radial distribution functions,etc.).125,127,128

AIMD has proven to be a remarkably accurate method forcomputationally determining bulk phase ion conductivity.Experimental measurements for LGPS placed the bulkconductivity at 12 mS cm�1 with an activation energy of 249meV (24 kJ mol�1).37 AIMD has predicted ionic conductivities onthe order 10–14 mS cm�1 with activation energies of 200–240meV.25,26,124 Moreover, AIMD has predicted several mechanisticaspects of ion diffusion that were later experimentallyobserved.25,71,129

5. Conclusion

Ceramic sulde solid electrolytes represent a promising direc-tion for the future of solid-state batteries. For commercialfeasibility, however, solid electrolytes must, at the very least,match liquid electrolytes in terms of both electrochemicalstability and ionic conductivity. To date, no solid electrolyte isknown that can simultaneously meet these demands intrinsi-cally. Ceramic sulde solid electrolytes have achieved remark-able ionic conductivities, even surpassing liquid electrolytes. Insome cases, ceramic suldes have also maintained comparablestability to their liquid counterparts but there exist manycomplicated reports and confusion in understanding. Majorchallenges remain in developing ceramic suldes to the levelneeded for commercialization. One of the most pressing chal-lenges is maintaining a wide voltage stability and interfacialstability window consistently.

Recent theoretical developments introduced in this reviewhave suggested that the discrepancies in the reported electro-chemical stabilities may not reect differences in the intrinsicmaterial-level stability but rather a difference in the mechan-ically induced metastability. In certain cases, by applyinga sufficiently rigid mechanical constraint, the stability windowof ceramic suldes can be opened from roughly 1.7–2.1 V withno constraint to nearly 0–5 V with a constraint. This behavior is

J. Mater. Chem. A

the result of the tendency of ceramic suldes to expand duringdecomposition. By applying a constraint that resists thesevolume expansions, the system can become metastable ina wide voltage range. This theoretical understanding alsoexplains why some high-temperature phases (e.g. Li7P3S11) areintrinsically unstable at room temperature but can be synthe-sized as a precipitate in a glassy matrix. That is, the glassymatrix serves as a mechanical constraint that impedes the decayof the high temperature phase when at room temperature.

This review paper has aimed to update the reader on thesedevelopments and provide a comprehensive introduction toimplementing mechanically induced metastable ceramicsuldes in solid-state batteries. A retrospective review of theexperimental history suggests that such mechanically inducedstability has been a key concept in ceramic suldes since therst glassy-ceramic suldes. Moreover, the importance of suchmechanical stabilization has grown by orders of magnitude asthe fraction of the ceramic material has increased to nearly pureor pure ceramic suldes. Computational methods weresurveyed for predicting the magnitude of mechanically inducedstability for a variety of constraining mechanisms. We envisionthat fully applying such a mechano-electrochemical effect iscritical to enabling the design of next generation solid electro-lytes with competitive performance for solid-state batteryapplications.

Conflicts of interest

There are no conicts to declare.

Acknowledgements

The work is supported by Dean's competitive fund for prom-ising scholarship at Harvard University and the GIC (GlobalInnovation Contest) of LG Chem, Ltd.

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