Energy and power densities of Li-garnet SSBs
To assess achievable energy and power density of Li-garnet SSBs, 1D-isothermal lithium-ion battery model with single-ion conducting solid electrolyte developed by COMSOL Multiphysics47,48 was applied to simulate their electrochemical performance during discharge. All equations governing the simulation can be found in the Supporting Information. The schematic of the model is depicted in Figure S1. Parameters used for simulation are summarized in Table S2. The following compositions of LCO-LLZO solid-state cathodes were modeled: 70 vol.% of LCO - 30 vol.% of LLZO, 60 vol.% of LCO - 40 vol.% of LLZO, 50 vol.% of LCO - 50 vol.% of LLZO and 40 vol.% of LCO - 60 vol.% of LLZO. Of note, in these simulations, we considered that no interfacial resistance is present at both LLZO/Li and LLZO/LCO interfaces, and no porosity was assumed to exist in the solid-state cathodes. Clearly, these conditions are oversimplified, but they enable to assess the highest reachable limits of energy and the power density of Li/LLZO/LCO SSBs. The simulation data obtained for the exemplary systems considering LLZO/Li (0.1 Ω cm2)49 and LLZO/LCO (50 Ω cm2)50 interfacial resistances, as well as the porosity in LCO/LLZO solid-state cathode, can be found in the Supporting Information.
Simulations were performed varying (i) the areal capacity of the cathode layer (0.5-5 mAh cm-2), (ii) the thickness of LLZO dense layer separating the cathode and Li anode layers (0.1- 90 µm), (iii) the temperature (30°C and 70°C), and (iv) the C-rate (0.5C-5C). Examples of the resulting voltage profiles simulated at different C-rates, cathode areal capacity of 4 mAh cm-2, and LLZO thicknesses of 30 µm are shown in Figures 2a and 2b (see Supporting Information, Figures S2-S25, for a complete set of simulated voltage profiles). The achievable energy and power densities were calculated from simulated voltage profiles at a specific C-rate and cathode mass loadings (areal capacities), average cell voltages, and total weight or volume of all cell components assuming a combination of 40 cathode/electrolyte/anode layers (see Figure S26 for details). Of note, the cell volume is calculated in the fully discharged state in which Li-garnet SSBs are to be assembled in practice. All parameters contributing to the mass and volume of the cell, such as the thickness of Cu and Al foils and the thickness of pouch Al foil are summarized in Table S3. Thickness of the Li metal anode was fixed, corresponding to 20% of the cathode areal capacity. For instance, Li anode thickness was 1, 3, and 5 µm for cathodic areal capacities of 1, 3, and 5 mAh cm-2, accordingly. It should also be pointed out that efficient operation of Li-garnet SSBs with high areal capacities of > 1mAh cm-2 can be practically achieved only at stack pressures that enable to mitigate the formation of voids at the LLZO/Li interface.19–22 As a result, the cell design requires integrating additional inactive components, which severely limits its energy density. Considering the lack of data on the optimal pressure at given current densities and the practical implementation of this requirement, we excluded this parameter from the energy and power density calculations.
Figures 2. (a, b) Simulated voltage profiles of Li/LLZO/LCO all-solid-state battery at different C rates (0.001C, 0.2C, 0.5C, 1C, 2C, and 5C) and temperatures (30°C and 70°C), using cathode constant areal capacity of 4 mAh cm-2 and LLZO thickness of 30 µm. (c, d) Gravimetric and volumetric Ragone plots of Li/LLZO/LCO solid-state battery simulated using cathode areal capacities of 0.5, 1, 2, 3, 4, and 5 mAh cm-2 at temperatures of 30°C and 70°C and constant LLZO thickness of 30 µm. The simulations were performed using LCO cathode that is composed of 70 vol.% of LCO and 30 vol.% of LLZO.
Next, we analyzed changes of the energy density of the studied solid-state system at gravimetric and volumetric power densities of 200 W kg-1 and 600 W L-1, corresponding to ca. 1h of a full discharge. The data derived from Figures 2c, d and Figures S27-S28 were plotted in the form of 3D maps governing the relationship between areal capacities of LCO cathodes, LLZO thicknesses, and the energy density (Figure 3). Additionally, state-of-the-art values for conventional LIBs are shown in Figure 3 as mesh area, where upper and lowest levels correspond to the energy densities of 18650 Panasonic (231 Wh kg-1, 636Wh L-1)41 and Samsung (180 Wh kg-1, 497 Wh L-1)42 LIBs at the gravimetric and volumetric power densities of 200 W kg-1 and 600 W L-1, accordingly. Considering 18650 Samsung battery as a reference system with the minimum necessary electrochemical performance, we identify LLZO thicknesses and areal capacities of Li-garnet SSBs required to match its energy density at 200 W kg-1 and 600 W L-1. Such values were named break-even thickness and areal capacities, following analogy to the break-even values in economics, representing a set of parameters at which total revenue and total expenses are equal. The break-even areal capacity-thicknesses curves for 30°C and 70°C are indicated in white. As follows from Figure 3a, at 30°C, gravimetric break-even LLZO thickness ranges from 5.5 to 59.5 µm for 1 mAh cm-2 and 5 mA cm-2, accordingly. However, in the case of 70°C, higher LLZO thicknesses of 5.8 to 86.9 µm (1 mAh cm-2 – 5 mA cm-2) can be used in order to reach the same energy density of 180 Wh kg-1 at 200 W kg-1. The volumetric break-even LLZO thicknesses were very similar at both temperatures: 15.8 – 66.2 µm and 15.7 – 67.5 µm for 0.5 – 1.5 mA cm-2 at 30 and 70°C, accordingly.
Notably, considering the employing of a 50 µm LLZO solid-electrolyte membrane, the gravimetric break-even cathode areal capacity equals 3.55, and 3.15 mAh cm-2 for the cells at 30°C and 70°C. Volumetric areal capacity of 1.2 mAh cm-2 was found to be the break-even value for both temperatures of 30°C and 70°C. Importantly, our calculations show that an increase of the Li anode excess has a moderate impact on the gravimetric energy density of Li-garnet SSBs (Figure S29a, b). For instance, when Li anode thickness was enlarged by a factor of 10, the gravimetric break-even LLZO thickness at a cathode areal capacity of 1.5 mAh cm–2 shifted only from 16.8 to 14.9 µm and from 16.8 to 15.4 µm at 30°C and 70°C, accordingly. Correspondingly, at a fixed cathode areal capacity of 1.5 mAh cm-2 and LLZO thickness of 15 µm, the gravimetric energy density decreases from 184.4 Wh kg-1 and 185.8 Wh kg-1 to only 180.2 Wh kg-1 and 181.2 Wh kg-1 (at 30°C and 70°C). With respect to the volumetric energy density, the picture is the opposite. Ten times higher Li anode amount changes significantly volumetric break-even thicknesses at a cathode areal capacity of 1.5 mAh cm–2, from 66.2 µm to 53.2 µm and 67.5 µm to 54.3 µm (at 30°C and 70°C, see Figure S29c, d). As a result, a substantial reduction of the volumetric energy density was found in the case of employing a 10-times thicker Li anode (at a fixed cathode areal capacity of 1.5 mAh cm-2 and LLZO thickness of 15 µm): from 939Wh L-1 to 774 Wh L-1 for 30°C and from 942 Wh L-1 to 777 Wh L-1 for 70°C.
Subsequently, we analyzed break-even dependences of cathode areal capacity and LLZO thickness for Li/LLZO/LCO solid-state battery on the vol. % of LLZO in LCO solid-state cathode, which are summarized in Figure 4. Figure 4a evidences that upon an increase of LLZO content in a composite cathode, higher areal capacity and lower LLZO solid electrolyte thickness should be used to attain the same energy densities of 180 Wh kg-1 and 497 Wh L-1 at gravimetric and volumetric power densities of 200 W kg-1 and 600 W L-1. Interestingly, assuming that the Li-garnet SSBs can be fabricated with 50 µm thick LLZO membrane, 50 vol.% of LLZO fraction in LCO cathode results in gravimetric energy densities not matching the energy density of a conventional Li-ion battery even at very high LCO areal capacity of 4 mAh cm-2, requiring LLZO thickness of < 40 µm. In the case of 60 vol.%, the maximal allowed LLZO thickness at LCO areal capacity of 4 mAh cm-2 equals 2 µm at 30°C, which can be slightly increased to 7 µm at a higher temperature of 70°C.
With regard to the volumetric performance, already at high LLZO loading of 60 vol. %, relatively thick LLZO membranes of 50 ‒ 90 µm at LCO areal capacities of 1.6 – 2.8 mAh cm-2 can be employed to reach volumetric energy density of 497 Wh L-1 at 600 Wh L-1 (30°C). Based on obtained results, below, we summarize recommended areal capacities of LLZO-LCO cathode at LLZO thickness of 10, 20, 30, and 50 µm and LLZO volumetric content of 30, 40, 50, 60% and temperatures of 30°C or 70°C (Table 1).
Table 1
Recommended areal capacities of LLZO-LCO cathode at given LLZO thickness and vol. % of LLZO in LCO solid-state cathode. Sign "-" means that at given temperature, LLZO thickness and LLZO content in the cathode, the Li-garnet SSB possess lower energy density values than the state-of-the-art value of 180 Wh kg-1 at a power density of 200 W kg-1.
T, °C
|
Vol.% of LLZO in LCO cathode
|
Thickness of LLZO, µm
|
Gravimetric break-even areal capacity, mAh cm-2
|
Volumetric break-even areal capacity, mAh cm-2
|
30°C
|
30%
|
20 µm
|
1.70
|
0.61
|
40 µm
|
2.84
|
1.03
|
70°C
|
30%
|
20 µm
|
1.66
|
0.61
|
40 µm
|
2.64
|
1.03
|
30°C
|
40%
|
20 µm
|
2.04
|
0.67
|
40 µm
|
3.67
|
1.1
|
70°C
|
40%
|
20 µm
|
1.98
|
0.67
|
40 µm
|
3.18
|
1.1
|
30°C
|
50%
|
20 µm
|
2.9
|
0.76
|
40 µm
|
-
|
1.22
|
70°C
|
50%
|
20 µm
|
2.72
|
0.76
|
40 µm
|
4.39
|
1.21
|
30°C
|
60%
|
20 µm
|
-
|
0.91
|
40 µm
|
-
|
1.43
|
70°C
|
60%
|
20 µm
|
-
|
0.91
|
40 µm
|
-
|
1.42
|
Practical challenges towards the fabrication of Li-garnet all-solid-state batteries
Apart from the importance of the above-discussed findings, which highlight the viability of solely garnet SSBs in respect of achievable energy and power densities, adopting the LLZO into the battery cell structure is challenging and requires new approaches in the fabrication of solid-state cathodes and cell design. The latter are primarily related to (i) the intrinsic volume changes of Li anode upon Li plating and stripping and (ii) the chemical reaction of cathode materials with LLZO, yielding non-Li ion conductance phases. These two factors were fully excluded from the simulations.
The volume change of Li is becoming a major challenge when it comes to the deposition of high areal capacities of 1-5 mAh cm-2 that correspond to 5-25 µm of Li. This means that, on the one hand, cell design should account for the dynamic expansion of Li anode upon charge. On the other hand, upon discharge, i.e., upon stripping of Li, stack pressure should be applied to the LLZO/Li interface to prevent the formation of cavities, which may arise from the insufficient rate of Li+ diffusion and applied pressure to replenish the Li being dissolved into LLZO.21 Contrarily, voids can accumulate at the LLZO/Li interface leading to increased local current density and the formation of Li dendrites upon cycling. A rough estimate for the required stack pressure range, provided by Kasemchainan et al.,51 is ca. 10 MPa, allowing to achieve stable cycling at current densities exceeding 1 mA cm–2. The external stack pressure is, however, a double-edged sword. Although it seems necessary to inhibit void formation during lithium stripping, some theoretical,20,52 and experimental reports53 indicated that stack pressure could lead to quicker cell failure due to increased mechanical stress. Therefore, research is ongoing on finding optimum pressure for Li stripping and the development of cell design enabling to accommodate the dynamical changes in lithium thickness. It should be noted, however, that one possible solution to avoid the Li volume change issue is to use a scaffold-type LLZO, since no external pressure is needed in this case. Thus, Li metal can be plated over the entire surface of the scaffold structure and stored in the pores. As a result, there is no dynamic change in the volume of the cell upon plaiting. Upon stripping, the voids are not forming due to the high surface area of the LLZO/Li interface. Another essential advantage of LLZO scaffolds is the possibility to increase applied current density upon Li plating/stripping up to 10 mA cm-2 without the formation of Li dendrites. For instance, as indicated by Wachsmann et al.,54 the current density of 10 mA cm-2 for porous LLZO configuration corresponds to the current density of 0.25 mA cm-2 for planar configuration, considering that the porous solid-state electrolyte might have up to ~ 40x higher surface area compared to the planar one.
As to the compatibility of LLZO with current cathode chemistries, this issue is mainly caused by the high-temperature co-sintering between LLZO and cathode active materials. For instance, upon heat-treatment of LLZO and LiCoO2 (LCO) cathode above 700°C, insulating decomposition reaction products were reported.48 High-voltage spinel cathodes (Li2NiMn3O8, Li2FeMn3O8, and LiCoMnO4) start to react with LLZO even at temperatures as low as 500°C.55 LiFePO4 (LFP) cathodes are difficult, if not impossible, to co-sinter with LLZO, as LFP phase decomposition already occurs above 400°C.24 To overcome this compatibility issue, a new design was recently proposed based on wet-chemical infiltration of the cathode active material precursors into porous LLZO solid-state electrolyte, serving as an as-sintered scaffold with their subsequent annealing at lower temperatures.24 Alternatively, as-synthesized cathode material can be infiltrated into LLZO scaffold, as was demonstrated for LiNi0.6Mn0.2Co0.2O2 (NMC622) particles by Doeff et al.56 Although both methods are interesting, they result in relatively low amounts of active materials, leading to low cathode areal capacities.