Numerical modelThe temporal evolution of the interfacial free energy in an inhomogeneous system is expressed as follows:32,33$$\frac{\partial \xi }{\partial t}=-{L}_{\sigma }^{\xi }\left(\frac{\partial {f}_{0}}{\partial \xi }+\frac{\partial {f}_{{{\rm{mech}}}}}{\partial \xi }-{\kappa }_{\xi }{\nabla }^{2}\xi \right),$$
(1)
where \({L}_{{{\rm{\sigma }}}}^{{{\rm{\xi }}}}\) is the interfacial mobility on the Li-metal phase, which is related to the interfacial velocity and the driving force according to the chemical rate theory34. In addition, f0 is an arbitrary double-well potential given by \({f}_{\!0}=A{\xi }^{2}{\left(1-\xi \right)}^{2}\), where the A is the barrier height for the LLZO/Li-metal interface with minima at ξ = 1, ξ = 0. Moreover, \({\kappa }_{{{\rm{\xi }}}}{\nabla }^{2}\xi\) is the gradient energy density that arises from spatial variations in the order parameters owing to chemical composition variations as well as structural changes at the interface, given by \({\kappa }_{{{\rm{\xi }}}}={\kappa }_{0}^{\xi }{\left[1+\omega \cos \left(\lambda \theta \right)\right]}^{2}\). θ is the angle between the reference axis and the normal direction of surface migration, \(\theta ={\tan }^{-1}\left(\frac{{{\rm{d}}}\xi /{{\rm{d}}}y}{{{\rm{d}}}\xi /{{\rm{d}}}x}\right)\), and λ is the mode of the anisotropic interfacial energy (λ = 4 for body-centered cubic Li metal)35. Based on previous first-principles calculations of the anisotropic surface energy of Li36, ω was set to 0.36 in this study. Finally, \({\kappa }_{0}^{\xi }\) is the gradient coefficient, defined as \(\kappa =\frac{3}{2}\gamma \delta\), where γ is the surface energy and δ is the interface thickness37. Previously reported phase-field simulations of ASSBs conventionally assumed a Li/SE interface thickness of 1 μm, a value prevalently employed in simulations of Li-metal batteries with liquid electrolytes38. However, this specific parameter has not been empirically or theoretically substantiated. In fact, this thickness is three orders of magnitude larger than those commonly applied in phase-field simulations in other areas of study, such as the solid–melt interface, where δ values typically range from 0.8 to 3 nm39,40.When the crystal lattice is continuous across the interface between two solid phases, and the dimensions of one of the lattices change during transformation, this creates a coherent finite-width interface (owing to the transformation of the strain tensor)40. To identify the domain where atomic disorder occurs at the Li/LLZO interface, we conducted first-principles simulations. The interface between Li(100) and the Zr-poor LLZO(100) face was chosen because its surface energy is the lowest41. The computational method is described in detail in Supplementary Note 3.The elastic energy density is expressed as$${f}_{{{\rm{mech}}}}=\frac{1}{2}\left({\varepsilon -\varepsilon }_{{{\rm{inel}}}}\right):\left(C:\left({\varepsilon -\varepsilon }_{{{\rm{inel}}}}\right)+2{\sigma }_{0}\right),$$
(2)
where C is the effective stiffness, and σ0 is the initial stress. Elastic strain εel is the difference between total strain ε and all inelastic strains εinel, including ε0 due to the volume expansion of Li metal during Li dendrite formation and plastic strain (εpl). The mathematical formulation of εpl is presented in Supplementary Note 4.In a previous study that employed phase-field simulations, the chemo-electro-mechanical properties of GBs were postulated by incorporating the corresponding properties of Li metal and SEs42. To refine the precision in characterizing the GB properties, we gleaned insights from recent studies using molecular dynamics (MD) and first principles specifically focused on GBs. These insights were then integrated into our overarching phase-field simulation model. Yu and Siegel43 investigated GBs in polycrystalline LLZO through MD and first-principles simulations; they discovered that the elastic modulus of GBs (CGB) is 50% lower than that observed in the SE grain interior (CSE). This notable difference was ascribed to an excess of free volume, which diminished the density, and an atomic structure with a bonding environment distinct from that of the bulk domain43. Hence, the effective stiffness of the system can be described by Eq. 3.$$C=\left\{\begin{array}{c}{C}_{{{\rm{Li}}}},\,\xi \, > \, 0.5+{{\rm{k}}}\\ {C}_{{{\rm{Li}}}}(0.5-{{\rm{k}}}-\xi )/2{{\rm{k}}}+{{{\rm{C}}}}_{{{\rm{SE}}}}(0.5+{{\rm{k}}}-\xi )/2{{\rm{k}}},\,0.5-k \, < \, \xi \, < \, 0.5+k\\ {C}_{{{\rm{GB}}}}, \, \xi \, < \, 0.5-k\end{array}\right.$$
(3)
Because the partial molar volume of lithium atoms is larger than that of lithium ions44, a Li-metal precipitate can generate substantial stress within the SE. The volume expansion of Li metal during the Li dendrite formation process can be expressed as ε0 = Kξ, where K is a constant diagonal matrix4. In addition to the interface thickness δ, another unrealistic assumption concerning the topology of GBs has prevailed, particularly regarding the thickness of the entire GB. Previously reported phase-field simulations assumed that LLZO GBs were thicker than 1 μm4; however, transmission electron microscopy45 and DFT results43 have indicated a GB thickness of only 2 nm. Given that this discrepancy is three orders of magnitude, such an assumption would lead to a significant overestimation of the stress development induced by the volume expansion of Li metal.The electrochemical reaction kinetics can be described using the Butler–Volmer equation,$$\frac{\partial \xi }{\partial t}=-{L}_{{{\rm{\eta }}}}{h}^{{\prime} }\left(\xi \right)\left[\exp \frac{\left(1-\alpha \right)F\eta }{{RT}}-{\check{c}}_{{{{\rm{Li}}}}^{+}}\exp \frac{-\alpha F\eta }{{RT}}\right],$$
(4)
where \({L}_{\eta }\) is the electrochemical reaction kinetic coefficient, and η is the surface overpotential incorporating the mechanical effect, i.e., η = φAnode – φSE – U, where φAnode is the applied electric potential at the Li-metal anode and U indicates the unstressed equilibrium potential, which was assumed to be zero for the reduction of lithium metal. In addition, \({\check{c}}_{{{{\rm{Li}}}}^{+}}\) is a dimensionless concentration of Li+ given by \({\check{c}}_{{{{\rm{Li}}}}^{+}}=\frac{{c}_{{{{\rm{Li}}}}^{+}}}{c0}\), where c0 is the concentration of mobile ions in LLZO. Finally, φ is the electrostatic potential.In a previous phase-field study, ion migration in the LLZO electrolyte was simulated based on a bulk Li-ion concentration of 42.2 mol∙L−1 for LLZO, which was calculated using an ideal LLZO supercell42. In principle, the bulk of the SE crystal lattice comprises four different constituents46: (i) immobile Li+, which does not participate in conduction; (ii) mobile Li+, activated by thermal or electrochemical energy from (i), denoted by cLi+; (iii) vacancies occupied by (ii) or accessible to Li+; and (iv) other immobile anions forming a background potential landscape. In inorganic SEs, anion mobility is negligible, and ions can be transported along GBs or inside grains. As only the mobile Li+ concentration is relevant to the redistribution of charges inside the SE, cLi+ serves as the central descriptor. Previous 7Li nuclear magnetic resonance47 and inductively coupled plasma optical emission spectroscopy studies48 revealed a mobile ion concentration of 5.8 mol∙L−1 for pure Li7-xLa3Zr2-xTaO12 (x = 1), representing only 14.0% of the total Li+ content in garnet LLZO47.Ion kinetics is also affected by the GB direction. A recent MD study on GB-dependent Li-ion transport behavior showed that Σ3(112) GBs exhibit relatively high Li-ion diffusivity, comparable to that of the bulk (DSE), which correlates with the smaller excess volume of this type of GBs47. Moreover, Li+ is much more immobile through Σ5(310), Σ5(210)49, and Σ1(110) GBs (DGB)27 than that in the vicinity of Σ3(112) GBs, and Li-ion conductivity at these GBs is an order of magnitude lower than DSE27,49. To evaluate the effect of the anisotropy of GBs on the mobility of ions (i), σGB and DGB are described as \({\sigma }_{{{\rm{GB}}},i}=\check{\sigma }\bullet {\sigma }_{{{\rm{SE}}}}\) and \({D}_{{{\rm{GB}}},i}=\check{D}\bullet {D}_{{{\rm{SE}}}}\), respectively, where \(\check{\sigma }\) and \(\check{D}\) are their corresponding ratios to the values for the bulk domain. Thus, Li+ transport in the system can be described as follows:$$\frac{\partial {\check{c}}_{{{{\rm{Li}}}}^{+}}}{\partial t}=\nabla \left[D\nabla {\check{c}}_{{{{\rm{Li}}}}^{+}}+\frac{D{\check{c}}_{{{{\rm{Li}}}}^{+}}}{{RT}}F\nabla \varphi \right]-\frac{{c}_{{{\rm{s}}}}}{{c}_{0}}\frac{\partial \xi }{\partial t},$$
(5)
$$D=\left\{\begin{array}{c}{{{\rm{D}}}}_{{{\rm{Li}}}},{\xi } \, > \, 0.5+{\mbox{k}}\\ {{{\rm{D}}}}_{{{\rm{Li}}}}(0.5{-}{\mbox{k}}{-}{\xi })/2{\mbox{k}}+{{{\rm{D}}}}_{{{\rm{GB}}},{{\rm{i}}}}(0.5+{\mbox{k}}{-}{\xi })/2{\mbox{k}},0.5{-}k \, < \, {\xi } \, < \, 0.5+k \\ {{{\rm{D}}}}_{{{\rm{GB}}}, {{\rm{i}}}},{\xi } \, < \, 0.5{-}k,\end{array}\right.$$
(6)
$$\sigma =\left\{\begin{array}{c}{{\sigma }}_{{{\rm{Li}}}},{\xi } \, > \, 0.5+{\mbox{k}}\\ {{\sigma }}_{{{\rm{Li}}}}(0.5{-}{\mbox{k}}{-}{\xi })/2{\mbox{k}}+{{\sigma }}_{{{\rm{GB}}},{{\rm{i}}}}(0.5+{\mbox{k}}{-}{\xi })/2{\mbox{k}},0.5{-}k \, < \, {\xi } \, < \, 0.5+k\\ {{\sigma }}_{{{\rm{GB}}},{{\rm{i}}}},{\xi } \, < \, 0.5{-}k.\end{array}\right.$$
(7)
The electrostatic potential distribution is described by a Poisson-type equation with a reaction-rate-related term (\({I}_{R}={nF}{c}_{{{\rm{s}}}}\frac{\partial \xi }{\partial t}\)) accounting for the temporal charge annihilation/generation at the anode surface:$$\nabla \cdot \left[\sigma \cdot \nabla \left(\varphi \left({{\boldsymbol{r}}},t\right)\right)\right]={I}_{{{\rm{R}}}}.$$
(8)
To study Li dendrite formation around these nanoscale GBs and interfacial nanovoids, we generated multiple GBs in an area of 200 nm × 300–400 nm, including the Li-metal anode and the SE having a rough surface with triangular protrusions (Fig. 2). The GB thickness was set to 2 nm. Previously reported atomic force microscopy results for the evaluation of the LLZO roughness indicated an Rq of 8–114 nm depending on the polishing method30,50,51. Thus, the peak-to-valley height (Rt) and roughness width (Ar) in this study were set to Rt = 50 nm and Ar = 200 nm to model the geometry of a typical defect. The yield stress of Li depends on temperature, decreasing by half within the range of 0–75 °C52. The evolution of Li dendrites at the Li metal/SE interface and the resultant short circuits are reportedly affected by the stack pressure and operational temperature (Supplementary Table 1). In light of existing research demonstrating that a stack pressure of 5.0 MPa is required for stable cycling at a current density of 1 mA∙cm–2 and 25 °C, the simulation was conducted under stack pressures of 1.0 and 5.0 MPa and a current density of 1 mA∙cm–2.Fig. 2Phase field simulation conditions: Model geometry (left side) and boundary conditions (right side) used to simulate Li dendrite formation.During the simulation, the continuous plastic deformation of the Li/SE contact first proceeded (Fig. 2i), followed by the phase-field simulation of Li dendrite formation (Fig. 2ii). In the plastic-flow simulation, constant stacking pressure was applied to the anode side. By applying the interfacial model after the plastic deformation of Li, the phase-field simulation was conducted to evaluate Li dendrite formation in the SE GBs near the Li/SE interface. The detailed boundary conditions are presented in Supplementary Note 5, and all parameters used in the model are summarized in Supplementary Table 2.Results of the numerical simulationThe Li/LLZO interfacial thickness (δ) was obtained by first-principles simulations, while the topological and chemo-electro-mechanical properties for GBs were taken from previous first-principles or observational studies27. Figure 3a,b show the magnitudes of the displacements of Li, La, Zr, and O atoms along the normal to the LLZO/Li-metal interfacial plane. The results indicate significant surface relaxation within the first 1.0 nm. Notably, the outermost Li atoms move toward LLZO by a maximum of 1.68 Å. This structural variation at the surface is expected to lead to mixing behaviors distinct from those observed in the bulk. For the LLZO/Li interfacial nanostructure, the inelastic strain induced by a change in the partial molar volume of Li is described as Kξ (Fig. 3c).Fig. 3: Atomic-level distortion at the Li(100)/LLZO(100) interface.a Schematic structural model adopted in our simulation of the LLZO/Li interface. The gray, blue, green, and red spheres represent Li, La, Zr, and O atoms, respectively. b Atomic displacements normal to the LLZO/Li interface (gray-shaded region) obtained through DFT calculations, using the atom coordinates before relaxation as a reference. Black and white circles represent Li in Li metal and LLZO, respectively, and blue, green, and red circles represent La, Zr, and O in LLZO, respectively. c y-component of the stress tensor near a Li dendrite at Σ1 after a simulation time (t) of 20 s, where the color scale from red to blue corresponds to stresses ranging from −5 to 5 MPa (inset).Accordingly, we simulated plastic flow at the Li/LLZO interface to obtain the interfacial model for the phase-field simulation. Figure 4a plots the morphology of the Li/SE interface after plastic deformation induced by static pressure in the absence of any charge/discharge process. To precisely simulate the non-linear deformation of Li, we employed a plasticity-hardening scheme based on previous experimental results revealing a yield stress (σyield) of 1.26 MPa and a hardening coefficient of 6.29 MPa20. Unlike the macroscopic creep model calibrated by cell-scale deformation data16 and studies that neglected surface effects in plastic deformation at the microstructure level16,17, our simulation results show a complex distribution of the intensity of plastic flow at the interface with surface irregularities (Fig. 4a).Fig. 4: Plastic deformation simulation results under different pressures.a Equivalent plastic deformation (\({\varepsilon }_{p}^{{eq}}\)), (b) first principal stress (\({\sigma }_{1}\)), (c) current density, (d) electronic potential, and (e) Li dendrite growth rate near GBs with \(\check{D}=\check{\sigma }=1\) at the Li/LLZO interface under pressures of (a-1, b-1, c-1, d-1) P = 1.5 MPa and (a-2, b-2, c-2, d-2) P = 5.0 MPa, along with the distributions of (b-3) \({\sigma }_{1}\) at the bottom edge of the Li metal and (c-3) the current density at the SE surface. In e, b-3, and c-3, blue and green lines represent pressures of 1.5 and 5.0 MPa, respectively.At the Li/SE interface at P = 5 MPa (Fig. 4a-2, b-2), Li and SE come into contact, in line with a previous observation of the pressure-dependent critical deposition current11. This result contrasts with that of the previous creep model, which assumed σyield to be 14 MPa, corresponding to compression test results for Li micropillars with a diameter of 9.45 μm15. This assumption led to a significant overestimation in the pressure required to form conformal contact at 15–40 MPa for a surface with Rq of 10–500 nm. In contrast, at P = 1.5 MPa, Li metal does not deform sufficiently to fill the interfacial voids (Fig. 4a-1, b-1), despite its stack pressure being higher than σyield. This is due to the heterogeneous pressure distribution, wherein stress is concentrated at the peak of the triangular protrusion in the SE, whereas Li metal in the valley domains of the rough SE surface experiences no compressive stress (Fig. 4b-3).The growth characteristics of Li dendrites are highly dependent on the applied stack pressure. At P = 1.5 MPa, the local current density at void edges in the interface can reach 9.2 mA∙cm–2 for an average cell current density of 1.0 mA∙cm–2 (Fig. 4c-1). This current concentration induced by interfacial voids is exacerbated by highly conductive dendrites, reaching as high as 71.6 mA∙cm–2 at the edge of the Li dendrite (Fig. 4c-3). Meanwhile, at P = 5 MPa, this current concentration decreases to 56.5 mA∙cm–2 at the Li/SE interface (Fig. 4c-2, 3). A heterogeneous Li/SE contact induces an uneven overpotential distribution with decreased η, specifically near the GBs (Fig. 4d-1), thereby increasing the dendrite growth rate (Fig. 4e). This finding confirms the possible enhanced formation of Li filaments in the presence of interfacial voids53. The dependency of the Li dendrite growth rate on the stack pressure corresponds with the results of previous experiments, where electrochemical cycling at P = 1 MPa caused the sudden formation of Li dendrites and a short circuit, even when the current density was as low as 0.75 mA∙cm–2, whereas increasing the stack pressure to 5 MPa permitted stable cycling at a current density of 1.0 mA∙cm–2 54.In conjunction with investigating the interfacial nanomorphology and substantiating the synergistic influence of interfacial nanovoids and the electrochemical properties of GBs, along with their anisotropy, we performed phase-field simulations for interfaces featuring Σ1 and Σ3 GBs. Figure 5 illustrates the morphology of Li dendrites in LLZO after the same evolution time with GBs having different anisotropy under a pressure condition of P = 1.5 MPa. In the Σ1 GB, the current is noticeably concentrated (white dashed circle, Fig. 5a-1) around the edges of the interfacial voids and Li dendrites, in contrast with the Σ3 GB (Fig. 5a-2).Fig. 5: Li dendrite growth and current density in LLZO over time.Distributions of (a) current density and (b) electric potential for the (a-1, b-1) Σ1 GB and (a-2, b-2) Σ3 GB, time development of (c) ∂ξ/∂t and (d) Li dendrite length, (e) distribution of first principal stress (σ1) around the Σ1 GB at t = 20 s, (f) trend in strain energy density, (g) x component of σ1 (σ1x) depending on the initial Li dendrite length for \(\check{C}\) = 0.5 (black circle) and 1.0 (black triangle) at t = 1 × 10−8 s, along with the condition for subcritical crack growth (blue line)58. In c, d, and f, the red, blue, and black lines represent the case of P = 1.5 MPa and Σ1 GB, Σ3 GB, and GB with \(\check{D}\) = \(\check{\sigma }\) = 1, respectively, and the dashed black line represents P = 5 MPa and Σ3 GB.The flow of current across the GB induces an abrupt potential drop (Fig. 5b-1) owing to its low ionic conductivity, which in turn induces a driving force for further dendrite growth (∂ξ/∂t) at the tips of dendrites (Fig. 5c).Consequently, the growth rate of Li dendrites at the Σ1 GB surpasses that at the Σ3 GB by 28.1% at a simulation time of 20 s (Fig. 5d). The distribution of the first principal stress (σ1) around the Li dendrite tip at the Σ1 GB (Fig. 5e) demonstrates that the GB below the Li dendrite tip is subjected to intensive tensile stress. GBs are recognized as pivotal nanostructural features contributing to mechanical degradation3. Many cycling studies have demonstrated that GBs serve as nucleation sites for lithium metal, resulting in crack propagation, and ultimately, the short-circuiting of cells3,8,9.Monroe and Newman hypothesized a stress-induced potential (μE) at the interface between solid polymer electrolytes (SPEs) and Li metal, and they posited that an increase in the stiffness of the SPE could prevent a Li dendrite from growing as μE increased at its tip55. However, two decades of research never revealed evidence of μE (i.e., that compression at the SPE/Li-metal interface generates a voltage, similar to that in the LLZO/LiCoO2 interface)56. Drawing on the μE concept, Barai et al.18 modeled this phenomenon because of the softening of GBs, indicated by a lower elastic modulus. However, in contrast with this expectation, previous MD simulations revealed that GBs exhibit brittle fracture behavior, characterized by the absence of dislocation activity ahead of the propagating crack tip, observed at a critical stress (σc) of 9.09 GPa at 300 K57. Complementing this atomic-scale theoretical analysis, a recent indentation study on polycrystalline LLZO crystals showed that when LLZO fractures, crack formation is preceded by subcritical crack growth at a much lower σc of 53 MPa58.With the growth of lithium dendrites, the strain energy density (Ws) consistently increases at an increasing rate in the Σ1 GB (Fig. 5f). To verify the dendrite length at which the tensile stress below the dendrite tip (σ1,tip) reaches σc, we conducted another phase-field simulation wherein we varied the initial Li dendrite length at GBs and \(\check{C}\). Contrary to Barai et al.’s assumption18, the elastic modulus of the GB being lower than that of the bulk domain of LLZO contributes to decreasing σ1,tip (Fig. 5g), thereby mitigating the risk of fracture. Despite the softening effect of GBs, σ1,tip reaches the σc for subcritical crack growth when the dendrite reaches a length approaches 1 μm (Fig. 5g), thus raising the necessity of preventing Li dendrite growth at GBs by quantitatively understanding the role of all the chemo-electro-mechanical properties of GBs.As is evident in Fig. 5d, Σ3 GBs with a stack pressure of 1.5 MPa fall short of effectively suppressing Li dendrite growth, thus necessitating the development of a combinatorial strategy involving a conformal Li/SE contact. However, a stack pressure of 5 MPa is sufficient to form a Li/SE contact, which agrees with previous electrochemical cycle test results (Supplementary Table 1). In the pragmatic deployment of ASSBs within multi-layer and multi-pouch cell stacks, the adoption of an elevated stack pressure introduces challenges because of the increased weight of cell modules required to maintain a consistent pressure while ensuring two-dimensional areal homogeneity59,60. However, the simulation results revealing the synergistic effect of interfacial nanovoids and the electrochemical properties of GBs highlight the tradeoff between stack pressure and Li dendrite formation at nanodefects in SEs. To resolve this dilemma, recent studies have utilized polymer-based interfacial ion-conductive layers, including poly(ethylene glycol) diacrylate/butyl acrylate/poly(vinylidene fluoride-co-hexafluoropropylene (σ at room temperature (σRT) = 0.18 mS∙cm−1 61), Lithium bis(trifluoromethanesulfonyl)imide/1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide/poly(methyl methacrylate) (σRT = 0.48 mS∙cm−1 62), (poly(ethylene glycol) dimethyl ether/trimethylolpropane trimethyllacrylate/1,6-hexanediol diacrylate (σRT = 0.48 mS∙cm−1 63), bis(fluorosulfonyl)imide doped polypropylene carbonate64, and perfluoropolyether (PFPE) (σRT = 0.5 mS∙cm−1 65). These layers exhibited notable cycling performance and prevented short circuits induced by Li dendrite formation. Although interlayers and surface coatings have proven effective in reducing the initial interfacial resistance stemming from interfacial voids by improving contact during cell assembly66, their long-term stability is limited to cycle under temperature elevated (≥ 45 °C) or low current densities (≤ 0.5 mA∙cm−1), particularly when employing interpolymers with insufficient ionic conductivity, such as poly(ethylene oxide) (PEO) with σRT = 0.01 mS∙cm−1 67,68,69. To confirm the synergetic effect of the GB properties and the interfacial layer, we conducted another simulation for the Li/interlayer/LLZO system, in which nanovoids at the Li/LLZO interface at P = 1.5 MPa were filled with interfacial polymers. For the ionic conductivity (σinter) and diffusivity (Dinter) of the interlayer in this simulation, we used values corresponding to those of PFPE-diol (σinter = 0.5 mS∙cm−1 65, Dinter = 3.0 × 10−7 cm2∙s−1 70) and PEO (σinter = 0.01 mS∙cm−1 69, Dinter = 1.0 × 10−8 cm2∙s−1 71).In the Σ3 GB with an interlayer having σinter = 0.5 mS∙cm−1 at a stack pressure of P = 1.5 MPa, the lithium dendrite growth rate decreases by 23.7% with respect to that observed at the Li/LLZO interface with the Σ3 GB having no interlayer. However, the application of an interlayer with σinter = 0.01 mS∙cm−1, corresponding to that of PEO, increases the overpotential (Figs. 6b-1,c). Consequently, owing to the relatively sluggish Li-ion conduction within the interfacial polymer compared to that in the LLZO bulk, ∂ξ/∂t exhibits a more discernible increase compared with that for the Li/LLZO interface with the Σ3 GB in the absence of an interpolymer. Therefore, increasing σinter can evidently mitigate lithium dendrite formation, highlighting the potential significance of applying an interlayer with σinter ≥ 0.5 mS∙cm−1 for the dynamics of deposition at the Li/LLZO interface with the Σ3 GB, particularly under a reduced stack pressure of 1.5 MPa.Fig. 6: Effect of interlayer at Li/LLZO interface with various GBs and pressures.a Comparison of ∂ξ/∂t for the Li/LLZO interface by varying the parameters for GB anisotropy, P, and σinter (*: σinter = 0.01 mS∙cm−1, **: σinter = 0.5 mS∙cm−1); shades of red refer to Σ1 GB, black and gray refer to Σ3 GB, filled bars represent P = 1.5 MPa, and open bars indicate P = 5.0 MPa; (b) electric potential at the Li-metal/interlayer/LLZO system with the (b-1,2) Σ3 GB and (b-3) Σ1 GB with (b-1) σinter = 0.01 mS∙cm−1 and (b-2,3) σinter = 0.5 mS∙cm−1; (b-4) electric potential distributions from the bottom of the LLZO at t = 1 μs; and (c) time development of Li dendrite growth. In c, the blue, red, and black lines represent the case of the GB with \(\check{D}\) = \(\check{\sigma }\) = 1, Σ1 GB, and Σ3 GB at P = 1.5 MPa; the gray line indicates the Σ3 GB with an interlayer (σinter = 0.5 mS∙cm-1) at P = 1.5 MPa; and the dashed black line represents the Σ3 GB at P = 5 MPa.In contrast, within the Σ1 GB at P = 1.5 MPa, a potential drop persists around the GBs, induced by the low ionic conductivity of the Σ1 GB and the co-presence of an interlayer with a slightly lower ionic conductivity than that of the LLZO bulk (Figs. 6b-3), leading to a larger driving force for Li dendrite growth (∂ξ/∂t) than that observed in the Σ1 GB without an interlayer at P = 1.5 MPa (Fig. 6c). This result indicates that the weak ion mobility of the Σ1 GB accelerates Li dendrite formation, even with an interlayer with σinter = 0.5 mS∙cm−1. It also suggests the necessity of a higher stack pressure of P = 5 MPa to suppress the dendrite growth rate to the same extent as that in the Σ3 GB with an interlayer having σinter = 0.5 mS∙cm−1 at P = 1.5 MPa (Fig. 6a).
Chemo-electro-mechanical phase-field simulation of interfacial nanodefects and nanovoids in solid-state batteries
