Abstract

Next-generation lithium ion batteries are expected to demonstrate superior energy and power density with longer cycle life for successful electrification of the automobile, aviation, and marine industries. Adoption of lithium metal anodes with solid electrolytes can help to achieve that goal given that the dendrite-related issues are solved eventually. Another possibility is to use Ni-rich high-capacity NMC cathode materials with liquid and/or solid electrolytes, which presently experiences rapid capacity fade while charged to higher voltages. Several mechanical and chemical degradation mechanisms are active within these NMC-based cathode particles. Recent experimental research activities attempted to correlate the mechanical damage with the capacity fade experienced by Ni-rich LiNixMnyCozO2 (x+y+z = 1) (NMC) cathodes. A computational framework is developed in this study capable of quantifying the evolution of inter primary particle and cathode/electrolyte interfacial fracture experienced by the poly- and single-crystalline NMC cathodes during charge/discharge operation. Influences of mechanical degradation on the overall cell capacity, while operating with liquid and/or solid electrolytes, are successfully characterized. Decreasing the size of the cathode primary particles, or the size of the single-crystalline cathodes, can mitigate the overall mechanical degradation, and subsequent capacity fade, experienced by NMC cathodes. The developed theoretical methodology can help the engineers and scientists to better understand the mechanical degradation mechanism prevalent in Ni-rich NMC cathodes and build superior lithium ion-based energy storage devices for the application in next-generation devices.

Introduction

Lithium ion batteries are extensively used in portable electronics and electric vehicle industries due to their superior energy density and long cycle life [1]. Further improvement in the energy and power density of lithium ion batteries is needed to mitigate the range anxiety experienced by the electric vehicles, and successful electrification of the aviation and the marine industries [2]. Two different pathways have been adopted to amplify the energy density of existing lithium ion-based energy storage devices:

  • Replacement of graphite anodes with lithium metal [3]

  • Increase the capacity of LiNixMnyCozO2 (x + y + z = 1) cathodes by increasing the amount of Ni [4,5]

Adoption of lithium metal anodes is heavily hindered by the formation of dendrites during charge at higher rates [6]. Solid electrolytes are expected to stabilize the deposition of lithium through the generation of a mechanical stress field around the dendritic protrusion [7,8]. However, the presence of inherent voids and defects within the ceramic-based solid electrolytes can act as nucleation points for the formation of detrimental lithium dendrites [9,10]. Research activities are still underway to stabilize the deposition of lithium with both liquid and solid electrolytes [6,11]. Conversely, it is possible to improve the capacity, and subsequently energy density, of lithium ion batteries by increasing the amount of Ni within the NMC-based cathode particles while operating within the same potential window [12]. Accordingly, NMC811 with 80% Ni, NMC900505 with 90% Ni, and LiNiO2 (or LNO) with 100% Ni are being studied extensively for use with both liquid and solid electrolytes [13,14]. Various doping and coating strategies are also being investigated to obtain stable cycle life from these Ni-rich NMC cathode materials with liquid as well as solid electrolytes [1517]. Adoption of high-capacity cathode materials are much closer to the industrial deployment because of the possibility of “drop in replacement” compared to lithium metal anodes, which may require major changes to the battery fabrication facilities.

The largest bottleneck preventing the widespread integration of Ni-rich cathodes within commercial lithium ion batteries containing liquid electrolytes is the rapid capacity fade experienced by them during long-term cycling under high voltage (upper cutoff around 4.2 V or 4.3 V) [18,19]. Several detrimental aspects within the cathode are assumed to be behind this degradation in cell capacity:

  • Evolution of spanning cracks within the cathode secondary particles that can possibly result in electrochemical isolation of segments of the secondary particle and eventual capacity fade [1921].

  • Release of oxygen from the electrochemically active surface of the cathode, which leads to surface reconstruction and formation of a resistive spinel/rocksalt layer at the expense of the desired layered one [22,23].

  • Due to the similar size of the Li and Ni ions, Li–Ni mixing can occur in Ni-rich cathodes that can possibly slow down the diffusion of lithium ions within active materials [24].

Various coating and doping strategies have already been implemented that can possibly help to stabilize the oxygen environment and minimize the formation of the resistive rocksalt layer [25,26]. Doping Ni-rich cathodes with multivalent cations (Mo, V, etc.) can possibly help to stabilize the layered phase through the “pillaring” mechanism even under extremely high levels of delithiation [16,27]. Extensive research activities are being conducted to elucidate the evolution of microcracks within cathode active materials through both computational and experimental means [2831]. Intrasecondary cathode particle cracking can occur through two different mechanisms:

  • Inter primary particle cracks evolve due to anisotropic expansion of the cathode primary particles with different orientations, which leads to strain accumulation at the grain boundaries [20,32,33].

  • Intra primary particle cracks are also observed during operation at very high voltages, which can possibly be attributed to the nucleation of oxygen vacancies and/or dislocation-induced defects within the bulk of the lattice structure [19,34].

Majority of the research activities focus on the formation of these cracks or possibly suggest ideas to mitigate them [3537]. However, very little experimental and computational research activities are underway to elucidate the electrochemical impact of these mechanical degradations on the overall cell capacity and performance [3840].

Ceramic-based (Li7La3Zr2O12 (LLZO), Li2S-P2S5 (LPS), Li3YCl6 (LYC)) and polymer-based (polyethylene oxide (PEO), polyacrylonitrile (PAN)) solid-state electrolytes are most commonly investigated for the application with lithium metal anodes [41]. Since the energy density and the safety of lithium ion batteries can possibly be improved by replacing liquid electrolytes with their solid-state counterparts, behavior of NMC cathodes in conjunction with these ceramic and polymer type electrolytes are also being studied thoroughly [42]. Several mechanical and electrochemical issues prevalent at the NMC cathode/solid electrolyte interface that can possibly lead to deterioration in cell performance are listed as follows [43]:

  • Mechanical detachment between the cathode and the solid electrolytes at their interface and loss of electrochemically active surface area [44].

  • Chemical interdiffusion of transition metal ions from cathode to the solid electrolyte, and vice-versa, and formation of resistive interphase layers, which can subsequently lead to performance decay [45,46].

  • Chemical decomposition of the polymer or the ceramic electrolyte itself when they come in contact with the delithiated high-voltage cathode particles, which can again cause enhancement in cell impedance [47].

The application of stable interphase layers are capable of minimizing the chemical degradations, but cannot necessarily mitigate the mechanical delamination [48]. Several experimental research activities attempted to characterize the impact of mechanical degradation on the performance decay experienced by the solid-state lithium ion cells [39,44,49]. Majority of the computational modeling activities focused mostly on the evolution of mechanical stress at the cathode/solid electrolyte interface [5052], whereas only a few studied the evolution of microcracks and their potential impact on cell performance [35,53]. It is worth noting that inter primary particle cracking within cathode secondary particles is possible while operating with solid electrolytes. Hence, NMC cathode particles are subjected to two types of mechanical degradations [43]:

  • Cathode/solid electrolyte interfacial delamination, which causes a loss in electrochemically active surface area.

  • Evolution of inter primary particle cracks within the polycrystalline cathodes, which can result in enhanced diffusion length and increased mass transport limitations.

Unlike liquid electrolytes, because of their inherent rigidity, solid electrolytes are not capable of flowing into the surface-connected cracks that evolve within the polycrystalline cathode secondary particles [54]. Subsequently, a general consensus is to use single-crystalline cathodes while operating with solid electrolytes, which can possibly minimize the inter primary particle cracking-induced increase in mass transfer resistance and subsequently mechanical degradation-induced capacity fade [39,55]. Till date, few computational methodology attempted to characterize the inter primary particle degradation and cathode/electrolyte interfacial delamination experienced by the NMC cathodes and their impact on overall cell performance, while operating with different ceramic- and polymer-based solid electrolytes [56,57].

In the present research, an already existing lattice spring-based computational framework [53] is adapted to study the inter primary particle detachment and interfacial delamination in both liquid and solid electrolytes, and their influence on the overall cell performance is studied. Inter primary particle cracks within the polycrystalline cathodes form because of the anisotropic volume expansion/contraction of the cathode primary particles due to a mismatch in their crystal orientation [28]. The flow of liquid electrolytes through the surface-connected inter primary particle cracks is modeled through the implementation of Butler–Volmer reaction kinetics not only at the electrode/electrolyte interface but also within the nodes adjacent to the surface-connected cracks [38,39]. Shrinkage of the cathode particles during delithiation results in tensile stress at the NMC cathode/solid electrolyte interface, which is modeled appropriately along with the possibility of the evolution of interfacial delamination and subsequent loss of electrochemically active surface area [43]. How the interparticle and interfacial mechanical degradations manifest itself within poly- and single-crystalline NMC cathode particles during cell operation will be discussed. Influence of the primary particle size on the mechanical deteriorations and impact of the size of the single-crystalline cathodes on the overall cell performance will also be elucidated using computational means [48,55].

Methodology

Investigation of the mechanical degradation experienced by NMC cathode particles while operating with liquid as well as solid electrolytes is the main aim of this article [38,44]. Impact of this cathode cracking on the capacity and performance demonstrated by the electrochemical cell is also studied [29,31]. A multiscale computational methodology, developed as part of an earlier study [53], is adapted to predict the extent of mechanical degradation that can occur within NMC cathodes during charge/discharge cycling. A decrease in cathode volume during the delithiation process leads to the evolution of tensile stress at the inter primary particle domains as well as cathode/solid electrolyte interface [49]. Excess strain energy is released through the evolution of microcracks within regions where the applied stress and/or strain exceeds the fracture threshold [58]. This stress release mechanism leads to fracture at the cathode inter primary particle domains, as well as the formation of microcracks in the cathode/solid electrolyte interface [56].

Formation and propagation of a crack within the cathode inter primary particle boundaries result in the loss of physical contact between two adjacent points, which also hinders the diffusion of lithium as well as blocks the migration of electrons [38]. In a fractured cathode particle, atoms and electrons take a longer pathway to travel from one point to the other, which effectively reduces the diffusion coefficient and electronic conductivity of the bulk material [59]. This increase in transport resistance is manifested as mass transport limitation within the cathode that results in capacity fade while operating with both liquid and solid electrolytes [12]. Inflow of liquid electrolytes into the bulk of the cathode through some of these surface-connected cracks is possible, which is also successfully captured within the developed computational framework [38].

Due to its inherent stiffness, solid electrolytes are incapable of maintaining complete contact with the cathode materials [60]. Delithiation of cathode particles during charge leads to a decrease in the volume, which induces tensile stress and eventually fracture at the cathode/solid electrolyte interface [53]. This particular mode of interfacial delamination between cathode and solid electrolytes is also simulated in the developed computational framework. The loss of contact between electrode and electrolyte leads to a decrease in the electrochemically active surface area and subsequently results in an enhanced charge transfer resistance and capacity fade [48].

To estimate the extent of mechanical degradation within the NMC cathode particles during the charge–discharge process, the following set of governing equations are solved at different domains, along with appropriate boundary conditions [50,61,62]:

  • Charge balance at the cathode and electrolyte (see Eqs. (4)—(8) in Table 1)

  • Mass balance within the cathode (see Eqs. (9)—(11) in Table 1)

  • Force balance at both cathode and electrolyte (see Eqs. (12)—(15) in Table 1)

Table 1

List of equations and boundary conditions solved in the continuum model

Governing equation or boundary conditionEquation applied in the electrolyteEquation applied in the cathode regionEq. no.
Charge transport equation for current distribution(κElecϕElec)=0(κCathodeϕCathode)=0(4)
Current boundary condition on the top and bottom of domainκElecϕElec|y=Topy=Bottom=0κCathodeϕCathode|y=Topy=Bottom=0(5)
Current boundary condition at the left (electrolyte) and right (cathode) boundaryκElecϕElec|x=0=IappκCathodeϕCathode|x=Lx=Iapp(6)
Current boundary condition at cathode/electrolyte interfaceκElecϕElec|x=Intf.=iBV (see Eq. (1))κCathodeϕCathode|x=Intf.=iBV (see Eq. (1))(7)
Lithium potentialϕElec|x=0 = 0 corresponding to the electrolyte domain only(8)
Diffusion equation for lithium atomsNo diffusion of Li+ within the electrolyte due to high lithium salt diffusivity in liquid electrolytes(DCathodecLi)=0(9)
Boundary condition for Li diffusion at cathode/electrolyte interfaceNot applicableDCathodecLi|x=Intf.=iBV/F (see Eq. (1))(10)
Boundary condition for Li diffusion at right cathode/current collector boundaryNot applicableDCathodecLi|x=Lx=0(11)
Equilibrium equation for mechanical forceσElec¯¯=0σCathode¯¯=0(12)
Displacement boundary condition at the left and right sideux(x = 0, y) = 0ux(x=Lx,y)=0
uy(x=Lx,y=(Ly/2))=0
(13)
Displacement boundary condition at Li/solid-state-electrolyte interfaceContinuity in force and displacement has been assumed at the cathode/electrolyte interface.
Force displacement constitutive relation for lattice springs{fafs}=[ka00ks]{uaus}(14)
Estimation of lattice spring constants from elastic modulika=YCathode/Elec(1+νCathode/Elec)thk23(1νCathode/Elec2)
ks=YCathode/Elec(13νCathode/Elec)thk23(1νCathode/Elec2)
(15)
Governing equation or boundary conditionEquation applied in the electrolyteEquation applied in the cathode regionEq. no.
Charge transport equation for current distribution(κElecϕElec)=0(κCathodeϕCathode)=0(4)
Current boundary condition on the top and bottom of domainκElecϕElec|y=Topy=Bottom=0κCathodeϕCathode|y=Topy=Bottom=0(5)
Current boundary condition at the left (electrolyte) and right (cathode) boundaryκElecϕElec|x=0=IappκCathodeϕCathode|x=Lx=Iapp(6)
Current boundary condition at cathode/electrolyte interfaceκElecϕElec|x=Intf.=iBV (see Eq. (1))κCathodeϕCathode|x=Intf.=iBV (see Eq. (1))(7)
Lithium potentialϕElec|x=0 = 0 corresponding to the electrolyte domain only(8)
Diffusion equation for lithium atomsNo diffusion of Li+ within the electrolyte due to high lithium salt diffusivity in liquid electrolytes(DCathodecLi)=0(9)
Boundary condition for Li diffusion at cathode/electrolyte interfaceNot applicableDCathodecLi|x=Intf.=iBV/F (see Eq. (1))(10)
Boundary condition for Li diffusion at right cathode/current collector boundaryNot applicableDCathodecLi|x=Lx=0(11)
Equilibrium equation for mechanical forceσElec¯¯=0σCathode¯¯=0(12)
Displacement boundary condition at the left and right sideux(x = 0, y) = 0ux(x=Lx,y)=0
uy(x=Lx,y=(Ly/2))=0
(13)
Displacement boundary condition at Li/solid-state-electrolyte interfaceContinuity in force and displacement has been assumed at the cathode/electrolyte interface.
Force displacement constitutive relation for lattice springs{fafs}=[ka00ks]{uaus}(14)
Estimation of lattice spring constants from elastic modulika=YCathode/Elec(1+νCathode/Elec)thk23(1νCathode/Elec2)
ks=YCathode/Elec(13νCathode/Elec)thk23(1νCathode/Elec2)
(15)

Note: These equations have been solved in both the electrolyte and the cathode domains.

One representative computational cathode/electrolyte microstructure adopted in the present analysis is shown in Fig. 1(a). The mass and charge balance equations are solved using a control volume approach, whereas force balance relations are satisfied using a lattice spring methodology [58,59,61]. Note that the diffusion coefficient that controls the mass transport process within the cathode active particles is assumed to be isotropic without invoking any crystal orientation-dependent anisotropy. The current density at the cathode/solid electrolyte interface is given by the Butler–Volmer equation (iBV), which is also used as the boundary condition in Eqs. (7) and (10) (see Table 1) [7,8,61]:
iBV=i0[exp(αaFηRT)exp(αcFηRT)]
(1)
where i0 is the exchange current density; αa and αc are the anodic and cathodic transfer coefficients, respectively; and F, R, and T are Faraday’s constant, the universal gas constant, and the absolute temperature, respectively. The surface overpotential, η, for this cathode–electrolyte interface is given by η = ϕsϕeU, where ϕs and ϕe are the potentials in the cathode and solid electrolyte phases, and U indicates the open-circuit potential within the cathode. The exchange current density, i0, is given by the following expression [63]:
i0=i0,ref(cs,maxcscs,max)αc(cscs,max)αa,wherei0,ref=Fkref(ce)αccs,max
(2)
where kref indicates the reference rate of reaction, ce denotes the concentration of lithium salt within the electrolyte adjacent to the electrode, cs indicates lithium concentration within the cathode, and cs,max denotes the maximum amount of lithium that can be inserted into the cathode material. To simplify the computational model, a constant magnitude of the reference exchange current density, i0,ref, is assumed for all liquid and solid electrolytes.
Fig. 1
Demonstration of cathode interparticle degradation in liquid electrolytes. (a) Initial cathode electrolyte microstructure without any degradation. Red, blue, and green colors indicate cathode primary particles with different crystallographic orientation. The white cross symbols at the cathode/electrolyte interface indicates electrochemically active surface. (b) The same cathode electrolyte microstructure after initial cycles with interparticle degradation, which is denoted by the black cross symbols. Inflow of electrolyte enhances the electrochemically active surface area shown by the white cross at the boundary of the primary particles. (c) Cathode/electrolyte microstructures after multiple cycles where not only an increase in electroactive area is observed but also the evolution of highly resistive electrochemically inactive blocked domains occurs due to the loss of electronic contact. (d) Voltage versus capacity performance curves under pristine condition (black line), after two cycles (blue line) and after several (hundreds) cycles (red line). An increase in capacity is attributed to the enhanced electroactive area, and a decrease in capacity is explained by the formation of resistive interphase layers and electrochemically blocked domains. (e) Capacity after the initial (two) cycles (black square) and after multiple (hundreds) cycles (blue open triangles), for poly- and single-crystalline cathodes. Different primary particle size for the polycrystals is investigated. For polycrystalline cathodes, interparticle degradation causes inflow of electrolyte, which initially helps to enhance cell performance. However, after multiple cycles, enhanced charge transfer resistance and mechanical degradation-induced formation of electrochemically inactive domains lead to severe capacity fade in polycrystalline cathodes with larger primary particles.
Fig. 1
Demonstration of cathode interparticle degradation in liquid electrolytes. (a) Initial cathode electrolyte microstructure without any degradation. Red, blue, and green colors indicate cathode primary particles with different crystallographic orientation. The white cross symbols at the cathode/electrolyte interface indicates electrochemically active surface. (b) The same cathode electrolyte microstructure after initial cycles with interparticle degradation, which is denoted by the black cross symbols. Inflow of electrolyte enhances the electrochemically active surface area shown by the white cross at the boundary of the primary particles. (c) Cathode/electrolyte microstructures after multiple cycles where not only an increase in electroactive area is observed but also the evolution of highly resistive electrochemically inactive blocked domains occurs due to the loss of electronic contact. (d) Voltage versus capacity performance curves under pristine condition (black line), after two cycles (blue line) and after several (hundreds) cycles (red line). An increase in capacity is attributed to the enhanced electroactive area, and a decrease in capacity is explained by the formation of resistive interphase layers and electrochemically blocked domains. (e) Capacity after the initial (two) cycles (black square) and after multiple (hundreds) cycles (blue open triangles), for poly- and single-crystalline cathodes. Different primary particle size for the polycrystals is investigated. For polycrystalline cathodes, interparticle degradation causes inflow of electrolyte, which initially helps to enhance cell performance. However, after multiple cycles, enhanced charge transfer resistance and mechanical degradation-induced formation of electrochemically inactive domains lead to severe capacity fade in polycrystalline cathodes with larger primary particles.
Close modal
To determine the local strain energy (Ψ), the mechanical equilibrium equations obtained by balancing the forces are solved along with appropriate boundary conditions (see Eqs. (12)—(15) in Table 1). During lithiation and delithiation of the cathode, its volume changes [49], which depends on the concentration of Li within the cathode (cs) and partial molar volume of lithium within the cathode material (V¯Cathode) [49,59]. Hence, the lithium concentration-dependent strain (ɛLi,ij) within the electrode can be estimated as follows [59]:
εLi,ij=(1/3)V¯Cathodeβijcs
(3)

Here βij denotes the anisotropy in lattice expansion as a function of lithium concentration, which is adopted from the existing literature [28,33]. Thus, variation in lithium concentration inside the cathode material impacts its volume and subsequently leads to generation of stress at the inter primary particle boundary and the cathode/solid electrolyte interface. Usually, more fracture is observed under tensile stress conditions than compression [59,61,62]. Hence, as the tensile strain energy within each element exceeds its fracture threshold (Ψt), it is removed from the lattice spring network, which manifests itself as a microcrack within the continuum [58]. Generation of microcracks within the cathode and solid electrolyte domains are denoted by the “black cross” symbols (as shown in Fig. 1(b)). Removal of multiple adjacent lattice spring elements located at the inter primary particle domains or cathode/solid electrolyte interface leads to the formation of spanning cracks. No ion, charge, or mass transfer occurs across these broken elements, which renders them as mechanically and electrochemically inactive. Hence, the evolution of mechanical degradation effectively deteriorates the transport properties of the cathode particles.

In the present context, the extent of mechanical degradation experienced by the NMC cathode particles are investigated during charge–discharge cycling under an applied current density of 1 mA/cm2, which approximately corresponds to 0.66 C. Constant current constant voltage (CCCV) charge and constant current (CC) discharge protocols are implemented within a potential window of 3.0 V 4.5 V. Three different polycrystalline cathode microstructures are studied with various primary particle sizes ranging between 1 µm and 5 µm, approximately. The ability of the single-crystalline cathodes in mitigating the mechanical degradation, while operating with both liquid and solid electrolytes, is also investigated. [64] Impact of the elastic stiffness of the solid electrolyte on the mechanical degradation experienced by NMC cathodes are also studied [50,52]. Along this direction, performance of NMC cathodes with three different solid electrolytes, LLZO, sulfides and halides, with very different elastic stiffness, are investigated. The following assumptions are applied to the developed computational modeling scheme:

  • Rate of lithium diffusion and electron migration is assumed to be same for the crystalline primary particles and through the primary particle boundaries. No variation in transport properties due to the presence of the grain boundaries are taken into consideration, even though some experimental and computational results conclude otherwise [65,66].

  • No mechanical degradation occurs within the bulk of the cathode primary particles [67]. As a result, single-crystalline cathodes operating in liquid electrolytes do not show any mechanical degradation according to the developed computational framework. Existing experimental results do indicate the formation of intra primary particle cracks in NMC [19,29].

  • Charge transfer resistance, and subsequently the reference exchange current density (i0,ref), between the cathode and the electrolyte is assumed to be constant for all types of solid and liquid electrolytes studied in this research.

  • Due to the extremely small size of the computational domain adopted here (∼10 µm), evolution of salt concentration gradient within the liquid electrolytes, and corresponding concentration polarization, are not taken into consideration. In realistic liquid electrolytes, concentration gradients do evolve, which are also associated with some potential drop [68].

  • Magnitude of lithium conductivity within the electrolyte is also assumed to be constant for liquid, LLZO, sulfides, and halide-based electrolytes due to the small size of the electrolyte domain, and its negligible impact on the overall cell performance compared to the other factors associated with the mechanical degradation of the NMC cathodes.

  • As soon as a surface-connected crack forms within the polycrystalline cathode particles, liquid electrolytes are assumed to flow through them instantaneously and do not depend on the extent of crack opening [38].

For the analysis being conducted here, the entire computational domain is discretized into 40 nodes along both horizontal and vertical directions. Each of the lattice spring elements are assumed to be of length 250 nm, which makes the entire domain length to be around 10 µm. A triangular lattice spring configuration is adopted, which allows for a coordination number of six for each node [59]. A single layer of lattice spring elements is assumed to exist at the electrode/electrolyte interface where Butler–Volmer equation (see Eq. (1)) prescribed reaction current density is applied [7,8]. All the parameters used in the present analysis are provided in Table 2.

Table 2

List of parameters used in the continuum model for capturing interfacial delamination at cathode/LLZO interface and subsequent capacity fade

Name of the parameterSymbolUnitValueReferences
Electronic conductivity in cathodeκCathodeS/m1.0[69]
Lithium atom diffusivity in cathodeDCathodem2/s1014[69,70]
Lithium ion conductivity in the electrolyte (assumed same for liquids, LLZO, sulfides, and halides)κElecS/m0.1[71]
Partial molar volume of lithium within cathodeV¯Cathodem3/molPolynomial expansion[53]
Anisotropy in lattice expansion/contractionβijAlgebraic expression[28]
Faraday constantFC/mol96,485
Universal gas constantRJ/(molK)8.314
TemperatureTK300
Anodic transfer coefficientαa0.5[63]
Cathodic transfer coefficientαc0.5[63]
Reference exchange current density at NMC/electrolyte interfacei0,refA/m21.9[48,53]
i0,ref for aged NMC/electrolyte interface after multiple cyclesi0,ref,mcA/m20.19Assumed
Young’s modulus of cathodeYCathodeGPa190[7276]
Young’s modulus at the boundary of the cathode primary particlesYPrimaryparticleboundaryGPa20Assumed from [72]
Poisson’s ratio of cathodeνCathode0.3[7376]
Young’s modulus of LLZOYLLZOGPa150[77,78]
Young’s modulus of sulfidesYSulfidesGPa21[79]
Young’s modulus of halidesYHalidesGPa35[80]
Young’s modulus of liquidsYLiquidsPa1Assumed
Poisson’s ratio of all electrolytesνElec0.27[77]
Inter primary particle fracture threshold energy in NMCΨ¯t,NMCJ/m21.0[72]
Fracture threshold energy at cathode/LLZO interfaceΨ¯Cath/LLZOJ/m22.0[53]
Fracture threshold energy at cathode/sulfides interfaceΨ¯Cath/SulfJ/m20.8[81,82]
Fracture threshold energy at cathode/halide interfaceΨ¯Cath/HalJ/m22.0Assumed
Name of the parameterSymbolUnitValueReferences
Electronic conductivity in cathodeκCathodeS/m1.0[69]
Lithium atom diffusivity in cathodeDCathodem2/s1014[69,70]
Lithium ion conductivity in the electrolyte (assumed same for liquids, LLZO, sulfides, and halides)κElecS/m0.1[71]
Partial molar volume of lithium within cathodeV¯Cathodem3/molPolynomial expansion[53]
Anisotropy in lattice expansion/contractionβijAlgebraic expression[28]
Faraday constantFC/mol96,485
Universal gas constantRJ/(molK)8.314
TemperatureTK300
Anodic transfer coefficientαa0.5[63]
Cathodic transfer coefficientαc0.5[63]
Reference exchange current density at NMC/electrolyte interfacei0,refA/m21.9[48,53]
i0,ref for aged NMC/electrolyte interface after multiple cyclesi0,ref,mcA/m20.19Assumed
Young’s modulus of cathodeYCathodeGPa190[7276]
Young’s modulus at the boundary of the cathode primary particlesYPrimaryparticleboundaryGPa20Assumed from [72]
Poisson’s ratio of cathodeνCathode0.3[7376]
Young’s modulus of LLZOYLLZOGPa150[77,78]
Young’s modulus of sulfidesYSulfidesGPa21[79]
Young’s modulus of halidesYHalidesGPa35[80]
Young’s modulus of liquidsYLiquidsPa1Assumed
Poisson’s ratio of all electrolytesνElec0.27[77]
Inter primary particle fracture threshold energy in NMCΨ¯t,NMCJ/m21.0[72]
Fracture threshold energy at cathode/LLZO interfaceΨ¯Cath/LLZOJ/m22.0[53]
Fracture threshold energy at cathode/sulfides interfaceΨ¯Cath/SulfJ/m20.8[81,82]
Fracture threshold energy at cathode/halide interfaceΨ¯Cath/HalJ/m22.0Assumed

Results and Discussion

The developed computational methodology is used to investigate the extent of the inter primary particle mechanical degradation and electrode/electrolyte interfacial delamination experienced by the NMC cathodes while operating with liquid and solid electrolytes [29,43]. Both hard and soft ceramic-based solid electrolytes are studied, for example, LLZO, sulfides (LPSCl), and halides (LYC) [83,84]. Finally, the possibility of minimizing the mechanical degradation and subsequent capacity fade experienced by the NMC particles by altering the size of their primary particles in polycrystalline cathodes will be elucidated [14]. Also, the propensity of improving the cell performance by decreasing the single-crystalline cathode particle size, while operating in conjunction with solid-state electrolytes, will be investigated [55]. The entire Results and Discussion section is divided into the following subsections:

  • Mechanical degradation in NMC cathodes while operating with liquid electrolytes

  • Mechanical fracture within NMC cathodes during operation with solid electrolytes

  • Impact of ceramic solid electrolyte type and cathode particle size on the overall mechanical deterioration and capacity fade experienced by the NMC cathodes

The main focus of this study is to provide a good understanding of the impact of the mechanical cracking experienced by NMC cathodes on the overall cell performance. No special strategy to mitigate the mechanical degradation (other than altering the particle size), and subsequent capacity fade, will be investigated as part of the present research.

Mechanical Degradation in NMC Cathodes While Operating With Liquid Electrolytes.

In commercially available lithium ion batteries, the NMC cathodes usually operate within a liquid electrolyte environment [85,86]. During the charge process, the cathode particles get delithiated, which results in a shrinkage in the lattice structure, and the overall cathode volume decreases. Conventional NMC cathode particles are polycrystalline in nature, where the individual grains, also known as the primary particles, demonstrate random orientation [28,87]. A similar cathode/liquid–electrolyte microstructure is shown in Fig. 1(a), where the location of the anode and positive electrode current collector are also shown explicitly. The red, green, and blue domains within the cathode indicate primary particles with different crystallographic orientations. The light blue region denotes liquid electrolyte, whereas the white cross symbols located at the cathode/electrolyte interface indicates electrochemically active surface where Butler–Volmer prescribed reaction current is implemented.

During charge–discharge operation change in lithium concentration within these cathode primary particles leads to anisotropic variation in lattice parameters, which causes orientation-dependent nonuniformity in volume change experienced by the cathode primary particles [28,31,49]. Even though anisotropic volume change of the cathode primary particles is taken into consideration, the lithium diffusion is assumed to be isotropic and independent of the crystallographic orientation. Anisotropy in volume expansion/contraction results in the evolution of tensile stress at the boundaries of the cathode primary particles, which can eventually lead to the formation of inter primary particle microcracks [30,35]. Formation of such detrimental interparticle cracks is denoted by the black cross symbols in Fig. 1(b). Neither the diffusion of lithium atoms nor the migration of electrons is allowed to occur across the broken elements located at the primary particle boundary. During the initial cycles, propagation of these microcracks tend to form spanning cracks connected to the surface of the cathode secondary particles, through which liquid electrolytes can flow to the interior domain of the cathode particles [38,39]. Since electrochemical reaction can occur at any cathode surface that is connected to the liquid electrolytes, all the cathode particles adjacent to the surface-connected cracks experience the Butler–Volmer prescribed electrochemical reaction and subsequent lithium intercalation. Electrochemically active primary particle boundaries are denoted by the white cross symbols in Fig. 1(b), which penetrates well inside the cathode secondary particles. Due to the formation of these surface-connected crack fronts within liquid electrolytes, a couple of beneficial aspects is observed within the cathode particles [38]:

  • The total electrochemically active surface area of the cathode increases.

  • Significant decrease in the diffusion length associated with the transport of lithium atoms within the cathode particles is observed.

As a result, the observable capacity of the cathodes increases due to better utilization of the stored lithium. The voltage versus capacity performance curves demonstrated by the pristine and cracked cathode particles is denoted in Fig. 1(d) by the black and blue solid lines, respectively. As already discussed, increase in capacity and energy density is observed within the cathode after initial cycles due to inflow of electrolyte through the surface-connected cracks, an increase in electrochemically active surface area, and a decrease in lithium ion diffusion length.

However, during long-term cycling, further evolution of the inter primary particle microcracks can possibly lead to isolation of cathodes, and subsequent capacity fade [20,88]. Various forms of chemical and electrochemical degradation that can occur at the cathode electrolyte interface, or within the cathode particle, which leads to decreased utilization of cathode particles, are provided as follows:

  • Phase change at the electrochemically active surface of the cathode particles leads to the formation of resistive spinel and/or rocksalt layer at the expense of the layered one, which tends to increase the charge transfer resistance at the cathode/electrolyte interface [89].

  • During operation at high voltages, the loss of lattice oxygen at the electrochemically active surface area is observed extensively in NMC cathodes. This oxygen-depleted zone can penetrate well into the bulk of the cathode, which can enhance the lithium–nickel mixing and subsequently lower the lithium diffusivity within the bulk of the cathode particles [22,23].

  • The third major mechanism of degradation associated with the evolution of microcracks is the formation of electrochemically inactive cathode surfaces due to detrimental surface reactions and loss of electronic connectivity with the current collectors, which renders that particular cathode surface incapable of conducting electrochemical reactions [88].

After multiple charge/discharge cycles, the surface-connected cracks propagate further inside the cathode particles, which is denoted by the whitish cross symbols in Fig. 1(c), and the electrochemically active surface area increases. However, restructuring of the layered phase to the spinel or rocksalt increases the charge transfer resistance at the surface of the cathode particles (indicated by the slight gray tinge in the cross symbols) [32,89]. The reference exchange current density at the degraded cathode/electrolyte interface is assumed to be approximately one order of magnitude smaller than the pristine material. The extent of interparticle cracks, not connected to the secondary particle surface also increases, which is evident from the higher number of black cross symbols at the primary particle boundaries shown in Fig. 1(c) (compared with Fig. 1(b)). Mechanical degradation-induced loss of electronic connectivity with the current collector, and detrimental side reaction-induced loss of electrochemically active surface area is taken into consideration in a hypothetical fashion, and not explicitly simulated using the developed computational scheme [90]. These mechanical and chemical degradations render some of the surface area in contact with the liquid electrolyte incapable of participating in electrochemical reaction (denoted by the brown shaded surface in Fig. 1(c)). To computationally simulate the formation of the electrochemically inactive cathode surface, the detrimental surface reactions need to be incorporated within the model, which is out of the present scope of the developed methodology, but can definitely be added in the future. While considering all these modes of chemical and mechanical degradation, the decay in voltage versus capacity cell performance curves after multiple cycles is denoted in Fig. 1(d) by the red curve. Enhanced charge transfer resistance along with rapid capacity fade is observed after hundreds of cycles, both of which can be attributed to the aforementioned modes of mechanical and chemical degradations.

Influence of the cathode primary particle size on the evolution of cell capacity is demonstrated in Fig. 1(e). The black solid line with square symbol (in Fig. 1(e)) indicates cell capacity after the initial few cycles experienced by single- and poly-crystalline cathode particles. As shown in Fig. 1(d), the polycrystalline cathode particles experience surface-connected cracks after the initial cycles, and flow of electrolyte through them leads to an increase in cell performance. Hence, polycrystalline cathodes with large grains, which are prone to high magnitudes of microcracking and subsequently enhanced the inflow of electrolyte through cracks, demonstrate substantial increase in cell capacity. In polycrystalline cathodes, decreasing the primary particle size helps to minimize the fraction of inter primary particle cracking. This can be attributed to the presence of larger quantities of the grain boundary domains in cathodes with smaller primary particle sizes. Due to their inherent softness, the grain boundaries can efficiently accommodate large volume change experienced by the cathode particles. Eventually, the presence of the softer grain boundary domains helps to relax some of the strain energy that develop at the primary particle boundaries and effectively lower the evolution of microcracks. Also note that in cathode particles with small primary particles, the total amount of microcracks is more than that observed in cathodes with larger primary particles. But fraction of ruptured grain boundaries decreases substantially with the decreasing primary particle size. In the remaining article, the terminology “evolution of microcracks” always denotes “evolution of fractional microcracks,” which is defined as the ratio between “total number of broken elements” and the “number of elements located at the cathode primary particle boundaries.” Hence, polycrystalline cathodes with smaller primaries experience less interparticle cracking, reduced evolution of surface-connected cracks, and finally a minimized enhancement in cell capacity after the initial few cycles [14].

On the contrary, single-crystalline cathode demonstrate better initial capacity than the polycrystalline cathodes with small primary particles (compare the left most and right most black squares in Fig. 1(e)). This can be possibly attributed to the formation of some microcracks within the polycrystalline cathodes that is not connected to the surface, which can substantially lower the effective lithium diffusivity and effective electronic conductivity within the solid cathode particles. Single-crystalline cathode particles never experience any intraparticle mechanical degradation [67], and their effective diffusivity and conductivity remain same as the initial value, which effectively keeps the cell capacity unaltered after the initial few cycles.

Capacity demonstrated by the same single- and poly-crystalline cathodes after multiple charge–discharge cycles is denoted by the blue dashed line and triangular symbols in Fig. 1(e). It is evident that large primary particles experience dramatic capacity fade, whereas the capacity fade experienced by polycrystalline cathodes with smaller primary particles is much less. The polycrystalline cathodes with larger primary particles demonstrate enhanced evolution of microcracks, and subsequently the isolation of domains is exacerbated, which leads to a rapid capacity fade (as already indicated in Fig. 1(d)). In polycrystalline cathodes, decreasing the primary particle size helps to mitigate the interparticle cracking due to the enhanced presence of the softer grain boundary domains, and subsequently, formation of the electrochemically isolated domains is also minimized. As a result, the capacity fade after multiple cycles experienced by the polycrystalline cathodes can be possibly mitigated by lowering the primary particle size. Also note that in the computational simulations, the extent of electrochemically blocked domains is assigned randomly, which is assumed to be proportional to the magnitude of inter primary particle cracks that evolve within the polycrystalline cathodes. Interestingly, the single-crystalline cathode particles never experience any intraparticle degradation. Such lack of mechanical deterioration ensures that the entire single-crystalline cathode always remains in contact with the current collectors, and no electronically isolated blocked domains evolve. Negligible capacity fade is observed in the single-crystalline cathodes due to minor increase in charge transfer impedance because of the formation of the resistive spinel/rocksalt layers at the electrochemically active surface of the cathode particles [89]. Also note that even though the evolution of intraparticle cracks have already been reported in various experimental observations, no such damage mechanism is taken into consideration in the present study [19,29]. Also note that in Figs. 1(d) and 1(e), even though the rapid capacity fade is reported to occur after hundreds of cycles, the computational brittle fracture evolution is simulated for only ten cycles because the brittle mechanical degradation tends to saturate after ten cycles or so [59,91,92]. However, an increase in charge transfer resistance through detrimental side reactions requires hundreds of cycles. Since, in the present context, both mechanical degradation and enhanced charge transfer resistance are taken into account, the total number of cycles required for dramatic capacity fade is reported to be in the range of hundreds. Note that fatigue failure of the cathode particles may continue over hundreds of cycles, which is again not considered in the present computational framework.

Mechanical Fracture Within NMC Cathodes During Operation With Solid Electrolytes.

Next-generation lithium ion batteries are expected to use solid electrolytes in combination with lithium metal anodes to enhance the energy density of the lithium-based energy storage devices [2,42]. However, NMC cathodes encounter a very different set of mechanical and chemical degradation while operating with solid electrolytes, compared to their liquid counterpart [39,43]. It is possible to form resistive interphase layers due to chemical reactions and/or interdiffusion of transition metal ions between the cathode and solid electrolytes, which can eventually lead to high charge transfer resistance and result in significant capacity fade [45,47]. In the present context, chemical degradation experienced by NMC while operating with various solid electrolytes is not investigated. Rather, two types of mechanical degradations experienced by the NMC cathodes are studied:

  • Inter primary particle degradation between NMC cathodes that increases the lithium and electron transport resistance within cathode active materials [55,64]

  • Interfacial delamination between NMC and the solid electrolytes that minimizes electrochemically active surface area [44,53]

A cathode/solid electrolyte microstructure at the pristine condition, without any degradation, is shown in Fig. 2(a). The gray domain indicates solid electrolyte, whereas the red, green, and blue regions denote NMC primary particles with different orientations. Similar to the earlier cathode/liquid electrolyte microstructures shown in Fig. 1(a), the white cross symbols indicate electrochemically active surface area where Butler–Volmer prescribed reaction kinetics between the cathode and the solid electrolytes is implemented. An NMC/solid electrolyte microstructure with inter primary particle degradation, but without any interfacial delamination, is shown in Fig. 2(b), where the black cross symbols indicate broken elements, which are inactive and cannot diffuse or migrate ions or electrons, respectively, across them. Another cathode/solid electrolyte microstructure with interfacial delamination but without any inter primary particle degradation is shown in Fig. 2(c). The two special scenarios demonstrated in Figs. 2(b) and 2(c) are generated by infinitely increasing the fracture threshold for the interfacial and interparticle degradations, respectively. When both the modes of mechanical degradation between NMC and solid electrolytes are considered, the deteriorated cathode electrolyte microstructure is shown in Fig. 2(d). One stark difference between liquid and solid electrolytes is the inflow of electrolytes through the surface-connected cracks, which is a dominant mechanism of enhancement in cell capacity in the liquid phase, but never occurs in the solid ion conductors due to their extremely high stiffness [39]. This major difference between the mechanoelectrochemical interaction between the NMC cathodes with liquid and solid electrolytes is successfully captured in the developed computational scheme.

Fig. 2
For LLZO solid electrolytes and NMC cathodes, electrode/electrolyte interfacial and cathode inter primary particle degradation are demonstrated. (a) Initial cathode/solid electrolyte microstructure without any degradation. White cross symbols indicate electrochemically active surface area. Red, green, and blue cathode primaries indicate different crystallographic orientations. (b) Cathode/solid electrolyte microstructure with interparticle degradation denoted by the black cross symbols (no interfacial delamination). No inflow of solid electrolyte is possible here through the surface-connected cracks. (c) Cathode/solid electrolyte microstructure with interfacial delamination but without any inter primary particle damage, again denoted by black cross symbols. Substantial decrease in electroactive surface area is evident. (d) Cathode/solid electrolyte microstructure with both interparticle and interfacial degradation. (e) Voltage versus capacity performance curves without any degradation (A, black), with only interparticle damage (B, blue), with only interfacial delamination (C, red), and with both interparticle and interfacial degradation (D, magenta). (f) Black symbols and lines indicate the correlation between electrode–electrolyte detachment and the capacity, which is shown in the left axis. The right axis indicates the interparticle degradation and its correlation with capacity by the magenta symbols and lines. A negative correlation between interfacial delamination and capacity is evident, whereas no clear correlation exists between interparticle degradation and cell capacity. (g) Negative correlation between cathode/solid electrolyte delamination and the inter primary particle detachment. Subsequent studies will only focus on the cell capacity and the electrode electrolyte delamination aspects, as their correlations are well defined.
Fig. 2
For LLZO solid electrolytes and NMC cathodes, electrode/electrolyte interfacial and cathode inter primary particle degradation are demonstrated. (a) Initial cathode/solid electrolyte microstructure without any degradation. White cross symbols indicate electrochemically active surface area. Red, green, and blue cathode primaries indicate different crystallographic orientations. (b) Cathode/solid electrolyte microstructure with interparticle degradation denoted by the black cross symbols (no interfacial delamination). No inflow of solid electrolyte is possible here through the surface-connected cracks. (c) Cathode/solid electrolyte microstructure with interfacial delamination but without any inter primary particle damage, again denoted by black cross symbols. Substantial decrease in electroactive surface area is evident. (d) Cathode/solid electrolyte microstructure with both interparticle and interfacial degradation. (e) Voltage versus capacity performance curves without any degradation (A, black), with only interparticle damage (B, blue), with only interfacial delamination (C, red), and with both interparticle and interfacial degradation (D, magenta). (f) Black symbols and lines indicate the correlation between electrode–electrolyte detachment and the capacity, which is shown in the left axis. The right axis indicates the interparticle degradation and its correlation with capacity by the magenta symbols and lines. A negative correlation between interfacial delamination and capacity is evident, whereas no clear correlation exists between interparticle degradation and cell capacity. (g) Negative correlation between cathode/solid electrolyte delamination and the inter primary particle detachment. Subsequent studies will only focus on the cell capacity and the electrode electrolyte delamination aspects, as their correlations are well defined.
Close modal

Impact of the aforementioned mechanical deterioration on the decrease in electrochemically active surface area and reduction in effective diffusivity and conductivity within the NMC cathode particles are successfully captured through the developed computational means. Voltage versus capacity performance curves demonstrated by the different NMC/solid electrolyte microstructures are shown in Fig. 2(e). Properties of LLZO are used to represent the solid electrolyte domain. The pristine cathode electrolyte microstructure demonstrates the maximum capacity denoted by the black line and also noted as “A.” Incorporation of interparticle degradation, without any interfacial delamination, reduces the cell capacity by some amount, which is shown in Fig. 2(e) by the blue line and also marked as “B.” Addition of interfacial delamination leads to a rapid fade in cell performance even without any interparticle degradation, which is depicted by the red line and denoted as “C.” Finally, the addition of both the interparticle and interfacial degradation demonstrates slightly better performance than “C,” which is shown by the magenta line in Fig. 2(e) and denoted as “D.” It is interesting to note that in the case of “D” even though both interparticle and interfacial degradations are considered, the cell demonstrates better capacity compared to case “C,” where only interfacial delamination was taken into account. This apparent mismatch in trends can be explained by the smaller interfacial delamination experienced in case “D” than case “C,” and the heavy dependence of the cell capacity on the amount of electrochemically active surface area. Incorporation of interparticle damage helps to release some of the strain energy within the primary particle boundaries, which helps to lower the delamination at the cathode solid electrolyte interface for case “D.”

To better understand the correlation among cathode inter primary particle cracking, cathode/solid electrolyte interfacial delamination, and cell capacity, the three interdependent descriptors are plotted in Fig. 2(f). The electrode/electrolyte interfacial delamination versus capacity data is shown along the left y-axis and denoted by the black square symbols. The extent of electrode/electrolyte delamination is defined as the ratio of the broken interfacial elements over the total number of elements located at the cathode/electrolyte interface. A negative correlation between the cell performance and interfacial deterioration is evident, even though the behavior is not strictly linear. On the contrary, the correlation between interparticle fracture and cell capacity is not well defined, which is denoted by the magenta circles along the right y-axis in Fig. 2(f). Hence, it can be concluded that the cell capacity is substantially dictated by the extent of interfacial delamination between the NMC cathodes and solid electrolytes and less influenced by the inter primary particle degradation. Note that the parameter “interparticle detachment” is defined as the ratio between the number of broken inter primary particle elements and the total number of elements located at the inter primary particle region.

The correlation between the electrode/electrolyte interfacial delamination and interparticle detachment is also worth studying, which is plotted in Fig. 2(g) by the blue triangles. The negative correlation between the two can be possibly attributed to the fact that increasing the inter primary particle fracture helps to release some strain energy within the cathode and eventually leads to a decrease in the overall interfacial detachment at the NMC/solid electrolyte interface. This inverse correlation between interparticle and interfacial degradation is in good agreement with the counterintuitive enhancement in cell capacity reported with both the modes of degradation (denoted as “D” in Fig. 1(e)) compared to the case with only interfacial delamination (marked as “C” in Fig. 1(e)). Due to the importance of the cathode/solid electrolyte interfacial delamination in determining the overall cell capacity [44,48] in the remaining portion of this article, only the delamination-induced mechanical degradation will be reported, without mentioning the inter primary particle degradation. Also note that the extent of interparticle damage is modeled computationally, and their impact on determining the interfacial delamination is still taken into consideration.

Impact of Ceramic Solid Electrolyte Type and Cathode Particle Size on the Overall Mechanical Deterioration and Capacity Fade.

Recently, several experimental research activities aimed at deciphering the advantages and disadvantages of using poly- and single-crystalline cathodes while operating with solid ceramic electrolytes [39,55,64,93,94]. It was successfully established in the previous section that the interfacial delamination between the cathode and solid electrolyte dictates the effective electrochemically active surface area and overall cell performance. However, altering the type of solid electrolyte (oxides, sulfide, or halides), or cathode primary particle size (in polycrystalline cathodes) can significantly influence the extent of interfacial delamination and subsequently the overall capacity fade [52,55]. Various poly- and single-crystalline cathode microstructures are studied in the present context, which are denoted in Figs. 3(a)3(d), where the primary particle size of the polycrystalline cathodes increase from 1 µm in Fig. 3(a) to 2.5 µm in Fig. 3(b), and finally 5 µm in Fig. 3(c). The arrows indicate the size of the primary particles being studied. The computationally simulated single-crystalline cathode particle with diameter around 7.5 µm is shown in Fig. 3(d). Influence of three different types of solid electrolytes on the overall mechanical degradation and subsequent capacity fade is also investigated [8084]:

  • Mechanically stiff LLZO, which demonstrates good adhesion with NMC cathodes

  • Mechanically softer sulfide electrolytes that shows lower fracture energy than LLZO

  • Mechanically soft halides with relatively high fracture energies at the cathode/electrolyte interface

Fig. 3
Impact of poly- and single-crystalline cathodes inside various solid electrolytes in determining capacity and electrode/electrolyte interfacial delamination. (a) Cathode/electrolyte microstructure with small primary particles with a size around 1 µm. (b) Polycrystalline cathode with a primary particle size around 2.5 µm. (c) Cathodes containing large primary particles of a size around 5 µm. (d) Microstructure of single-crystalline cathode of size around 7.5 µm along with the adjacent solid electrolyte. (e) Interfacial delamination at the electrode/electrolyte interface for poly- and single-crystalline cathodes. Less interfacial degradation is observed for polycrystalline cathodes with smaller primary particles. Due to its lower stiffness and higher fracture energies, halide-based solid electrolytes tend to demonstrate minimum interfacial delamination, whereas LLZO experiences maximum degradation. (f) Capacity after one or two cycles as a function of the primary particle size. It is evident that decreasing the primary particle size helps to obtain enhanced cell capacity. Single-crystal cathodes are better than polycrystals with large primary particles, but demonstrate poor performance than smaller primaries. Performance also varies with the type of the LLZO-, sulfide-, and halide-based solid electrolytes.
Fig. 3
Impact of poly- and single-crystalline cathodes inside various solid electrolytes in determining capacity and electrode/electrolyte interfacial delamination. (a) Cathode/electrolyte microstructure with small primary particles with a size around 1 µm. (b) Polycrystalline cathode with a primary particle size around 2.5 µm. (c) Cathodes containing large primary particles of a size around 5 µm. (d) Microstructure of single-crystalline cathode of size around 7.5 µm along with the adjacent solid electrolyte. (e) Interfacial delamination at the electrode/electrolyte interface for poly- and single-crystalline cathodes. Less interfacial degradation is observed for polycrystalline cathodes with smaller primary particles. Due to its lower stiffness and higher fracture energies, halide-based solid electrolytes tend to demonstrate minimum interfacial delamination, whereas LLZO experiences maximum degradation. (f) Capacity after one or two cycles as a function of the primary particle size. It is evident that decreasing the primary particle size helps to obtain enhanced cell capacity. Single-crystal cathodes are better than polycrystals with large primary particles, but demonstrate poor performance than smaller primaries. Performance also varies with the type of the LLZO-, sulfide-, and halide-based solid electrolytes.
Close modal

The extent of fracture and capacity decay experienced by the combinations of various cathodes with different primary particle sizes, and solid electrolytes with different mechanical stiffness, will be discussed next.

Extent of interfacial delamination between cathode and the solid electrolyte is demonstrated in Fig. 3(e) for the poly- and single-crystalline cathode particles. It is evident that in polycrystalline cathodes, decreasing the size of the primary particles help to minimize the interfacial delamination. This can be attributed to the enhanced presence of the softer grain boundary regions in cathodes with smaller primary particles [72], which can help to release some strain energy stored within the bulk of the cathode particles and effectively lower the evolution of cathode/electrolyte interfacial microcracks. This particular trend of less delamination with smaller primaries is consistent across all the three types of solid electrolytes studied here—LLZO, sulfides, and halides, which are denoted by the yellow, magenta, and green bars, respectively. Adoption of single-crystalline electrode active particles does not necessarily ensure a decrease in cathode/electrolyte detachment. Rather, a combination of single-crystalline cathodes with mechanically stiff LLZO can aggravate the NMC/LLZO interfacial delamination, which can be possibly attributed to the absence of the softer grain boundary domains within the single-crystalline cathodes. Soft grain boundaries are capable of shading some strain energy stored within the bulk of the electrode particles through enhanced deformation or mechanical degradation, which can effectively help to minimize the electrode/electrolyte delamination. Changing the type of the solid electrolyte from mechanically stiff LLZO to softer sulfide- or halide-based electrolytes [83] can lead to different magnitudes of cathode/electrolyte interfacial degradation. This can be attributed to the fact that the evolution of strain energy at the electrode/electrolyte interface minimizes when mechanically softer electrolytes are used [53]. Hence, with softer solid electrolytes, less microcracks need to be formed at the cathode/electrolyte interface to release the smaller magnitudes of strain energy that evolves during the charge–discharge process. Lower magnitudes of fracture energy for sulfides than halides can cause enhanced mechanical delamination in the sulfide-based solid electrolytes, even though the former demonstrate slightly lower mechanical stiffness than the later [79,80,83].

The discharge capacity experienced by the combination of NMC cathodes with different primary particle sizes, and solid electrolytes with different stiffness, is demonstrated in Fig. 3(f). Irrespective of the solid electrolyte, the lowest discharge capacity is reported for the polycrystalline cathodes with large primary particles. It is evident that for polycrystalline cathodes, lowering the primary particle size leads to enhanced cell capacity, which is again true irrespective of the type of the adopted solid electrolyte. This particular trend of enhancement in capacity with smaller primary particles can be attributed to the decrease in interfacial delamination for smaller primaries, and preservation of large amount of the electrochemically active surface area, as already reported in Fig. 3(e).

It is also evident from Fig. 3(f) that single-crystalline cathodes demonstrate enhanced capacity retention than the polycrystals with larger primary particles. According to our understanding developed in Fig. 2, cathode capacity should be inversely proportional to the interfacial delamination. Enhanced capacity retention of single-crystalline cathode compared to polycrystals with larger primaries should indicate smaller magnitudes of interfacial delamination in the single-crystalline cathode particles. Compared with the extent of electrode/electrolyte delamination reported in Fig. 3(e), even though the trend is consistent for sulfide and halide-based softer solid electrolytes, LLZO experiences enhanced delamination with single-crystalline cathodes. Observation of higher capacity in single-crystalline cathode/LLZO systems even with enhanced delamination can be possibly attributed to the absence of inter primary particle degradation in single crystals. The polycrystalline cathodes with larger primaries are subjected to large magnitudes of inter primary particle microcracks, which significantly decreases the lithium diffusivity, lowers the electronic conductivity within the cathodes, and effectively increases the mass transport resistance.

Other than a few exceptions, softer sulfide- and halide-based solid electrolytes demonstrate higher discharge capacity compared to LLZO in Fig. 3(f), as they are also associated with less interfacial mechanical degradation in Fig. 3(e). It is worth noting that the chemical degradation experienced by NMC cathodes with LLZO-, sulfide-, and halide-based solid electrolytes can be very different, and the experimentally observed capacity for these three solid electrolytes can demonstrate a very different trend than that predicted in Fig. 3(f). Also, commercially available lithium ion batteries are operated for several hundreds of cycles, but in the present context, the mechanical degradations are investigated for only the first few cycles. This apparent mismatch can be attributed to the fact that evolution of only the mechanical degradation is studied here, and the evolution of microcracks tend to stabilize after the initial few cycles [59,91,92] unless fatigue failure of the cathode particles is taken into consideration.

Several experimental studies have reported that single-crystalline NMC cathode particles demonstrate enhanced performance than the polycrystalline ones [55,64]. It is worth investigating how the adoption of single-crystalline cathode helps to obtain enhanced performance than the polycrystalline ones. It is clearly depicted in Fig. 3(f) that single-crystalline cathodes perform better than polycrystals with large primary particles from the standpoint of total discharge capacity. However, it is also demonstrated in Fig. 3(e) that single-crystalline NMC cathodes experience quiet severe interfacial delamination, which can be possibly mitigated to some extent by the adoption of softer sulfide- and/or halide-based solid electrolytes. The single-crystalline cathode analyzed in Fig. 3 demonstrated large particle size of approximately 7.5 µm. The majority of the experimental studies used single-crystalline cathodes, which are much smaller in size [55,64,93,94]. Accordingly, two other single-crystalline cathode/solid electrolyte microstructures are generated with particle sizes 1.5 µm and 4 µm, which are clearly shown in Figs. 4(a) and 4(b), respectively. The electrochemically active surface area is marked by the white cross symbols in between the gray solid electrolytes and blue single-crystalline cathode particles. Electrode/electrolyte delamination and discharge capacity experienced by the single-crystalline cathodes with different particle sizes, while operating with various solid electrolytes, will be discussed next.

Fig. 4
Influence of single-crystalline cathode particle size on capacity retention and electrode/electrolyte interfacial delamination. (a) Small cathode of size around 1.5 µm located inside solid electrolyte. (b) Medium-sized (4 µm) single-crystalline cathode particle located within the solid electrolyte. (c) Interfacial delamination between the cathode and solid electrolytes for different cathode particle sizes. The extent of interfacial damage seems to be less dependent on the size of the single-crystalline cathodes. (d) Cell capacity after the initial cycles as a function of the cathode particle size. It is evident that higher capacity is obtained in smaller particles. Electrolyte type can also influence the magnitude of capacity. The enhanced capacity in smaller single-crystalline cathode particles can be attributed to the shorter diffusion length.
Fig. 4
Influence of single-crystalline cathode particle size on capacity retention and electrode/electrolyte interfacial delamination. (a) Small cathode of size around 1.5 µm located inside solid electrolyte. (b) Medium-sized (4 µm) single-crystalline cathode particle located within the solid electrolyte. (c) Interfacial delamination between the cathode and solid electrolytes for different cathode particle sizes. The extent of interfacial damage seems to be less dependent on the size of the single-crystalline cathodes. (d) Cell capacity after the initial cycles as a function of the cathode particle size. It is evident that higher capacity is obtained in smaller particles. Electrolyte type can also influence the magnitude of capacity. The enhanced capacity in smaller single-crystalline cathode particles can be attributed to the shorter diffusion length.
Close modal

The extent of interfacial delamination experienced by the single-crystalline NMC cathode/solid electrolyte interface is shown in Fig. 4(c). In general, the interfacial delamination remains almost independent of the cathode particle size [55]. Some solid electrolyte-dependent trends are observable; for example, with LLZO, the interfacial delamination decreases slightly with decreasing the cathode particle size. This particular trend can be possibly attributed to the higher stiffness of LLZO and a minor reduction in local volumetric strain due to the adoption of smaller cathode particles [52]. Interestingly, no particular trend in mechanical degradation is observed for sulfide- and halide-based solid electrolytes due to their lower stiffness, and the extent of interfacial delamination remains almost constant for all the three cathode particle sizes.

On the contrary, the capacity demonstrated by the single-crystalline cathode particles increases substantially with the decreasing particle size, which is clearly denoted in Fig. 4(d). The increase in capacity with the decreasing cathode size is evident for all the three solid electrolytes. The trend is most evident while operating single-crystalline NMC cathodes with LLZO solid electrolytes, which is consistent with the decrease in interfacial delamination with the decreasing cathode size reported in Fig. 4(c). However, for sulfide- and halide-based solid electrolytes even though the interfacial degradation remains independent of the cathode particle size, the discharge capacity demonstrates a stark increase with smaller cathodes. Since smaller cathode particles are associated with shorter diffusion lengths [38,39], the enhancement in capacity reported for single-crystalline NMC cathodes with small size can be attributed to the enhanced lithium transport, higher electrochemically active surface area, and better utilization of the lithium stored within the particles during the discharge process [55]. Hence, one can conclude that by the adoption of smaller single-crystalline cathodes, the interfacial delamination cannot be minimized substantially, and the enhancement in cell capacity is due to the decrease in diffusion length associated with the cathode particles and increase in electroactive area.

Conclusion

In the present context, a computational methodology is developed that is capable of predicting the extent of mechanical degradation experienced by single- and poly-crystalline NMC cathode particles while operating with liquid and solid electrolytes. Two types of mechanical degradations are computationally simulated, and their influence on cell capacity is investigated [94]:

  • Evolution of inter primary particle microcracks capable of hindering the diffusion and migration of lithium and electrons within the bulk of the cathode particles, which eventually leads to an increase in mass transport resistance [32].

  • Interfacial delamination between the cathode and solid electrolytes and subsequent loss of electrochemically active surface area, which leads to an enhancement in charge transfer resistance and subsequent capacity fade [44,48].

It is interesting to note that the flow of liquid electrolytes through surface-connected microcracks lead to an increase in cell capacity after the initial few cycles [38]. However, after multiple charge–discharge cycles, due to the formation of a resistive interphase layer and evolution of electrochemically isolated inactive domains, substantial capacity fade is observed in cathodes operating with liquid electrolytes [20,30,35]. Decreasing the cathode primary particle size, or adoption of single-crystalline cathode particles, can help to minimize the mechanical degradation, and subsequent capacity fade, experienced by the NMC cathode particles in both liquid and solid electrolytes [12,14]. Adoption of single-crystalline cathodes with a smaller particle size can possibly help to minimize the extent of cathode/solid electrolyte interfacial delamination and maximize their discharge capacity due to smaller diffusion lengths [55]. It is worth noting that in the present context, only mechanical degradation of cathode particles is taken into consideration. Other forms of chemical degradation, such as interdiffusion of ions and reaction between the delithiated cathodes and electrolytes, can lead to the formation of resistive interphase layers, which under extreme scenarios can render the cathode particle completely useless [45,47,95]. Hence, future computational models of NMC cathode particles should take into consideration both the modes of mechanical and chemical degradation to obtain better correlation with experimental observations.

Acknowledgment

This research is supported by the Vehicle Technologies Office (VTO), Department of Energy (DOE), USA, through the Battery Materials Research (BMR) program. Argonne National Laboratory is operated for DOE Office of Science by UChicago Argonne, LLC under the contract number DE-AC02-06CH11357.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Appendix: Concentration and Strain Energy Profiles

Rupture of cathode particles depend heavily on the evolution of concentration during the charge and discharge processes. It is worth investigating how the concentration profile within the cathode particles impacts the distribution of strain energy, while operating with liquid and solid electrolytes. For the ease of representation, the magnitude of strain energy is normalized by the strain energy threshold before plotting. Figure 5 demonstrates the concentration and strain energy profiles experienced by the cathode particles toward the end of the charge, while operating with liquid electrolytes. Fracture is observed only at the inter primary particle domains, and some of those cracks are also connected to the surface, which is clearly denoted by the white cross symbols in Fig. 5(a). Flow of electrolyte through those surface-connected cracks causes enhanced electrochemical reaction at the particle interior, which is also evident in the concentration profile shown in Fig. 1(b). The normalized strain energy contour shown in Fig. 1(c) indicates some domains with negligible strain energy, and some other regions with normalized strain energy close to unity. These elements with normalized strain energy slightly less than one (1.0) are the possible locations where more microcracks can evolve next. Note that in liquid electrolytes, no microcracks evolve at the cathode electrolyte interface due to the soft nature of the liquids.

Fig. 5
(a) Cathode/liquid electrolyte microstructure toward the end of the charge process. Inter primary particle microcracks evolve, some of which are connected to the surface and electrochemically active (denoted by white cross symbols), and some are isolated (denoted by black cross symbols). The red, blue, and green domains indicate cathode primary particles with different orientation, whereas light blue indicates the liquid electrolyte. (b) Concentration contour within the cathode active particle toward the end of charge. Inflow of electrolyte toward the particle interior through surface-connected cracks, and subsequent electrochemical reactions are evident within the concentration contour. (c) Normalized strain energy profile toward the end of charge, where values close to unity indicate possible locations where the next fracture event can occur.
Fig. 5
(a) Cathode/liquid electrolyte microstructure toward the end of the charge process. Inter primary particle microcracks evolve, some of which are connected to the surface and electrochemically active (denoted by white cross symbols), and some are isolated (denoted by black cross symbols). The red, blue, and green domains indicate cathode primary particles with different orientation, whereas light blue indicates the liquid electrolyte. (b) Concentration contour within the cathode active particle toward the end of charge. Inflow of electrolyte toward the particle interior through surface-connected cracks, and subsequent electrochemical reactions are evident within the concentration contour. (c) Normalized strain energy profile toward the end of charge, where values close to unity indicate possible locations where the next fracture event can occur.
Close modal

Lithium concentration and strain energy profiles within cathode active particles toward the end of charge, while operating with LLZO solid electrolytes, are shown in Fig. 6. Inter primary particle microcracks as well as cathode/solid electrolyte interfacial delamination is observed, which is clearly denoted in Fig. 6(a) by the black cross symbols. Due to the inherent rigidity of the solid electrolytes, the flow of electrolytes through the surface-connected cracks is not possible. Any form of inter primary particle microcracks hinder the lithium diffusion and electronic conduction within the solid active cathode. Concentration profile toward the end of charge is shown in Fig. 6(b), where concentration-depleted zones are observed, which can be attributed to the evolution of inter primary particle microcracks and almost complete isolation of that particular domain. The normalized strain energy contour is shown in Fig. 6(c), where the locations with normalized strain energy close to unity indicate the regions where the next fracture can occur. Unlike liquid electrolytes, enhanced strain energies are observed at both inter primary particle as well as cathode/solid electrolyte interfacial regions, while operating with LLZO.

Fig. 6
(a) Cathode/solid electrolyte microstructure with both inter primary particle as well as cathode/electrolyte interfacial microcracks (denoted by black cross symbols). The electrochemically active domains are indicated by the white cross symbols. The red, blue, and green domains indicate cathode primary particles with different orientations, whereas gray domain indicates the LLZO-based solid electrolyte. (b) Concentration profile within the cathode active particle toward the end of the charge process. Concentration-depleted zone on the left of the active particle got generated due to almost complete isolation of this region through the evolution of microcracks. (c) Contour plot of the normalized strain energy toward the end of the charge process, where regions close to unity indicates domain for further microcrack evolution.
Fig. 6
(a) Cathode/solid electrolyte microstructure with both inter primary particle as well as cathode/electrolyte interfacial microcracks (denoted by black cross symbols). The electrochemically active domains are indicated by the white cross symbols. The red, blue, and green domains indicate cathode primary particles with different orientations, whereas gray domain indicates the LLZO-based solid electrolyte. (b) Concentration profile within the cathode active particle toward the end of the charge process. Concentration-depleted zone on the left of the active particle got generated due to almost complete isolation of this region through the evolution of microcracks. (c) Contour plot of the normalized strain energy toward the end of the charge process, where regions close to unity indicates domain for further microcrack evolution.
Close modal

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