The performances of rechargeable batteries are significantly influenced by macroscopic structure, such as the morphology of electrodes, the particle size and shape, and the property of the solid electrolyte interface (SEI). It is the reason why a great many useful characterization and simulation tools have been used to extract the macroscopic information.

Scanning electron microscopy (SEM) has been one of the most popular tools in investigating the macroscopic morphology and topography of battery materials by means of collecting secondary electrons and backscattered electrons. Combining with a microbattery design, it is feasible to achieve real-time observation of the microbattery during discharge and charge, which is called in situ or operando SEM.^[12,13] But SEM can only acquire surface and topography information. In contrast, transmission electron microscopy (TEM) collects the transmission electrons and can provide internal information of materials, for example, the thickness of the shell in a core–shell structure nanoparticle.^[14,15] Other methods to image the macroscopic morphology such as transmission x-ray microscopy (TXM)^[16,17] have not been used comprehensively. In other words, SEM and TEM have dominated the field of macroscopic real space detection of battery materials because of their high spatial resolution and convenience, and other techniques are still needed to be studied and optimized.

Macroscopic level simulations can help us to understand macroscopic in-depth phenomena in rechargeable batteries, such as stress, thermal stability, flow, multi-field coupling, and failure mechanism. So far, researchers have used phase-field models to study grain growth and roughening, crack evolution, the interaction of dislocations and solute, electromigration, multicomponent interdiffusion, etc. For example, Zuo et al. put forward a phase-field model coupling lithium diffusion, stress evolution, and crack propagation.^[18] The model was applied to a silicon thin film electrode to explore the coupling effects on diffusion and crack propagation paths. Hu et al. developed a phase-field based multiscale model that enables generating nanoporous microstructures of different porosity and connectivity patterns based on the depth and energy of the surface (pore/electrolyte interface) to predict both the microstructure patterns and the effective properties of heterogeneous solid electrolytes.^[19] Zhang et al. developed a nonlinear phase-field model for predicting Li dendrite growth at the electrode/electrolyte interface during the electrochemical deposition involving highly nonequilibrium processes. In the model, the Butler–Volmer type electrochemical kinetics was automatically reproduced at the moving diffusion interface and a revised Poisson–Nesters–Planck equation was further solved for ionic transport and local overpotential variation.^[20]

When the scale of the phase-field model is larger than the micron scale or the free-boundary condition is to be dealt with, the finite element method is a better choice. The finite element method can help to understand some macroscopic engineering problems, such as the thermal stability and mechanical failure mechanism of batteries. The temperature distribution in the batteries has a significant impact on their safety and longevity. Guo et al. used a finite element method to develop a three-dimensional thermal abuse model on LIB (Fig. 1), which was coupled with electrochemical reactions and thermal responses to study in detail the temperature field distribution and evolution inside the cell.^[21] Bower et al. described a finite element method for modeling deformation, diffusion, fracture, and electrochemical reactions in materials used as lithium-ion intercalation electrodes.^[22] Vijayaraghavan et al. developed a finite element based neural search analytical model to analyze the crash for understanding the effect of various uncertainties in the LIB pack.^[23] The intergranular and intragranular cracks in electrodes, SEI, and solid-state electrolyte are inevitable during the cycling of batteries and severely cause battery performance degradation. Today, many studies have focused on the cracking mechanism of battery materials.^[24,25] Yan et al. analyzed the driving forces for crack propagation in LiNi_0.6Mn_0.2Co_0.2O₂ (NMC622) particles.^[26] With the combination of inhomogeneous lithium distribution, phase transformation, crack surface pressure, and heat treatment, the coupling of thermal and mechanical effects can contribute to a high driving force for crack propagation and performance degradation of the NMC622 cathode. In conclusion, macro-scale simulation is challenging and meaningful for solving practical problems in batteries.

Fig. 1.

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	Fig. 1. Distribution of temperature at 155 °C using finite element modeling among different time scopes: (a) 1200 s, (b) 3600 s.[21]

Most of the active materials in batteries are crystal or short-range ordered amorphous materials. The ability to probe and simulate the crystal structure is critical for linking the electrochemical performances and materials’ structure. To date, the diffraction techniques such as x-ray diffraction (XRD), neutron diffraction (ND), and electron diffraction are the most powerful tools to study the crystal lattice by a basic principle: incident microscopic particle interacts with crystal atoms, resulting in wave interference effect. Different crystal planes have different atomic arrangements, thus different planes have various diffraction directions. The relationship between different crystal plane and diffraction direction is given by the famous Bragg’s law

XRD utilizes x-rays (photons) as the incident particles. Collecting the data of θ and diffraction intensity and comparing them with standard substance information can provide the specific crystal structure and crystallinity of the sample. By Rietveld refinement, a great deal of useful information including lattice constant, atomic occupancy, and chemical stoichiometry of the material can be acquired to study the crystal structure and structure–activity relationship. It is worth mentioning that XRD provides the long-range average information because of the difficulty in converging the x-rays. On the other hand, in situ experiments are suitable for XRD. Synchrotron radiation source is able to offer higher intensity and photon flux than laboratory x-rays by several orders of magnitude. Combining synchrotron radiation source and in situ experiment techniques with XRD, real-time ultrafast data collection and deep penetration depth are satisfied with recent battery studies.^[9]

Wu et al. demonstrated the crystal structure evolution of Na_xCu_0.27Zn_0.06Mn_0.67O₂ (NCZM) during the charge and discharge procedures of the sodium ion batteries by in situ synchrotron XRD.^[27] In the region of 0.51 < x < 0.78 of Fig. 2, the (002) peak position (2θ value) and intensity subtly decreased, which indicated a solid solution process. When the cathode was charged to 3.8 V that was the region of 0.42 < x < 0.51, a significant peak position move and intensity change could be attributed to a phase transition reaction, which was verified by the result of electron energy-loss spectrum (EELS). The black arrow of the (002) peak suggested a highly disordered OP4 phase instead of the original P2 phase at 4.1 V, which demonstrated the stability of NCZM below 4.1 V.

Fig. 2.

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	Fig. 2. Selected regions of in situ synchrotron XRD data and the sodium content–voltage curve.[27]

In contrast to x-rays, the scattering cross section of neutrons is irrelevant to atomic number Z, so it is better to distinguish light atoms and elements which have similar Z or isotopes than XRD. In addition, neutrons only interact with the atomic nucleus (different from x-rays that interact with electrons), resulting in a good penetration ability. However, there are some intrinsic limitations in ND. On the one hand, ND needs a large amount of materials. On the other hand, H atom strongly disturbs the analysis of the diffraction data. What is more, high-flux spallation neutron sources (SNS) which are urgently needed for ND technique are very scarce and the in situ experiments of ND are much more difficult than XRD.^[9] To some extent, ND and XRD techniques complement each other in many different aspects.

Bruce’s group investigated Na_2/3Ni_{1/3 − x}Mg_xMn_2/3O₂ crystal lattice evolution with different substitution amount of Mg via ND and XRD.^[28] Because of the different neutron scattering lengths of Mg and Mn, it is easy to characterize Mg²⁺/Mn⁴⁺ ordering by ND. The comparison between XRD and ND data is shown in Fig. 3(a), in which ND shows more detail diffraction information. A series of ND diffraction data of Na_2/3Ni_{1/3 − x}Mg_xMn_2/3O₂ is shown in Figs. 3(b) and 3(c). By combining with selected Rietveld refinement, they found that the crystallographic parameters are increasing with the replacement of Mg²⁺ instead of Ni²⁺ because of the larger size of Mg²⁺. In Fig. 3(c), the reflection at 4.1 Å implies the interplane Ni(Mg)/Mn long-range ordering by (011) crystal facet even at large magnesium content, which is different from a previous Na_2/3Ni_1/3Mn_2/3O₂ report.^[29]

Fig. 3.

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	Fig. 3. (a) X-ray and neutron diffraction data comparison for x = 0. (b) Neutron diffraction data for 0 ≤ x ≤ 0.2. (c) Zoomed-in yellow region of (b).[28]

The principle of electron diffraction is similar to that of ND and XRD. Electron diffraction technique is always combined with TEM, thereby acquiring atomic and crystallographic information at the same time. The outstanding advantages of electron diffraction are the high intensity and the ability to analyze at nanoscale. However, the difficulties in quantitative analysis and the presence of the electron beam damage are still limiting this widely used diffraction technique. Nowadays, ultrafast electron diffraction (UED) technique equips with MeV electrons which differs from electron diffraction in TEM is used to study structural dynamics in many fields.^[30–33] We will discuss more electron diffraction technique combing with TEM and electron energy loss spectrum (EELS) in the following section. In short, x-ray, neutron, and electron diffraction methods have their own respective advantages. Therefore, they are complementary techniques in detecting the crystal structure of battery materials to some extent.

In the field of simulation of crystal structure evolution, molecular dynamics and Monte Carlo simulations can both visually observe the migration of ions during electrochemical processes in the scale of crystal lattice level. Ma et al. created a dynamically adaptive approach in molecular dynamics simulations (Fig. 4) to reveal the molecular mechanisms and the reaction pathways in the conversion reaction of the FeF₂ electrode.^[34] Intercalation along [001] rapid transport channels is accompanied by a slight reduction of charge density on multiple nearby Fe ions per Li ion until enough Li saturates a region, which causes the nearby Fe to lose sufficient charge and become destabilized, eventually forming Fe⁰ nanocluster. The resultant nanostructures are fully consistent with the TEM observations. Methekar et al. used a kinetic Monte Carlo simulation to understand the passive SEI layer, the simulation results showed that the active surface coverage remains constant for the initial charging cycles and then decreases monotonically with the number of charging cycles.^[35]

Fig. 4.

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	Fig. 4. Simulated reaction between Li and FeF2 on the (001) surface of FeF2. Fe–F bond is yellow, and Li–F bond is red. (a) System with 72 Li+ already shows the growth of Fe metal cluster. (b) 288 Li+ with a glassy Li–F region. (c) 360 Li+, crystalline LiF is observed at the left corner. (d) 864 Li+, crystalline LiF grows.[34]

The atomic structure of defects and interfaces has a great influence on the performance of full batteries, so the capability to probe atomic information of materials is essential for the performance optimization of batteries. To date, many microscopic techniques have achieved sub-nanometer or even sub-angstrom resolution with different methods, such as scanning probe microscopy (SPM), high-resolution transmission electron microscopy (HRTEM), and scanning transmission electron microscopy (STEM).

SPM includes scanning tunneling microscopy (STM), atomic force microscopy (AFM), etc. which are based on quantum tunneling effect or atomic force and have atomic resolutions. STM^[36,37] and AFM^[38,39] have already been used to observe the atomic structure of battery materials for a long time and brought a novel view for surface information, especially for the phase interface. However, SPM is limited to the surface region. Hence, the bulk atomic information of electrodes and solid-state electrolytes cannot be acquired by SPM. That is where the electron microscopy is required.

HRTEM is an atomic scale technique with a long history and it has the ability to probe bulk information. In brief, it is an imaging mode of TEM and can directly image atomic columns by phase interference between diffracted beams and transmission beams.^[40] To confirm the existence of SEI between the Mo₆S₈ anode and aqueous electrolyte, Suo et al. directly observed the SEI via HRTEM which is shown in Figs. 5(a) and 5(b).^[41] TFSI⁻ in the aqueous electrolyte is electrochemically reduced to LiF on the surface of Mo₆S₈ anode. The interplanar spacing of the LiF indicates its imperfect crystallinity. This crystalline ∼ 15 nm thick LiF-based SEI seems to differ from the composite interphase in nonaqueous electrolytes.^[42]

Fig. 5.

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	Fig. 5. HRTEM images of (a) pristine Mo6S8 and (b) cycled Mo6S8.[41]

Instead of utilizing the static incident electron beams of TEM, STEM scans the electron beams parallel to the optical axis and employs an annular detector to collect the scattered electrons.^[40,43] Respectively, Pennycook et al. and Okunishi et al. proposed high angle annular dark field (HAADF)^[44] and annular bright field (ABF)^[45] imaging techniques in 1988 and 2009. The electron signal intensity in HAADF mode is almost proportional to Z^1.7 which is suitable for imaging relative heavy atoms^[46,47] and in ABF mode is approximate Z^1/3 which is sensitive to light elements,^[48] such as lithium and oxygen.

Gu’s group constructed an all-solid-state nanobattery that consists of a LiCoO₂ cathode, Y and Ta doped LLZO solid-state electrolyte (Li_6.75La_2.84Y_0.16Zr_1.75Ta_0.25O₁₂), and a gold anode on a biasing nanochip by focus ion beam (FIB) milling.^[49] The delithiation of the LiCoO₂ cathode was observed by HAADF and ABF after a high voltage biasing, which is an appropriate example for explaining the different features of HAADF and ABF. The pristine single crystal LiCoO₂ became nanosized polycrystal after delithiation and figure 6 shows its grain boundaries structure. Geographical phase analysis (GPA) was used for identifying the orientation of grains in Fig. 6(a), in which different colors indicate different orientations. Two types of boundaries were found that coherent twin boundaries are between different oriented grains and antiphase domain boundaries are between similarly oriented grains. The HAADF and ABF micrographs of coherent twin boundaries and antiphase domain boundaries are displayed respectively in Figs. 6(b)–6(e). It is obvious that only Co ion can be observed in the HAADF micrographs because of the weak signal of light elements. On the contrary, Li and O atoms can be distinguished clearly in the ABF micrographs, which is attributed to the Z^1/3 signal intensity relationship. Combining with theoretical calculations, the pathway of Li⁺ along the boundaries is concluded for illuminating the lithium ion transportation mechanism in LiCoO₂ cathode.

Fig. 6.

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	Fig. 6. (a) HAADF image of delithiated LiCoO2 using the GPA method. (b) and (c) are HAADF and ABF images from the yellow region in (a), and (d) and (e) are HAADF and ABF images from the pink region in (a).[49]

STEM has a sub-angstrom resolution, which can directly reveal significant information on the physical and chemical properties of materials at the atomic level, such as phase transformation, surface/interface structure evolution, microscopic mechanisms of lithium ion diffusion and storage, and so on. Nevertheless, STEM still has some limitations. For example, the strong radiation of STEM can rapidly damage samples and both STEM and TEM images are actually two-dimensional projections of three-dimensional samples, which can be misleading. Therefore, the combination of computation and TEM imaging is very necessary, as the calculation can make up for the shortcomings of TEM imaging. The calculation methods are more applicable and not affected by the radiation damage, regardless of whether the sample is conductive or not. What is more, calculation methods can construct various periodic, even nonperiodic models, such as surface/interface models, which can provide a convenient interpretation of two-dimensional TEM images. Based on this, Yue et al. provided further insight on the intercalation/deintercalation process of Li and Na ions into Fe₂(MoO₄)₃ combining the first-principle thermodynamic calculations and direct atomic-scale observation by STEM.^[50] With the combination of STEM and calculation, the “discrete occupation” and “pseudo-continuous” were proposed to describe the distinctly different occupation paths of Li and Na ions into Fe₂(MoO₄)₃.

The energy of a phonon mode is on the order of 10–10² meV, therefore an energy transfer around vibration energy must be achieved to characterize the vibrational modes of materials. At present, many different techniques have successfully probed the phonon dispersion. Inelastic scattering techniques including inelastic x-ray scattering^[64,65] and inelastic neutron scattering^[66,67] are old-style methods, but they are rarely used in battery research. Optical spectroscopy exploits the inelastic scattering of photons to detect the vibrational modes, for example, Raman spectroscopy, which has been widely applied for detecting the structural variations of battery materials.^[68] Zaghib et al. used in situ Raman spectroscopy to investigate the vibrational modes in Cr/Co-doped LiMn_1.5Ni_0.5O₄ cathode and study the valence state change of Ni and Mn in real time.^[69]

Two-dimension materials are of great importance in the field of rechargeable batteries. Recently, Kazu et al. reported a novel method to simultaneously map the vibration in graphene nanostructures in real space and momentum space.^[70] Different from low-spatial-resolution inelastic x-ray (neutron) scattering techniques and low-momentum-transfer optical spectroscopy, EELS in transmission can provide local vibrational modes of two-dimension monolayer materials for several Brillouin zones at the nanometer scale. There must be a tradeoff between spatial resolution and momentum resolution because of the uncertainty principle. With the energy resolution of 30 meV full width at half maximum (FWHM), the momentum resolution of ± 0.1–0.2 Å⁻¹, and the probe size of 10–40 nm, phonon dispersions along different momentum space directions are measured and they are perfectly accord with simulated results. Except for the missing of the low-energy region, details of the phonon dispersions are mostly described.

Yao et al. used first-principles density functional theory (DFT) calculations to investigate both the disordered rock salt-type Li₄Mn₂O₅ structure and the ordered ground-state structure.^[71] From Fig. 10(a), the energy of Li₄Mn₂O₅ is slightly higher than that of Li₂O and LiMnO₂, so Li₄Mn₂O₅ is not stable at 0 K. Their DFT-calculated phonon dispersion of the Cmmm Li₄Mn₂O₅ is provided in Fig. 10(b), and no imaginary phonons are shown, which indicates that Li₄Mn₂O₅ is dynamically stable. By computing the harmonic phonons and vibrational entropies of Li₄Mn₂O₅, LiMnO₂, and Li₂O, the relationship between free energy and temperature has been revealed, as shown in Fig. 10(c).

Fig. 10.

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Fig. 10. Thermodynamic and dynamic stabilities of Li4Mn2O5. (a) Calculated Li–Mn–O (T = 0 K) phase diagram. The Li4Mn2O5 phase is slightly higher in energy (13.6 meV per atom) relative to the ground-state phase: a mixture of Li2O and LiMnO2. (b) Phonon dispersion of the ground-state Li4Mn2O5 and (c) calculated temperature-dependent free energy of Li4Mn2O5 (red dashed line), Li2O (orange dotted line), and LiMnO2 (green dotted line), as well as the stability (purple solid line) of Li4Mn2O5 versus temperature relative to Li2O and LiMnO2 phase mixtures. Li4Mn2O5 is dynamically stable and can be entropically stabilized at ∼ 1350 K.[71]

The electronic energy band of solid materials is very important for battery design, for it describes the quantum-mechanic-allowable electron energy state which strongly influences the electrical property of electrodes and solid-state electrolytes. The electronic structure of the battery material is closely related to their electrochemical properties, for example, the chemical stability of the interface between the electrode and the electrolyte can be derived from the density of energy states,^[72] the rate performance is related to the electronic conductivity of the electrodes,^[73] solid electrolyte materials require electronic insulation properties, which are related to the width of the energy gap.^[74]

Nevertheless, experimental characterization of the energy band is still limited to a few techniques such as angle-resolved photoemission spectroscopy (ARPES) and resonance Raman spectroscopy (RRS). ARPES directly observes the distribution of electrons in momentum space by photoemission electrons and it has become one of the most indispensable techniques for characterizing the physical property.^[75] Usachov et al. employed ARPES to study the energy band of N-doped graphene.^[76] The nitrogen impurities could tune the band structure and carrier concentration of N-doped graphene for optimizing the performance of energy devices.

If the energy of the incoming or outgoing photon matches the electronic transition energy of the sample, the Raman cross section will notably increase, which is called RRS.^[77,78] As a result, RRS relates the Raman signals to the electronic energy band. Today, the energy band structure of many types of materials has been studied by RRS.^[79,80] These kinds of momentum-related characterizations in the momentum space enlighten the followers to discover the quality of battery materials from a brand-new angle.

The calculation of energy band is scarce in the field of rechargeable batteries none the less. Chen et al. demonstrated that carbon foams (CFs) exhibit good stabilities and pore-size dependent electronic properties, which are related to the size-dependent band gaps of graphene nanoribbons (GNRs) through first-principles calculations.^[81] Then they used 48Z_S_I as an example to calculate the band structures of monolayer graphene nanoribbons-based asymmetric zigzag CFs to find out the rules (Fig. 11). Based on this, they found that: when l, m, and n all equal to 3n or 3n + 2, if at least one is equal to 3n, the CF is a wide-band-gap semiconductor, otherwise, it is a narrow-band-gap semiconductor. When only one of the three widths is equal to 3n + 1, the CF has a small E_g, if more than one, it is metallic. However, researchers seem to pay more attention to the density of states (DOS) of electrons. Seo et al. used ab initio calculations to demonstrate which specific chemical and structural features lead to electrochemically active oxygen states in cathode materials by calculating the projected DOS (pDOS) of the oxygen 2p states of the three oxygen environments.^[82]

Fig. 11.

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Fig. 11. The schematics of asymmetric 48Z_SI(l, m, n) networks and the corresponding band structures. (a) Three-wing GNRs building block of asymmetric CFs and three width degrees of freedom, l, m, n, are considered. (b) and (c) m = n and m ≠ n asymmetric CFs, respectively. The orange and cyan sticks indicate the sp3 and sp2 C atoms, respectively. (d) The band structures of (5, 3, 2), (5, 3, 3), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 5, 2), (5, 5, 3), (5, 5, 4), and (5, 6, 6).[81]