Probing the range of applicability of structure- and energy-adjusted QM/MM link bonds III: QM/MM MD simulations of solid-state systems at the example of layered carbon structures

The previously introduced workflow to achieve an energetically and structurally optimized description of frontier bonds in quantum mechanical/molecular mechanics (QM/MM)-type applications was extended into the regime of computational material sciences at the example of a layered carbon model systems. Optimized QM/MM link bond parameters at HSEsol/6-311G(d,p) and self-consistent density functional tight binding (SCC-DFTB) were derived for graphitic systems, enabling detailed investigation of specific structure motifs occurring in graphene-derived structuresv i a $$ via $$ quantum-chemical calculations. Exemplary molecular dynamics (MD) simulations in the isochoric-isothermic (NVT) ensemble were carried out to study the intercalation of lithium and the properties of the Stone-Thrower-Wales defect. The diffusivity of lithium as well as hydrogen and proton adsorption on a defective graphene surface served as additional example. The results of the QM/MM MD simulations provide detailed insight into the applicability of the employed link-bond strategy when studying intercalation and adsorption properties of graphitic materials.

Replica exchange molecular dynamics for Li-intercalation in graphite: a new solution for an old problem

Li intercalation and graphite stacking have been extensively studied because of the importance of graphite in commercial Li-ion batteries. Despite this attention, there are still questions about the atomistic structures of the intermediate states that exist during lithiation, especially when phase dynamics cause a disordered Li distribution. The Li migration event (diffusion coefficient of 10-5 nm2 ns-1) makes it difficult to explore the various Li-intercalation configurations in conventional molecular dynamics (MD) simulations with an affordable simulation timescale. To overcome these limitations, we conducted a comprehensive study using replica-exchange molecular dynamics (REMD) in combination with the ReaxFF force field. This approach allowed us to study the behavior of Li-intercalated graphite from any starting arrangement of Li at any value of x in LixC6. Our focus was on analyzing the energetic favorability differences between the relaxed structures. We rationalized the trends in formation energy on the basis of observed structural features, identifying three main structural features that cooperatively control Li rearrangement in graphite: Li distribution, graphite stacking mode and gallery height (graphene layer spacing). We also observed a tendency for clustering of Li, which could lead to dynamic local structures that approximate the staging models used to explain intercalation into graphite.

Towards hybrid quantum mechanical/molecular mechanical simulations of Li and Na intercalation in graphite - force field development and DFTB parametrisation

In this work a previously established QM/MM simulation protocol for the treatment of solid-state interfaces was extended towards the treatment of layered bulk materials enabling for instance investigation of metal intercalation in graphitic carbon materials. In order to study the intercalation of Li in graphite, new density functional tight binding (DFTB) parameters for Li have been created. Molecular dynamics (MD) simulations at constant temperatures (273.15, 298.15 and 323.15 K) have been carried out to assess the performance of the presented DFTB MD simulation approach. The intercalation of variable lithium and sodium content was investigated via z-distribution functions and analysis of the diffusivity in the direction parallel to the graphene plane. Both the calculated diffusion coefficients and the activation energy in case of lithium are in good agreement with experimental data. The comparison of the QM/MM MD simulation results provide detailed insights into the structural and dynamical properties of intercalated metal ions.

Aqueous electrolyte-mediated reversible K+ ion insertion into graphite

Herein, reversible K+ ion insertion into graphite in an aqueous electrolyte is illustrated. It is shown that more facile diffusion of K+ ions is possible in natural graphite than in pyrolytic graphite.

A Figure of Merit for Fast-Charging Li-ion Battery Materials

Rate capability is characterized necessarily in almost all battery-related reports, while there is no universal metric for quantitative comparison. Here, we proposed the characteristic time of diffusion, which mainly combines the effects of diffusion coefficients and geometric sizes, as an easy-to-use figure of merit (FOM) to standardize the comparison of fast-charging battery materials. It offers an indicator to rank the rate capabilities of different battery materials and suggests two general methods to improve the rate capability: decreasing the geometric sizes or increasing the diffusion coefficients. Based on this FOM, more comprehensive FOMs for quantifying the rate capabilities of battery materials are expected by incorporating other processes (interfacial reaction, migration) into the current diffusion-dominated electrochemical model. Combined with Peukert's empirical law, it may characterize rate capabilities of batteries in the future.

Na Diffusion in Hard Carbon Studied with Positive Muon Spin Rotation and Relaxation

The diffusive nature of Na⁺ in Na-inserted hard carbon (C _x Na), which is the most common anode material for a Na-ion battery, was studied with a positive muon spin rotation and relaxation (μ⁺SR) technique in transverse, zero, and longitudinal magnetic fields (TF, ZF, and LF) at temperatures between 50 and 375 K, where TF (LF) denotes the applied magnetic field perpendicular (parallel) to the initial muon spin polarization. At temperatures above 150 K, TF-μ⁺SR measurements showed a distinct motional narrowing behavior, implying that Na⁺ begins to diffuse above 150 K. The presence of two different muon sites in C _x Na was confirmed with ZF- and LF-μ⁺SR measurements; one is in the Na-inserted graphene layer, and the other is in the Na-vacant graphene layer adjacent to the Na-inserted graphene layer. A systematic increase in the field fluctuation rate (ν) with increasing temperature also evidenced a thermally activated Na diffusion, particularly above 150 K. Assuming the two-dimensional diffusion of Na⁺ in the graphene layers, the self-diffusion coefficient of Na⁺ (D _Na ^J) at 300 K was estimated to be 2.5 × 10^-11 cm²/s with a thermal activation energy of 39(7) meV.

Na-ion mobility in P2-type Na0.5MgxNi0.17-xMn0.83O2 (0 ≤ x ≤ 0.07) from electrochemical and muon spin relaxation studies

Sodium transition metal oxides with a layered structure are one of the most widely studied cathode materials for Na⁺-ion batteries. Since the mobility of Na⁺ in such cathode materials is a key factor that governs the performance of material, electrochemical and muon spin rotation and relaxation techniques are here used to reveal the Na⁺-ion mobility in a P2-type Na_0.5Mg_xNi_0.17-xMn_0.83O₂ (x = 0, 0.02, 0.05 and 0.07) cathode material. Combining electrochemical techniques such as galvanostatic cycling, cyclic voltammetry, and the galvanostatic intermittent titration technique with μ⁺SR, we have successfully extracted both self-diffusion and chemical-diffusion under a potential gradient, which are essential to understand the electrode material from an atomic-scale viewpoint. The results indicate that a small amount of Mg substitution has strong effects on the cycling performance and the Na⁺ mobility. Amongst the tested cathode systems, it was found that the composition with a Mg content of x = 0.02 resulted in the best cycling stability and highest Na⁺ mobility based on electrochemical and μ⁺SR results. The current study clearly shows that for developing a new generation of sustainable energy-storage devices, it is crucial to study and understand both the structure as well as dynamics of ions in the material on an atomic level.

Structural Evolution and Transition Dynamics in Lithium Ion Battery under Fast Charging: An Operando Neutron Diffraction Investigation

Fast charging (<15 min) of lithium-ion batteries (LIBs) for electrical vehicles (EVs) is widely seen as the key factor that will greatly stimulate the EV markets, and its realization is mainly hindered by the sluggish diffusion of Li+ . To have a mechanistic understanding of Li+ diffusion within LIBs, in this study, structural evolutions of electrodes for a Ni-rich LiNi0.6 Mn0.2 Co0.2 O2 (NMC622) || graphite cylindrical cell with high areal loading (2.78 mAh cm-2 ) are developed for operando neutron powder diffraction study at different charging rates. Via sequential Rietveld refinements, changes in structures of NMC622 and Lix C6 are obtained during moderate and fast charging (from 0.27 C to 4.4 C). NMC622 exhibits the same structural evolution regardless of C-rates. For phase transitions of Lix C6 , the stage I (LiC6 ) phase emerges earlier during the stepwise intercalation at a lower state of charge when charging rate is increased. It is also found that the stage II (LiC12 ) → stage I (LiC6 ) transition is the rate-limiting step during fast charging. The LiC12 → LiC6 transition mechanism is further analyzed using the Johnson-Mehl-Avrami-Kolmogorov model. It is concluded as a diffusion-controlled, 1D phase transition with decreasing nucleation kinetics under increasing chargingrates.

How Li diffusion in spinel Li[Ni1/2Mn3/2]O4 is seen with μ ±SR

The diffusive behavior in a spinel-type Li+ ion battery material, Li[Ni1/2Mn3/2]O4, has been studied with positive and negative muon spin rotation and relaxation (μ ±SR) measurements in the temperature range between 200 and 400 K using a powder sample. The implanted μ + locates at an interstitial site near O2− ion so as to form a O–H like bond, while the implanted μ − is mainly captured by an oxygen nucleus, resulting in the formation of muonic oxygen. This means that local magnetic environments in Li[Ni1/2Mn3/2]O4 were investigated from the two different sites in the lattice, i.e., one is an interstitial site for μ +SR and the other is an oxygen site for μ −SR. Since both μ +SR and μ −SR detected an increase in the fluctuation rate of a nuclear magnetic field for temperatures above 200 K, the origin of this increase is clearly confirmed as Li diffusion. Assuming a random walk process with the hopping of thermally activated Li+ between a regular Li site and the nearest neighboring vacant octahedral sites, a self-diffusion coefficient of Li+ was found to range above 10−11 cm2/s at temperatures above 250 K with an activation energy of about 0.06 eV.

In Situ Diffusion Measurements of a NASICON-Structured All-Solid-State Battery Using Muon Spin Relaxation

In situ muon spin relaxation is demonstrated as an emerging technique that can provide a volume-averaged local probe of the ionic diffusion processes occurring within electrochemical energy storage devices as a function of state of charge. Herein, we present work on the conceptually interesting NASICON-type all-solid-state battery LiM2(PO4)3, using M = Ti in the cathode, M = Zr in the electrolyte, and a Li metal anode. The pristine materials are studied individually and found to possess low ionic hopping activation energies of ∼50-60 meV and competitive Li+ self-diffusion coefficients of ∼10-10-10-9 cm2 s-1 at 336 K. Lattice matching of the cathode and electrolyte crystal structures is employed for the all-solid-state battery to enhance Li+ diffusion between the components in an attempt to minimize interfacial resistance. The cell is examined by in situ muon spin relaxation, providing the first example of such ionic diffusion measurements. This technique presents an opportunity to the materials community to observe intrinsic ionic dynamics and electrochemical behavior simultaneously in a nondestructive manner.

Honeycomb layered oxides: structure, energy storage, transport, topology and relevant insights

The advent of nanotechnology has hurtled the discovery and development of nanostructured materials with stellar chemical and physical functionalities in a bid to address issues in energy, environment, telecommunications and healthcare. In this quest, a class of two-dimensional layered materials consisting of alkali or coinage metal atoms sandwiched between slabs exclusively made of transition metal and chalcogen (or pnictogen) atoms arranged in a honeycomb fashion have emerged as materials exhibiting fascinatingly rich crystal chemistry, high-voltage electrochemistry, fast cation diffusion besides playing host to varied exotic electromagnetic and topological phenomena. Currently, with a niche application in energy storage as high-voltage materials, this class of honeycomb layered oxides serves as ideal pedagogical exemplars of the innumerable capabilities of nanomaterials drawing immense interest in multiple fields ranging from materials science, solid-state chemistry, electrochemistry and condensed matter physics. In this review, we delineate the relevant chemistry and physics of honeycomb layered oxides, and discuss their functionalities for tunable electrochemistry, superfast ionic conduction, electromagnetism and topology. Moreover, we elucidate the unexplored albeit vastly promising crystal chemistry space whilst outlining effective ways to identify regions within this compositional space, particularly where interesting electromagnetic and topological properties could be lurking within the aforementioned alkali and coinage-metal honeycomb layered oxide structures. We conclude by pointing towards possible future research directions, particularly the prospective realisation of Kitaev-Heisenberg-Dzyaloshinskii-Moriya interactions with single crystals and Floquet theory in closely-related honeycomb layered oxide materials.

DFTB Modeling of Lithium-Intercalated Graphite with Machine-Learned Repulsive Potential

Lithium ion batteries have been a central part of consumer electronics for decades. More recently, they have also become critical components in the quickly arising technological fields of electric mobility and intermittent renewable energy storage. However, many fundamental principles and mechanisms are not yet understood to a sufficient extent to fully realize the potential of the incorporated materials. The vast majority of concurrent lithium ion batteries make use of graphite anodes. Their working principle is based on intercalation, the embedding and ordering of (lithium-) ions in two-dimensional spaces between the graphene sheets. This important process, it yields the upper bound to a battery's charging speed and plays a decisive role in its longevity, is characterized by multiple phase transitions, ordered and disordered domains, as well as nonequilibrium phenomena, and therefore quite complex. In this work, we provide a simulation framework for the purpose of better understanding lithium-intercalated graphite and its behavior during use in a battery. To address large system sizes and long time scales required to investigate said effects, we identify the highly efficient, but semiempirical density functional tight binding (DFTB) as a suitable approach and combine particle swarm optimization (PSO) with the machine learning (ML) procedure Gaussian process regression (GPR) as implemented in the recently developed GPrep package for DFTB repulsion fitting to obtain the necessary parameters. Using the resulting parametrization, we are able to reproduce experimental reference structures at a level of accuracy which is in no way inferior to much more costly ab initio methods. We finally present structural properties and diffusion barriers for some exemplary system states.

Li-ion transport at the interface between a graphite anode and Li2CO3 solid electrolyte interphase: ab initio molecular dynamics study

Understanding and the control of Li-ion (Li+) transport across the interface between the anode and solid electrolyte interphase (SEI) film or electrolyte is a key issue in battery electrochemistry and interface science. In this study, we investigated the structural, electronic and free energy properties of Li+ migration between a Li-intercalated graphite anode LiCx and Li2CO3 SEI film, by using ab initio molecular dynamics and free energy calculations. We compared three types of graphite edges: H-, OH- and mixed (H, OH, COOH)-terminations, and three cases of transferred Li-ions: Li+ constructing the SEI, excess Li+ and excess Li0 (excess Li+ + e- in anode). After validation of our calculations with Li2CO3 and LiCx bulk systems, we sampled the interfacial structures under thermodynamic equilibrium and demonstrated that the OH- and mixed-terminations had larger binding energies. The calculated free energy profiles of Li+ intercalation from the Li2CO3 SEI to LiC24 showed barriers larger than 1.2 eV irrespective of the terminations and Li+ cases. We also clarified that the charges of Li ions did not change much upon the intercalation. Based on these results and the calculated Li chemical potential, we constructed the probable free energy profile of Li+ between the anode and cathode under charging and discharging. This profile model suggest a possible electric field approximation for the charging stage, and the resultant free energy profiles with such fields gave a ca. 0.5 eV barrier under charging, which was consistent with the experimental values. The present picture will give a crucial insight into Li-ion transport at the battery interfaces.