Influence of elastic strain on the thermodynamics and kinetics of lithium vacancy in bulk LiCoO2

The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO2 is evaluated by means of first-principles calculations within density functional theory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor (Gij) for ground state and saddle point configurations. We analyze finite size-effects in the calculation of Gij, compare the predictions of the linear elastic model with those obtained from direct calculations of defective cells under strain and discuss the differences. Based on our data, we calculate the variations in vacancy concentration and mobility due to the presence of external strain in bulk LiCoO2 cathodes. Our results reveal that elastic in-plane and out-of-plane strains can significantly change the ionic conductivity of bulk LiCoO2 by an order of magnitude and thus strongly affect the performance of Li-secondary batteries

On the origin of incoherent magnetic exchange coupling in MnBi/Fex_xCo1−x_{1-x} bilayer system

In this study we investigate the exchange coupling between the hard magnetic compound MnBi and the soft magnetic alloy FeCo including the interface structure between the two phases. Exchange spring MnBi-Fe$_x$Co$_{1-x}$ (x = 0.65 and 0.35) bilayers with various thicknesses of the soft magnetic layer were deposited onto quartz glass substrates in a DC magnetron sputtering unit from alloy targets. Magnetic measurements and density functional theory (DFT) calculations reveal that a Co-rich FeCo layer leads to more coherent exchange coupling. The optimum soft layer thickness is about 1 nm. In order to take into account the effect of incoherent interfaces with finite roughness, we have combined a cross-sectional High Resolution Transmission Electron Microscopy (HR-TEM) analysis with DFT calculations and micromagnetic simulations. The experimental results can be consistently described by modeling assuming a polycrystalline FeCo layer consisting of crystalline (110) and amorphous grains as confirmed by HR-TEM. The micromagnetic simulations show in general how the thickness of the FeCo layer and the interface roughness between the hard and soft magnetic phases both control the effectiveness of exchange coupling in an exchange spring system

Theoretische Untersuchung des Ladungstransports in Li-basierten Batterien

The performance of Li-ion batteries is mainly determined by ionic and electronic conductivities of the electrode materials. Both transport properties were studied in this dissertation using ab initio-based calculations together with thermodynamic and kinetic analysis in three electrode materials. Here, the Li transport in Si as a future anode material as well as LiCoO2 as the most commonly used and Li2S as a promising cathode materials were investigated. Each of them shows a distinct Li diffusion mechanism and hence different ionic transport properties. In addition, effect of stress/strain on the ionic and electronic mobilities in bulk LiCoO2 were evaluated within the theory of elasticity. In the first section, lithiation of the crystalline silicon anode (c-Si), which results in the formation of a two- phase system consisting of amorphous Li2Si (a-Li2Si) as shell around c-Si as core, was investigated. The lithiation of silicon nanowires, which is accompanied by an anisotropic swelling, is governed by the motion of the interfaces between a-Li2Si and c-Si. To reveal the origin of this phenomenon, adsorption and migration of Li were first evaluated at the three most stable surfaces of c-Si. It was shown that the adsorption of Li initially starts from the (110) surface with the lowest Li migration energy at the highest Li concentration. Afterwards, Li migration was estimated at three explicitly- modeled interfaces of a-Li2Si/c-Si corresponding to the three surfaces of c-Si. It was found that the origin of the anisotropic swelling is not due to a faster ionic diffusion at the interfaces but it is because of thermodynamic reasons related to various interface stabilities. Thus, the growth process at the interfaces of a-Li2Si/c-Si is orientation dependent. The a-Li2Si/c-Si(110) interface has the highest formation energy, lowest stability and hence highest interface mobility among the others which is in agreement with experimental findings. In the second section, thermodynamics and kinetics of defects in Li2S cathode material were studied. To find the origin of the low ionic conductivity in Li2S, the formation and migration of defects in this material were investigated. It was demonstrated that the Li diffusion in Li2S is driven by the formation of Frenkel pairs and migration of single Li vacancies since migration of interstitials Li is not energetically favorable. The lithiation process in Li2S is accompanied by a high activation energy. Therefore, since the formation energies for Li vacancy and interstitial are almost the same, the ionic conductivity is controlled by the kinetic, i.e. the migration energy of single Li vacancies. For LiCoO2 cathode material with a layered structure, first the mechanisms of Li migration both in bulk and on the (10-14) surface were investigated. It was shown that the planar lithiation in both bulk and (10-14) surface occurs via the diffusion of Li into a divacancy of Li on a curved pathway. This process, in the case of the topmost layer of (10-14) surface, takes place with no energy barrier. The lithiation process in LiCoO2 is accompanied by hole-polaron hopping, which can only be detected using a DFT functional corrected with an onsite Hubbard term for Co, and as a result increases the migration energy of lithium. Estimated electronic conductivity in bulk LiCoO2 is in good agreement with experimental value. Additionally, the effect of stress/strain on charge carriers mobilities was investigated in bulk LiCoO2 by means of the “elastic dipole tensor (EDT)” method. Li diffusion energy barrier decreases with lateral tensile strain while the formation energy of Li vacancy increases, however, the effect of strain on the migration energy is stronger. 1% longitudinal strain in bulk LiCoO2 can change the ionic conductivity more than one order of magnitude. The effect of stress/strain on electronic conductivity is opposite and less pronounced than that of the ionic one. The results obtained from the computationally efficient EDT method for both ionic and polaronic transports are in very good agreement with the conventional computationally-demanding method.Die Leistung von Li-Ionen-Batterien wird hauptsächlich durch ionische und elektronische Leitfähigkeiten der Elektrodenmaterialien bestimmt. Beide Transporteigenschaften wurden in dieser Dissertation mit ab initio-basierten Berechnungen zusammen mit thermodynamischen und kinetischen Analysen in drei Elektrodenmaterialien untersucht. Hier wurden den Li-Transport im Si als zukünftiges Anodenmaterial, LiCoO2 als das am häufigsten verwendete und Li2S als ein sehr vielversprechendes Kathodenmaterial untersucht. Jedes von ihnen zeigt einen anderen Li-Diffusionsmechanismus und damit unterschiedliche ionische Transporteigenschaften. Darüber hinaus wurde die Wirkung von Stress/Dehnung auf ionische und elektronische Mobilitäten in Bulk LiCoO2 innerhalb der Theorie der Elastizität ausgewertet. Im ersten Abschnitt wird die Lithiierung von einer kristallinen Silizium-Anode (c-Si) untersucht, die durch die Bildung eines Zweiphasensystems entsteht, mit amorphem Li2Si (a-Li2Si) als Hülle um c-Si als Kern. Die Lithiierung von Silizium- Nanodrähten, die begleitet wird von einer anisotropen Ausdehnung, erfolgt durch die Bewegung der Grenzflächen zwischen a-Li2Si und c-Si. Um den Ursprung dieses Phänomens zu enthüllen, wurden zuerst Adsorption und Migration von Li an den drei stabilsten Oberflächen von c-Si ausgewertet. Es wurde gezeigt, dass die Adsorption von Li zunächst auf der (110) Oberfläche mit der niedrigsten Li-Migrationsanergie bei der höchsten Li- Konzentration beginnt. Danach wurde die Li-Migration für drei explizit modellierte Grenzflächen von a-Li2Si/c-Si, die den drei Oberflächen von c-Si entsprechen, untersucht. Die Ergebnisse zeigten, dass der Ursprung der anisotropen Ausdehnung nicht auf eine schnellere ionische Diffusion an den Grenzflächen zurückzuführen ist, sondern auf thermodynamischen Gründen, die sich auf verschiedene Grenzflächenstabilitäten beziehen. Daher ist der Wachstumsprozess an den Schnittstellen von a-Li2Si/c-Si orientierungsabhängig. Die a-Li2Si/c-Si(110) Grenzfläche besitzt die höchste Grenzflächenbildungsenergie, die niedrigste Stabilität und damit die höchste Mobilität der untersuchten Grenzflächen, was mit dem Experiment übereinstimmt. Im zweiten Abschnitt wurden die Thermodynamik und Kinetik von Defekten im Li2S Kathodenmaterial untersucht. Um den Ursprung der niedrigen Ionenleitfähigkeit in Li2S heraus zu finden, wurden die Defektbildung und -migration in diesem Material untersucht. Es wurde gezeigt, dass die Li-Diffusion in Li2S durch die Bildung von Frenkel- Paaren und die Migration von einzelnen Li-Leerstellen angetrieben wird, da die Migration von interstitiellen Li-Ionen energetisch nicht günstig ist. Der Lithiierungsprozess wird von einer hohen Aktivierungsenergiebarriere begleitet. Daher wurde gefolgert, dass, da die Formationsenergien für Li- Leerstellen und Interstitiale fast gleich sind, die Ionenleitfähigkeit wird durch kinetische gesteuert, und damit die Migrationsenergie einzelner Li- Leerstellen. Für das LiCoO2 Kathodenmaterial mit einer Schichtstruktur, wurden zunächst die Mechanismen der Li-Migration sowohl im Bulk als auch auf der (10-14) Oberfläche untersucht. Es wurde gezeigt, dass die planare Lithiierung sowohl im Bulk als auch der (10-14) Oberfläche über die Diffusion von Li in eine Divakanz von Li auf einem gekrümmten Weg erfolgt. Dieser Vorgang, im Falle der oberste Schicht der (10-14) Oberfläche, erfolgt ohne Energiebarriere. Der Lithiierungsprozess in LiCoO2 wird von einem Loch- Polaron-Hopping begleitet, das nur mit einem DFT-Funktional erkannt werden kann, das mit einem lokalen-Hubbard-Term für Co korrigiert wird und die Migrationsenergie von Lithium erhöht. Die berechnete elektronische Leitfähigkeit in Bulk LiCoO2 ist in sehr guter Übereinstimmung mit dem experimentellem Wert. Darüber hinaus wurde die Wirkung von Stress/Dehnung auf Ladungsträger-Mobilitäten mittels des ”elastischen Dipol-Tensors (EDT)” Verfahrens in Bulk LiCoO2 untersucht. Die Li-Diffusionsenergiebarriere nimmt mit lateraler Zugbeanspruchung ab, während die Vakanz-Bildungsenergie zunimmt, jedoch ist der Effekt der Dehnung auf die Migrationsenergie stärker. 1% Längsdehnung in Bulk LiCoO2 kann die Ionenleitfähigkeit mehr als eine Größenordnung verändern. Dieser Effekt ist gegenüber und weniger ausgeprägt im Fall der elektronischen Leitfähigkeit. Die Ergebnisse aus dem rechnerisch effizienten EDT Verfahren stimmen sowohl für ionische als auch polaronische Transporte mit dem konventionellen rechnerisch anspruchsvollen Verfahren ausgezeichnetüberein

Effect of lattice and dopant–induced strain on the conductivity of solid electrolytes: application of the elastic dipole method

Here, we studied the possibility of applying the elastic dipole method (EDM) to predict the response of defect formation and migration energy to an external strain field (ϵij) in Al-doped cubic Li6.25Al0.25La3Zr2O12 (Al-LLZO) and Li10GeP2S12 (LGPS). It is shown that EDM can quantitatively provide accurate values for Li-defect formation energy as a function of ϵij. EDM can also predict, qualitatively, how the migration barrier varies with ϵij. In both Al-LLZO and LGPS systems, the formation energy of Li vacancy decreases (increases) by applying a tensile (compressive) strain, which is because the lattice parameters tend to expand by formation of a Li vacancy. An opposite behavior is found for the formation energy of interstitial Li. Furthermore, we found that a compressive strain decreases the diffusion barrier in Al-LLZO, while it increases it in LGPS. The lowering of migration barrier in Al-LLZO is in spite of contraction of bottleneck width of Li diffusion in this system. This finding is in line with a recent experimental study. Analysis of EDM results shows that the lowering (rising) in the migration barrier of Li in Al-LLZO (LGPS) under a compressive strain is due to tendency of the system to contract (expand) Li–O (Li–S) bond lengths in the transition states where Li ions are at the bottlenecks of diffusion pathways. We finally show that the result of Li migration barrier as a function of strain in a non-doped solid electrolyte can be used to predict the global effect of substitution/doping on the conductivity of that system

Defect chemistry in cubic Li6.25Al0.25La3Zr2O12 solid electrolyte: A density functional theory study

Al-doped Li7La3Zr2O12 is a promising solid electrolyte material for all-solid-state batteries. In this study, by applying Coulomb energy analysis, density functional theory (DFT) calculations, and thermodynamics considerations, we have investigated defect chemistry in Li6.25Al0.25La3Zr2O12 (Al-LLZO). Defect formation energy plots indicate that decreasing or increasing of Li+ concentration in Al-LLZO is unfavorable. To preserve the charge neutrality, any removed (added) Li+ must be compensated by adding (removing) Li+, which can be viewed as a rearrangement of Li+ ions. The energy cost for Li+ displacement is very low (∼0.1 eV), which is in line with the (Li) ionic-conductive nature of Al-LLZO. For a wide range of Li chemical potentials, under Zr poor condition, a complex defect type consisting of 2 added Li+ together with one removed O2− and one removed Zr4+ is the most favorable. Under O poor condition, a Schottky-like defect comprising of a cluster of 2Li+ and O2− vacancies with ≈0.2 eV higher formation energy is the second most favorable defect. In addition, we found that for a narrow range of low (high) Li chemical potentials, removed (added) neutral Li is the most favorable defect type. Our results show that decreasing or increasing of Li content in bulk Al-LLZO is only possible through the formation of complex defects or neutral removed/added Li under Li poor/rich conditions

Thermodynamics and kinetics of defects in Li2S

Li2S is the final product of lithiation of sulfur cathodes in lithium-sulfur (Li-S) batteries. In this work, we study formation and diffusion of defects in Li2S. It is found that for a wide range of voltages (referenced to metal Li) between 0.17 V and 2.01 V, positively charged interstitial Li (Li+) is the most favorable defect type with a fixed formation energy of 1.02 eV. The formation energy of negatively charged Li vacancy V(Li,-) is also constant, and it is only 0.13 eV higher than that of Li+. For a narrow range of voltages between 0.00 V and 0.17 V, the formation energy of neutral S vacancy is the lowest and it decreases with decreasing the cell voltage. The energy barrier for Li+ diffusion (0.45 eV), which takes place via an exchange mechanism, is 0.18 eV higher than that for V(Li,-) (0.27 eV), which takes place via a single vacancy hopping. Considering formation energies and diffusion barriers, we find that ionic conductivity in Li2S is due to both Li+ and V(Li,-), but the latter mechanism being slightly more favorable

The influence of anisotropic surface stresses and bulk stresses on defect thermodynamics in LiCoO2 nanoparticles

The demand for higher specific capacity and rate capability has led to the adoption of nanostructured electrodes for lithium-ion batteries. At these length scales, surface effects gain an appreciable impact not only on the electrochemical and mechanical behavior of the electrode material, but also on defect thermodynamics. The focus of this study is the distribution of surface-induced bulk stresses in a LiCoO2 nanoparticle and their impact on the migration of Li vacancies. LiCoO2 is a prototypical cathode material, where the diffusion of Li is mediated by the vacancy mechanism. For this investigation, elastic parameters and anisotropic surface stress components are computed using Density Functional Theory calculations. They are incorporated into a surface-enhanced continuum model, implemented by means of the Finite Element method. The particle geometry is derived from a Wulff construction, and changes in the formation energy and migration barriers of a Li vacancy are determined using the defect dipole tensor concept. Within the considered nanoparticle, the surface stresses result in a highly heterogeneous bulk stress distribution with a vortex-like transition region between the tensile particle core and its non-uniformly stressed boundaries. Both the center and the exterior of the particle show enhanced formation energy and migration barriers for of a Li vacancy. These experience a reduction in the transition region in the particle, culminating in a peak increase in vacancy diffusivity and ionic conductivity by circa 10% each. For a particle at a length-scale of 10 nm, this yields an overall increase in ionic conductivity by a mere 0.8%. This surface stress-enhanced conductivity decays rapidly with increasing particle size. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved