@PhdThesis{duepublico_mods_00039980,
  author = 	{Amanieu, Hugues-Yanis},
  title = 	{Nanomechanics of Li-ion battery materials},
  year = 	{2015},
  month = 	{Dec},
  day = 	{14},
  keywords = 	{nanoindentation AFM akkumulator},
  abstract = 	{This document deals with the research that the author, Hugues-Yanis Amanieu, carried out between 2012 and 2015 in order to obtain the academic grade of Doctor of Engineer- ing (Dr.-Ing.) delivered by the University of Duisburg-Essen, Germany. The present work was included in two larger projects: Nanomotion, funded by the European Commission through a Marie-Curie actions program, and ReLiOn, funded by the German Federal Ministry of Education and Research. The goal of the former is to design new nanoscale characterization techniques to study electrochemical systems. The latter has for objective to better understand mechanical reliability of battery materials. The work described in this manuscript consequently had for objective to develop new characterization techniques in order to obtain material parameters which are fundamental to numerical simulations allowing a better understanding of mechanical failure in active particles of lithium-ion batteries. In part I, there is a description of the functioning of lithium-ion batteries (LiB) and of the state-of-the-art of the most important characterization techniques. As explained in section 1.1, LiB is an electrochemical system where two electrodes exchange ions within the system and electrons in an external circuit. These electrodes contain active particles where lithium can reversibly intercalate. The ions are extracted and reintroduced repeatedly which can lead to mechanical failure of the particles (see section 1.2). In fact the speed of ions in the host material controls the gradient of ionic concentration upon cycling. This gradient provokes tensile and compressive stresses. The former can reach a critical value where fracture or disordering occurs. This process depends on some key material parameters, namely the elastic modulus E, the fracture toughness K C , and the diffusion coefficient D Li . The material of study is spinel lithium manganese(III,IV) oxide (LiMn 2 O 4 ), which is described in section 1.3. Instrumented indentation testing (IIT), or nanoindentation, is then outlined in section 2.1. It is a tool which consists in driving a stiff diamond tip into a sample surface. Using the Oliver and Pharr (1992) method, the elastic modulus and the hardness of a homogeneous sample can be quantified. It was extended by Ulm and Vandamme (2007) for heterogeneous materials by implementing statistical deconvolution on a large data set. Section 2.2 deals with atomic force microscopy (AFM)-based techniques. The first one consists of measuring the topography of a crack in order to determine its crack- opening displacement (COD) and subsequently estimate the fracture toughness using Irwin's near field theory. Then contactresonance atomic force microscopy (CR-AFM) is introduced. The elastic properties can be estimated through the resonance frequency of the cantilever when in contact with the sample surface. Last electrochemical strain microscopy (ESM) is presented. Here the AFM cantilever vibration amplitude is measured during application of a AC excitation between the AFM tip and the sample. The vibration is mediated via a mechanism which depends on the lithium concentration. Time spectroscopy measurements can be carried out by monitoring the signal after applying a DC pulse: a typical relaxation process is detected and its speed depends on the ionic diffusion coefficient D Li . However the underlying mechanisms are still unknown to quantify it. A Vegard's deformation generated by ionic diffusion was first assummed but it seems unlikely as the displacement would not be detectable. As listed in part II, the objectives of the work were to implement Ulm's nanoindentation statistical method and to suggest alternative methods such as CR-AFM in order to quantify E, to propose new instruments to estimate the K C of micrometric particles, and last to suggest a new model in order to make ESM a quantitative technique. Sample preparation and experiments are described in part III. LiMn 2 O 4 cathodes obtained from fresh cells and from aged cells at different states of charge were embedded in epoxy and then prepared as polished cross-sections. Laboratory-grade reference powders of SiO 2 , MnO 2 and LiMn 2 O 4 were also similarly prepared. A LiMn 2 O 4 -based wafer oriented in the {\{}111{\}} direction was synthesized (see chapter 3). The different instruments used in the course of the work are mentioned in chapter 4. Among these, AFM topography measurements of the COD were numerically modeled as described in chapter 5. It is shown in part IV that Ulm's statistical deconvolution technique cannot be directly used on the battery samples as many spurious peaks appear in the distribution of the measurements. This part therefore relates to a method, called selective nanoindentation, that was specifically developed in order to obtain reliable measurements of the elastic moduli and the hardnesses of each phase of heterogeneous samples. It consists of filtering each experimental data by checking its consistency with the Oliver and Pharr method. First it is checked if the load-displacement curve has a quadratic shape. Second it is checked if no structural compliance induced by the epoxy matrix influences the measured stiffness. Third the filtered data are deconvoluted and compared to scanning electron microscopy (SEM) micrograms of the indented surfaces. The SiO 2 -based sample was used to verify the reliability of the method. Part V deals with the modeling of the ESM system. A COMSOL model was developed to describe the change in the lithium concentration field in a LiMn 2 O 4 body during and after the application of a DC pulse. Its novelty is twofold. D Li is not constant but depends on the lithium concentration. More importantly, the ESM signal is not physically described like in previous work where Vegard's deformation in the frequency domain is computed. Instead, the signal is estimated to be linearly dependent with the mean Lorentz electric force applied by the AC excitation on the lithium ions, denoted F AC . All of the results are listed in part VI. First, chemical analyzes of the samples are given in chapter 13. X-ray diffraction (XRD) measurements showed that every sample contains a single spinel phase. This result was nuanced by energy dispersive X-ray analysis (EDX) and inductively coupled plasma optical emission spectrometry (ICP-OES) as cobalt oxide particles (up to 2 {\%}) were detected but also other impurities. SEM showed also that these commercial particles can be porous agglomerates of nanoparticles as well as large single grains. The wafer exhibited two phases: the main one is spinel LiMn 2 O 4 as expected but also a Mn 2 O 3 bixbyite phase was found. Only the former was characterized by the other methods. Nanoindentation results are reported in chapter 14. The particles are quite brittle: chipping occurs around the indents and cracks grow from them. Electron backscatter diffraction (EBSD) qualitatively revealed that the mechanisms depend on the crystal orientation. IIT measurements reported an elastic modulus of around 90 GPa and a Berkovich hardness of 7 GPa. This is lower than what was previously reported on LiMn 2 O 4 thin films by Zhu and Zeng (2012), certainly because they did not take pile-up into account, hence overestimating the properties, but also because our samples are made of factory-grade particles of lower quality. These two properties increase of more than 10 {\%} upon delithiation. We associated this behavior with Mn−O bonds which are stiffer when the valence of the transition metal increases. The average Mn valence goes from +3.5 for LiMn 2 O 4 to +4 for $\lambda$−MnO 2 . An exception was detected for the specimen obtained from a 25 {\%} SoC cell where the hardness was much lower (6.5 GPa), which could be caused by a less hard non-stoichiometric LiMn 2 O 4 . Micro- Raman spectroscopy combined with CR-AFM revealed that neighboring particles can have different lithium concentrations, hence difference stiffnesses accordingly with the nanoindentation results. CR-AFM was also used on the reference LiMn 2 O 4 powder and it was shown that the spinel is isotropic, at least within the detection limit of the instrument. Quantitative implementation of CR-AFM was unsuccessful. Using the traditional crack-length measurement method on the wafer, a K C of 0.23 MPa{\textperiodcentered}m 1/2 was found. As the unusual crack configuration around the indents of the particles do not allow this method to be used, COD measurements were carried out. A K C of about 0.9 MPa{\textperiodcentered}m 1/2 was measured for the commercial particles and of about 0.8 MPa{\textperiodcentered}m 1/2 for the wafer. It was also found by EBSD that cracks always propagate in the <121> direction in the wafer. They open {\{}101{\}} planes just below the surface and deviate of 30 to 40 ◦ after about 100 nm. These data are given in chapter 15. ESM measurements as well as data from the model are reported in chapter 16. It was demonstrated that the experimental signal is qualitatively similar to F AC . The concentration dependent D Li can explain the asymmetrical hysteresis loops. Using a constant D Li , it was established that time spectroscopy relaxation of F AC follows a power law of the form (at + 1) 1/p . Here p is only slightly dependent on the diffusivity 1/2 and the contact radius while a strongly depends on them and is linear with D Li /R tip . Experimentally, the relaxation process was much slower for the aged sample while no significant differences were reported for the fresh samples with different states of charge (SoCs). Discussions of the different results are depicted in part VII. A critique of the Ulm and Vandamme (2007) method of is discussed in chapter 17. Pavel Trtik et al. (2009) consider indeed that spurious peaks cannot be avoided when indenting heterogeneous materials. A response is given by Ulm and Vandamme (2010) which proves that their results are due to the three-dimensional configuration of their model. In our case, spurious peaks were detected nonetheless but could simply be eliminated using the selective nanoindentation method. An important drawback is that much more measurements must be performed to reach statistically significant numbers. In the same chapter, it was discussed that CR-AFM was a valuable extension to nanoindentation as qualitative stiffness maps with a nanoscale precision can be acquired within minutes. Nanoindentation still has the advantage of quantification as the AFM-based method was unreliable and much too slow. Last the COD measurements are discussed. It was shown that the user interpretation of the data is not so significant as a sample of 9 analysts found similar K IC and K IIIC on the simulated cracks as well as on two real measurements. However it is believed that the method greatly overestimates the toughness as one of the Irwin's condition is not met: the crack walls are not traction-free due to residual tensile stresses originating from the indent plastic zone. This explains the discrepancy between the two values measured on the wafer. It was suggested to use instead the pillar splitting method developed by Sebastiani et al. (2014), as they found a likely K C of about 0.3 MPa{\textperiodcentered}m 1/2 on our samples. The origin of the ESM signal is discussed in chapter 18. It is suggested that other electromechanical couplings, such as electrostriction or flexoelectricity, should be considered. Moreover, the AC electric field could hypothetically interact with the transition metals rather than with the lithium ions. The coupling between the mechanical properties and the lithium concentration is compared with that of other similar ceramics in chapter 19. In general, a longer bond length lead to a more compliant material, whether it is induced by an increasing or decreasing lithium concentration. Then the fracture toughness is compared with that of LiCoO 2 . It was reported to be higher for the pristine material: 1 MPa{\textperiodcentered}m 1/2 . But as soon as the material is electrochemically activated, the K C drops to similar values as ours, about 0.25 MPa{\textperiodcentered}m 1/2 . In the end a brief conclusion is given that first sums up the key results for people working with battery simulation. Secondly, an overview of the reliability of the different characterization methods is given.},
  url = 	{https://duepublico2.uni-due.de/receive/duepublico_mods_00039980},
  file = 	{:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00040465/DissAmamieu.pdf:PDF},
  language = 	{en}
}