Quantitative spatiotemporal Li profiling using nanoindentation

Abstract

The rate capability and lifetime of Li-ion batteries is largely dictated by the composition dynamics of the electrodes. We set forth a nanoindentation approach to probe the spatiotemporal Li profile using the functional dependence of the mechanical properties on Li composition. This mechanics-informed material dynamics allows us to measure the composition-dependent diffusivity, assess the rate-limiting process in Li reactions, and quantitatively evaluate the stress regulation on Li transport. The experiments show that Li diffusivity in amorphous Si varies exponentially by three orders of magnitude from the pristine to the fully lithiated state. Lithiation in amorphous Si is limited by diffusion at the micron scale. We further evaluate the thermodynamic driving force for Li diffusion by including the material non-ideality and mechanical stresses. Through computational modeling, we find that the composition dependence of the Li diffusivity in general creates an asymmetry on the rate capability during lithiation versus delithiation. In Si, the exponential dependence results in a fast lithiation that proceeds via a steep concentration gradient compared to a slow and relatively smooth delithiation. This asymmetric behavior appears to be a root cause of Li trapping and loss of the deliverable capacity in Si. This work sheds light on the thermodynamics of Li transport and the lithiation kinetics of amorphous Si. It demonstrates the potential of operando nanoindentation in the mechanics-informed understanding of Li chemistry and aiding battery research beyond mechanical measurement.

Introduction

The kinetics of Li reactions plays a decisive role in the rate capability and cyclic life of Li-ion batteries. Charge heterogeneity is a prevalent feature in the composite electrodes (Xu et al., 2019; Yang et al., 2019). The inhomogeneous distribution of Li is associated with issues such as underused and abused regions in the redox active materials and heterogeneous mechanical failure due to the localized strains and damage (McDowell et al., 2012; Xu et al., 2016). The spatiotemporal distribution of Li provides essential information needed to identify the underlying rate-limiting mechanisms and to determine the material properties. The combination of chemical, temporal and spatial measurements on battery materials is a vast challenge because the instrument must be able to probe the sample without exposure to the atmosphere while still accommodating all necessary components to control the reactions and maintaining experimental accuracy.

Advanced techniques with the capability of probing the Li element are under fast development; nonetheless, current solutions still hold many practical limitations and are not easily accessible (Hoffmann et al., 2015; Wolf et al., 2017). Because of the low atomic number, Li detection is challenging and requires ultra-sensitive spectroscopy techniques such as electron loss spectroscopy (EELS) (Wang et al., 2011), secondary-ion mass spectrometry (SIMS) (Bordes et al., 2015), and Auger electron spectroscopy (AES) (Radvanyi et al., 2013). Neutron diffraction is sensitive to Li, but the neutron resources are very limited (Mu et al., 2019; Sharma et al., 2010). Hence, most studies rely on indirect measurements to infer the local Li content. For instance, X-ray diffraction (XRD) tomography and atomic force microscopy (AFM) can be used to estimate the composition through local changes in density and volume (Balke et al., 2010; Beaulieu et al., 2003). Optical microscopy and colorimetry are able to estimate the approximate Li content based on the changes in the optical spectrum (Chen et al., 2019; Ghannoum et al., 2016; Harris et al., 2010). One of the most popular approaches is the measurement of lithiation state from the lattice parameters and crystal structures through transmission electron microscopy (TEM) and XRD tomography (Finegan et al., 2019; Lim et al., 2016). A combination of different techniques is also often used to complement the capabilities and correlate different processes taking place at different scales (Pietsch et al., 2016; Wu and Liu, 2018). In this work, we use nanoindentation to probe the spatial distribution of Li over time by making use of the functional dependence of the mechanical properties of elastic modulus and hardness on Li composition (de Vasconcelos et al., 2017). We choose an amorphous Si (a-Si) thin film as a model system.

The incorporation of Si nanoparticles to graphite electrodes in recent years has enabled a 6% improvement in the specific capacity of commercial Li-ion batteries (Mims, 2018). The research aimed at improving the reliability of Si anodes continues to grow worldwide, and pure Si electrodes represent an untapped potential for increasing the cell capacity by 40% (Mims, 2018). A major challenge in Si-dominant anodes (Li et al., 2017; Yu et al., 2015) and other high-energy-density electrodes as well (Beaulieu et al., 2001; Laforge et al., 2008; Xu et al., 2018; Zhang et al., 2019) is the suppression of the mechanical degradation resulting from the inherently large strains associated with lithiation. Information on the kinetic processes associated with Li reactions is crucial to understand and manage mechanical stability as they dictate the buildup of mechanical stresses (Xu and Zhao, 2016).

Despite the commercial interest in Si anodes, the kinetics of Li reactions in a-Si remains unclear. In 2013, two in-situ TEM studies under a large bias voltage (McDowell et al., 2013; Wang et al., 2013) and later a potentiostatic study (Miao and Thompson, 2018) found that the first lithiation of a-Si took place via the propagation of a sharp interface between lithiated and pristine Si, but the following delithiation and cycling proceeded with an evolving, smooth concentration gradient. The sharp interface is a common phenomenon in reactions involving phase transformation; however, Si remains amorphous in these experiments. This observation sparked a debate concerning the underlying rate-limiting process, whether reaction-limited (McDowell et al., 2013; Wang et al., 2013) or diffusion-limited (Miao and Thompson, 2018; Wang et al., 2017), and on the structural changes of amorphous Si upon lithiation (Cubuk and Kaxiras, 2014). Another group compared the rate performance of Si films during lithiation versus delithiation and found that amorphous Si exhibited better rate performance during delithiation, which was attributed to the cut-off voltage being more sensitive to the ohmic polarization during lithiation (Li et al., 2015). In contrast, a few recent studies proposed that the incomplete delithiation by Li trapping is one of the causes of fade in the cyclic efficiency of Si (Lindgren et al., 2019; Rehnlund et al., 2017; Zhu et al., 2019).

The complexity of the Li kinetics in Si and the limitation of existing experimental methods are underscored by another discrepancy in the literature about the Li diffusion coefficient in Si which spans over 8 orders of magnitude (Hü et al., 2018; Simolka et al., 2019; Xie et al., 2010; Yoshimura et al., 2007). It is worth mentioning that electroanalytical techniques such as galvanostatic and potentiostatic intermittent titration (GITT and PITT) are amidst the most popular characterization tools. At the same time, many assumptions of the classical models for GITT and PITT may not uphold in Li-ion applications due to uncertainties arising from parasitic charge injections, varying or not well-defined active surface area (expanding and fracturing surfaces), additional rate-limiting effects (e.g., interfacial reactions), and stress effects on diffusion (Jerliu et al., 2017a; Li et al., 2012; Tripuraneni et al., 2018).

This work sets forth a nanoindentation approach to probe the spatiotemporal Li profile in the electrodes of LIBs. Fig. 1 outlines the structure of the work. The nanoindentation experiments are performed on an a-Si thin film in contact with a Li metal and undergoing chemical lithiation in an argon-filled glovebox (step 1). The outcome of the experiments is the spatial maps of the hardness and elastic modulus of the sample at various lithiation times which spans over several days. The central circle in the sketch represents previous operando nanoindentation measurements of the mechanical properties and the size of lithiated Si upon controlled electrochemical lithiation (de Vasconcelos et al., 2017). The combination of the two experiments yields a spatiotemporal Li concentration map (step 2) that enables the calculation of the apparent diffusivity and tracer diffusivity of Li in Si as a function of the material composition (step 3). The knowledge about the Li distribution and internal stresses in the Si thin film allows a quantitative assessment of stress regulation on Li diffusion. The experimental conditions are simulated using finite element analysis (FEA). The numerical simulations employing a two-way coupling between stress and diffusion validate experimental findings and elaborate the implications on the battery performance (step 4).

This work introduces a new characterization method on Li chemistry using the mechanics tool and provides valuable insights into the kinetic behaviors of battery materials. We find that the diffusion coefficient of Li in a-Si electrodes varies by at least three orders of magnitude with the Li composition. The highly concentration-dependent diffusivity leads to an asymmetrical rate capability and thus an asymmetrical accessible capacity of Si during lithiation versus delithiation. More broadly, this work demonstrates the potential of operando nanoindentation in aiding the research on redox active materials beyond simple mechanical characterization. We present one such application where the local mechanical response is used to inform the local chemical composition. Such an interdisciplinary platform does not only expand the experimental toolbox to detect the Li concentration which is difficult to achieve, but also makes it possible to evaluate the competing factors of chemical and mechanical driving forces of Li transport in a quantitative manner.