Cycling-Induced Microstructural Changes in Alloy Anodes for Lithium-Ion Batteries

The lithium-ion battery (LIB) plays a key role in current and future technology. Our existing and future technology hinges on the ability to store and transport energy more efficiently. Lithium-ion batteries have a relatively high energy density and a decreasing cost which has made them the choice for many applications today and sparked an interest in the research of LIBs. Graphite anodes are the most common choice for many commercial lithium-ion batteries. However, when the capacity of graphite (372 mAh g⁻¹) is considered, it becomes clear that there is room for improvement. For LIBs, high-capacity anode development based on tin (Sn) and silicon (Si) can achieve an order of magnitude higher specific capacity compared to the conventional graphite anode. The Li storage capacity of Sn has a theoretical value of 991 mAhg⁻¹, and the Li storage capacity of Si has a theoretical value of 3579 mAh/g which are both significantly higher than that of graphite [1–6]. Both of these high-capacity options have failure mechanisms that must be mitigated in order to effectively utilize their high capacity. Tin alloys will be the primary interest herein, as it presents a promising performance in both lithium-ion and beyond lithium-ion chemistries.

Pure Sn undergoes excessive (300%) volume change when alloying with lithium. This volume change causes dramatic structural changes and leads to capacity fade during electrode cycling. To overcome the adverse effects of lithiation and volume expansion, various routes, such as developing alloys and nano-materials, have been explored to accommodate expansion and reduce fracture [1,7–18]. Among these routes, Sn-based intermetallic compounds, Sn_xM_y (M: Cu, Ni, Fe, Co), have been explored where the lithium alloying reaction forms a Li–Sn alloy within a relatively ductile host matrix that accommodates strain [2]. For example, Cu-based porous foam structures coated with Sn can serve the dual purpose of the electrode and current collector [2,19–23]. In this case, the Cu foam serves as a distributed current collector within the porous electrode. Depending on the preparation, the foam may be applied without a foil current collector [2,19,21] or integrated with the foil current collector through deposition methods [20,22,23]. The porous foam architecture is believed to allow shorter lithium transport pathways through the active coating and increase electrochemically active interfacial area with higher porosity, resulting in improved electrochemical performance [2]. However, substantial capacity fade has been observed in intermetallic alloy anodes during cycling.

Capacity fade in intermetallic electrodes has been attributed to several potential mechanisms, which include (1) expulsion of inactive material from the composite microstructure; (2) mechanical disintegration of microstructure; (3) Li₂O formed from metal oxide impurities; and (4) solid electrolyte interface formation and reformation after mechanical disintegration. For the intermetallic alloy Cu₆Sn₅, the first of these mechanisms relates to the chemical reactions that occur during lithiation [24]. Above 0.2 V versus Li/Li⁺, an intermediate ternary alloy, Li₂CuSn, is formed during lithiation of Cu₆Sn₅, and some expulsion of Cu from the alloy matrix occurs. Cycling down to 0 V versus Li/Li⁺ leads to complete Cu expulsion from the alloy material. Mechanical disintegration also occurs during lithiation. For the first reaction step, a volume change of ∼45% has been noted, while full lithiation increases expansion to ∼180% [2]. This expansion fractures the active material and may lead to microstructural collapse after extended cycling [25]. Such behavior has been observed for particle-based and foil electrodes [20,26] as well as electrodes employing more novel mesoporous structures [2,21–25]. The content herein focuses on the observation and characterization of the microstructural changes that are introduced to Cu₆Sn₅ electrodes during various cycling conditions.

X-ray tomography, both on the micro- and nanoscale, is an effective way of quantifying and evaluating the characteristics of material structures. Being able to capture an image of the structure of materials at various states under various conditions allows us to attribute the reason for particular structural changes in materials. Herein, X-ray microtomography (µCT) is used to image the three-dimensional (3D) microstructure of samples extracted from pristine and cycled electrodes. The reconstructed samples are segmented using grayscale thresholding informed by the histograms of background and pristine sample regions. The phase size distributions, specific surface areas, and tortuosity of the anode phases are compared to quantify and assess the impacts of lithiation and delithiation on high-capacity anode materials.

In order to observe and quantify the microstructural effects of lithiation and delithiation, electrode pellet samples were fabricated, cycled, and then X-ray µCT was performed on the pellet samples. Synthesis of Cu₆Sn₅ pellet electrodes was performed following the methods of Kepler et al. [26]. Further details of the alloy synthesis, X-ray diffraction (XRD), and electrode fabrication are given in Ausderau et al. [27]. A significant majority of the pellet electrodes were found to be Cu₆Sn₅ with smaller amounts of Cu₃Sn, Sn, and Cu. No significant quantities of Sn or Cu oxides were observed. For electrochemical testing, pellet electrodes 13 mm in diameter and 1 mm thick were produced. Lithiation and cycling were performed on these electrodes to observe the structural effects of electrochemical cycling. Cu₆Sn₅ pellets were used as the working electrode in a half cell assembled in an argon-filled glove box. These cells included a lithium foil counter electrode and glass fiber separator along with ∼200 µl of 1 M LiPF₆ in diethyl carbonate (DEC) as an electrolyte. Lithiation and delithiation were performed in two voltage windows 0.2−1.5 V versus Li/Li⁺ and 0–1.5 V versus Li/Li⁺. The upper cutoff voltage of 1.5 V versus Li/Li+ is commonly applied in studies of Cu₆Sn₅ [2,19]. The lower voltages were selected to better observe the multistep lithiation process of Cu₆Sn₅ electrode [2,24,26]. Above approximately 0.2 V versus Li/Li⁺ a ternary alloy, Li₂CuSn, is formed with partial copper expulsion and moderate structural change. Full lithiation of the Sn to Li_4.4Sn occurs as the electrode approaches 0 V versus Li/Li⁺. This full lithiation is accompanied by complete expulsion of the Cu and further structural change. To permit more extensive lithiation of the pellet electrode surfaces, the lithiated samples were held at their respective lower voltage limits. Further details of the electrode testing have been provided by Ausderau et al. [27].

To better understand the coupling of microstructural changes and cycling for alloy anodes, a combined electrochemical and µCT study was performed. Galvanostatic lithiation and delithiation were performed on Cu₆Sn₅ pellet electrodes. After cycling, the half cells were disassembled in a controlled atmosphere glove box (∼1 ppm H₂O). The surfaces of the Cu₆Sn₅ pellets exhibited a black coating along the exterior surface adjacent to the separator, suggesting lithiation of that surface [19]. This reacted layer was removed from a portion of the pellets for use in nanoscale X-ray imaging [27]. Synchrotron-based X-ray µCT was also performed on larger samples extracted from the pellet electrodes prior to surface layer removal. These µCT samples were placed in plastic pipette tips and cast in epoxy prior to imaging. X-ray imaging was performed at a resolution of 1.3 µm (0.65 µm pixel size) using beamline 2-BM-A at the Argonne National Laboratory Advanced Photon Source (APS). The µCT scans were performed in white beam mode with an exposure time of 50 ms per projection image. Each tomographic scan contained 1500 projection images equally spaced over 180 deg of rotation.

The projection image data are used to reconstruct a 3D image for each pellet sample that was scanned. The reconstruction process was completed using a filtered back-projection algorithm within the TomoPy software [28]. A cross section from the reconstructed image of each pellet sample that was scanned and used for the present analysis is shown in Fig. 1. Where applicable, the cycling conditions are included. The difference between the (de)lithiated samples in Figs. 1(a)–1(d) and the pristine samples in Fig. 1(e) can be seen clearly. The samples subject to full lithiation or cycling (Figs. 1(a), 1(b), and 1(d)) show a distinct pulverized edge region, with interior regions that are comparable with the pristine pellet (Fig. 1(e)), which shows a consistent structure throughout. The samples subject to partial lithiation (Fig. 1(c)) show slight changes near the edge regions, but they share the more consistent structure seen in the pristine sample. Further discussion of these features is given in Sec. 3.1. Here, it should be noted that the sample on the left in Fig. 1(a) has fractures that occurred in the pellet as the result of sample preparation. These regions of the sample were avoided when selecting sample regions for analysis. Furthermore, multiple sample regions were selected from each sample image to ensure that any related variations would be accounted for when considering mean values for microstructural properties.

The reconstructions of the pellet samples shown in Fig. 1 are analyzed to acquire parameters that can quantitatively describe the microstructure of each sample. Two sample image stacks were used from each cycling condition, shown at left and right in Figs. 1(a)–1(e). From these 3D image stacks, smaller sample regions were taken and treated as individual samples in the microstructural analysis. Preliminary analysis was completed using three 270 × 270 × 270 voxel edge sample regions and one 180 × 180 × 180 voxel center sample regions from each of the sample images (giving a total of eight sample regions for each cycling condition). These sample regions were used to calculate the continuous phase size distribution and specific surface areas for the microstructure [29]. All other analyses herein were conducted by taking four 180 × 180 × 180 voxel edge sample regions and two 180 × 180 × 180 voxel center sample regions from each sample image. This subdivision yielded a total of eight sample edge regions for each cycling condition. The edge sample regions were used to evaluate the microstructural changes due to cycling. The center sample regions were unreacted and were compared to each other and to the pristine sample to confirm the consistency in the determined properties of the unreacted structure. The analyzed sample set came to a total of 60 sample regions that were used in the characterization analysis. The reason for the smaller volume regions in the latter analysis is to accommodate the computational limitations of the code used in determining the tortuosity. Although this volume is smaller, trade studies for comparing the characterization results show that the smaller volume regions are sufficiently large to be a representative volume of the entire sample image.

Quantifying microstructural parameters from these X-ray images consist of two main processes: segmentation and analysis. The segmentation and analysis processes were carried out primarily with FIJI and matlab. The segmentation process is done to isolate different materials of interest that reside in the pellet samples for later analysis. The method of segmentation used is a strict thresholding process based on grayscale limits informed by the sample image histogram. This thresholding process consists of establishing ranges of gray values that encompass each material of interest and then using these ranges to isolate a specific material of interest during analysis. The most difficult part of the segmentation process is establishing gray value ranges that can accurately encompass a material of interest without being so broad that the range also encompasses materials of other phases. Gray values can be used to isolate individual materials because the gray value of each voxel in the image has a direct correlation to the attenuation of the object at that location. This attenuation is specific to each material, which makes the gray values specific to each material.

To establish ranges of gray values for each material of interest, specific regions of the image were isolated for observation. For the purpose of the analysis presented herein, the image can be broken up into three phases: “reactants” to be lithiated (the high attenuation solids Cu₆Sn₅ and Sn), “products” of the lithiation process (intermediate attenuation solids including Li₂CuSn, Li_4.4Sn, and Cu), and the background (low attenuation epoxy and open-pore regions). These materials are considered to be the bulk content of the three phases distinguished by thresholding. However, additional compounds may be present including solid electrolyte interphase (SEI) within the lithiated regions and Cu₃Sn and Sn within the reactant regions [27]. During electrochemical testing, a voltage plateau corresponding to electrolyte decomposition on Sn was observed, suggesting the occurrence of SEI formation [27]. The µCT method lacks the resolution to directly observe details of the SEI structure.

To establish the gray value ranges for these three regions, a large area is selected from the image that contains only what is known to be part of the background, as shown in Fig. 2(a). A histogram is then calculated for this selected region. Typically, since this entire selected region is known to be background, the histogram of the gray values contained in this selection forms a well-defined normal distribution. This normal distribution is used to choose a range of gray values that would encompass the distribution of all background voxels. Figure 2(b) shows a histogram that was observed to determine the gray value range for the background region shown in Fig. 2(a). The upper and lower limits for background thresholding are shown as well. It should be noted that the negative values in this histogram data are the result of phase-contrast data retrieved from the tomographic reconstruction. Specifically, some of the voids present in the epoxy can be seen in Fig. 2(a) (indicated by the arrows).

Every voxel in the image that has a gray value that falls in the range defined in Fig. 2(b) is considered to be part of the background and thresholded with a value of “NaN.” This setting allows the background voxels not to be considered in future histograms while preserving the grayscale values of the remaining voxels. At this point, all that remains in the image is solid material since the background voxels have essentially been nulled. A depiction of an image that just contains solid material is shown in Fig. 2(c).

This solid material, as stated earlier, is broken into two phases of interest. In Fig. 1, it can be seen that for all of the samples, other than the pristine samples, the innermost region consists primarily of the reactants that are not lithiated, while the outermost region of the samples is where most of the products from the lithiation process reside. With this information, a region toward the center of the sample is selected that can be assumed to consist primarily of Cu₆Sn₅ and Sn. An example of a selection of the center of a pellet sample is depicted in Fig. 2(c). A histogram is calculated for all the voxels in this selected region. The histogram of the center region of the sample is considered a left-skewed distribution, the left tail of which is believed to be due to imaging artifacts as well as small amounts of materials other than Cu₆Sn₅ and Sn that skew the gray value distribution to the left. These artifacts can include ring artifacts, beam hardening, and phase-contrast effects in the tomographic reconstruction. The next step is to establish another range of gray values that just encompass the material consisting of Cu₆Sn₅ and Sn. Establishing the gray values range from this histogram is a bit more complicated than establishing a range from the background data, because these data are skewed, rather than being strictly a normal distribution.

For establishing this range of gray values, it is assumed that the distribution of gray values for the material containing Cu₆Sn₅ and Sn follows the central limit theorem. This assumption is validated by calculating a histogram of the material in the pristine samples of primarily Cu₆Sn₅ and the minor components identified by XRD. As shown in Fig. 3, distribution is formed for the pristine sample that is approximately normal and follows the central limit theorem. Furthermore, this pristine sample exhibits a distribution and mean values comparable to the interior region of interest for the cycled samples (Fig. 2(d)).

Under the consideration that the Cu₆Sn₅ and Sn gray value distribution follows the central limit theorem, the peak of the left-skewed distribution is located and said to be the mean of the Cu₆Sn₅ and Sn gray values distribution. Next, an upper limit that will encompass the gray values to the right of the peak is determined. The peak value and upper limit are compared to determine the number (n) of standard deviations (σ) to the right of the peak that will encompass all gray values to the right of the peak. Once this number of standard deviations is determined, a lower limit for the range is established that is symmetric to the upper limit that was established. This process establishes upper and lower limits that are symmetric about the peak of the distribution. This symmetry then falls in line with the assumption that the gray values containing Cu₆Sn₅ and Sn follow the central limit theorem when unaffected by artifacts, imperfections, and small amounts of foreign material in the microtomography. Figure 2(d) depicts the histogram of the gray values for the region containing primarily Cu₆Sn₅ and Sn with the upper and lower limits established.

With a range of gray values established for the Cu₆Sn₅/Sn regions in the sample, the images can be segmented into the three regions of interest. There is now a range of gray values that encompass the background and a range of gray values that encompass the reactant materials. The remaining unclassified voxels in the image have gray values that fall between these two ranges and are deemed products from the lithiation process.

Using the ranges of gray values for each phase of interest, analysis is performed on each individual phase. The main procedures for analysis that is carried out on each phase are phase size distribution (PSD), continuous phase size distribution (CPSD), cumulative size distribution (CSD), specific surface area calculation, and tortuosity calculations.

The PSD, CPSD, and CSD analyses are distinct ways of quantifying the volumetric distribution of phase in the electrode. The PSD is calculated following the method of Münch and Holzer [30]. This approach uses successive dilation of the distance map for a thresholded image to estimate phase sizes. This approach was implemented in FIJI. The CPSD and CSD analyses were run using the methods developed by Grew et al. [31,32]. This approach was implemented using a combination of matlab and fortran routines which utilize a ray-tracing method on the segmented microstructural images to calculate ray lengths extending across individual pores/particles. These rays can then be related back to the pore/particle size and thus used to derive the CPSD, which outlines the respective volume fractions of phase sizes. The CSD is derived through the integration of the CPSD.

The specific surface area calculation is started by creating a matlab isosurface from the microtomography data that can serve as a detailed 3D spatial representation of the phase of interest. To create this isosurface, the gray value ranges are used to convert the microtomography data into a binary 3D matrix that can visually and mathematically represent the geometry of the material of interest. This 3D matrix is then used to create the isosurface, which uses linear interpolation to create a smooth continuous surface with the three-dimensional binary matrix. The isosurface is defined by a set of triangular facets characterized by face numbers and the related Cartesian coordinates representing the vertices of each triangular facet.

The tortuosity calculations were also completed using a combination of matlab and fortran routines that were developed by Grew et al. [31,32]. For this calculation, the segmented morphology is discretized and a finite difference method is used to obtain a solution to Laplace’s equation across the structure in the direction of interest. Since Laplace’s equation is found in the equation describing diffusion through a porous medium, the diffusivity factor can be calculated. This diffusivity factor is analogous to the tortuosity, and thus, the tortuosity can be calculated with the diffusivity factor and volume fractions of the phase of interest [31,32].

The goal herein is to quantify the changes to the microstructure of the alloy anode samples described in Sec. 2.2. The samples analyzed are shown in aggregate in Fig. 1. Samples subject to electrochemical testing are shown in Figs. 1(a)–1(d), while the pristine sample is shown in Fig. 1(e). As noted, the samples subject to full lithiation or cycling (Figs. 1(a), 1(b), and 1(d)) show a distinct pulverized edge region, with interior regions that are comparable to the pristine pellet Fig. 1(e). The samples subject to partial lithiation Fig. 1(c) shows slight changes near the edge regions, but they share the more consistent structure seen in the pristine sample. The pristine sample shows a consistent structure through the thickness of each pellet. These changes reveal the destructive effects of full lithiation and delithiation which are quantified further below. For the samples shown in Figs. 1(a) and 1(b), the insertion of lithium causes an expansion of the structure. The subsequent removal of the lithium leads to a collapse of the structure as the expansion is reversed. Full lithiation also yields a pulverized structure (Fig. 1(d)), where regions of products from the electrochemical reaction can be readily observed.

An example of the microstructural changes for the fully lithiated sample can be seen in further detail in Fig. 4. This figure contains a partial image of the microstructure of Sample 4. The unreacted Cu₆Sn₅ phase can be seen toward the center of the sample as the lithiation process does not penetrate this far into the samples. Sample 4 was lithiated to 0 V versus Li/Li⁺, and the reaction products of this lithiation process can be observed on the left of Fig. 4(b). The two solid phases are distinguished by the different grayscale values of the image. As shown in Fig. 4, the unreacted Cu₆Sn₅ shows a brighter grayscale value than the lithiated products. It also can be seen that as one moves from the interior to the exterior of the sample, the structure becomes more pulverized. The pulverization and the related microstructural changes are due to several key processes. As the voltage approaches 0 V versus Li/Li⁺, lithium reacts with the Sn from the Cu₆Sn₅ to form Li_4.4Sn. As with the lithiation of pure Sn, this lithiation results in a significant expansion of the active material, which generates internal stress leading to fracture. In addition to the Sn lithiation, the electrochemical reaction of Cu₆Sn₅ results in the expulsion of Cu from the alloy. This process yields a more ductile Cu buffer region that interacts with the expanding active material. When the lithium is removed, the expanded lithiated region contracts, and further pulverization occurs, as shown in Figs. 1(a) and 1(b).

The varied structure from the exterior to the interior of the sample is also influenced by transport processes. The edge surfaces seen in the samples of Figs. 1(a)–1(d) and Fig. 4 were in direct contact with the electrolyte and therefore served as the main active interface for the electrochemical reaction. In these pellet samples, the slow diffusion of Li in Sn yielded a reaction region that advances from the exterior to the interior of the pellet. Thus, the image in Fig. 4 shows the end result of the complex coupling between the mechanical, electrochemical, and transport processes that occur within high-capacity battery electrodes.

It was assumed that the grayscale values of the solid phase of the pristine sample would accurately represent the unreacted Cu₆Sn₅ phase for each of the other samples. This would mean that the material properties should be similar for the unreacted regions of all samples. This was evaluated by comparing the CPSD, PSD, connectivity, tortuosity, and interfacial area of the center samples to the pristine sample. These results showed that for interior regions of Samples 3 and 4, the parameters noted were consistent with those of the pristine sample (Sample 5). However, Samples 1 and 2 tended to deviate from the results for the pristine sample. This can be attributed to a few factors. First, both Samples 1 and 2 have sample images that were taken of smaller volumes compared to the other samples (Fig. 1). This leads to deeper penetration of the lithiation processes into the sample, and thus, there is not an unreacted region at the center of these smaller samples like there is for the other samples. Second, as it was attempted to obtain multiple sample regions of the central regions that were 180 × 180 × 180 voxels in size, it is evident for Samples 1 and 2 that some of the reacted regions were captured in some of these sample regions of the center. These captured reacted regions within the sample regions made it no longer an unreacted structure and rather a combination of reacted and unreacted, which caused the results to deviate from that of the pristine sample.

The distinct changes in the electrode structure that can be seen in Figs. 1 and 4 are further illustrated in Fig. 5. In Figs. 5(a)–5(c) pristine, fully lithiated, and partially dlithiated samples are compared in segmented cross sections. A comparison of the 3D structures for these regions is shown in Fig. 5(d). These figures provide qualitative visual evidence of the degrading effects due to lithiation and delithiation. The breakup and pulverization of the lithiated and delithiated samples can be observed.

For the execution of PSD calculations, three 5.41 × 10⁶µm³ regions are selected along the edge of each pellet sample. This gives a total of six regions that can be analyzed for every set of cycling conditions. Once the microtomography data for each pellet have been subjected to the PSD calculation methods noted earlier, results for the PSD can be used to compare and quantify the microstructural changes that have taken place due to the different lithiation and delithiation processes that are involved with the use of this alloy anode.

Regarding the PSD results for the Cu₆Sn₅ phase, some tendencies can be seen of the alloy anode as it undergoes cycling. First, from the PSD results, it can be said that the alloy anodes undergo more severe phase size reductions during the delithiation process as lithium is extracted from the Cu₆Sn₅ anode and the supporting structure collapses. This can be seen by comparing Samples 2 and 3, both tested within the potential window of 0.2–1.5 V versus Li/Li⁺ (Fig. 6(a)). Since both samples were lithiated to the 0.2 V, the microstructural changes due to the lithiation process should be comparable in each case. This would correspond to the formation of Li₂CuSn. From Fig. 6, it can be seen that the PSD data show Sample 2 has a greater degree of pulverization, reflected by a smaller PSD than that of Sample 3. This observation supports the conclusion that the alloy anode tends to see destructive microstructural changes during the delithiation process. This same tendency can also be seen in the PSD data for Samples 1 and 4 from Fig. 6(a). This behavior is also seen for the lithiation of Sn-based anodes [33–35].

As stated, there are destructive microstructural changes that are introduced during the process of delithiation. However, the Cu₆Sn₅ anodes are also affected by the lithiation process. When the Cu₆Sn₅ anodes are lithiated, they undergo volumetric expansion, which plays a role in the destructive changes that occur during the delithiation process, but it also causes some microstructural changes in itself. The PSD data suggest that there is a difference in the severity of destructive microstructural changes that occur depending on the amount of lithiation that is done with the anode. For instance, Sample 4, which was fully lithiated to 0 V, shows the Cu₆Sn₅ phase to have a smaller continuous PSD and to be much more pulverized than the Cu₆Sn₅ phase in Sample 3, which was only partially lithiated to 0.2 V. The increased pulverization in the fully lithiated sample results from the higher volume expansion (∼180%) associated with the formation of Li_4.4Sn. Above 0.2 V, the ternary alloy Li₂CuSn is formed, a process that entails a volume expansion of ∼45% [2]. This comparison can be observed in Fig. 6(a). This decreased PSD due to lithiation can be seen in the overall solid phase of the pellets as well (Fig. 6(b)). Another possible cause for this decrease in PSD, other than strictly volumetric expansion, can be due to Cu₆Sn₅ and Sn reacting with Li⁺ during lithiation and decreasing the amount of Cu₆Sn₅ and Sn phases in the pellet. The lithiated phases have a lower X-ray attenuation since Li is a light elemental that does not absorb a significant amount of the incident X-ray. Therefore, these lithiated phases are not classified as higher attenuation Cu₆Sn₅ or Sn during segmentation.

More examples of the impact of the lithiation condition can be seen when Samples 1 and 2 are compared. Sample 1 was fully lithiated and only delithiated to 0.2 V, but shows the Cu₆Sn₅ phase at a more pulverized state than that of Sample 2, which was lithiated to 0.2 V and delithiated all the way to 1.5 V. These two comparisons help illustrate that the destructive microstructural changes are lessened by limiting the amount lithiation of the anodes. However, this comes with the price of limiting the electrode capacity.

For the execution of CPSD calculations utilizing the ray-tracing scheme, four 180 × 180 × 180 voxel regions are selected along the edge of each pellet sample. This gives a total of eight edge regions that can be analyzed for every set of cycling conditions. The reason for decreasing the total voxel size of the selected regions was to accommodate the tortuosity calculations that were executed with the same code as the CPSD calculations. Once the microtomography data for each pellet have been subjected to the ray-tracing CPSD calculation method, similar results for the PSD can be used to compare and quantify the microstructural changes of the pellet samples as was done with the continuous PSD.

When the CPSD results from the ray-tracing method are observed, similar conclusions about the effects that cycling conditions have on the Cu₆Sn₅/Sn phase can be drawn as with the PSD results. First, the results show that the anodes undergo more severe pulverization due to being lithiated and delithiated rather than just being lithiated. This can be seen by comparing the area under the curve for Sample 2 and Sample 3 in Fig. 7 and also by comparing the mean phase diameter for Samples 2 and 3 in Table 1. Again, since both of these samples were lithiated to the same potential of 0.2 V versus Li/Li⁺, the degradation caused by the lithiation should be comparable. This allows us to infer that the more severely pulverized state of Sample 2 can be attributed to delithiation. This same trend can be seen by comparing the CPSD curves and mean phase diameters for Sample 1 and Sample 4. Both of these samples were lithiated down to 0 V, but Sample 1 was delithiated to 0.2 V and resulted in a more pulverized structure than that of Sample 4, which was held at 0 V. These effects can be seen quantitatively in the mean and peak diameters shown in Table 1. The mean and peak diameters show a decrease for the delithiated samples when comparing Sample 1 to Sample 4 and Sample 2 to Sample 3. The process of extracting Li from the expanded active material leads to a collapse of the overall electrode structure and a reduction in phase diameters.

The same trends described by comparing the mean phase diameters in Table 1, and the curves in Fig. 7 can also be seen in Fig. 8. This figure shows the pore/phase size distribution for each sample relative to the three phases that make up the structure. This allows us to see that the largest phase diameters for all samples, as expected, is the Cu₆Sn₅/Sn phase. The figure also shows the more pulverized samples show the curve peaks farther to the left of the graph, which reflects that more pores/particles are smaller in size than if the curve peak was shifted to the right. So, the CPSD curve for Sample 1 peaks farther to the left than Sample 4 and Sample 2 peaks farther to the left than Sample 3. Figures 8(i) and 8(j) can be compared to the other graphs in Fig. 8 to see that the pristine sample has the largest phase diameters of the other samples. This is a result of the volumetric expansion that occurs upon lithiation. It is also seen that the pore size distribution is also affected by the delithiation as the pore phase is at a more pulverized state in Sample 1 than in Sample 4 and also in Sample 2 than in Sample 3. The reduced size of the pore phase is due to the pulverization of the solid phases, which leads to the decrease in the contiguous path sizes and can restrict transport associated with the pore region. This trend can be seen by comparing Figs. 8(a) and 8(b) to Figs. 8(g) and 8(h) as well as comparing Figs. 8(c) and 8(d) to Figs. 8(e) and 8(f).

When the specific surface area is calculated for each pellet sample, all of the tendencies that were seen from the PSD of the Cu₆Sn₅/Sn phase are confirmed. The alloy anodes tend to have an increased specific surface area when they are delithiated as compared to the anodes that were just lithiated. The increase in surface area can be attributed to the reduction in phase size that comes with delithiation. As Li is extracted from the active material the expanded active material contracts and breaks apart, a process referred to as pulverization. The fracture of the material reveals a more active material area for reaction. The phase size reduction results in a higher surface area per unit volume since finer microstructures yield higher surface area per unit volume. This tendency can be seen by comparing Samples 2 and 3 as well as Samples 1 and 4. This is another example of how the delithiation process introduces destructive microstructural changes in the anodes. The reason that this change in the microstructure is destructive is that the increased surface area can free up the area for SEI formation and contribute to a capacity loss in the electrode. This SEI formation reduces the total Li inventory in the battery, which decreases battery performance. The Cu₆Sn₅ anodes also tend to have a higher specific surface area when they are fully lithiated to 0 V as compared to when they are just partially lithiated to 0.2 V. This increase in specific surface area can be noticed in the comparison of Samples 3 and 4. These comparisons all follow the comparisons that are made when observing the PSD data. Figure 9 shows the normalized results of the specific surface area ratio calculations. The data for each phase were normalized by the maximum specific surface area for each phase to provide a clear comparison between phases.

As discussed earlier, the tortuosity is calculated by iteratively solving Laplace’s equation for the segmented microstructure of interest. All samples were checked for sufficient convergence, with representative results provided in the Supplemental Information available in the Supplemental Materials on the ASME Digital Collection. After comparing the tortuosity results, it was noticed that there were some potential outliers. These outliers could be due to a localized inconsistency with the bulk structure or image artifacts. In order to mitigate these outliers, Chauvenet’s criterion was used. Chauvenet’s criterion provides a statistical measure of whether a given data point falls outside of a likely band of deviation for the data set, established as a multiple of the standard deviation (σ) based on the sample size [36]. For each imaged sample, tortuosity was analyzed for eight regions, so results that were outside of the 1.87σ band were considered outliers and discarded in the results reported. Further details of this calculation and the tortuosity data with outliers indicated are provided in the Supplemental Information available in the Supplemental Materials on the ASME Digital Collection. When the tortuosity is calculated for each pellet sample, all of the tendencies that were seen from the PSD of the Cu₆Sn₅/Sn phase are confirmed once again. The alloy anodes tend to have a higher tortuosity when they are delithiated as compared to the anodes that were just lithiated. This is shown by the fact that Sample 2 shows a higher tortuosity than that of Sample 3 and Sample 1 shows a higher tortuosity than that of Sample 4 in Fig. 10. This reaffirms the trends that show the delithiation process introducing destructive microstructural changes in the anodes. The destructive impact of delithiation has been observed in prior studies of Cu₆Sn₅ cycling [37,38]. These studies include ex situ X-ray μCT and scanning electron microscope observations [37] as well as nanoscale in operando X-ray imaging [38]. The reason that this is a destructive microstructural change is due to the fact that tortuosity can be correlated with ionic and electronic conductivity, so the decrease in the tortuosity upon delithiation implies a decrease in the effective conductivity and Li diffusivity of the anode, thus hindering performance. Similar to what was seen in the other results, the anodes also tend to show a higher tortuosity when they are fully lithiated to 0 V as compared to when they are just partially lithiated to 0.2 V. This trend is observed upon the comparison between Samples 3 and 4 in Fig. 10. In addition to comparing the tortuosity values for each of the samples, the variation of the values for a given sample can also be useful. The tortuosity values for Samples 1, 2, and 4 show a larger standard deviation than those from Samples 3 and 5. This variation in tortuosity values suggests a varying tortuosity throughout the electrode structure which in turn is due to a breakdown of the structure.

There is a capability for the advancement of the electrochemical capacity of LIB electrodes by utilizing Sn-alloy electrodes. These alloy anodes show great potential for advancing battery performance due to the high capacity of tin. However, the destructive effects of volumetric expansion must be mitigated in order to sustain this high capacity during extended cycling. One of the ways these effects can be mitigated is by alloying Sn with more malleable metals. By forming this active–inactive alloy, the anode can attempt to accommodate the severe volumetric expansion with a malleable inactive metal such as copper, while retaining some of the high capacity of Sn. Since the expansion is mitigated with an inactive metal, there are losses in the potential capacity of the anode. Another way to accommodate the extreme volumetric expansion of Sn is by forming an alloy with another active metal. This active–active approach results in a higher theoretical capacity than the active–inactive alloy since the secondary metal participates in the lithiation process.

In order to evaluate the effectiveness of this approach, the microstructural changes due to volumetric expansion were produced by conducting lithiation and delithiation tests of Cu₆Sn₅ pellet electrodes. Ex situ X-ray microtomography was performed on these pellet electrodes after electrochemical testing, and these microtomography data were used to quantify the microstructural changes that occur during lithiation and delithiation. The microtomography data were segmented into three distinct phases to evaluate certain characteristics of the samples. The calculations that were used to characterize the microstructural changes are continuous phase size distribution (PSD), specific surface area, tortuosity, connectivity, and interface area between phases.

When evaluating the PSD of each electrode sample, it can be seen that the electrodes lithiated to 0 V versus Li/Li⁺ and then delithiated to 0.2 V versus Li/Li⁺ showed the most substantial reduction in overall phase sizes compared to the other samples. This suggests that full lithiation of the Sn present in the alloy electrodes followed by partial delithiation of the Li_4.4Sn to Li₂CuSn can cause substantial microstructural changes related to volume expansion on lithiation and structural collapse upon delithiation. The electrodes fully lithiated to 0 V versus Li/Li⁺ and not delithiated show a higher overall phase size distribution, including all solid phases, than the pristine sample and the electrode samples that were partially lithiated to 0.2 V versus Li/Li⁺ and delithiated to 1.5 V versus Li/Li⁺. The higher overall phase size distribution that is shown by the sample that was fully lithiated and not delithiated is evidence of the significant volumetric expansion of the Cu₆Sn₅ compound due to lithiation. During this process of volumetric expansion, the phase size distribution of the Cu₆Sn₅/Sn phase is shown to decrease as lower attenuation lithiated phases develop. When the volumetric expansion of the lithiated electrode samples and the volumetric contraction of the delithiated electrode sample are considered together, it can be inferred that the microstructural changes that are observed, such as the decrease in phase size distribution of the Cu₆Sn₅/Sn phase, can be attributed to the volumetric expansion and contraction of the compound during the lithiation and delithiation processes. Specifically, the expansion and contraction of the active material lead to the pulverization of the anode active material, yielding reduced phase sizes.

When considering other microstructural characteristics, the tortuosity for the electrodes lithiated to 0 V versus Li/Li⁺ and then delithiated to 0.2 V versus Li/Li⁺ shows the highest tortuosity compared to other samples. This also suggests that full lithiation of the Sn present in the alloy electrodes followed by partial delithiation of the lithiation products can cause substantial microstructural changes related to volume expansion upon lithiation and structural decomposition upon delithiation. The electrodes fully lithiated to 0 V versus Li/Li⁺ and not delithiated show a lower tortuosity of the Cu₆Sn₅/Sn phase, than the pristine sample and the electrode samples that were partially lithiated to 0.2 V versus Li/Li⁺ and not delithiated. The higher tortuosity that is shown by the electrode that was fully lithiated rather than partially lithiated is evidence of the destructive effects associated with the full lithiation of the alloy. It can be inferred that the increase in tortuosity is caused by the significant volumetric expansion of the electrodes during lithiation.

In addition to evaluating the effects of cycling conditions on tortuosity, other characterization properties are determined and considered. These additional characterization calculations include connectivity and interfacial areas between phases. When the connectivity and interfacial areas are evaluated, it can be seen that the electrode samples lithiated all the way down to 0 V versus Li/Li⁺ and not delithiated show a lower connectivity in the pore phase and a smaller interfacial area between the Cu₆Sn₅/Sn and pore phase than the pristine sample and the electrode samples that were partially lithiated to 0.2 V versus Li/Li⁺ and delithiated to 1.4 V versus Li/Li⁺. These results show that in addition to the mechanical degradation of the electrodes, excessive volume expansion can also influence transport networks in the active material and supporting phases of the electrode. The less pulverized Cu₆Sn₅ microstructure in some samples may increase battery performance by creating fewer regions of isolated active material and a more streamlined path for the flow of electrons. This smaller specific surface area can help prevent the formation of SEI and other unwanted compounds that can decrease the amount of Li⁺ available for storage in the anode, which has a negative effect on battery performance.

A thorough assessment of X-ray microtomography imaging data was performed to understand structural degradation caused by cycling of alloy anodes for lithium-ion batteries. The studies focused on Cu₆Sn₅ pellet electrodes cycled against lithium counter electrodes. Samples from these pellet electrodes were imaged used X-ray microtomography. Segmentation of samples was performed with guidance from the sample histogram data. The segmented microstructural data were then analyzed with a suite of microstructural characterization tools.

Comparing the images and phase size distributions, the anodes subject to full lithiation or cycling (lithiation and delithiation) show a distinct pulverization and phase size reduction in regions experiencing electrochemical reactions. The anodes subject to partial lithiation only show slight changes in these regions. Furthermore, quantitative assessment of the phase size distributions shows that the delithiation process results in decreased phase sizes, and an indicator of pulverization and structural collapse that occurs on the extraction of Li from the Sn active material. The pulverization process leads to increased exposure of active material, as seen in the specific surface area assessment. This exposed active material can support further SEI formation, which reduces Li inventory and contributes to capacity fade. Increased tortuosity, and variation in tortuosity, for samples subjected to delithiation suggests that microstructural networks supporting transport and electrochemical reactions are adversely impacted by the significant structural changes seen during the cycling of high-capacity materials.

The observations of structural change enabled by the above studies give more understanding of why alloy anode materials, like Cu₆Sn₅, show signs of fatigue very early into use as a battery anode. It is evident that as the anodes are lithiated, there is a significant volumetric expansion that results in material degradation and when the samples are delithiated continue to see degradation. These changes and their negative effects can be seen in both pulverization of the active material and increased tortuosity of the active material. These observations for pellet electrodes complement prior observations of chemical and structural changes in alloy electrodes [27,37,38]. While based on studies, the active–inactive alloy Cu₆Sn₅ for lithium-ion battery applications, the methodology described herein could be applied to other alloys used for energy storage. The methodology supports nano-materials with nano-scaled images. In the realm of other metallic alloys, it would be useful to further explore active–active alloys such as SnSb, Al–Sn, or silicon/carbon composites. The insights obtained are therefore expected to be applicable to other alloy electrodes and battery chemistries.

Financial support from the National Science Foundation through a Collaborative Research Award (Grant No. CBET-1438683) is gratefully acknowledged. This research used the resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The authors would like to thank Professor Wilson K.S. Chiu from the University of Connecticut for the use of microstructural characterization codes for calculating phase size distributions and tortuosity.

There are no conflicts of interest.

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.