Document [original]

Quantitative Comparison of Different Approaches for

Reconstructing the Carbon-Binder Domain from

Tomographic Image Data of Cathodes in Lithium-Ion

Batteries and Its Inﬂuence on Electrochemical Properties

Benedikt Priﬂing,* Matthias Neumann, Simon Hein, Timo Danner, Emanuel Heider,

Alice Hoffmann, Philipp Rieder, André Hilger, Markus Osenberg, Ingo Manke,

Margret Wohlfahrt-Mehrens, Arnulf Latz, and Volker Schmidt

1. Introduction

Because of their outstanding energy density,

low self-discharge rate, and high power den-

sity, lithium-ion batteries are the most

widely used technology for storing electrical

energy.

[1–4]

However, further optimization

of the performance is necessary due to

the continuously growing requirements

for electric vehicles and a general need for

reducing carbon dioxide emissions to miti-

gate global warming.

[5,6]

As it is well known

that the 3D microstructure of battery

electrodes strongly inﬂuences the resulting

electrochemical performance,

[7–12]

tailoring

the morphology of the 3D microstructure

by speciﬁcally developed structuring

concepts seems to be a promising approach.

Obviously, the manufacturing process

consisting, among others, of mixing,

[13,14]

drying,

[15,16]

and calendering

[17–19]

has a

signiﬁcant impact on the electrode morphol-

ogy.

[20]

Although the carbon-binder domain

(CBD) is regarded as passive constituent of

the electrode morphology, its spatial

distribution is particularly crucial for the

resulting electrochemical properties of cathodes

[13,21–23]

and ano-

des.

[24,25]

Thus, the segmentation of tomographic image data into

three phases, namely, active material, CBD, and pores, is

It is well known that the spatial distribution of the carbon-binder domain (CBD)

offers a large potential to further optimize lithium-ion batteries. However, it is

challenging to reconstruct the CBD from tomographic image data obtained by

synchrotron tomography. Herein, several approaches are considered to segment

3D image data of two different cathodes into three phases, namely, active

material, CBD, and pores. More precisely, it is focused on global thresholding, a

local closing approach based on energy-dispersive X-ray spectroscopy data, a

means clustering method, and a procedure based on a neural network that has

been trained by correlative microscopy, i.e., based on data gained by synchrotron

tomography and focused ion beam scanning electron microscopy data repre-

senting the same electrode. The impact of the considered segmentation

approaches on morphological characteristics as well as on the resulting per-

formance by spatially resolved transport simulations is quantiﬁed. Furthermore,

experimentally determined electrochemical properties are used to identify an

appropriate range for the effective transport parameter of the CBD. The devel-

oped methodology is applied to two differently manufactured cathodes, namely,

an ultrathick unstructured cathode and a two-layer cathode with varying CBD

content in both layers. This comparison elucidates the impact of a speciﬁc

structuring concept on the 3D microstructure of cathodes.

B. Priﬂing, M. Neumann, P. Rieder, V. Schmidt

Institute of Stochastics

Ulm University

89081 Ulm, Germany

E-mail: benedikt.priﬂing@uni-ulm.de

The ORCID identiﬁcation number(s) for the author(s) of this article

can be found under https://doi.org/10.1002/ente.202200784.

This is an open access article under the terms of the Creative Commons

Attribution License, which permits use, distribution and reproduction in

any medium, provided the original work is properly cited.

DOI: 10.1002/ente.202200784

S. Hein, T. Danner, A. Latz

German Aerospace Center (DLR)

Institute of Engineering Thermodynamics

705696 Stuttgart, Germany

S. Hein, T. Danner, A. Latz

Computational Electrochemistry

Helmholtz Institute for Electrochemical Energy Storage (HIU)

89081 Ulm, Germany

E. Heider, A. Hoffmann, M. Wohlfahrt-Mehrens

Accumulators Materials Research (ECM)

ZSW-Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-

Württemberg

89081 Ulm, Germany

RESEARCH ARTICLE

www.entechnol.de

necessary to adequately describe the 3D microstructure of battery

electrodes. On the one hand, a high resolution of 3D image data

up to the nanometer scale, which can be achieved by focused ion

beam scanning electron microscopy (FIB-SEM) tomography, ena-

bles for the application of segmentation techniques, which distin-

guish between these three phases. Disadvantageously, FIB-SEM

tomography provides only a small ﬁeld of view such that the result-

ing 3D image of the electrode is often not sufﬁciently representa-

tive. On the other hand, X-ray-based imaging techniques such as

synchrotron tomography allow for a nondestructive measurement

of a comparatively large cutout of the electrode. The technique has

been applied successfully for the analysis of a wide range of elec-

trode materials, including transition metal oxides,

[26–28]

lithium-

iron phosphates,

[29]

and organic active materials.

[30]

However,

the contrast between CBD and pores is comparatively low in many

cases such that a frequently used approach is to segment only the

active material and its complement (see refs. [29,31–34]). Several

studies then use modeling approaches for inserting the CBD in a

subsequent step (see refs. [19,35–37]).

In the present article, we consider four conceptually different

data-driven approaches to reconstruct the microstructure of

two differently manufactured cathodes using tomographic

image data. While in ref. [37], the CBD is virtually included based

on different geometric models for a given segmentation of active

material; the novelty of the present article consists of the

quantitative comparison between data-driven three-phase

reconstructions. These segmentation approaches include global

thresholding, k-means clustering, machine learning trained by

correlative microscopy, and a reconstruction based on energy-

dispersive X-ray spectroscopy (EDX) data. This comparison

elucidates the impact of different segmentation approaches on

morphological and electrochemical properties of the resulting

electrode microstructures. Moreover, we determine the effective

transport parameter of the CBD for each segmentation approach

by validating the output of spatially resolved half-cell simulations

with experimentally determined electrochemical data. This

approach allows us to specify a range in which the effective trans-

port parameter is located. Thereby, the presented approach takes

the important aspect of uncertainty during the reconstruction

process

[38]

into account when analyzing the microstructure of

battery electrodes based on 3D image data.

This article is organized as follows. In Section 2, we describe the

manufacturing process of two different cathodes as well as the

tomographic imaging procedure. Next, we present four different

approaches of segmenting active material, CBD, and pores from

3D image data in Section 3. The computation of electrochemical

properties by spatially resolved numerical simulations is described

in Section 4. In Section 5, the inﬂuence of the different trinariza-

tion approaches on the 3D microstructure is quantitatively inves-

tigated by means of statistical image analysis. In addition, we

present results regarding simulated electrochemical properties,

where a particular focus is put on the effective transport parameter

of the CBD, which is ﬁtted via experimentally determined lithia-

tion curves. Finally, the article is concluded with a summary of the

main results and an outlook to possible future research.

2. Experimental Section

In this section, manufacturing, material composition and the

tomographic imaging of the cathode materials considered in

the present article are described.

2.1. Materials and Cathode Manufacturing

We investigate two different cathode samples, the 3D microstruc-

ture of which is quantitatively characterized based on different

segmentation approaches. Moreover, an additional electrode is

considered, which is solely used for the trinarization approach

based on correlative microscopy in Section 3. In the following,

we describe four different suspensions, denoted by A, B, C,

and D, which were used to manufacture these samples. Note that

one of the electrodes is a two-layer electrode, where the two layers

are prepared with different suspensions. All suspensions share the

underlying materials, but differ with regard to their composition.

Commercially available LiNi0.6Co0.2Mn0.2O2(BASF), shortly

denoted by NMC, was mixed and dispersed with carbon black

(SuperP, Imerys) and graphite (SFG6L, Imerys) as conducting

additive and polyvinylidene ﬂuoride (PVdF, Solvay Solexis) as

a binder, where the union of carbon black, graphite, and binder

forms the CBD. N-methyl-2-pyrrolidone (NMP, Sigma-Aldrich)

was used as a solvent. Note that all materials were utilized as

delivered without further treatment. Because two suspensions

were needed simultaneously for the manufacturing of the two-

layer electrode, different mixers applying the same working prin-

ciple were used for the preparation of the cathode suspensions.

To be precise, a 10 dm

planetary mixer (Netzsch, Germany) and

a 1.6 dm

planetary mixer (Grieser, Germany) were used. Both

mixers were equipped with two agitators, a cross-bar stirrer

(CS) and a butterﬂy stirrer (BS) running at low and high speed,

respectively. In the case of the 10 dm

mixer, an axially double

butterﬂy stirrer was used while the 1.6 dm

mixer contained a

single butterﬂy stirrer. Transport of the components into the

mixing zone was ensured by a wall scraper rotating at slow speed.

For each suspension, the solid material composition and the type

of mixer used for the preparation are given in Table 1.

The suspensions were prepared starting from a binder solu-

tion containing 7–10 wt% of PVdF which was dissolved in NMP

at room temperature. First, carbon black and then graphite were

added to the binder solution and dispersed, respectively. After

A. Hilger, I. Manke

Institute of Applied Materials

Helmholtz-Zentrum Berlin für Materialien und Energie

14109 Berlin, Germany

M. Osenberg

Department of Materials Science and Technology

TU Berlin

10623 Berlin, Germany

A. Latz

Institute of Electrochemistry

Ulm University

89081 Ulm, Germany

www.advancedsciencenews.com www.entechnol.de

that, NMC was added stepwise and dispersed after each addition.

Finally, the viscosity of each suspension was adjusted for appli-

cation by thinning with NMP. From the suspensions, ultrathick

electrodes were produced using a pilot line coating machine

(LACOM, Germany). A single-layer electrode (abbreviated by

SL) was prepared from the suspension A using a single slot

die. A two-layer electrode (abbreviated by TL) was prepared by

simultaneous slot die coating with a double slot die applying sus-

pension B at the bottom and suspension C at the top. The sus-

pensions were cast onto an aluminum foil (Korff, Switzerland). A

drying oven with a total length of 8 m, separated into four drying

stages, independently adjustable in temperature, was used for

evaporation of the solvent. The belt speed was 0.8 m min

1

and the temperatures of the ovens were 50, 70, 95, and 110 °C

for both electrodes. The mass loading resulted in 51 and

53 mg cm

2

for the single-layer and the two-layer electrode,

respectively. After drying, the electrodes were calendered using

a pilot line calender (KKA, Germany) with a line pressure

restricted to a maximum value of 208.3 Pa m

1

and rolls heated

to 100 °C. The ﬁnal density of the electrode composites was

3.1. g cm

3

for both electrodes. Note that the single-layer and

the two-layer cathode share the following volume fractions:

59.54% active material, 11.54% CBD, and 28.92% pore space.

These volume fractions are computed from the density of the

electrode as well as the material composition (i.e., the weight per-

centage as well as the density of the individual solid constituents).

In addition, a third cathode sample is considered, image data

of which is solely used in Section 3 for establishing a trinariza-

tion approach based on correlative microscopy. This sample is

manufactured with suspension D analogously to the single-layer

and the two-layer cathode, except for a slower belt speed of

0.6 m min

1

and a slightly lower mass loading of 49.1 mg cm

2

2.2. Tomographic Imaging

First, we describe the imaging procedure of the single-layer and

the two-layer cathode. The tomography measurements of these

cathode samples have been conducted at the P05 beamline (Petra

III, DESY, Germany).

[39,40]

More precisely, a monochromatic

nearly parallel X-ray beam is guided on the rotating sample with-

out the use of X-ray focusing optics. Behind the sample, the

transmitting beam is detected with a setup consisting of a

CdWO

scintillator for X-ray to light transformation, an optical

microscope, and a CMOS camera. The samples have been

measured with an energy of 28 keV to assure an optimal image

contrast, where a double crystal monochromator is used for

selection. Both samples have been measured as close as

possible to the scintillator screen to reduce phase contrast.

During the tomography each sample was constantly rotated while

2401 images have been captured using a KIT CMOS camera

(5120 3840 pixel) with an exposure time of 130 ms.

Combined with the 10 times optics this resulted in a voxel size

of 0.642 μm. For the reconstruction the normalized data were

denoised using a total variation minimization ﬁlter

[41]

and then

reconstructed using the gridrec routine based on the ﬁltered back

projection.

[42]

Note that all subsequent results regarding the

single-layer and the two-layer sample are based on three nonover-

lapping equal size cutouts, where the entire thickness is used in

through-plane direction.

With regard to the third cathode sample, which is used for

establishing the neural network approach based on correlative

microscopy, imaging by synchrotron tomography as well as by

FIB-SEM tomography has been carried out. First, synchrotron

tomography has been conducted at the P05 beamline (Petra III,

DESY, Germany) using the μ-CT setup. For the tomography, a

beam energy of 25 keV was found to yield optimal transmission

contrast. The energy was ﬁltered using a double multilayer mono-

chromator. The sample that was ﬁxated on the translation/rotation

stage was positioned 15 mm away from the CdWO

scintillator.

Behind the scintillator the portion of the signal that has been trans-

formed into visible light was magniﬁed (10 times magniﬁcation)

by the microscope optics and redirected into the camera system. A

KIT CMOS camera equipped with a CMOSIS CMV 20 000 sensor

(5120 3840 pixel) was then used to capture the signal with an

exposure time of 130 ms. The whole tomography consisted of

3000 projections; for ring artifact reduction, a center of rotation

variation protocol was used. The whole setup yielded a

0.642 μm raw pixel size. The synchrotron tomography was recon-

structed using the P05 in-house reconstruction tools based on the

ﬁltered back projection algorithm. After reconstruction, an addi-

tional nonlocal means denoising step was performed.

[43,44]

The FIB-SEM tomography has been conducted at Helmholtz-

Zentrum Berlin (HZB) using the ZEISS Crossbeam 340. For this

purpose, the sample that previously was measured at P05 has

been ﬁxated on an aluminum sample holder. For better orienta-

tion on the sample, a ﬁrst low-resolution large-scale surface scan

was performed. The scan was then aligned with the 3D synchro-

tron tomography reconstruction using the SIFT algorithm.

[45]

Afterward, using the synchrotron tomography, a suitable ROI

has been selected for FIB-SEM tomography. For the FIB-SEM

tomography, a Gallium ion milling source with 30 keV and

300 pA ion current was used. The Gemini electron gun was oper-

ated at 2 keV. For imaging the SE2 chamber detector (i.e., a detec-

tor for low-resolution secondary electrons) with an image capture

rate of 30 s per image was used. The pixel size was set to 10 nm,

which also corresponds to the thickness of the slices that have

been cut by the FIB. Finally, the 3D image data obtained by

FIB-SEM tomography were manually aligned with the synchro-

tron tomography data set using Fiji/ImageJ.

[46]

A 3D rendering

of the complete 3D FIB-SEM data together with the image data

obtained by synchrotron tomography is shown in Figure 1.

In addition, 2D EDX data have been gathered for the local closing

approach described in Section 3.4. For this purpose, cross sections

Table 1. Material compositions and mixers for the four different

suspensions, which are used to manufacture the cathode samples

considered in the present article.

Suspension ABCD

Content in solid mass ½wt%

NMC 93.5 91.5 95.5 93.0

Carbon black 2.0 2.0 2.0 2.0

Graphite 1.0 1.0 1.0 1.0

PVdF 3.5 5.5 1.5 4.0

Mixer Grieser Netzsch Grieser Netzsch

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of electrodes were prepared perpendicular to the electrode surface

by a broad Arþion beam milling device (Hitachi IM4000Plus) at an

accelerating voltage of 5 kV for 2–3 h depending on the electrode

thickness. A subsequent analysis of the electrode microstructure

was conducted with scanning electron microscopy (SEM, accelerat-

ing voltage between 4 and 5 kV) using a LEO1530VP (Zeiss)

equipped with a thermal ﬁeld emission gun. To determine the

locally resolved elemental distribution of ﬂuorine, EDX (X-

Max50, Aztec Advanced Software, Oxford Instruments) was used.

Characteristic X-rays of ﬂuorine were used as a measure for the

spatial distribution of PVdF within the electrode.

3. Phase-Based Segmentation

This section covers four different approaches to reconstruct the

3D image data obtained by synchrotron tomography. Each of

these trinarization methods is designed in such a way that the

experimentally determined volume fractions of all three phases

can be matched. However, it is not possible to resolve the inner

structure of the CBD based on synchrotron image data because

the resolution is too low. Thus, we assume that each CBD voxel

contains an inner porosity, sometimes called nanoporosity, of

50%, which is close to inner porosities of 47% and 58% reported

in refs. [47,48], respectively. Therefore, a voxel labeled as CBD

also contains nanopores, which cannot be resolved by synchro-

tron tomography, whereas voxels labeled as pores correspond to

the larger macropores. Finally, a voxel-based analysis is carried

out to obtain a ﬁrst impression about potential differences

between the four segmentation approaches. A visualization of

these different segmentation approaches, which are described

in detail in the following, is shown in Figure 2.

3.1. Global Thresholding

To begin with, we consider the trinarization of 3D image data

by two global thresholds,

[49–51]

which are chosen in such a way

that the experimentally determined volume fractions of all

three phases are matched. For this purpose, we choose a sufﬁ-

ciently large sampling window, which does not contain void

space outside the electrodes to avoid edge effects. The size

of this cutout is given by 1500 900 250 voxels (two-layer

cathode) and 1000 800 220 voxels (single-layer cathode),

respectively. In the following, we refer to this approach

as Thresholding. A visualization of the grayvalue histogram

together with two thresholds as vertical lines is shown in

Figure 2.

3.2. Clustering Approach

A further method for the segmentation of 3D image data repre-

senting three-phase materials is based on a hard clustering

approach, such as k-means clustering with k=3.

[52–54]

In partic-

ular, this kind of unsupervised learning has been successfully

applied to cathodes in lithium-ion batteries.

[55]

In the present

article, we slightly modify the algorithm considered in ref. [55]

in order to ensure that the experimentally determined volume

fraction of each phase is matched. In general, each voxel will

be classiﬁed based on the grayvalues in its 3 33 neighbor-

hood. However, arranging these 27 values in a ﬁxed order is not

meaningful because, e.g., rotating or ﬂipping the 3 33

neighborhood would signiﬁcantly change the feature vector.

To overcome this problem, we sort the grayvalues in ascending

order. To additionally increase the information content of the fea-

ture vector, we further group the voxels in the local neighborhood

by their distance to the currently considered voxel. Thus, the ﬁrst

entry of the feature vector contains the grayvalue of the current

voxel, the next six entries correspond to the sorted grayvalues of

the 6-neighborhood, the subsequent 12 entries belong to the vox-

els with distance ﬃﬃﬃ2

p, and the remaining 8 entries correspond to

the voxels with distance ﬃﬃﬃ3

p. The ith cluster Ciwith i∈f1, 2, 3g

(corresponding to the three phases such as active material, CBD,

and pores) is now given by

Figure 1. Left: 3D rendering of a cutout (640 μm640 μm182 μm) of the grayscale image obtained by synchrotron tomography, where the current

collector is located at the bottom. Right: 3D rendering of the trinarized FIB-SEM data (15 μm14 μm27 μm), where active material, CBD, and pores

are shown in gray, red, and black, respectively.

www.advancedsciencenews.com www.entechnol.de

Ci=vj∶i=argmin

l=1,2,3

wl⋅X

m=1

xm⋅fðmÞ

jμðmÞ



()

(1)

where vjdenotes the jth voxel, fj=ðfð1Þ

j,:::,fð27Þ

jÞ∈ℝ27 the cor-

responding feature vector, and μl=ðμð1Þ

l,:::,μð27Þ

lÞ∈ℝ27 the

cluster centroids in the feature space. The phase weights

w1,w2,w3>0 and the feature weights x1,:::,x27 >0 can

now be chosen in such a way that we match the experimentally

determined volume fractions of each phase. For this purpose, we

choose w1=1 and x1=1 as reference. Moreover, we further

reduce the number of parameters which have to be optimized

by assuming equal weights for voxels with the same distance

to the currently considered voxel, i.e., we assume that

x2=::: =x7,x8=::: =x19 and x20 =::: =x27. This leads

to ﬁve parameters, which are computed by minimizing the cost

function P3

l=1ðεl,exp bεlÞ2, where εl,exp denotes the experimen-

tally determined volume fraction of phase land bεlequals the

volume fraction of phase lestimated on the segmented 3D

image data obtained by running the k-means algorithm. This

optimization is carried out with Powell’s BOBYQA algorithm.

[56]

As the segmentation result depends on the initial cluster cent-

roids,

[57]

we initialize the active material cluster by the feature

vector associated with the brightest voxel and the pore cluster

by the one associated with the darkest voxel. The CBD cluster

is initialized with the feature vector that is most similar to the

average of the feature vectors of the initial active material and

pore centroid. In the following, we refer to this approach as

k-means. In Figure 2, a 2D sketch of this segmentation approach

is shown, where three different colors are used to highlight the

three clusters, whose centroid is marked with a large blue dot.

3.3. Neural Network

In order to train a neural network that classiﬁes each voxel

according to the grayvalues in the synchrotron images, we make

use of correlative microscopy. More precisely, a small cutout of

the electrode has been imaged by FIB-SEM tomography after

measuring the whole electrode sample by synchrotron tomogra-

phy as described in Section 2.2. This approach relies on the fact

that a three-phase reconstruction of 3D FIB-SEM data is possible

due to the better contrast compared to image data obtained by

synchrotron tomography. More precisely, a global threshold

determined by Otsu’s method is used to segment the active mate-

rial,

[58]

whereas a U-Net is trained to distinguish between pores

and CBD.

[59]

Finally, a slicewise ﬂood-ﬁlling algorithm has been

applied to the active material phase in order to remove inclusions

of CBD or pores.

[50,51]

Due to the different voxel sizes of both

kinds of image data, each synchrotron voxel corresponds to

128 128 128 voxels in the FIB-SEM data. Thus, we can

compute the material composition—i.e., a 3D vector containing

the volume fractions of active material, CBD, and pore space—

for each synchrotron voxel, for which FIB-SEM data are available.

This information serves as ground truth for training a feed-

forward neural network, which uses the grayvalues of an input

voxel and its 5 55 neighborhood. The neural network is a

multilayer perceptron consisting of ﬁve hidden layers with 75

units each and a softmax output layer with three units represent-

ing the predicted material composition of the input voxel.

[60,61]

As the physical size of the FIB-SEM cutout is comparatively

small (only 2541 voxels as training data), we make use of a data

augmentation for the training data, where we ﬂip and/or rotate

the 5 55 neighborhood.

[61–64]

As these kind of transforma-

tions do not change the material composition, we increase the

size of the training data by a factor of 48, which corresponds

to the number of elements of the symmetry group of a hexahe-

dron.

[65]

The data points are randomly shufﬂed and split into

60% training data, 20% validation data, and 20% test data.

The validation data are used for early stopping in case of ten sub-

sequent epochs with a nondecreasing error on the validation set.

The network consists of ﬁve hidden layers with 75 nodes

each.

[60,61]

The mean squared error, which is used as loss

Figure 2. Comparison of different trinarization approaches for a 2D slice.

www.advancedsciencenews.com www.entechnol.de

function, has been optimized using Nesterov’s accelerated sto-

chastic gradient descent

[66]

with a learning rate of 0.01 and a

momentum coefﬁcient of 0.99. After training the network is

applied to the synchrotron image data of the single-layer and

the two-layer sample, respectively. For each sample, this results

in a 3D image, where for each voxel the material composition is

predicted. This kind of information can be either interpreted as

fuzzy membership or as probability of belonging to a certain

phase.

[67,68]

The top left plot in Figure 2 shows the prediction

accuracy on the test set of the trained neural network for each

of the three phases, which indicates that the material composi-

tion can be reliably predicted.

In order to transform the output of the neural network into a

segmentation with three classes, we consider two procedures.

The ﬁrst approach relies on the experimentally determined mate-

rial composition as well as on a predeﬁned ordering of the three

phases, denoted by P1,P

2, and P3. More precisely, we assign the

voxels with the highest predicted probability of belonging to

phase P1to P1until the target volume fraction of P1is matched.

This procedure is then repeated for P2, except that we no longer

consider voxels already classiﬁed as P1. In the following, this

approach will be abbreviated as NN–P1–P2–P3with

P1,P

2,P

3∈fAM;CBD;Pg. For example, ﬁrst segmenting the

active material and then assigning the CBD lead to the trinariza-

tion NN–AM–CBD–P. The second possibility for transforming

the material composition by the neural network to a trinarization

is based on conditional probabilities, where the ﬁrst phase P1is

obtained analogously to the ﬁrst approach. However, we then

compute the conditional probabilities of voxels belonging to

P2and P3conditioned on the event that these voxels are not clas-

siﬁed as P1. As these two conditional probabilities add up to one,

there is—given that the phase P1is ﬁxed—exactly one possibility

to obtain a trinarization, which matches the experimentally deter-

mined material composition. This trinarization method will be

denoted by NN–P1–Cond in the following. For example, ﬁrst

classifying the active material and then assigning the CBD

and pore space based on the conditional probability that a certain

voxel is not classiﬁed as active material leads to the trinarization

NN–AM–Cond. In total, there exist six different orderings

of the three phases required for the ﬁrst approach, as well as

three different trinarizations based on the conditional

probability approach, leading to nine different neural network

segmentations.

3.4. Local Closing Based on EDX Data

Similar to ref. [13], 2D image data obtained by EDX are used to

estimate the corresponding CBD gradient along the transport

direction, which is then ﬁtted by a linear function (see Figure 3).

The ﬁrst step to obtain a 3D segmentation that reﬂects the

linear CBD gradient is to use the active material obtained by

the k-means segmentation. Afterward, the CBD is inserted

by a morphological closing of the active material phase,

where the structuring element is given by a ball with some loca-

tion-dependent radius r>0.

[69,70]

Note that it has been shown in

ref. [37] that using a morphological closing is an appropriate

model for inserting the CBD. As described in ref. [13], the closing

radius rdepends on the distance to the separator such that the

slice-dependent amount of CBD is proportional to the estimated

CBD gradient, where the known CBD volume fraction is

matched by multiplying the EDX intensity values by a constant

that is computed with the bisection method.

[71]

In the following,

we refer to this approach as EDX-Closing.

3.5. Voxel-Based Comparison of Trinarization Approaches

Before investigating the inﬂuence of the different trinarization

approaches on morphological and electrochemical properties

in Section 5, we perform a quantitative voxel-based analysis to

obtain a ﬁrst impression regarding the potential differences

between the segmentation approaches described above. Before

we quantify the inﬂuence of the trinarization approach on geo-

metric descriptors of the resulting 3D microstructures in

Section 5.1, we ﬁrst quantify the difference between the pre-

sented three-phase reconstructions by the fraction of equally

assigned voxels as well as the Jaccard index

[72]

(see Figure 4).

Both measures take values between zero and one, where lower

values correspond to more pronounced differences between two

0 20 40 60 80 100 120 140 160

Distance to separator [µm]

0.4

0.6

0.8

1.2

1.4

1.6

1.8

EDX intensity

Two-layer: EDX

Single-layer: EDX

Two-layer: Linear fit

Single-layer: Linear fit

Figure 3. Left: EDX image (ﬂourine mapping) of the single-layer cathode. Right: CBD gradient computed from EDX data (dots) and corresponding linear

ﬁt (solid line) for SL and TL.

www.advancedsciencenews.com www.entechnol.de

trinarizations. In the present setting, the Jaccard index compares

the spatial distribution of a predeﬁned phase between two differ-

ent trinarizations by computing the ratio of the intersection vol-

ume and the volume of the union. Note that the fraction of

equally assigned voxels and the Jaccard index corresponding

to a certain phase are symmetric characteristics such that the

entries below the main diagonal in Figure 4 contain the informa-

tion regarding the single-layer cathode, whereas the entries above

the main diagonal correspond to the two-layer cathode. On the

one hand, the top left plot shows that there exist non-negligible

differences between the neural network approaches, i.e., the

method for converting the output of the neural network to a tri-

narization has an inﬂuence on the resulting three-phase recon-

struction. On the other hand, there are even more pronounced

differences between the neural network trinarizations and the

remaining three approaches, namely, k-means, EDX-Closing,

and Thresholding. In addition, the remaining three plots in

Figure 4 indicate that the least differences between the

trinarization approaches are observed with regard to the segmen-

tation of active material, which is most likely caused by the high

contrast between active material and the remaining two phases.

Furthermore, there are negligible differences between the

single-layer and the two-layer cathode, except for the trinarization

obtained by global thresholding.

4. Simulation of Electrochemical Properties

The electrochemical simulations are conducted using the

research branch of the framework BEST, which is developed

in collaboration between the DLR Institute of Engineering

Thermodynamics and the Fraunhofer Institute for Industrial

Mathematics (ITWM) (https://www.itwm.fraunhofer.de/best).

Focus of this work is on the inﬂuence of the CBD on electro-

chemical reactions and transport. Therefore, we will describe

our CBD model and assumptions in more detail in subsequent

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing 0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Fraction of equally assigned voxels

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing 0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Jaccard index of AM

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Jaccard index of CBD

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

NN-AM-CBD-P

NN-AM-P-CBD

NN-CBD-P-AM

NN-CBD-AM-P

NN-P-AM-CBD

NN-P-CBD-AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Jaccard index of P

Figure 4. Fraction of equally assigned voxels (top left) as well as Jaccard index for active material (top right), CBD (bottom left), and pores (bottom right).

Note that the entries above the main diagonal correspond to the two-layer cathode, whereas the entries below the main diagonal refer to the single-layer

cathode. Due to the high accordance with regard to the spatial distribution of active material, the corresponding color bar only ranges from 0.6 to 1.

www.advancedsciencenews.com www.entechnol.de

paragraphs. A derivation of the governing equations and a

description of our numerical framework can be found in previ-

ous publications.

[37,73,74]

To provide a systematic overview of the

electrochemical simulation approach, we summarize the model

equations, boundary conditions, initial conditions, and parame-

ters in the supporting information. More speciﬁcally, the govern-

ing equations in the different phases are listed in Table S2,

Supporting Information. Interface and boundary conditions

are given in Table S3, Supporting Information. Interface models

between active materials and electrolyte are listed in Table S4,

Supporting Information.

As described in the previous section, the 3D image data of

both cathodes are segmented into three distinct phases, namely,

cathode active material, CBD, and porosity. However, the inner

structure of the CBD cannot be resolved by means of synchrotron

tomography, which has been also discussed at the beginning of

Section 3. Therefore, the CBD in our simulations on the elec-

trode scale actually contains two materials, namely, the solid car-

bon and binder matrix as well as liquid electrolyte. Similarly, the

porous separator contains both the glass-ﬁber material and liquid

electrolyte. In our simulations, we do not resolve the actual

microstructure of these materials. We rather use a homogeniza-

tion approach

[75]

to simulate the effective transport through these

mixed domains. This approach is computationally much more

efﬁcient and enables simulations on the cell scale; however,

requires additional input parameters for our model.

The relevant transport coefﬁcients which need to be corrected

due to the internal microstructure of the materials are the diffu-

sion coefﬁcient of lithium in the electrolyte (De) and the ionic

and the electronic conductivity (κeand σs) of the electrolyte

and solid phase, respectively. We determine the effective trans-

port parameters based on the concept of effective tortuosity using

the general expression given by Equation (2).

Xd;eff

p=γd

p⋅Xbulk

pwith X∈fD,σ,κg(2)

The effective transport parameter Xd;eff

pis deﬁned for a phase

p, which can be electrolyte (e) or solid (s), in a domain d, which is

the CBD or the separator. The effective parameter γd

pis deﬁned

using the respective volume fraction εd

pand the effective tortuos-

ity τd

pby

γd

εd

τd

with phase p∈fe,sgand domain d∈fCBD;Sepg. (3)

We assume that the inner porosity of the CBD is equal to 50%.

Hence, the effective tortuosity of the electrolyte part of the CBD

τCBD

ecan be computed based on γCBD

eusing the relationship

τCBD

εCBD

γCBD

2⋅γCBD

(4)

The effective tortuosity of the solid part in the CBD and the

electrolyte part of the separator are computed likewise. The elec-

trochemical parameters used in the simulations within this arti-

cle are listed in the Supporting Information (see Table S5,

Supporting Information).

In the previous paragraph, we provide a qualitative description

for the inﬂuence of the porous phases on the transport phenom-

ena. Additionally, these porous materials also have an impact on

the reactive surface effective at the interface to the active material.

At the interfaces, where the active material is in contact with a

porous electrolyte domain, we multiply the intercalation current

with the porosity of the electrolyte phase. In the case of the inter-

face between CBD domain and active material domain, the reac-

tion current is given by Equation (5).

iCBDAM

react =ireactεCBD

e(5)

The list of all interface conditions can be found in Table S3,

Supporting Information.

To evaluate the impact of different methods for CBD recon-

struction we performed two different types of virtual experi-

ments: 1) constant current lithiation in half-cell conﬁguration

with six different currents (1, 3, 6, 8, 10, and 12 mA cm

2

);

and 2) impedance spectroscopy in symmetrical cell conﬁguration

under blocking condition.

The simulation domains for the lithiation and the symmetrical

impedance simulations are shown in Figure 5.

Three different cutouts of the electrode tomography are used

as simulation domain for each trinarization approach and elec-

trode type. The trinarized 3D microstructures are cropped to a

lateral size of 200 voxels for the electrochemical simulations

due to computational constraints. This modiﬁcations keeps

the thickness of the electrode and areal capacity unchanged.

Impedance spectra are calculated using the step excitation

method. Details of the approach are also provided in ref. [37].

All electrochemical simulations are conducted using the HPC

resources of JUSTUS2.

(a) (b)

Figure 5. Simulation domains used for lithiation simulations in half-cell conﬁguration (a) and impedance spectroscopy simulations in symetrical cell

conﬁguration (b).

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5. Results and Discussion

This section covers the quantitative analysis of the different tri-

narization approaches with regard to their morphological prop-

erties by means of statistical microstructure analysis as well as

the resulting electrochemical behavior based on spatially and

temporally resolved numerical simulations.

5.1. Inﬂuence of Selected Trinarization Approach on

Morphological Descriptors

In this section, we discuss the inﬂuence of the different trinari-

zation approaches described in Section 3 on the morphology of

the resulting three-phase microstructures. For the sake of

clarity, we only discuss the three trinarizations corresponding

to the conditional probability approach, whereas the results

for the remaining six neural network trinarizations can be found

in the Supporting Information. Considering the 2D slices in

Figure 2, one can already observe visual differences with regard

to the morphological properties of the three phases. The CBD

phase determined by morphological closing based on EDX data

is accumulated around the active material, which, in turn, leads

to the formation of relatively large pores. Thereby, this approach

differs clearly from the other approaches. On the other hand, the

neural network approach results in a ﬁnely structured pore space.

Moreover, by visual inspection it is hard to detect differences

between the segmentation based on global thresholds and the

one obtained by k-means clustering. Recall from Section 3 that

all segmentation approaches are calibrated such that the volume

fractions of active material and CBD phase coincide with the

experimentally determined values. In order to quantitatively evalu-

ate the different trinarization approaches, we consider several

microstructure characteristics for each of the three phases, which

are considered as random closed sets,

[76]

denoted by ΞAM,ΞCBD,

and ΞP.

We begin with the surface area per unit volume. This quantity

is estimated from voxelized 3D image data as described in

ref. [77]. Besides the surface area per unit volume of each phase,

denoted by SAM,SCBD, and SP(see Table 2), the surface area per

unit volume of the interface between active material and the pore

space is of interest from an electrochemical point of view because

the intercalation takes place at this surface. Due to the inner

porosity of the CBD, this characteristic, denoted by SInt, is given

by SInt =SAM;Pþ0.5 ⋅SAM;CBD. For this purpose, the surface area

per unit volume of the interface between two phases is

computed as described in ref. [78]. Interestingly, the surface area

per unit volume of all three phases does not depend on the

underlying trinarization approach. Thus, there are only minor

differences between the values of SInt.

Additionally, the microstructure descriptors rmax and rmin are

given in Table 2, where the descriptor rmax denotes the 50%-

quantile of the so-called continuous pore size distribution.

Similarly, the descriptor rmin denotes the 50%-quantile of a phase

size distribution obtained by a geometric simulation of mercury

intrusion and can be considered as the radius of the typical

bottleneck. By means of rmax and rmin, the constrictivity

β=r2

min=r2

max ∈½0, 1can be deﬁned, which is a measure for

the strength of bottleneck effects and a meaningful characteristic

Table 2. Scalar microstructure characteristics for different trinarization approaches.

Sample AM–Cond CBD–Cond P–Cond Thresholding k-means EDX-Closing

SAM ½μm1TL 0.925 0.925 0.925 0.925 0.918 0.918

SAM ½μm1SL 0.925 0.925 0.924 0.918 0.924 0.924

SCBD ½μm1TL 0.360 0.361 0.36 0.359 0.369 0.374

SCBD ½μm1SL 0.362 0.362 0.362 0.360 0.361 0.370

SP½μm1TL 0.272 0.271 0.273 0.273 0.27 0.265

SP½μm1SL 0.271 0.271 0.272 0.279 0.272 0.263

SInt½μm1TL 0.672 0.672 0.672 0.672 0.664 0.662

SInt½μm1SL 0.671 0.671 0.671 0.668 0.671 0.667

rmin;AM ½μmTL 1.81 1.78 1.86 1.90 2.12 2.12

rmin;AM ½μmSL 1.83 1.80 1.84 1.93 2.17 2.17

rmin;CBD ½μmTL 0.66 0.75 0.23 0.21 0.22 0.78

rmin;CBD ½μmSL 0.60 0.73 0.24 0.21 0.21 0.78

rmin;P½μmTL 0.21 0.21 0.70 0.76 0.80 0.00

rmin;P½μmSL 0.22 0.21 0.69 0.78 0.78 0.00

rmax;AM ½μmTL 3.11 2.88 3.13 3.63 3.74 3.74

rmax;AM ½μmSL 3.19 3.12 3.17 3.66 3.80 3.80

rmax;CBD ½μmTL 1.03 1.23 0.67 0.48 0.52 1.26

rmax;CBD ½μmSL 0.96 1.14 0.70 0.46 0.47 1.27

rmax;P½μmTL 0.93 0.64 1.16 1.53 1.57 2.61

rmax;P½μmSL 0.97 0.67 1.15 1.47 1.55 2.58

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for effective transport properties.

[79–81]

With respect to these

microstructure descriptors, formally deﬁned in ref. [82], clear dif-

ferences between the considered trinarization approaches can be

observed, whereas there are no signiﬁcant differences between

the single-layer and the two-layer cathode. In particular,

Figure 6 shows that EDX-Closing leads to signiﬁcantly larger

pores, which, in turn, leads to the largest value of rmax.

Furthermore, k-means and Thresholding lead to nearly identical

continuous phase size distributions for all three phases, whereas

the neural network trinarizations differ from each other with

regard to the continuous phase size distribution of the CBD

as well as the pores. It is also interesting to note that with regard

to the CBD as well as the pore space, the neural network segmen-

tation based on conditioning on the respective phase leads to

larger clusters of this phase. With regard to the simulated mer-

cury intrusion porosimetry (see Figure 7), we observe that the

curves corresponding to the CBD and the pores are prone to dis-

cretization errors. Considering the active material, there are only

slight differences, which, in turn, leads to similar values for rmin.

Furthermore, the approach based on EDX data is the only case,

where clear differences between the single-layer and the two-

layer cathode can be observed. These differences are quantiﬁed

by means of the simulated mercury intrusion porosimetry of the

pore space. In Figure 6 and 7, the curves corresponding to the

segmentation approaches based on correlative microscopy are

shifted to the left compared to the remaining three-phase recon-

structions when considering the pore space.

Moreover, the distribution of geodesic tortuosity is consid-

ered. This is a purely geometric quantity, in contrast to the effec-

tive tortuosity considered in Section 4, providing the distribution

of the length of shortest paths through a predeﬁned phase in the

electrode divided by the thickness of the electrode (see ref. [82]

for a formal deﬁnition). Note that different concepts of tortuosity

exist in the literature,

[83–86]

where in the case of geodesic tortu-

osity Dijkstra’s algorithm is used to estimate this quantity from

voxelized image data.

[87]

As shown in Figure 8, the distribution of

geodesic tortuosity of the active material neither depends on the

selected trinarization approach nor on the considered cathode

sample. In contrast, the length of shortest paths through the

CBD as well as the pore space is larger for the trinarizations

obtained by the neural networks compared to the remaining

three segmentation approaches. These differences between the

four trinarization approaches considered in this article are stron-

ger than the differences between the single-layer and the two-

layer cathode.

In addition, the centered two-point coverage probability func-

tion is considered (see Figure 9). For stationary and isotropic

random closed sets Ξi,Ξjin the 3D Euclidean space ℝ3with

i,j∈fAM, CBD, Pg, this characteristic is deﬁned via CijðrÞ=

ℙð0∈Ξi,x∈ΞjÞεiεjfor any x∈ℝ3and r=jxj≥0, where

εi,εjdenotes the volume faction of Ξi,Ξj, respectively. This func-

tion is also called covariance function in the literature.

[69,88]

Due

to the normalization by subtracting the product of the volume

fractions, a value of zero implies that the events 0 ∈Ξiand

012345678

Radius [µm]

100

Normalized CPSD of AM [%]

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Radius [µm]

100

Normalized CPSD of CBD [%]

0 0.5 1 1.5 2 2.5 3 3.5 4

Radius [µm]

100

Normalized CPSD of P [%]

Figure 6. Continuous phase size distribution of active material (left), CBD (center), and pore space (right) for the two-layer cathode (dashed curves) and

the single-layer cathode (solid curves).

0 0.5 1 1.5 2 2.5 3 3.5

Radius [µm]

100

Normalized MIP of AM [%]

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

0 0.5 1 1.5

Radius [µm]

100

Normalized MIP of CBD [%]

0 0.5 1 1.5 2 2.5 3

Radius [µm]

100

Normalized MIP of P [%]

Figure 7. Simulated mercury intrusion porosimetry of active material (left), CBD (center), and pore space (right) for the two-layer cathode (dashed

curves) and the single-layer cathode (solid curves).

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x∈Ξjare stochastically independent. Positive values of Ci,jðrÞ

can be interpreted as a positive correlation between those two

events, whereas negative values correspond to a negative corre-

lation. Typically, choosing equal phases (i.e., i=j, see top row of

Figure 9) leads to a monotonously decreasing function

taking non-negative values, which approaches zero for large

radii r. On the other hand, considering two different phases

(i.e., i6¼ j, see bottom row of Figure 9) leads in most cases to

a monotonously increasing function approaching zero from

below. Figure 9 shows that there are no differences between both

samples regardless of the phases under consideration.

Furthermore, the curves in the top row of Figure 9 show the

same qualitative behavior as the continuous phase size distribu-

tion in Figure 6. The most noticeable effect is the unique

behavior of the closing approach based on EDX data with regard

to the bottom right plot in Figure 9. More precisely, the remain-

ing segmentation approaches show a peak at around 2 μm, which

corresponds to an increased likelihood of observing CBD and

pores 2 μm away from each other. The curves corresponding

to EDX-Closing show a steadily increasing two-point coverage

probability function instead.

Finally, we consider the volume fraction of each phase in

dependence of the distance to the separator (see Figure 10).

With respect to the spatial distribution of active material, there

is a clear difference between the single-layer and the two-layer

cathode regardless of the trinarization approach. More precisely,

the two-layer sample shows a pronounced drop of the volume

fraction of active material at 80 μm, i.e., at the interface between

012345678910

0.05

0.1

0.15

0.2

0.25

CAM, AM

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

012345678910

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

CCBD, CBD

012345678910

-0.02

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

CP, P

012345678910

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0.02

CAM, CBD

012345678910

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0.02

CAM, P

012345678910

-0.05

-0.04

-0.03

-0.02

-0.01

0.01

0.02

CCBD, P

Figure 9. Top row: Centered two-point coverage probability function of active material, CBD, and pore space (from left to right). Bottom row: centered

two-point coverage probability functions CAM;CBD,CAM;P, and CCBD;P(from left to right). Note that dashed curves are used for the two-layer cathode,

whereas the solid curves correspond to the single-layer cathode.

1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1

Geodesic tortuosity of AM []

Density []

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

1 1.05 1.1 1.15 1.2 1.25

Geodesic tortuosity of CBD []

Density []

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Geodesic tortuosity of P []

Density []

Figure 8. Geodesic tortuosity of active material (left), CBD (center), and pore space (right) for the two-layer cathode (dashed curves) and the single-layer

cathode (solid curves).

www.advancedsciencenews.com www.entechnol.de

both layers. With regard to the CBD, there are clear differences

between the results obtained for each of the trinarization

approaches, where all three-phase reconstructions except

EDX-Closing indicate a larger amount of CBD at the interface.

This peak is most pronounced for k-means and Thresholding.

Obviously, EDX-Closing reﬂects the linear gradient estimated

from EDX data. Note that this linear gradient is estimated from

a single 2D EDX image and is thus subject to a larger uncertainty

compared to the information extracted from 3D image

data. Therefore, segmentation approaches not reﬂecting the lin-

ear gradient observed in EDX data are not automatically consid-

ered as unrealistic. Interestingly, this does not lead to a linear

behavior of the distance-dependent porosity. Except for

EDX-Closing, there are comparatively small differences between

both samples (see the plots on the right-hand side of Figure 10).

5.2. Inﬂuence of Selected Trinarization on Electrochemical

Properties

The inﬂuence of the selected trinarization approach on the elec-

trochemical simulations is investigated using half-cell lithiation

simulations and symmetrical impedance simulations. The only

free parameter to achieve a good agreement between experi-

ments and simulations is the effective transport parameter

τCBD within the electrolyte part of the CBD. Relevant transport

mechanisms in a thick NMC electrode are the electronic conduc-

tivity through the solid phase and the lithium transport through

the electrolyte. Both quantities strongly depend on the distribu-

tion and morphology of the CBD. Especially, the electrolyte trans-

port depends on the local effective tortuosity in the CBD. The

electronic conductivity depends both on the conductive network

of the CBD and the conductivity of the active material, were the

latter is additionally dependent on the state of charge. However,

at larger CBD contents losses due to electronic transport are

minor compared to transport losses in the electrolyte.

Therefore, we use the lithiation simulation at a current of

6mAcm

2

to identify the local effective tortuosity of the CBD

that leads to the best agreement between experiment and simu-

lations. Note, at low CBD contents this assumption can be invalid

and contribution of the two processes cannot be deconvoluted

unambiguously. The best matching effective transport parame-

ters are identiﬁed for both electrode types (single-layer

cathode and two-layer cathode) with three cutouts each and all

trinarization approaches except for NN–CBD–P–AM and

NN–P–CBD–AM. In previous studies, we have shown that the

EDX-Closing trinarization is able to provide a reasonable

agreement between electrochemical measurements and

simulations.

[13,89]

Figure 10 visualizes the impact of the effective

γ-parameter on the lithiation simulation for the EDX-Closing tri-

narizations of the two-layer electrode in comparison to the exper-

imental results. Lithiation curves with a current of 6 mA cm

2

serving as target for our parameter optimization are highlighted

by the green symbols.

The impact of the spatial distribution of the CBD on the cell

voltage and the achievable lihtiation capacity is apparent. A

smaller value for the effective transport parameter γwill reduce

the achievable lihtiation capacity of the simulated electrode. In

turn, increasing the value of γreduces the transport resistance

in the electrolyte allowing to access larger electrode capacity.

A value of γ=0.12 provides the best match between simulations

and experiments for the two-layer electrode created using the

EDX-Closing method presented in Figure 11. This parameter

value corresponds to a local effective tortuosity of the electrolyte

phase of the CBD of 4.2.

The simulation results for all six currents for the selected

effective transport parameter (γtwolayer

EDX =0.12) within the CBD

are shown in Figure 11b. The numerical results show some

spread for higher currents due to local ﬂuctuations in the three

electrode cutouts. Nevertheless, the simulated cell voltages are in

excellent agreement with the experimental data for all currents.

However, as shown in Figure 11c applying the same procedure to

the k-means trinarization will result in a similar match between

experiments and simulations. In this case, the resulting effective

tortuosity of the CBD is somewhat larger (γ=0.06, 8.3). Similar

results can be reported for all cases studied in this work. The

ﬁgures used for both electrodes and all trinarizations to select

the best matching effective tortuosity are shown in the

Supporting Information (see Figure S8, Supporting

Information). The corresponding values for the ten different tri-

narizations and the two different electrode types are also listed in

Table 3.

The impact of the trinarization on the electrode performance

differs between the methods investigated in this work. Yet, the

two-layer electrode and the single-layer electrode exhibit the same

0 20406080100120140160

Distance to the separator [µm]

Volume fraction of AM [%]

NN-AM-Cond

NN-CBD-Cond

NN-P-Cond

Thresholding

k-means

EDX-Closing

0 20406080100120140160

Distance to the separator [µm]

Volume fraction of CBD [%]

0 20 40 60 80 100 120 140 160

Distance to the separator [µm]

Volume fraction of P [%]

Figure 10. Volume fraction of active material (left), CBD (center), and pores (right) in dependence of the distance to the separator for the two-layer

cathode (dashed curves) and the single-layer cathode (solid curves).

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trends. A smaller effective tortuosity indicates that the CBD is

distributed in the electrode such that even a small local transport

resistance will reduce the overall transport through the electrode.

The EDX-Closing trinarization leads to the smallest effective tor-

tuosities for the single-layer and two-layer electrodes due to the

distribution of the CBD at the bottlenecks of the active material

microstructure. The k-means and thresholding approach, on the

other hand, result in the largest effective tortuosities, which

implies that the spatial distribution of CBD created by these tri-

narization methods is not fully covering the bottlenecks for the

electrolyte transport. The results obtained for the trinarization

based on neural networks are qualitatively in between these

two extremes.

Additional analytical techniques are required to probe the

inﬂuence of the CBD distribution. As shown above, the distribu-

tion and corresponding effective tortuosity values have a signiﬁ-

cant inﬂuence on lithium ion transport in the electrolyte.

Impedance spectroscopy on symmetrical cells in blocking

(a) (b)

(c)

Figure 11. Impact of the effective transport through the CBD for the two-layer electrode. Further details can be found in the captions of the respective

graphs.

Table 3. List of effective tortuosity values providing the best match to the

corresponding electrochemical data.

Method Single-layer Two-layer

τSL τSL 1

τTL τTL

k-means 0.02 50 0.12 8.3

DX-Closing 0.18 5.6 0.24 4.2

Thresholding 0.02 50 0.12 8.3

NN–AM–CBD–P 0.09 11.1 0.18 5.6

NN–AM–Cond 0.09 11.1 0.18 5.6

NN–AM–P–CBD 0.03 33.3 0.18 5.6

NN–CBD–AM–P 0.09 11.1 0.18 5.6

NN–CBD–Cond 0.09 11.1 0.18 5.6

NN–P–AM–CBD 0.03 33.3 0.18 5.6

NN–P–Cond 0.03 33.3 0.18 5.6

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conditions has become a standard tool for the characterization of

the pore transport resistance.

[90–92]

Therefore, we additionally

performed impedance simulations on symmetrical cells to inves-

tigate the impact of the different trinarization methods. The cor-

responding impedance spectra for the single-layer and two-layer

cathode are shown in Figure S6a and S6b, Supporting

Information, respectively. However, the different trinarizations

result in very similar impedance spectra which will not allow

to discern distribution-related effects in corresponding imped-

ance measurements. Therefore, also the electrode impedance

does not provide a hint on the most favorable trinarization

method.

In summary, we demonstrate that it is possible to identify one

effective tortuosity per electrode type and trinarization method

such that the simulations are in fair agreement with the experi-

mental data for all currents. However, there are large variations

in the effective tortuosity of the CBD between the different tri-

narization methods. None of the individual techniques is able to

provide a consistent representation for all electrode samples

investigated in this work. Hence, we could not determine the tri-

narization method providing the best representation of the elec-

trode microstructure. High-resolution image data of the CBD

might yield additional information on the effective CBD conduc-

tivity which then eventually will allow to choose the most suitable

trinarization technique.

6. Conclusion and Outlook

In the present article, 3D image data of a single-layer and a two-

layer cathode obtained by synchrotron tomography have been

segmented into active material, the CBD, and the pore space

by four different approaches, where the approach based on cor-

relative microscopy allows for nine different trinarizations by

altering the way of converting the material composition predicted

by the neural network to a three-phase reconstruction. The dif-

ferent segmentation approaches, which are designed to match

the experimentally determined volume fractions, are quantita-

tively compared by means of statistical image analysis as well

as spatially and temporally resolved simulations of electrochemi-

cal properties. It turns out that there are non-negligible differen-

ces between the proposed trinarization approaches. Among

others, the geodesic tortuosity as well as the continuous phase

size distribution of both - the CBD and the pores - depend on

the chosen segmentation approach. Furthermore, it has been

shown that there are clear differences between the trinarizations

obtained by correlative microscopy. Thus, the rule for converting

the material composition predicted by the neural network to a

three-phase reconstruction is of importance, even though the dif-

ferences compared to the remaining three approaches are more

pronounced. However, a high level of agreement between the

experimental measurements and the lithiation simulations can

be achieved for all trinarization methods by adjusting the effec-

tive transport parameter of the CBD. Note that using a ﬁxed cur-

rent for ﬁtting this parameter allows us to match the

experimental curves for ﬁve different currents, which indicates

that each trinarization approach is reasonable. By doing so, the

effective tortuosity within the CBD is restricted to the interval

½4.2, 50. This large range indicates that further research is

required to determine the best trinarization approach. For exam-

ple, the high-resolution 3D FIB-SEM data could be used to quan-

titatively investigate ionic transport within the nanopores.

Nevertheless, this approach based on spatially resolved numeri-

cal simulations allows to predict the optimal spatial distribution

of the CBD in lithium-ion battery electrodes, leading to an

improved electrochemical performance.

Supporting Information

Supporting Information is available from the Wiley Online Library or from

the author.

Acknowledgements

The presented work was ﬁnancially supported by the German Ministry

“Bundesministerium für Bildung und Forschung”within the projects

HighEnergy and HiStructures under the reference numbers 03XP0073C

and 03XP0243C/D/E as well as within the framework of the program

“Vom Material zur Innovation.”This study contributes to the research per-

formed at CELEST (Center for Electrochemical Energy Storage Ulm

Karlsruhe). The work by M.N. was partially funded by the German

Research Foundation (DFG) under Project ID 390874152 (POLiS

Cluster of Excellence, EXC 2154). The authors acknowledge support by

the state of Baden-Württemberg through bwHPC and the German

Research Foundation (DFG) through grant no. INST 40/575-1 FUGG

(JUSTUS 2 cluster). The authors thank Christian Dreer for working out

the production process for the single-layer and two-layer electrodes and

their manufacturing and Claudia Pfeifer for the preparation and EDX anal-

ysis of the electrode cross sections. All responsibility for the content of this

publication is assumed by the authors.

Open Access funding enabled and organized by Projekt DEAL.

Conﬂict of Interest

The authors declare no conﬂict of interest.

Data Availability Statement

Research data are not shared.

Keywords

3D imaging, carbon-binder domain, electrochemical performance, image

segmentation, microstructures, modeling and simulation, structuring

concept for lithium-ion batteries

Received: July 18, 2022

Revised: August 19, 2022

Published online: September 14, 2022

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