Electrochemical

characterization of

LiNi1/3Mn1/3Co1/3O2 at

different stages of lifetime

MARIA VARINI

Doctoral Thesis, 2020

KTH Royal Institute of Technology

School of Engineering Sciences in Chemistry,

Biotechnology and Health

Department of Chemical Engineering

Division of Applied Electrochemistry

SE-100 44 Stockholm, Sweden

TRITA-CBH-FOU-2020:13

ISBN 978-91-7873-457-3

Akademisk avhandling som med tillstand av KTH i Stockholm framlaggs till

offentlig granskning for avlaggande av teknologie doktorsexamen fredagen den 27

mars kl.10:00 i sal K2, KTH, Teknikringen 28, Stockholm.

I am the bone of my sword.Steel is my body, and fire is my blood.I have created over a thousand blades,unaware of loss,nor aware of gain;withstood pain to create weapons,waiting for one’s arrival.I have no regrets.This is the only path.My whole life was Unlimited Blade Works.

Shirou Emya, Fate/Stay Night: Heaven’s Feel

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Abstract

Li-ion batteries have entered our everyday life first as power sources forsmall electronics, and recently for electric vehicles and stationary sto-rage applications. As the requirements on the performance and lifetimeof Li-ion batteries increase and diversify, it becomes paramount to pro-perly understand their electrochemical performance at single-electrode le-vel, and their evolution over cycling. This is crucial for both the designof improved electrode materials, better suited for the most recent ap-plications, but also for accurately predicting the performance decay ofexisting devices. As the component of focus, the positive electrode waschosen, since it limits both power and energy in Li-ion batteries. Speci-fically, the material investigated was LiNi1/3Mn1/3Co1/3O2 (NMC111), astate-of-the-art, fully commercial electrode, as well as the precursor for Ni-rich LiNixMnyCo1–x –yO2, towards which research is very active. Startingat Beginning of Life, NMC111 was characterized though a combinationof electrochemical techniques at varying temperatures (Constant Currentcycling, Cyclic Voltammetry, Galvanostatic Intermittent Titration Techni-que, and Electrochemical Impedance Spectroscopy), which were comparedand discussed in terms of electrode response and suitability. Thermody-namic and dynamic properties were obtained, and supported the designof a semi-empirical model for predicting LIBs voltage characteristics. Thisknowledge was also used to monitor the evolution of NMC111’s performan-ce under high voltage operation, and the possibility of connecting changesin the electrochemical response to specific ageing phenomena: this infor-mation could support the creation of physics-based predictive models.

Keywords: Li-ion battery, positive electrode, LiNi1/3Mn1/3Co1/3O2,electrochemical characterization, ageing, semi-empirical model.

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Sammanfattning

Litiumjonbatterier ar numera en del av var vardag och har sedan langeanvants som energilager i konsumentelektronik och har pa senare ar avenblivit en viktig del i elektrifierade fordon samt for stationar energilag-ring. Nar kraven pa prestanda och livslangd for litiumjonbatterierna okaroch diversifieras blir det viktigare att forsta den elektrokemiska prestan-dan pa elektrodniva och hur egenskaperna forandras vid cykling. Detta aravgorande for utformning av forbattrade elektrodmaterial som ar battrelampade for framtida applikationer, samt ocksa for att kunna forutsagabatteriprestandaforlust i befintliga applikationer. Detta arbete har fokuse-rat pa den positiva elektroden eftersom den ar begransande bade gallandeeffekt och energi i litiumjonbatterier. ElektrodmaterialetLiNi1/3Mn1/3Co1/3O2 (NMC111), ett kommersiell tillgangligt och ofta anvantelektrodmaterial i dagens litiumjonbatterier har undersokts i detta ar-bete. Detta material ar foregangare till de nickelrika elektrodmaterial(LiNixMnyCo1–x –yO2) dar intensiv forskning sker idag. Undersokning avnytt NMC111-material utfordes med en kombination av tekniker vid va-rierande temperaturer (konstantstromcykling, cyklisk voltammetri, galva-nostatisk intermittent titreringsteknik och elektrokemisk impedansspekt-roskopi) och resultaten jamfordes och diskuterades med avseende pa elek-trodrespons och lamplighet. Termodynamiska och dynamiska egenskapererholls och stodde utformningen av en semi-empirisk modell for att forutsagaspanningsegenskaper hos litiumjonbatterier. Denna kunskap anvandes ocksafor att overvaka forandringen av egenskaperna hos NMC111 vid cykling tillhogre spanningsnivaer samt for att forsoka sammankoppla forandringar avelektrokemiska egenskaper till specifika aldringsfenomen: denna informa-tion kan stodja skapandet av fysikbaserade prediktiva modeller.

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List of papers

The thesis is based on the following papers:

I. M. Varini, J. Y. Ko, M. Klett, H. Ekstrom, G. Lindbergh, ”Electro-chemical techniques for characterizing LiNixMnyCo1–x –yO2 batteryelectrodes”, Manuscript

II. J. Y. Ko, M. Varini, M. Klett, H. Ekstrom, G. Lindbergh, ”PorousElectrode Model with Particle Stress Effects for Li (Ni1/3Co1/3Mn1/3)O2

Electrode”, Journal of The Electrochemical Society, 166(13):A2939-A2949, 2019.

III. M. Varini, J. Y. Ko, P. Svens, U. Mattinen, M. Klett, H. Ekstrom,G. Lindbergh, ”Quantitative study of Li-ion battery ageing: the caseof LiNi1/3Mn1/3Co1/3O2 under high voltage operation”, Manuscript

IV. M. Varini, P. Campana, G. Lindbergh, ”A semi-empirical, electro-chemistry - based model for Li-ion battery performance predictionover lifetime”, Journal of Energy Storage, 25:100819, 2019.

V. F. Benavente, M. Varini, A. Lundblad, S. Cabrera, G. Lindbergh,”Effect of partial cycling of NCA/graphite cylindrical cells in dif-ferent SOC intervals”, Submitted to Journal of the ElectrochemicalSociety

Author contribution

In Paper I, I performed the majority of the experiments, and wrote thearticle under the guidance of the co-authors. The EIS measurements in3-electrode cell were performed by Matilda Klett. The implementation ofthe P2D model and the fitting of EIS results were performed by Jing YingKo.

In Paper II, I performed all the experiments. The design and implemen-tation of the modified P2D model, as well as the fitting of experimentalGITT curves, was performed by Jing Ying Ko.

In Paper III, I performed the majority of the experiments, and wrote

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the article under the guidance of the co-authors. The design and imple-mentation of P2D model, as well as the fitting of the experimental EISresults, was performed by Jing Ying Ko. The structure of the articlewas drafted by Pontus Svens. The operando MS measurements were per-formed by Ulriika Mattinen. The SEM/EDX analysis was performed byBjorn Ericksson, and the XRD measurements by Jekabs Grin at Stock-holm University (SU).

In Paper IV, I designed the semi-empirical model, performed the fittingand validation, and wrote the article under the guidance of the co-authors.

In Paper V, I performed a significant amount of the reference performancetests. The design of the testing protocol, the post mortem characterizationand DVA analysis were performed by Fabian Benavente.

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Acronyms

AC Alternate Current.

BMS Battery Management System.

BOL Beginning of Life.

CC Constant Current.

CL Capacity Loss.

CP Constant Potential.

CV Cyclic Voltammetry.

DC Direct Current.

DOD Depth of Discharge.

DST Dynamic Stress Test.

DVA Differential Voltage Analysis (dV/dQ).

EIS Electrochemical Impedance Spectroscopy.

EOL End of Life.

EV Electric Vehicle.

FUDS Federal Urban Driving Schedule.

GITT Galvanostatic Intermittent Titration Technique.

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ICA Incremental Capacity Analysis (dQ/dV).

LAM Loss of Active Material.

LCO LiCoO2.

LFP LiFePO4.

LIB Li-ion battery.

LLI Loss of Li+ inventory.

LMO LiMn2O4.

NCA LiNi0.8Co0.15Al0.05O2.

NMC LiNixMnyCo1–x –yO2.

NMC111 LiNi1/3Mn1/3Co1/3O2.

OCP Open Circuit Potential.

ODH Oxygen Dumbbell Hopping.

ORP Odd Random Phase (EIS).

P2D Pseudo 2 Dimensional.

PV Photo Voltaic.

RUL Remaining Useful Lifetime.

SEI Solid Electrolyte Interface.

SOC State of Charge.

SOH State of Health.

TSH Tetrahedral Site Hopping.

USABC United Sates Advanced Battery Consortium.

XRD X-Ray Diffraction.

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List of Symbols

α Barrier factor.

c Concentration/ mol cm−3.

cdl Double layer capacitance per active material surface area/ F m−2.

cdl, cc Double layer capacitance on current collector/ F m−2.

dEconc/γpos Thermodynamic factor/ V.

∆rG Gibbs free energy of reaction/ kJ mol−1.

∆rH Enthalpy of reaction/ kJ mol−1.

∆rS Entropy of reaction/ kJ mol−1 K−1.

Ds,eff Effective diffusion coefficient/ cm2 s−1.

E Voltage/ V.

E0 Steady-state voltage/ V.

EA Activation energy/ kJ mol−1.

ηdiff Diffusive overpotential/ V.

ηkin Kinetic overpotential/ V.

F Faraday constant/ A mol−1.

γstress Stress factor/ V.

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I Current/ A.

i0 Exchange current density/ A m−2.

J Interaction parameter.

k Kinetic rate constant/ m s−1.

Kdiff Diffusive resistance/ Ω.

Kkin Kinetic resistance/ Ω.

Qnom Nominal capacity/ A h.

Q(t) Actual capacity/ A h.

Rcc Resistance between current collector and porous electrode per geo-metric area/ Ω m2.

R Universal gas constant/ J mol−1 K−1.

Rohm Ohmic resistance/ Ω.

t Time/ h.

T Temperature/ K.

V0 Open Circuit Potential (OCP)/ V.

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Contents

1 Introduction 11.1 Li-ion batteries (LIBs) . . . . . . . . . . . . . . . . . . . . . 11.2 Ageing in LIBs and its detection . . . . . . . . . . . . . . . 21.3 Electrochemical techniques for LIBs . . . . . . . . . . . . . 3

1.3.1 Galvanostatic cycling . . . . . . . . . . . . . . . . . 41.3.2 Galvanostatic Intermittent Titration Technique

(GITT) . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.3 Cyclic Voltammetry (CV) . . . . . . . . . . . . . . . 61.3.4 Electrochemical Impedance Spectroscopy (EIS) . . . 7

1.4 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 LiNi1/3Mn1/3Co1/3O2 (NMC111) . . . . . . . . . . . . . . . 10

2 Scope of the thesis 13

3 Experimental 153.1 Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Electrochemical testing . . . . . . . . . . . . . . . . . . . . . 16

3.3.1 CC cycling . . . . . . . . . . . . . . . . . . . . . . . 163.3.2 GITT and equilibrium potential curves . . . . . . . 183.3.3 EIS . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.4 CV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Semi-empirical model . . . . . . . . . . . . . . . . . . . . . . 19

4 Results and Discussion 214.1 Electrochemical characterization of NMC111 . . . . . . . . 21

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4.1.1 Characterization at BOL . . . . . . . . . . . . . . . 214.1.2 Characterization at EOL . . . . . . . . . . . . . . . 36

4.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.1 Semi-empirical model . . . . . . . . . . . . . . . . . 434.2.2 Ageing protocols . . . . . . . . . . . . . . . . . . . . 46

5 Conclusions 51

6 Acknowledgements 54

References 56

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Chapter 1

Introduction

1.1 Li-ion batteries (LIBs)

Batteries can be classified as primary or secondary, according to whethertheir chemical reactions are reversible or not [1]. Li-ion batteries (LIBs)are secondary energy storage devices characterized by an exceptional energy-to-weight ratio [2], lack of memory effect, fast response, high power ca-pability, long cycle lifetime, and low self-discharge rate [3]. Due to allthese advantageous properties, LIBs have been dominating the market ofportable electronics; in addition, they are the main power source in elec-tric vehicles (EVs) [4], and help balancing the intermittency of renewableenergy sources (such as sun and wind) in the energy grid [5] [6]. In orderto fulfil the needs of these diversified applications, extensive engineeringhas brought to different LIB configurations (pouch, cylindrical, or pris-matic) and performances (power- or energy-optimized) through advancedcell design, and broad electrode material development.

The different applications notwithstanding, all conventional LIBs arebased on the reversible (de)intercalation of Li+ in the positive and neg-ative electrodes. This reaction occurs in solid-state, and since solid-stateprocesses are generally several orders of magnitude slower than in liquid[7], the electrodes are considered performance-limiting components [8] [9].The positive electrode is typically a Li metal oxide, with either a layeredor tunnelled structure. One of the first commercial positive electrodes hasbeen LiCoO2 (LCO), which is being replaced by less costly materials, as

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LiMn2O4 (LMO), LiFePO4 (LFP) and LiNixMnyCo1–x –yO2 (NMCs), orwith higher specific capacity, as LiNi0.8Co0.15Al0.05O2 (NCA) [10]. Thenegative electrode is mostly graphitic carbon, which has been employedsince early prototyping of LIBs, and is still hard to replace [10]. In boththese electrodes, the intercalation of Li+ is composed by an heterogeneouscharge transfer at the electrode/electrolyte interface (Li+ + e− + M →LiM, where M is the host electrode), accompanied by Li+ mass transfer(i.e. solid-state diffusion) in the bulk of the material [8][11]. Limitations inany of these steps increase the total polarization in the cell, thus decreas-ing its power and energy density [12]. Understanding the impact of bothcharge transfer and solid-state diffusion in the total polarization alreadyat Beginning of Life (BOL) is a valuable input for the design of improvedelectrode materials, and overall battery performance enhancement [9] [13].

1.2 Ageing in LIBs and its detection

The performance at BOL in LIBs undergoes a gradual degradation overlifetime, both during use (cycling) and on storage (calendar ageing) [14].This degradation, quantified by means of the State-of-Health (SOH) in-dicator [14], manifests itself in the form of an impedance increase (powerfade) and/or capacity fade at full cell level [15] [16]. Impedance increasecan be induced by the formation of passive films at the surface of the activeparticles of both the positive and negative eletrode, due to the electrolyte’sdecomposition [16]. Another possible cause for impedance increase is theloss of electrical contact within the porous electrode [16] due to structuraland mechanical degradation (cracking, loss of contact, and insulation) [17].Capacity fade, on the other hand, can be caused by (i) Loss of Li+ In-ventory (LLI), a degradation at cell level: Li+ is no longer available toshuttle between the electrodes, because it has been consumed by parasiticreactions (film formation, electrolyte decomposition, Li plating); and/or(ii) Loss of Active Material (LAM), a degradation at the single electrodesresulting from structural changes (phase transitions, oxygen release, ortransition metal dissolution), particle cracking or de-cohesion related tomechanical stress during operation [14]. LAM also affects the total cell’sperformances, particularly when it leads to a different extent of capacityfade in the two electrodes, whose half-cell voltage characteristics and rel-

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ative SOC become offset due to the incomplete intercalation [18]. Thisleads to stoichiometric drift, and loss of capacity at full-cell level.

This shows how the overall degradation of LIBs stems from severalageing processes occurring at single-electrode level, which have an impacton the full cell since they are inter-connected [14] [19]. An example of thisconvoluted degradation occurs while operating LIBs at high voltage, inorder to enhance their energy density. These cycling conditions, particu-larly detrimental for LIBs’ cycle life, lead to the degradation of the positiveelectrode and trigger the electrolyte’s decomposition, as well as the forma-tion of an anomalous Solid Electrolyte Interface (SEI) on graphite, whichin turn leads to severe LLI at full-cell level [20]. In the meantime, theelectrolyte decomposition induces the formation of films as well as gassingat both electrodes, and possible shuttling of the gases from one electrodeto the other [21].

Therefore, in all ageing scenarios it is necessary to first identify andde-convolute the different ageing modes occurring at single-electrode level[16], and then to quantify their impact on the total performance, in orderto understand the root causes behind the overall degradation. A com-bination of non-destructive and destructive testing is generally used forthe purpose. Non-destructive analysis, as part of the diagnostic protocol(often called the reference performance test) performed during cycling, isused to quantify the total cell performance, and to monitor its degradationas a function of the cycling conditions [16]. However, post-mortem charac-terization (which is destructive, as it requires the disassembly of the cell) isgenerally more effective for a deeper investigation at single-electrode level[14]. Identifying the limiting electrode, and the main ageing modes activein it, is key for understanding the degradation at full cell level (PaperV), as well as for a correct interpretation of the electrochemical responseof aged electrodes (Paper I), and the design of better-performing LIBs(Paper III).

1.3 Electrochemical techniques for LIBs

Investigating LIBs performance at all stages of lifetime is commonly doneby means of electrochemical techniques: a class of analytical methods inwhich the system is driven away from steady-state by perturbing the cur-

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rent or voltage, and the response of the other is recorded [22]. Commonelectrochemical techniques are Galvanostatic (or Constant Current (CC))cycling, Galvanostatic Intermittent Titration Technique (GITT), CyclicVoltammetry (CV) and Electrochemical Impedance Spectroscopy (EIS)[22], and they allow for (non-invasive) study of thermodynamic and dy-namic properties [23]. CC cycling, GITT, and CV are time-dependent,i.e. the rate of the measurement has to be comparable to the rate of thephenomena investigated. EIS is frequency-dependent, since it is measuredas a function of time, but processed in the frequency domain: in this way,several phenomena can be detected in the framework of the same exper-iment, even if their time constants differ of several orders of magnitude[24]. The electrochemical techniques here considered are not concurrent[23], i.e. they deliver different information, and are characterized by adifferent level of features and detail. As a consequence, it is of impor-tance to choose the right techniques for characterizing a certain aspect ofthe cell/electrode, maximizing the amount of information extracted fromsimple spectral observation. However, an overview of all these techniques(some of which are rather underused) for the characterization of LIBs israrely found: this leads to loosing valuable information that might arisefrom spectral comparison.

1.3.1 Galvanostatic cycling

Galvanostatic cycling consists in applying a constant current (CC) to thebattery, and reading the related voltage response. The measurement isterminated either after a certain amount of time (charge) has passed, orwhen a certain voltage has been reached [25]. A plot of voltage vs. ca-pacity (time) is thus obtained, often denoted as the voltage characteristic.The length of the curve represents the accessible capacity (of a full-cell,or of a single electrode) under certain testing conditions [23] [25]. Voltagecharacteristics contain both thermodynamic and kinetic contributions [25].Consequently, the shape of the curve is determined by several factors, in-cluding a) the chemistry and crystallographic structure of the electrode(s)[23]; b) the current applied (often referred to in terms of C-rate, i.e. theworking capacity of the electrode, divided by the desired amount of timefor a full (dis)charge), and c) the cycling history of the device [25]. Forsuch reasons, CC cycling is commonly used:

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• as the first experiment performed on a novel electrode material [25];

• for setting up (standard) cycling protocols mimicking real-life usageof LIBs [23];

• for characterizing (aged) cells and electrodes.

However, the separation of thermodynamic and kinetic responses in volt-age characteristics is not straightforward [25], even at slow C-rates (wherethe polarization is minimized [23]), unless a model is used. Furthermore,voltage characteristics are rather featureless, and small voltage variations(as those induced by a change in the electrode’s properties, or stoichiomet-ric drift in the full cell) are difficult to visualize, unless amplified throughdifferentiation [23] [25]. Two common differential methods are the In-cremental Capacity Analysis (ICA, also known as dQ/dV) and the Dif-ferential Voltage Analysis (DVA, also known as dV/dQ). Both ICA andDVA possess a higher sensitivity than a conventional voltage character-istic [26] [27], and don’t require additional measurements. However, apost-processing of the experimental signal is required, involving both thedifferentiation and noise cleaning, by which these techniques are severelyaffected [23] [25].

1.3.2 Galvanostatic Intermittent Titration Technique(GITT)

GITT consists in applying a series of CC pulses, each followed by a re-laxation (in which no current passes through the cell) long enough forthe electrodes to reach their equilibrium potential [25]: the correspond-ing voltage response is registered. The cell potential varies proportionallyto the ohmic drop, the charge transfer resistance, and the concentrationgradient in the electrolyte and solid phase [23]. A typical GITT measure-ment is performed on single electrodes [23], and it allows to retrieve boththeir thermodynamic and kinetic parameters [28] in the framework of asingle measurement [25]. In particular, GITT measurements are mostlyknown for providing solid-state diffusion coefficients [29] and equilibriumpotential of LIBs electrodes [23].

As far as solid-state diffusion coefficients are concerned, although theirextraction can be done analytically from GITT curves, the underlying

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theory implies several assumptions, which do not always hold valid forLIB electrodes: among others, a dense planar electrode, uniform cur-rent distribution, and a constant diffusion coefficient across the currentpulse. Therefore, obtaining the diffusion coefficients through this routemight lead to inaccurate results [30]. On the other hand, GITT mea-surements are considered among the most accurate for quantifying theequilibrium potential at different degrees of lithiation, since kinetic con-tributions are removed during relaxation [23]. Plotting the equilibriumpotential as a function of capacity allows to build an equilibrium curve,which is paramount in Battery Management Systems (BMS) for the esti-mation of State of Charge (SOC) [27]. All active electrode materials havedifferent equilibrium curves, due to their different chemical compositionand/or crystallographic structure [23]. In general, a flat plateau repre-sents a two-phase reaction (constant chemical potential), while a slopingbehaviour (changing chemical potential) indicates a change in the solidsolution concentration [25]. For some electrode materials, a thermody-namic hysteresis between charge and discharge might arise, due to theco-existence of several equilibria at the same SOC [27], or the occurrenceof apparent equilibria caused by the presence of phase boundaries [31].

1.3.3 Cyclic Voltammetry (CV)

CV is performed by applying a linear potential scan on the working elec-trode, and the current response is recorded [32]; by varying the scan rate,the time scale of the processes under study can be explored [33]. Assuch, it is a technique mostly suitable for single electrodes, since onlythe response of the working electrode is recorded [32]. In other electro-chemical systems than LIBs, CV is considered one of the most effectivetechniques for the direct investigation of reaction mechanisms, as it canbe used for identifying the limiting reaction steps, quantifying the num-ber of exchanged electrons, the equilibrium potential of the reaction, andits reversibility [32] [33]. When employed for the characterization of LIBelectrodes, the voltammograms resemble ICA plots [7], although the in-formation contained in them differs: firstly, these two measurements areperformed at different rates (very slow for ICA, and variable for CV), andsecondly, CV is characterized by a varying C-rate across the scan, sincethe current (which in this case is the dependent variable) is not constant

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[7].Performing CV on LIBs electrodes allows to identify the redox species

involved, as well as the particle size and crystalline properties of the ma-terial [33]; however, CV is possibly the most underused technique amongthose here considered, one of the reasons being the difficult interpretationof the voltammograms. CV of intercalating materials implies that theinvariant bulk concentration approximation [34] at the core of CV math-ematical description [35] cannot be fulfilled. A direct consequence is thatclassical CV analysis tools, as Randles-Sevcik equation (for extraction ofdiffusion coefficients) and the reversibility criteria [35], do not hold theirvalidity. Although different mathematical descriptions of the voltammo-grams of LIB electrodes have been proposed [36] [9] [34], they mostlyapply for limiting cases, i.e. experiments either fully in kinetic or diffusivecontrol; these conditions can be obtained experimentally only by meansof tailor-made electrodes [36] [34], which strongly differ from commercialformulations.

1.3.4 Electrochemical Impedance Spectroscopy (EIS)

EIS is a relatively specialized, but widely applied technique for character-izing LIBs [23][37]. The measurements are performed by applying a smallsinusoidal Alternate Current (AC) voltage perturbation (with varying fre-quency) on top of the controlled Direct Current (DC) voltage (usually atequilibrium). In this case, the current response is recorded (potentiostaticEIS) [23] [25]; alternatively, a sinusoidal current may be applied, and thesubsequent potential response measured (galvanostatic EIS). In an idealcase, both yield to the same result [23]. EIS can be performed both at full-cell level, and on single electrodes; performing both allows to understandthe single electrode’s contributions to the total cell impedance, since thisvariable is additive [10].

EIS enables both the qualitative and quantitative analysis of electrontransport, reaction rate and mechanisms, intercalation processes, masstransport and electrode structure [38] [39]. For such reason, it can be usedto determine the limiting factors in an electrode’s performance [40]. Thissupports the diagnostic of failure mechanisms (since impedance growthis strongly associated with SOH) [20] and the prediction of LIBs lifetime(since impedance changes over lifetime, and it is influenced by the previ-

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ous history) [39] [40]. Among various ways to present the results of EISmeasurements, the so-called Nyquist plot is commonly used [25], wherethe real and imaginary contribution to the total impedance are displayedon separate axes. This plot contains information about the charge trans-fer and diffusion, as well as the (possible) presence of insulating layers[41]. Although EIS is dense in information about the system, its quan-titative analysis relies on fitting a model to the data, in order to extractthermodynamic, transport, and/or kinetic parameters [39]. In addition,even the qualitative analysis of the spectra might be complicated, sinceLIB electrodes are porous materials characterized by several overlappingcharge-transfer processes due to their large, inhomogeneous surface area[23].

Finally, for an EIS measurement to be representative of the systemconsidered, the conditions of causality, linearity and stationarity have to bemet [41]. Causality is met if the impedance response stems only from theapplied signal and the experimental noise; linearity implies a linear relationbetween voltage and current, normally met by applying a small-amplitudeperturbation. Finally, stationarity is met if the response of the system isinvariant during the entire measurement, i.e. if the Open Circuit Potential(OCP) remains constant during the experiment [42]. Among the differentmethods to assess the fulfilment of these conditions, Odd Random Phase(ORP) EIS is able to measure and quantify the level of the disturbingnoise, of the non-linear distortions, and of the non-stationary behaviourin the framework of the same experiment. A more detailed explanation ofthe technique can be found in Breugelmans et al. [24].

1.4 Modelling

The electrochemical response of LIBs (and of LIB electrodes in particu-lar) to the different perturbations applied provides information about theirthermodynamic and kinetic properties. However, it might be difficult toseparate these two contributions, or to perform a direct quantificationof physically-meaningful parameters, unless models are developed to fitthem: in such case, parametrization can be performed, i.e. the quantifica-tion of thermodynamic and dynamic parameters from experimental data.The knowledge of these parameters deepens the understanding of LIBs’

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electrochemical response, supporting the development of predictive modelsfor estimating status figures (as SOC and SOH), and ultimately predictingLIBs’ performances at different stages of lifetime. Four different classes ofmodels can be found in the literature for LIBs:

1. empirical models, as mathematical equations and equivalent circuitmodels (ECMs);

2. electrochemical models, as the pseudo 2 dimensional (P2D) model[43], and the single particle model;

3. multi-physics models, i.e. models including both the electrochemi-cal response, and the impact of external variables (most commonly,temperature);

4. molecular and atomistic models [2].

Each modelling approach has its advantages and drawbacks. For exam-ple, increasing the level of detail brings to a higher computational cost [2],as in the case of multi-physics, molecular and physics-based models [44].Physics-based models are computationally heavy, due to the need of solv-ing differential equations [45]; in addition, they require a high number ofinput parameters, to be obtained through a complex and time-consumingparametrization [46]. Nevertheless, these approaches are characterized bya high accuracy [47], and the extracted parameters hold a physical mean-ing, thus a more general validity. For example, physics-based modellingapproaches allow to quantify the exchange current density i0, and Li+

solid-state effective diffusion coefficient1 Ds,eff, both material-dependentparameters that can provide insight into the limiting factors of an elec-trode’s performance. On the other hand, a good fitting of the experimentalresults can be achieved only by knowing the undergoing mechanisms atdifferent stages of LIBs’ lifetime [48] [49], an information not always vi-able, due to the already-discussed complexity and inter-relation of ageingphenomena [50].

Conversely, empirical models allow for very fast computation [2], andrequire a low number of input parameters. This makes them relevant in

1The effective diffusion coefficient (also referred to as the apparent diffusion coeffi-cient) in a solid polycrystalline material is thus called, since it is a weighted average ofthe grain boundary diffusion coefficient and the lattice diffusion coefficient.

9

industrial field, thanks to their easy implementation into the modellingof larger systems (as energy grids), or the possibility of performing real-time predictions (as on-board of EVs). However, the empirical characterof these approaches makes them poor descriptive models: in ECMs, theimpact of several variables is often underestimated (particularly SOC) [51],while the fitting parameters in low-order algebraic equations (as Shepherd,Unnewehr universal and Nernst models [52]) cannot be connected directlyto specific processes occurring in the battery. Semi-empirical models arean in-between solution, with the computational efficiency of an empiricalapproach (thus easily implementable in the description of larger systems),and the added value of providing physically-meaningful information aboutthe processes in the battery.

1.5 LiNi1/3Mn1/3Co1/3O2 (NMC111)

In the previous Sections, it has been discussed how the total cell behaviourin LIBs is strongly determined by the performance of the single electrodes.Therefore, for a better understanding of the electrochemical behaviour ofLIBs across their lifetime, the characterization (both experimental, andmodel-based) should start at single electrode level. When selecting whichelectrode to consider, the positive one is of particular interest, since itis the source of cyclable Li+ in LIBs, thus limiting their capacity [12].Among the layered oxide positive materials, research is particularly activeon NMCs, isostructural modifications of LCO with improved performanceand stability, as well as reduced cost [53]. In these materials, the Li+

content (1 - xLi+) (with xLi+ representing the fraction of vacant sites[43]) determines the capacity provided during Li+ (de)insertion, and inPaper IV it is linked directly to State-of-Charge (SOC).

Among NMCs, LiNi1/3Mn1/3Co1/3O2 (NMC111) has established itselfover LCO in several applications, and it is now broadly commercialized[54]. NMC111 is a layered compound, with space group R-3m and overallhexagonal symmetry [55]. It displays no bulk phase change in its standardoperating voltage window, which is between +3.6 V and +4.1 V vs. Li(corresponding to 1 < (1- xLi+) < 0.4). On the other hand, while the bulkremains unchanged, a few nm-thick surface reduced layer with rock-saltphase is formed [56] [57] during the very first cycle, in the instant the ma-

10

terial is put in contact with the electrolyte [58], and/or a polarization isapplied [11]. An irreversible bulk phase transition to rock-salt is observedonly near complete de-lithiation, which is rarely reached, since it corre-sponds to ∼ +5 V, +5.2 V vs. Li [53]. The absence of phase transitionsnonetheless, NMC111’s crystal lattice adjusts during cycling to accommo-date Li+, with a simultaneous expansion along the c axis and contractionalong a denoted as lattice breathing [59], and leading to an almost nullvolume change [54]. This ”breathing” of NMC111 obeys Vegard’s empir-ical law for 1≤ (1 - xLi+) ≤ 0.5, indicating that the material behaves asan ideal solid solution [54]. The ”breathing” is caused by the change inoxidation state and ionic radius of the redox couples in the lattice frame,which electronically compensate the (de)insertion of Li+. It is generallyagreed that Ni2+/Ni4+ has a dominant role in the charge compensation,while Mn is electrochemically inert, and the role of Co is still debated [60][61]. Since the Ni2+/Ni4+ couple provides the major reversible capacityin NMCs [62], much effort has been put in progressively increasing the Nifraction, thus creating Ni-rich NMCs (Ni > 0.6 [53]). The Ni enrichmentallows the cycling of these materials at higher cut-off voltages (≥ +4.6V vs. Li) than NMC111, resulting in the extraction of a higher capac-ity [63]; however, it also causes serious capacity degradation upon cycling[59] [62]. A better understanding of the electrochemical performance ofNi-rich NMCs is thus needed, and since the majority of NMCs displaysimilar structural [53] and electrochemical behaviour [64], the knowledgeacquired on NMC111 can be transferred to other materials of the sameclass, thus helping to further their development.

As far as NMC111 electrochemical behaviour is concerned, a high num-ber of publications involving its (electro)chemical characterization can befound in the literature. The equilibrium potential response is of particu-lar interest, since it contains information about NMC111’s thermodynamicproperties. The CC curves of NMC111 are widely established, and knownto be rather featureless; detailed studies about the distribution of polar-ization in these curves have been performed [12], with a particular focus inKasnatscheew et al. [65] on the very first cycle of pristine NMC111. On theother hand, CV curves are rarely included into testing protocols for LIBmaterials, and when done, barely commented upon [66]. Only recently,the voltammetric response of NMC111 have been specifically addressed in

11

Vassiliev et al. [9] and Palagonia et al. [7], specifically focussing on thedevelopment of physics-based models for describing it. As far as GITT isconcerned, several papers focus on the quantification of Li+ solid-state dif-fusion coefficients through analytical or model-based approaches [67] [68][69] [70]. Several reports of EIS for NMC111 are also available, particularlyin the framework of ageing studies; however, it is generally uncommon tofind EIS spectra reported for more than a single SOC [8] [40]. In addition,the impact of temperature on the electrochemical response of NMC111is rarely considered. As a result, a somewhat incomplete electrochemicalcharacterization of NMC111 emerges from the literature, where specifictechniques are neglected, or the impact of relevant variables (temperatureabove all) is not considered. In addition, when it comes to the character-ization of NMC111, although these techniques can be found in separatepublications, they are rarely collected and discussed in the framework ofthe same study. Consequently, a comparison in terms of their advantagesand limitations, and the possible information that can be extracted fromthem, is missing. This would allow to better understand NMC111’s ther-modynamic and dynamic behaviour at BOL, as well as its evolution afterprolonged cycling.

12

Chapter 2

Scope of the thesis

The scope of the present thesis is the electrochemical analysis of LIBsat single-electrode level, with a focus on the comparison and discussionof four standard techniques (CC cycling, GITT, CV and EIS) to quan-tify and distinguish electrode dynamics. The component of choice is thepositive electrode, with a specific focus on NMC111, a state-of-the-artcommercial electrode. Firstly, a detailed characterization of NMC111 atBOL is performed, with the purpose of extracting both qualitative andquantitative information about its thermodynamic and kinetic properties(Paper I and II). The information learned on NMC111 at BOL are used todevelop a semi-empirical model for predicting CC voltage curves of LIBs,which is demonstrated to successfully apply to commercial LIBs with dif-ferent layered oxide materials (Paper IV). The characterization at BOLsets a baseline for comparison with NMC111 aged under high voltage op-eration, a cycling protocol designed for enhancing the energy density ofLIBs, but also associated with pronounced degradation (Paper III). Theuse of different characterization techniques at EOL gives the opportunityto discuss which information can be obtained, how can they be connectedto different ageing modes, and ultimately, which method is to be preferredfor addressing a specific phenomenon (Paper I).

Cycling LIBs at high voltage can increase the driving range of EVs,or decrease their costs. This would favour their large-scale diffusion, thusreducing the emissions from the personal transport sector: as such, itaddresses the UN goal 13, Climate Action. The design of a semi-empirical

13

model to be included in the design of larger systems supports a higherinclusion of renewable energy sources in the energy grid, thus contributingto the UN goal 7, Affordable and Clean Energy. A larger inclusion ofrenewable energy sources in the electricity production also implies thereduction of CO2 emissions in a particularly impactful sectors: as such,this also covers the UN goal 13, Climate Action.

14

Chapter 3

Experimental

3.1 Set-up

LIBs characterization can be performed at full-cell, or at single-electrodelevel. Full-cell characterization was performed either in commercial 18650cells (cylindrical), or in lab-scaled pouch cells. Testing cylindrical cellsprovide findings directly applicable to commercial batteries; however, theyare characterized by added complexity, due to the wound geometry gener-ating inhomogeneity in current and temperature across the jelly roll [71].For this reason, lab-scaled pouch cells in full-cell configuration(NMC111/graphite) are of interest, since they remove the geometric fac-tor, thus strongly simplifying the modelling of the system, and allowingto better target specific phenomena.

For the characterization at single-electrode level, lab-scaled pouch cellsare the set-up of choice, with different configurations: half-cells (electrodeof interest/Li), and 3-electrode cells. With the introduction of a pseudoreference electrode [72], 3-electrode cells remove the polarization contribu-tion of the counter electrode of choice. For this reason, they are normallymore accurate, but also more complex to handle, as the pseudo referenceelectrode is very sensitive towards design [73] and experimental conditions[72], particularly during prolonged cycling. On the other hand, half-cellsare easier to handle, but their electrochemical response might containartefacts introduced by the polarization of the counter electrode. An ad-ditional configuration was used for EIS measurements, for distinguishing

15

between the contribution of positive and negative electrodes: symmetriccells [74]. They were assembled using identical electrodes, in an arrange-ment with limited supply of Li+ to be transferred between them [75].

3.2 Materials

In the present work, NMC111 was the material of choice. The datasets inPaper IV and the commercial cells in Paper V contained different layeredoxide positive electrodes (NCA, NMCs, LCO), to investigate the transfer-ability of the findings on NMC111 to other materials of the same class.When working in lab-based pouch cells, NMC111 was either purchasedas dry electrode (from Electrodes and More) and used as received, orharvested from commercial prismatic cells (40 A h). The purchased elec-trode, denoted as (A), was characterized by a capacity of 1.49 mA h cm−2

(measured at C/20 between +2.7 V and +4.4 V vs. Li). The electrodeharvested from commercial cells, denoted as (B), was characterized by acapacity of 3.25 mA h cm−2 (measured at C/60 between +2.7 V and +4.6V vs. Li). In these cells, the electrolyte of choice was BASF LP40 (1M LiPF6 in ethylene carbonate: diethylene carbonate, 1:1 wt%), withoutany additive.

3.3 Electrochemical testing

The electrochemical techniques mentioned in the Introduction (CC cy-cling, GITT/OCP, EIS and CV) were used for characterizing NMC111 atdifferent stages of lifetime. In addition, CC and EIS were also used onfull-cells in the framework of the reference performance test of commercialLIBs in Paper IV and V. During BOL characterization, these techniqueswere performed at three different temperatures (10, 25 and 40 C), while25 C was the temperature of choice for all post mortem characterization.

3.3.1 CC cycling

CC cycling has a crucial role in LIBs ageing studies, as it is involved in allthe steps of testing. Specifically, it is used for a) developing most cycling

16

protocols, b) in the framework of the reference performance test acrosscycling, and c) for BOL and post mortem analysis.

a) In order to address the ageing of LIBs for a specific application, itis crucial to design a testing protocol representative of the desiredusage. The cycling protocols can be simplified, or more complex,with the purpose of mimicking electric drives, or stationary storageloads. A simplified protocol is proposed for targeting high voltageoperation, which increases the energy density of LIBs, and is thusrelevant for EVs (increased driving range). The commercial LIBs inPaper IV are tested under several standardized protocols for EVs1.On the other hand, the testing of stationary LIBs is less defined[76]: for this reason, a testing protocol is proposed in Paper V, formimicking the operation of off-grid, PhotoVoltaic (PV)-connectedLIBs.

b) When performed at slow C-rate (C/20 in Paper V, C/60 in PaperIV) in the framework of the reference performance test, CC cyclingallows to quantify the actual capacity loss at full-cell level, and tobuild the capacity fade vs. time/cycle number plot. These plots arevital for estimating SOH at cell level, and to indicate when a cellhas reached its EOL criterion.

c) CC at BOL is the first measurement performed to characterize anew material. In case of pristine NMC111, this procedure allows tostudy its formation. In Paper I, an additional Constant Potential(CP) ”recovery” step of variable duration was added at the end ofthe very first discharge, as suggested in [65], to address the charac-teristic Capacity Loss (CL). In Paper III, during post mortem, slowrates were used for quantifying the actual residual capacity in eachelectrode.

1Some examples are the Dynamic Stress Test (DST) and the Federal Urban DrivingSchedule (FUDS) from the United Sates Advanced Battery Consortium (USABC), andECE-15 from the United Nations Economic Commission for Europe.

17

3.3.2 GITT and equilibrium potential curves

GITT measurements were performed by alternating C/20 and C/10 pulses,with variable rest time (3 and 2 h respectively) in-between. At BOL, thepulses were performed only in the charging direction, while at EOL in bothcharge and discharge (starting from the latter). Only the pulses at C/20and relative relaxation were used to build the equilibrium curves, whichwere then aligned with CC curves (assuming symmetric overpotential be-tween charge and discharge [12]), and differentiated (ICA) for comparisonwith CV.

3.3.3 EIS

EIS was performed galvanostatically with a reduced frequency interval at50% SOC on the cylindrical cells, in the framework of the reference per-formance test. Galvanostatic EIS is recommended for LIBs with smallinternal resistance, to minimize the risk of damage during the measure-ment2. Potentiostatic EIS with a broader frequency interval was used onpouch cells of any configuration instead. At BOL, the impact of temper-ature and of different SOC was considered, the latter also by means ofORP-EIS, to confirm the reliability of the measurements.

3.3.4 CV

CV was generally performed at slow scan rates (0.01 mV s−1): since themeasurements were performed in half-cells (i.e. without a reference elec-trode), the slow rate helped minimizing the possible artifacts stemmingfrom the counter/reference electrode. Due to the slow rate chosen, noohmic drop correction was performed, as negligible on the total voltage(based on the ohmic resistance measured through EIS). The scan rate wasincreased only for the purpose of Randall-Sevcik analysis at BOL. Also atBOL, different temperatures were investigated, as well as the formation ofpristine NMC111 by means of a CP ”recovery” procedure mimicking theone for CC cycling.

2https://www.gamry.com/application-notes/EIS/eis-measurement-of-a-very-

low-impedance-lithium-ion-battery/ https://www.gamry.com/application-notes/

EIS/eis-potentiostatic-galvanostatic-mode

18

3.4 Semi-empirical model

The model proposed in Paper IV was formulated as follows:

E = E0 + IRohm + ηkin + ηdiff (3.1)

with E0 being the steady-state voltage (in V), IRohm the ohmic drop(in A Ω = V), ηkin the overpotential towards charge transfer (in V), andηdiff the overpotential towards mass limitation (also in V). The separatedmathematical equations for each term of Equation 3.1 were the following:

• Steady-state voltage, E0:

E0 = V0 +RT

Flog

(Qnom −Q(t)

Qnom

)+ J

(0.5− Q(t)

Qnom

)(3.2)

being V0 the OCP value provided by the manufacturer (in V), Qnom

the nominal capacity of the cell (in Ah), and Q(t) =∫It the actual

battery capacity (also in Ah). Equation 3.2 describes the OCP - SOCrelation in terms of Frumkin isotherm, i.e. a gas lattice isothermmodified to take into account the lateral Li+ - Li+ interactions inthe crystal lattice [77] [78]. J is the interaction parameter (dimen-sionless), and it is strongly impacted by the presence (or absence) ofphase change(s) in the materials considered [77].

• Kinetic overpotential, ηkin:

ηkin =RT

0.5F

I

Kkin

(Q(t)Qnom

(Qnom−Q(t)

Qnom

))0.5

(3.3)

Equation 3.3 describes the charge transfer overpotential through alinearised Butler-Volmer equation. Kkin (in Ω) is a lumped parame-ter, called kinetic resistance, which represents the hindrance towardscharge transfer.

• Diffusive overpotential, ηdiff:

ηdiff =RT

FIKdiff

[Qnom(Q(t)/Qnom)0.5

Qnom −Q(t)

](3.4)

19

Equation 3.4 describes the overpotential towards mass transfer as an(approximated) semi-infinite linear diffusion in a current-controlledexperiment, with quasi-reversible one-electron process [35]. The ap-proximation taken consists in using an average Li+ concentrationinstead of separate bulk and surface Li+ concentrations, which arehard to quantify experimentally. Kdiff (in Ω) is a lumped parameter,called diffusive resistance, which represents the hindrance towardsmass transport.

Kkin and Kdiff together represents the internal resistance of the battery,divided into its kinetic and diffusive contributions. This is due to the factthat the internal resistance is actually an impedance (Z(Im) 6= 0) in themid-low frequency range (∼ 1 Hz) [40], thus positioned in a region of mixedkinetic control where both charge transfer (occurring in the mid frequencyrange) and mass limitations (occurring in the low frequency interval) areinfluential [79].

The evolution of the fitting parameters J , Kkin and Kdiff is assumedto capture LIBs performance over cycling, without the need of additionalterms describing specific degradation phenomena.

20

Chapter 4

Results and Discussion

4.1 Electrochemical characterization of NMC111

4.1.1 Characterization at BOL

Galvanostatic cycling

0 50 100 150

3

3.5

4

CL1st

ds

Capacity / mAhg−1NMC111

E/V

(vs.

Li/Li+)

10 C 1st cycle

10 C 2nd cycle

25 C 1st cycle

25 C 2nd cycle

40 C 1st cycle

40 C 2nd cycle

Figure 4.1: First and second CC cycles (∼ C/7) of pristine NMC111 (A,10 mm )/Li cells, cycled between +2.7 V and +4.1 V vs. Li at 10, 25and 40 C. The CL at the end of the first discharge is marked.

The voltage characteristics of NMC111, recorded at slow C-rate (∼

21

C/7), are reported in Figure 4.1 for different temperatures. In all cycles,the curves are characterized by a sloped behaviour, with a change in slopeat around +3.85 V vs. Li. Only between the first and second cycle,a temperature-dependent CL occurs at the end of the first discharge; asignificant portion of it can be retrieved in the next cycle by means of aCP ”recovery” procedure, as depicted in Figure 4.2. However, as shown

0 20 40 60 80 100 120 140 160 180 200

2.8

3.2

3.6

4.0

4.4CR from1st ds CP

Capacity / mAhg−1NMC111

E/V

(vs.

Li/Li+)

1st

2nd (no rec.)

2nd (6 h rec.)

2nd (24 h rec.)

2nd (48 h rec.)

2nd (96 h rec.)

Figure 4.2: First and second CC cycles (∼ C/7) of pristine NMC111 (A,10 mm )/Li between +2.7 V and +4.3 V vs. Li at 25 C, without andwith the CP ”recovery” step (at +2.7 V vs. Li, and variable duration:, 6,24, 48 and 96 h) at the end of the first discharge. The Capacity Recovery(CR) during the CP ”recovery” step is visible at the end of the secondcharge.

in Table 4.1, this recovered CL is newly lost unless a CP ”recovery” stepis performed at the end of every discharge, a procedure not feasible inpractical applications.

The causes behind the sloped voltage profile in all CC curves in Figure4.1, as well as the CL displayed during formation, could be better under-stood by de-coupling the electrochemical response into its thermodynamicand dynamic contributions.

22

Table 4.1: Capacity (in mA h g−1NMC111) delivered by NMC111 (A, 10 mm

)/Li cells at the end of the first three CC cycles (charge and discharge),without and with CP ”recovery” step (6 and 96 h).

1st ch 1st ds 2nd ch 2nd ds 3rd ch 3rd ds

no CP 180 162 162 162 - -6 h CP 179.1 159.4 172.3 159.2 160.7 159.196 h CP 180.9 161.3 179.3 161.1 162.4 160.7

Equilibrium voltage and GITT curves

The thermodynamic and dynamic contributions in Figure 4.1 can be visu-ally separated by comparison with the steady-state response of NMC111,i.e. its experimental equilibrium curves (Paper I). These curves, shown inFigure 4.3, are characterized by the absence of thermodynamic hystere-sis, and virtually no temperature dependency. The lack of temperaturedependency is explained knowing that the steady-state voltage E0 can beexpressed as:

E0 = −∆rG

F= −∆rH

F+T∆rS

F(4.1)

where ∆rG, ∆rH and ∆rS are the Gibbs free energy, entropy and enthalpyof the considered reaction (Li+ intercalation in the present case). Thetemperature dependency of ∆rG in Equation 4.1 is dominated by theT∆rS term, which means that in Figure 4.3 ∆rS assumes small values forNMC111 in the temperature interval considered; this is in agreement withwhat reported in Viswanathan et al. [83].

Similarly to Figure 4.1, a change in slope around +3.85 V vs. Li isobserved in Figure 4.3, matching several structural and electronic tran-sitions at the crystal level reported in the literature for pure NMC111:specifically,

• the change in charge-compensating couple from Ni2+/Ni3+ to

Ni3+/Ni4+ [60];

• the sudden increase in the electronic conductivity of pure NMC111(which is a semiconducting material) [80] caused by the narrowingof the HOMO-LUMO gap [60];

23

0.30.40.50.60.70.80.911.1

3.6

3.8

4

4.2

beginningofLi+

extraction

Ideal solid solution (Vegard) behaviour

H1 phaseNi2+ → Ni3+

Oxygen DumbbellHopping (ODH)

H2 phaseNi3+ → Ni4+

TetrahedralSite Hopping(THS)

H1→

H2;

conductivityincrease

endof

Vegard

beh

aviour

Calculated (1 - xLi+)

E/V

(vs.

Li/Li+)

10 C discharge10 C charge

25 C discharge25 C charge

40 C discharge40 C charge

Figure 4.3: Equilibrium voltage curves of NMC111 (A, 10 mm )/Li cellsbetween +3.6 V and +4.3 V vs. Li at 10, 25 and 40 C. (1 - xLi+) iscalculated from the measured capacity, with (1 - xLi+) = 0 correspondingto the maximum theoretical capacity of NMC111 (278 mA h g−1

NMC111).The structural and electronic properties of NMC111 are obtained from[54] [60] [80] [81] [82].

• the need of two different hexagonal cells (H1 and H2) to describethe crystal lattice [81];

• a change in Li+ diffusive pathway inside the crystal slab, specificallyfrom Oxygen Dumbbell Hopping (ODH) to Tetrahedral Site Hopping(TSH) [82].

By aligning the equilibrium voltage and CC curves in Figure 4.4, it isnow clarified that the double-slope behaviour stems from thermodynamicproperties, while the (load-induced) hysteresis and the temperature de-pendency are related to kinetic. Kinetic behaviour is indeed described byArrhenius relation, which relates the activation energy (EA) to the rate ofthe process (r) [84]:

r = A exp

(−EART

)(4.2)

24

This relation implies that the higher the temperature, the higher the rateof the kinetic processes, thus the lower the polarization. This explains whythe highest capacity in Figure 4.1 is delivered at the highest temperature;additionally, it indicates that the CL in Figure 4.1 is kinetic in nature, inagreement with Kasnatscheew et al. [65]: specifically, a hindered, but stillpossible re-lithiation at high Depth of Discharge (DOD).

0 20 40 60 80 100 120 140 160 180

3

3.5

4

Capacity / mAhg−1NMC111

E/V

(vs.

Li/Li+)

10 C CC10 C OCP25 C CC25 C OCP40 C CC40 C OCP

Figure 4.4: CC curves from Figure 4.1 (2nd cycle), aligned with the equi-librium voltage curves in Figure 4.3.

From Figure 4.4 alone, it is not possible to further separate the kineticcontribution into charge transfer and diffusion, unless a model is used.More suited experimental techniques are available for such purpose, oneof them being the GITT measurements used for building the equilibriumcurves in Figure 4.3. Since GITT measurement are characterized by alter-nated polarized and non-polarized phases, the relaxation contains purelythe diffusive behaviour of the material of choice. In Figure 4.5, the high-est polarization can be observed at 10 C during the polarized steps, aswell as the slowest relaxation during the rest phases, in agreement withEquation 4.2. The curves in Figure 4.5 also reveal a decrease in relax-ation rate above +3.85 V vs. Li at all temperatures, at the point thatthe equilibrium voltage is not reached even after 3 h of rest (Papers I andII). When the curves in Figure 4.5 are described by means of the standard

25

3.7

3.8

3.9

4

4.1

E/ V

vs.L

i10 oC25 oC40 oC

6

1210-5

I/ A

0 10 20 30 40t/ h

1.5

0.5

10-2

E -

E0/

Vvs

.Li

0 2t/ h

0.5

1.510-2

E -

E0/

Vvs

.Li

0 2t/ h

0 2t/ h

0.2

0.6

110-2

E -

E0/

Vvs

.Li

Figure 4.5: GITT curves of NMC111 (A, 10 mm )/Li cells performedbetween +3.6 V and +4.05 V vs. Li at 10, 25 and 40 C. A comparisonbetween low voltage (+3.73 V vs. Li, continuous line) and high voltage(+3.92 V vs. Li, dashed line) pulses is performed for the three temper-atures. For such purpose, a normalization on voltage is performed, withE0 being the OCP at the end of the precedent relaxation.

P2D model, the slow relaxation at high voltage cannot be captured, unlessby extending the model with the addition of diffusion-coupled mechani-cal stress on the particle surface. The fitting of Figure 4.5 by means ofthe extended P2D model allows to extract parameters as the kinetic rateconstant k1, and Li+ effective solid-state diffusion coefficient Ds,eff. Boththese parameters strongly depend on (1 - xLi+), displaying in Figure 4.6 avariation of several orders of magnitude in the voltage window considered.Secondly, these two parameters have opposite trends, with k increasingat higher voltages (faster charge transfer), and Ds,eff decreasing (slower

1The kinetic rate constant is directly connected to the exchange current density i0,according to:

i0 = Fkαaa kαc

c cαaa cαc

c (4.3)

where α is the barrier factor, kc represents the kinetic rate constant for the cathodicreaction, ka for the anodic reaction, ca and cc the concentrations of oxidized and reducedspecies [85].

26

0.550.60.650.70.750.80.850.90.95

10−12

10−11

10−10

∼+3.85V

vs.

Li

(1 -xLi+)

k/m

s−1

10 C25 C40 C

(a)

0.550.60.650.70.750.80.850.90.95

0

2

4

6

8

·10−18

∼+3.85

Vvs.

Li

(1 - xLi+)D

s,e

ff/cm

2s−

1

10 C25 C40 C

(b)

Figure 4.6: a) Kinetic rate constant (k) and b) Li+ solid-state effectivediffusion coefficient (Ds,eff) obtained from the fitting of the GITT curvesin Figure 4.5, by means of the modified P2D model proposed in Paper II.

solid-state diffusion).

27

EIS

10−3 10−2 10−1 100 101 102 103 104

10−4

10−3

10−2

10−1

100

101

Frequency / Hz

Mod(Z

)/Ω

+3.75 V+3.75 V noise

+3.75 V noise + nn stat.+3.75 V noise + nn lin.

+3.95 V+3.95 V noise

+3.95 V noise + nn stat.+3.95 V noise + nn lin.

+4.1 V+4.1 V noise

+4.1 V noise + nn stat.+4.1 V noise + nn lin.

Figure 4.7: Bode modulus of NMC111 (A, 18 mm )/Li 3-electrode cellsat 25 C and variable voltage (+3.745 V, +3.945 V and +4.096 V vs.Li), with the calculated noise, noise + non-stationarity, and noise + non-linearity curves from ORP-EIS measurements.

EIS also allows to separate the kinetic contribution into charge trans-fer and diffusion. The reliability of EIS measurements at different SOCis firstly assessed by means of ORP-EIS in Figure 4.7, where the Bodemodulus diagram is compared with the noise, non-stationarity and non-linearity levels. A similar noise is registered at all voltages, indicatinga similar experimental error at all SOC considered. The noise increasesat the lowest frequencies, but an acceptable signal-to-noise ratio is stillmaintained, since the noise is two orders of magnitude lower than thecorresponding Bode modulus. The non-stationarity (quantified as the dif-ference between the noise and the noise + non-stationarity curves in Figure4.7) displays an overall increase between 1 kHz and 1 Hz, which in Zhuet al. [86] has been associated with the occurrence of the charge trans-fer, due to either the highly active electrode surface, or the solid-statebehaviour of the electrode material. In any case, the non-stationaritylevel also remains considerably lower than the Bode modulus. Finally,the non-linearity curve is parallel to the non-stationarity one, possibly an

28

0 20 40 60 80 100

−20

0

20

40

60

Re(Z) / Ω cm2NMC111

-Im

(Z)

/Ω

cm2 NM

C111

+3.75 V +3.8 V+3.85 V +3.9 V+3.95 V +4.0 V+4.1 V +4.2 V

(a)

10−3 10−2 10−1 100 101 102 103 104 105

0

5

10

15

20

25

30

35

Frequency / Hz

-Im

(Z)

/Ω

cm2 NM

C111

+3.75 V+3.8 V+3.85 V+3.9 V+3.95 V+4.0 V+4.1 V+4.2 V

(b)

Figure 4.8: a) Nyquist plot of NMC111 (B, 18 mm )/Li 3-electrode cellsat 25 C, and variable OCP (+3.75 V, +3.8 V, +3.85 V, +3.9 V, +4.0 V,+4.1 V, and +4.2 V vs. Li); b) Corresponding -Im(Z) vs. frequency plot.

artefact from the non-stationarity (associated with the applied algorithmfor quantification of the distortions) [42]. The results obtained from theORP-EIS measurements in Figure 4.7 indicate that the EIS measurementsof NMC111 at BOL and different SOC fulfil the criteria of causality, lin-earity and stationarity, and can hence be considered for further analysis.

The corresponding Nyquist and -Im(Z) vs. frequency plots are re-ported in Figure 4.8. The impedance response of NMC111 is generallycharacterized by one (or more) large semicircle in the mid-frequency re-gion (1 kHz - 1Hz), followed by a straight tail at low frequencies (< 1 Hz).The mid-frequency semicircle is generally associated with charge-transferphenomena, with the frequency at which its local maximum occurs (fmax,or the corresponding time constant τ = (2πfmax)−1) defining the rate ofthe process [40]. The low frequency tail, on the other hand, is associatedwith (Warburg-type) diffusion, both in liquid and in solid state [41]. InFigure 4.8a, the charge-transfer semicircle is strongly affected in termsof height, diameter, and positioning. Specifically, the spectrum at thelowest SOC (+ 3.75 V vs. Li) is characterized by the lowest time con-stant. This indicates that NMC111 displays the slowest charge transfer atlow voltages, in agreement with the values of k extracted at 25 C (Fig-

29

2 4 6 8 10 12 14 16 18 20

−5

0

5

10 +3.95 V

Re(Z) / Ω cm2NMC111

-Im

(Z)

/Ω

cm2 NM

C111

10 C25 C40 C

(a)

10−3 10−2 10−1 100 101 102 103 104 105 106

0

10

20

30

+3.95 V

Frequency / Hz

-phase

10 C25 C40 C

(b)

Figure 4.9: a) Nyquist plot of NMC111 symmetric cells (A, 10 mm ) at+3.95 V vs. Li, measured at 10, 25, 40 C; b) corresponding Bode phasediagram.

ure 4.6). Since the EIS spectra depict the kinetic behaviour of NMC111,they are expected to display a temperature dependency in agreement withEquation 4.2. And indeed, the charge-transfer semicircle in Figure 4.9a isparticularly impacted by the variation in temperature, with a slower timeconstant, and a higher height of the semi-circle at 10 C.

On the other hand, the low-frequency tail in Figure 4.8, which con-tains the diffusive contribution [40], does not display a significant SOC-dependent variation: thus, the slow relaxation in Figure 4.5 cannot beobserved as straightforwardly in the EIS response. However, the modifi-cation proposed in Paper II to P2D model, i.e. the extra term to accountfor the particles’ surface stress, has to be considered when fitting the EISspectra as well (Paper I), and the results of the fitting are presented inTable 4.2. Overall, a good agreement is achieved between the fitted resultsfrom the two techniques: the parameters are within an order of magnitudedifference, and display the same trend as a function of temperature. Thethermodynamic and stress parameters (dEconc/dγpos and γstress) are smallerfor EIS, likely due to the smaller perturbation applied. This is rarely foundin literature, where the cross-parametrization between AC/DC techniquesoften display inconsistencies [30] [87]. This indicates that the slow relax-

30

Table 4.2: Parameters extracted from the fitting of EIS spectra in Figure4.9, compared to those extracted from GITT pulses at the same voltage(from Paper I).

10 C 25 C 40 CGITT EIS GITT EIS GITT EIS

Ds,eff/ m2 s−1 1.7e-18 9.6e-18 7.8e-19 1.6e-18 7.0e-19 3.5e-18k/ m s−1 0.074 0.32 2.22 3.95 5.93 9.36cdl/ F m−2 - 0.76 - 3.5 - 2.4

dEconc/dxpos/ V 1.32 0.37 1.35 0.49 1.18 0.47γstress/ V 1.09 0.27 1.28 0.47 1.15 0.43

β 1.5 1.0 1.5 1.7 1.5 1.5Rcc/ Ω m2 - 1.0e-5 - 1.2e-5 - 1.7e-5cdl,cc/ F m−2 - 0.40 - 0.45 - 0.23

ation, although not directly visible in the EIS spectra, is also present inthem, and needs to be accounted for when describing the EIS response ofNMC111 at BOL.

CV

Knowing more about charge transfer and diffusion in NMC111 providesadditional insights for understanding another technique with convolutedthermodynamic and dynamic contributions: CV. The voltammograms inFigure 4.10 are characterized by a single peak in each potential sweep, lo-cated between +3.75 V and +3.85 V vs. Li (depending on the temperatureand cycle number), followed by a linear i vs. E region at higher voltages.This implies that, from the peak onset on, capacity is delivered uninter-ruptedly across the entire voltage window, a behaviour reported for LCOas well [9] [88], but not for phase-changing materials as LFP and graphite,where all the available capacity is located in the peak features [34] [66].The region most affected by changes in the operational conditions (eithertemperature, or cycle number) is the peak area, which is characterizedby a higher ”C-rate” than the rest of the voltammogram, and thus by ahigher polarization [12]. This results in an ”amplification” of the signal,which is however localized: virtually no temperature dependency can be

31

3.2 3.4 3.6 3.8 4 4.2 4.4

−20

0

20

40

E / V (vs. Li/Li+)

i/mAg−1

NM

C111

10 C 1st cycle

10 C 2nd cycle

25 C 1st cycle

25 C 2nd cycle

40 C 1st cycle

40 C 2nd cycle

Figure 4.10: First and second CV cycles (scan rate = 0.01 mV s−1) ofpristine NMC111 (A, 10 mm )/Li cells at 10, 25 and 40 C, measuredbetween +3.2 V and +4.3 V vs. Li.

observed above +3.95 V vs. Li, although it is known to be present fromthe CC, GITT and EIS measurements displayed so far. This is possiblydue to the small currents in this region of the voltammogram (∼ C/60):this indicates a varying sensitivity of CV measurements in the voltagerange considered.

Following the reasoning in Figure 4.4, a comparison between CV andequilibrium voltage responses is attempted for visually separating the ther-modynamic and kinetic contributions. For this purpose, the equilibriumcurves in Figure 4.3 are differentiated to obtain the corresponding ICAplot, since at steady-state CV and ICA responses coincide [7]. In Figure4.11, a peak can be observed already at steady-state, as a mathemati-cal consequence of the slope change around +3.85 V vs. Li in Figure4.3. In addition, a peak in solid-state CV indicates a solid solution withperfectly miscible components [33], which well describes NMC111 in thevoltage interval considered [54]. The peaks at steady-state are symmetric,in the sense that the peak position, height and width are the same betweencathodic and anodic scan. The symmetry between anodic and cathodicpeaks is normally described in classic CV in terms of adsorption processes

32

3.2 3.4 3.6 3.8 4 4.2 4.4

−20

−10

0

10

20

30

x=

1

x∼

0.65

x∼

0.45

E / V (vs. Li/Li+)

i/mAg−1

NM

C111

OCP 10 COCP 25 COCP 40 C

Figure 4.11: ICA plot of the equilibrium curves in Figure 4.3, overlayedwith the 2nd cycle of the experimental CV curves from Figure 4.10.

[32]; adsorption isotherms have also been demonstrated to suitably de-scribe Li+ intercalation [88], and are used in Paper IV for modelling thethermodynamic response of LIBs.

In Figure 4.4, any difference between the equilibrium voltage andCV responses was attributable to polarizations. However, in Figure 4.11this is possibly true only for the peak region, where the polarization ishigh enough to detect changes in the set-up. Under dynamic load, atemperature-dependent narrowing of the anodic peak width, as well as ashift in the positioning and onset of both anodic and cathodic peaks, canbe observed. While the absolute value of this peak shift is approximatelythe same between anodic and cathodic scan, its direction is opposite, as itfollows the direction of the voltage sweep. These changes in the voltammo-gram, attributed to kinetics, are associated with the highest polarization,in agreement with Equation 4.2. In addition, the mirrored peak shiftbetween anodic and cathodic sweep is compatible with the symmetric po-larization in NMC111 between charge and discharge, in agreement withKasnatscheew et al. [12]. According to this finding, the anodic peakin the first cycle (Figure 4.10) indicates a more polarized condition atall temperatures, compared to the following cycles. If a CP ”recovery”

33

2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4

−20

−10

0

10

20

30

40

E/ V vs. Li/Li+

i/mAg−1

NM

C111

1st cycle

2nd cycle (no rec.)

2nd cycle 24 h rec.

(a)

Capacity/mA h g−1

NMC111

1st 177.3

2nd (no CP) 167

2nd (after CP) 170.2

(b)

Figure 4.12: a) First and second CV cycles (scan rate = 0.01 mV s−1) ofpristine NMC111 (A, 10 mm )/Li cells measured at 25 C between +2.7V and +4.3 V vs. Li, without and with the CP ”recovery” step at theend of the first cathodic sweep (+2.7 V vs. Li, 24 h). b) Capacity (inmA h g−1

NMC111) delivered in Figure 4.12a at the end of the first and secondanodic sweeps, without and with a preceding CP ”recovery” step.

step is performed at the end of the first cathodic sweep, although a par-tial recovery of the lost capacity is achieved (Table 4.12b), the shape ofthe voltammogram is equal to the one without the recovery step (Figure4.12a), thus indicating that the highly polarized state in the first cycle

34

3.4 3.6 3.8 4 4.2

−400

−200

0

200

400

600

800

E/ V (vs. Li/Li+)

i/m

Ag−1

NM

C111

0.01 mV s−1

0.05 mV s−1

0.1 mV s−1

0.5 mV s−1

(a)

0 0.4 0.8 1.2 1.6 2 2.4

·10−2

−0.5

0

0.5

1

0.01 mV s−1

0.05 mV s−1

0.1 mV s−1

0.5 mV s−1

ν1/2 / (V/s)1/2

i/A

g−1

NMC111

(b)

Figure 4.13: a) CV of NMC111 (A, 10 mm )/Li cells measured at 25 Cbetween +3.4 V and +4.2 V vs. Li, and variable scan rates (0.01, 0.05,0.1, 0.5 mV s−1). b) Plot of the peak current Ip (of anodic and cathodicpeak) vs. the square root of the scan rate ν1/2 from a).

cannot be restored. This initial resistance, also observable at low degreesof de-lithiation in the first charge of Figure 4.1, is possibly due to theremoval of (carbonate) layers on the surface of the pristine electrode ma-terial, or to the formation of the surface reduced layer characteristic ofNMCs [56] [58].

Classical CV is commonly diffusion-limited, which means that all thedynamic contributions can be ascribed to this process, and Randles-Sevcikequation is applicable for quantifying diffusion coefficients [35]. The linearIp vs. ν1/2 relation found in Figure 4.13b would alone indicate that Li+

intercalation in NMC111 is limited by solid-state diffusion in the scan rateinterval considered [88]. However, an increase in the scan rate is also asso-ciated with a pronounced peak shift in the direction of the scan in Figure4.13a, which is a sign of decreased reversibility of the charge transfer [32][35]. This indicates that Li+ intercalation in Figure 4.10 happens undermixed kinetic control, i.e. both charge transfer and diffusion contributesto the electrochemical response: this is a realistic scenario for commercialelectrodes, and supports the assumption of quasi-reversibility in PaperIV. In addition, the extracted parameters in Figure 4.6 have revealed that

35

the relative contributions of charge transfer and solid-state diffusion inNMC111 are not constant in the voltage and temperature interval con-sidered (Figure 4.6). In an extreme case, this might lead to a varying”weight” of the charge transfer and diffusive contributions towards thetotal polarization below and above +3.85 V vs. Li. This is an importantdetail to consider for an accurate and physically-meaningful modelling ofCV curves.

In conclusion, the characterization of NMC111 at BOL reveals a neg-ligible temperature dependency at steady-state. On the other hand, whenthe system is perturbed from equilibrium, the dynamic response is temperature-dependent, and overall symmetric between charge and discharge (with theonly exception at high DOD, due to re-lithiation hindrance). This can beobserved directly in GITT and EIS measurements; in CC cycling, theseaspects better emerge by comparison with the equilibrium curves. OnlyCV is unable to capture the dynamic response at voltages above +3.9 V vs.Li, where rather low currents are registered. Furthermore, the dynamicresponse also depends on the degree of lithiation: this aspect is betterinferred (both qualitatively and quantitatively) from EIS and GITT. Thelatter in particular is the only technique to visually capture a slow re-laxation occurring above +3.85 V vs. Li, hypothesized to be caused byincreasing mechanical stress on the particles’ surface.

4.1.2 Characterization at EOL

After clarifying NMC111’s electrochemical behaviour at BOL, its elec-trochemical response is compared to the one of NMC111 cycled at highvoltage (Paper III). The specific cycling protocol chosen targets the high-end of a full-cell’s voltage window, between +3.8 V and +4.6 V vs. Li. Inaddition, it considers different cell configurations, i.e. different stages ofstoichiometric drift as it might occur in different locations of a jelly rollin a commercial LIB. In Figure 4.14, where Li plating on graphite mightoccur, a significant degradation is observed particularly for the cells at40 C, characterized by a capacity fade to 50% of the original value dur-ing the first 60 cycles, while the cells cycled at 25 C show a stablerperformance. All electrochemical characterization techniques are used toidentify the modifications induced in NMC111’s response by the specificcycling protocol chosen, for understanding the role of NMC111 in the total

36

0.6

1.3

Cap

acit

y/ m

Ah

cm-2

2

Cap

acit

y/ m

Ah

cm-2

Figure 4.14: Charge/discharge end capacity for NMC111(B, 22 mm)/graphite cells cycled at high voltage (between +3.8 V and +4.5 Vvs. graphite) and two different temperatures (25 and 40 C).

cell degradation.

CC cycling

In Figure 4.15a, a comparison is performed between NMC111 at BOL,and the one harvested from the most degraded full cell in Figure 4.14:specifically, the one cycled at 40 C. A capacity loss of 50% of its originalvalue is observed for the aged NMC111 electrode, in the form of a shortervoltage curve at EOL. This considerable capacity loss on NMC111 whencycled at high voltage has not been previously reported in the literature;instead, NMC111 is generally considered to have a negligible role in theoverall capacity fade, and to impact instead the impedance rise [89]. Addi-tionally, when repeating the CC cycling after 1 month rest in Figure 4.15b,the capacity loss is partially regained (∼ 25%), indicating the (partially)reversible nature of the main ageing phenomenon hindering NMC111’sperformance at high voltage: specifically, the formation (and dissolution)of insulating layers on NMC111’s surface, caused by the decomposition ofthe electrolyte.

Another ageing-induced change can be observed in the CC curves inFigure 4.15: a small polarization between +3.8 V and +2.8 V vs. Li, re-ported for other positive electrodes under different cycling protocols [90][91], and associated with inhomogeneous current distribution [92]/ uneven

37

E/ V

vs.

Li

Capacity/ mAh cm-2

0 1.0 2.1 3.22.5

3.5

4.5

EOL40 C

50%cap. loss

BOL40 C

(a)

25%capacity loss

(b)

Figure 4.15: a) Residual capacity (measured at C/60 in NMC111 (B, 22mm )/Li cells, at 25 C) for NMC111 after high-voltage cycling at 40C(showed in Figure 4.14). b) Newly-measured residual capacity (measuredin NMC111 (B, 10 mm )/Li cells at C/10, 25 C) after the conclusion ofthe post mortem analysis, followed by 1 month rest.

Li+ concentration in the electrode [90]. This is compatible with the pres-ence of a non-uniform, insulating layer on the surface of the electrode,which would generate inactive domains in NMC111.

CV

In Figure 4.16, the CV response of aged NMC111 is also modified by theoperation at high voltage. The total area of the voltammogram is reducedby 25% of the original value, in agreement with Figure 4.15b (after whichthe CV measurement was performed). Differently than in CC curves, thecapacity loss appears to be voltage-dependent, with the largest loss locatedin the peak region: however, this is a consequence of the ”amplification”effect already observed and discussed at BOL, which makes the peak regionmore sensitive towards external changes. Compared to the CV responseat BOL, the voltammogram at EOL is characterized by a further shiftof the peak position in the direction of the scan, indicating an increasedpolarization: this is compatible with the increased impedance observed inFigure 4.17. In addition, an asymmetry occurs between the anodic andcathodic scans: specifically, the cathodic peak is characterized by a lowerintensity and broader width compared to the anodic one. Since at BOL

38

3.4 3.6 3.8 4 4.2 4.4 4.6−0.3

−0.2

−0.1

0

0.1

0.2

0.3

E / V (vs. Li/Li+)

i/mAcm

−2

BOLaged

Figure 4.16: CV response (scan rate: 0.01 mV s−1) of NMC111 at EOL(measured in NMC111 (B, 10 mm )/Li cells at 25 C) after the cyclingat 40 C in Figure 4.14, the post mortem analysis, and 1 month rest.

the anodic and cathodic scans were overall symmetrically altered by thepolarization (Figure 4.11), this asymmetry has been induced by the cyclingconditions, and the consequent degradation. A variation in the cathodicpeak well correlates with the modification induced by the same cyclingconditions in the CC curves in Figure 4.15: specifically, the polarizationtowards the end of discharge, due to inhomogeneous current distribution.Overall, the information extracted from the CC curves in Figure 4.15 canbe equivalently obtained from CV.

39

EIS

EOL40 C

50 100 150 200 250-50

-25

0

25

50

EOL25 C

BOL25 C

+ 4.15 V vs. Li

NMC111

NMC111

1 kHz1 Hz

10 mHz

-Z(I

m)/

Ohm

cm

2

Z(Re)/ Ohm cm2

0

4

8

0 4 8 12 16

-Z(I

m)/

Ohm

cm

2

Z(Re)/ Ohm cm2

BOL25 C

EOL25 C

1 kHz

1 Hz

NMC111

Graphite

NMC111

Li

Disassemblyinto half-cells Slow

CC cycle(C/60)

NMC111

NMC 1 11

Into symmetric cells

Potentiostatic EIS

Figure 4.17: Potentiostatic EIS response of NMC111 symmetric cells (B,10 mm ), measured at +4.15 V vs. Li and 25 C, after the cycling inFigure 4.14 at 40 C.

EIS of the aged NMC111 electrode, measured in symmetric cells, allowsto investigate the root causes behind the lost capacity in Figures 4.15 and4.16. The Nyquist plot in Figure 4.17 displays an increasing impedancein both semi-circles, caused by the degradation phenomena occurring inNMC111 at different interfaces. This is demonstrated in Paper III bycombining a DC/AC physics-based model with different analytical tech-niques. Specifically, NMC111’s electronic pathway has degraded at thecurrent collector/electrode and electrode/carbon interfaces, while the in-terfacial features have suffered extensive degradation: the high impedanceon the second semicircle is dominated in particular by the layer formed onthe electrode’s particles, and the film between the electrode and the sep-arator, observed by means of Raman and Scanning Electron Microscopy(SEM). These layers would be responsible for the formation of inactivedomains in NMC111, and thus the capacity loss in Figure 4.15.

40

GITT

While CC and EIS measurements are commonly found in literature withthe purpose of investigating ageing, GITT and CV are rarely used for thispurpose. However, if the characterization of NMC111 at EOL should beperformed as at BOL, the first step would consist in obtaining the ther-modynamic response of NMC111 at EOL by means of GITT measure-ments. In Figure 4.18a, the GITT curve for NMC111 at EOL is displayed,

0 10 20 30 40 50 60

3.6

3.8

4

4.2BOL40 C

EOL40 C

t/ h

E/V

vs.

Li

(a)

0 0.5 1 1.5 2 2.5 3 3.5

3.6

3.8

4

4.2

4.4

Capacity/ mAh cm−2

E/V

vs.

Li

(b)

Figure 4.18: a) Comparison (in the same lithiation interval) between GITTcurves of NMC111 at BOL and EOL (measured in NMC111 (B, 10 mm)/Li cells at 25 C), after high voltage cycling at 40 C. b) (Non-steady-state) OCP response, derived from GITT measurements performed be-tween +3.6 V and +4.5 V vs. Li on aged NMC111 under high voltageoperation at 40 C.

measured with the same protocol as at BOL (C/10 - C/20 pulses with3 h relaxation). In this plot, the relaxation is almost never achieved inthe framework of 3 h rest, even at voltages inferior to +3.85 V vs. Li.This indicates that the time constants of the kinetic processes in the agedNMC111 electrode have become slower than the allocated time for relax-ation. In addition, the GITT curves in Figure 4.18a once again displaya different behaviour before and after +3.85 V vs. Li: at lower voltages,a higher polarization in all CC phases notwithstanding, the same SOC

41

is reached at the end of relaxation, indicating that the same amount ofcharge is injected in the material both at BOL and EOL. On the otherhand, above +3.85 V vs. Li the capacity delivered by the aged NMC111electrode is systematically inferior to the one at BOL, as it is observed inthe relaxation phases ending at a lower SOC. This seemingly points to anoxidative parasitic reaction occurring in the polarized phases of the GITTmeasurement, and the most voltage-dependent degradation mode identi-fied in Paper III is the decomposition of the electrolyte, triggered above+4.2 V vs. Li already at BOL. Moreover, ageing is known to increase thereactivity of NMC111’s surface, which might have decreased the thresholdfor the electrolyte’s degradation: therefore, the loss of capacity observedin Figure 4.18b above +3.85 V vs. Li would be due to a lowered onsetof the decomposition of the electrolyte. This information cannot be ob-tained directly from the CC cycling in Figure 4.15 (unless combined withoperando Mass Spectrometry measurements), or the CV response in Fig-ure 4.16, where the voltammogram is almost unaltered from BOL in thehigh voltage window. Additionally, the presence of an oxidative parasiticreaction could be causing the asymmetry between anodic and cathodicscans in Figure 4.16. As a consequence, if an OCP curve is built from therelaxation phases in Figure 4.18a, it could not be considered at steady-state, since it would contain not only the thermodynamic behaviour ofaged NMC111, but also its dynamic response, and the occurrence of par-asitic reactions. And indeed, when such a curve is built in Figure 4.18b,a measurement-induced hysteresis [27] appears, which is not due to ther-modynamic changes in NMC111 (Paper III).

The first consequence is the impossibility of using the OCP curve inFigure 4.18a for performing a comparative analysis as in Figures 4.4 and4.11. Additionally, and more importantly, for building actual equilibriumvoltage curves at different stages of lifetime, the decrease in rate of thekinetic processes due to ageing must be taken into account. Incorrectcurves where steady-state is not reached could lead to a wrong estimationof SOC, which is problematic for practical applications: among others, theestimation of the residual driving range in EVs.

In conclusion, applying the different characterization techniques onNMC111 at EOL after high operation allows to obtain an overview of itsdegradation. Specifically, the designed protocol leads to a considerable,

42

partially reversible capacity loss on NMC111 due to LAM, not often re-ported in the literature. This degradation can be identified through CCcycling, and also CV measurements, provided that its varying sensitivityis duly taken into account. On the other hand, the expected impedancerise on NMC111 is captured by EIS in both semicircles of the Nyquistplot, indicating that the degradation occurs at different interfaces in theelectrode. A modelling approach supported by analytical characterizationreveals that the measured LAM and impedance rise are in fact connected,since the first would be caused by the formation of insulating layers onNMC111’s surface. The formation of these layers occur due to the oxida-tive decomposition of the electrolyte on NMC111’s surface: this parasiticreaction is successfully captured by means of GITT measurements, per-formed with the same protocol as at BOL. On the other hand, by usingthis protocol, NMC111 does not fully relax to steady-state at any of thevoltages considered: this is due to the fact that the time constants havebeen slowed down by the ageing, at the point that the time scale of themeasurement is unable to properly capture them. This indicates the needof re-designing testing protocols across LIBs lifetime, in order to avoidfaulty measurements that might cause wrong estimations, and severe im-pact on the end-users.

4.2 Applications

4.2.1 Semi-empirical model

From the previous Section, it emerges how the electrochemical responseof NMC111 towards different excitation signals is often the result of aconvolution of its thermodynamic and dynamic behaviour, the latter con-sisting of both charge transfer and diffusion. Consequently, understandingthe role and the extent of the thermodynamic and dynamic contributionsin NMC111’s electrochemical response allows to artificially ”re-build” theexperimental results, i.e. to predict its electrochemical performance. Thisconcept is expanded in Paper IV, where a semi-empirical model is proposedfor predicting CC voltage characteristics. The forecasting of voltage char-acteristics supports the proper estimation and prediction of LIBs statusfigures, the most important being SOC, SOH, and Remaining Useful Life-

43

time (RUL), which are hardly inferred from experimental measurements,and often need to be calculated based on measurable parameters (as volt-age, current and internal resistance) [50] [51]. The model proposed inPaper IV is built upon the thermodynamic and kinetic properties of LIBelectrodes, also observed for NMC111 in the previous Section; specifically:

• Frumkin isotherm is chosen for describing steady-state behaviour,this is compatible with the dual slope in NMC111’s equilibriumcurves at BOL.

• Semi-infinite linear diffusion is assumed for describing Li+ solid-statemass transport; this is compatible with the Warburg behaviour ob-served in the EIS spectra of NMC111.

• Quasi-reversibility is also assumed, and is compatible with NMC111’sCV response at different scan rates.

Ideally, the proposed approach can be applied to full cells containing differ-ent layered oxide positive electrodes. This assumption is tested in practicein Paper IV, by applying the proposed model to the voltage characteristicsof different commercial LIBs, cycled under different cycling protocols forboth stationary and automotive applications, and at different tempera-tures. The proposed model proves able to predict these voltage responseswith an accuracy of 1% error on the predicted voltage, which is consid-erably higher than the one of other models from the same class (5 - 20%[93]). Although the fitting performed is based on several approximations,the evolution of the fitted parameters as a function of time/cycle numbercan be considered a rough qualitative indication of the limiting processesduring cycling. Specifically, the parameters are J , Kkin and Kdiff, whichrepresent the thermodynamic, charge-transfer and diffusive portions of thevoltage response respectively. In the framework of a capacity fade dynamic(30% capacity loss at EOL), the largest variation is observed for J andKdiff, while Kkin remains constant (Figure 4.19a), pointing to a growingdiffusion limitation across cycling, with a coupled thermodynamic changein the electrodes’ bulk. This is compatible with the increasing diffusivehindrance in graphite due to mechanical stress at low SOC, as reportedin [94] [95]. In the framework of a rapid power fade dynamic, on theother hand, Kkin steadily increases over cycling (Figure 4.19b), indicating

44

0 100 200cycle number

-0.7

-0.6

-0.5

-0.4J,

ch

0.6

0.8

1

1.2

J,ds

0 100 200cycle number

0.99

0.995

1

1.005

1.01

Kki

n,ds

107

0 100 200cycle number

-5

0

5

10

15

Kdi

ff,d

s

(a)

2

t/h

-0.4

-0.3

-0.2

-0.1

0

J

0

0.5

1

1.5

0 10 20 30-5

0

5

I/A

0

0.5

1

1.5

2

Kkin

1011

0

5

10

151010

t/h0 10 20 30

-5

0

5I/A

-10

0

10

20

30

Kdiff

-5

0

5

I/A

t/h0 10 20 30

chargedischarge

(b)

Figure 4.19: Evolution of the fitting parameters J , Kkin and Kdiff (fromPaper IV) as a function of cycle number/time for a) a capacity fade dy-namic and b) a power fade dynamic (under variable current) in commercialLIBs at 25 C.

charge transfer as limiting. Although charge transfer is generally consid-ered a fast process, a large increase in its impedance has been observed inLIBs containing layered oxide electrodes, due to the formation of films atthe positive electrode’s surface [96].

Even if mostly based on NMC111’s properties, the semi-empiricalmodel proposed provides a good experimental fitting for full cells underrather diversified cycling protocols; in addition, a rough identification ofthe main limiting processes over cycling can be obtained at full-cell level,

45

although based on several strong approximations. This information can beused for quick failure detection, battery sizing and design, system designand optimization of operational strategies.

4.2.2 Ageing protocols

(a)

(b)

Figure 4.20: a) Normalized discharge capacity (measured with slow CCcycling in the framework of the reference performance test) vs. equivalentcycle number of commercial LIBs, cycled under a stationary protocol (Pa-per V) in different SOC ranges. b) Galvanostatic EIS response (between1 kHz and 25 mHz) of the cells in a), measured at 50% SOC.

46

For the validation of the semi-empirical model, online databases wereused, where LIBs were cycled according to generic protocols for mimickingelectric drives, and stationary storage. However, for targeting specificapplications, the design of cycling protocols which would better approachthe real usage of LIBs is still necessary. This aspect is addressed in PaperV, where a testing protocol for PV-connected, off-grid LIBs is proposed.This protocol also addresses a gap in the standardization of LIB cycling,which mostly focuses on automotive use, and is left rather undefined whenit comes to stationary applications [76]. For better relating the designedprotocol to real-life conditions, the testing procedure is extracted frompower usage data in the rural region of interest. These data pointed to theoverall use of low currents (∼ C/20 cycling) and different SOC intervals,depending on the application and the time of the year. This led to acampaign of experiments spanned over two years, during which commercialLIBs with layered oxide positive electrodes were cycled according to theproposed procedure. In order to maintain the relatability to real usageconditions, no accelerated ageing procedure was applied. The capacityloss displayed by these devices across the two years of cycling is displayedin Figure 4.20a. Only LIBs cycled in the highest SOC interval (65 - 95%SOC) reach the EOL criterion of 20% loss on the nominal capacity. Thiscycling condition also corresponds to the EIS spectrum with the highestmid-frequency semicircle in Figure 4.20b, i.e. the highest fmax: this is asign that the kinetics are most impeded in the cycling protocol involvingthe high-end of the SOC window. Additionally, the EIS spectrum in the65 - 95% SOC range is also characterized by the appearance of a secondsemi-circle at mid-high frequencies, not entirely resolved, and associated(among other reasons) with the formation of layers on the electrodes’surface [41]. This is in agreement with the findings from DVA in PaperV, which point to SEI growth as the main cause behind LLI at full-celllevel. This indicates that, in the specific application considered (off-grid,PV-connected LIBs), the combination of a narrow SOC interval and theuse of a high voltage cut-off has the most impact on LIB’s lifetime. Thisinformation can be used for defining the optimal operational strategies forLIBs in off-grid systems: specifically, these strategies should minimize thetotal system cost by extending LIB’s lifetime.

Ideally, lifetime testing should always be performed on commercial

47

LIBs, in order to be as close as possible to the real set-up and usageconditions; however, this might not be always advantageous, or feasible.One disadvantage of using commercial LIBs is the difficulty of describingthem through physics-based models, which would allow for a more precisedescription and quantification of ageing mechanisms than (semi)empiricalapproaches, and for a better generalization of the results. This is due tothe fact that physics-based models, already computationally expensive [45][47], further increase in their cost and complexity when considering com-mercial LIBs, due to the local, geometry-induced effects to be consideredin the form of added dimensions [2]. Furthermore, some testing conditionsmight not be practically applicable to commercial LIBs. One example ishigh voltage operation, already considered in the previous Section: thevast majority of these studies is necessarily performed in lab-scaled cells,due to the unavailability of mass-produced commercial LIBs design forthis purpose. However, this approach misses the complexity of commer-cial LIBs with wound configuration: one of the aspects overlooked, forexample, is the occurrence of uneven electrode slippage across the jellyroll [71] [97]. This aspect is specifically addressed in Paper III, by apply-ing the chosen testing protocol to lab-scaled cells in different stoichiometricconfigurations: half cells, and full cells where graphite is in excess, or withforced Li plating. We here focus on one of the most undesired situationsin a full-cell, whose effects have already been displayed in Figure 4.14: Liplating, as might locally occur in the jelly-roll of commercial LIBs. Inthe cells in Figure 4.14, two LLI mechanisms are likely to be present: 1)anomalous SEI growth due to transition metal dissolution and 2) Li plat-ing, due to the fact that graphite initially reaches 0 V vs. Li. This leads toa pronounced slippage between the electrodes over cycling, and two stagescan be considered in particular:

1. Graphite has not yet slipped to a point of completely matchingNMC111 when fully charged (Figure 4.21b). Up until this point,NMC111 reaches voltages of + 4.5 V vs. Li, as the Li plating ongraphite induces 0 V vs. Li as negative electrode potential whenfully charged [98];

2. Graphite has slipped passed the point shown in Figure 4.21b, andforces NMC111’s potentials above +4.5 V vs. Li during charging (as

48

+4.5 Vupper voltage cut-off

+4.5 Vupper voltage cut-off

+4.5 Vupper voltage cut-off

(a)

(b)

(c)

+3.9 V

Figure 4.21: (a) Unbalanced NMC111/graphite cells at BOL (ex-perimental data). (b) and (c) Simulated scenarios for unbalancedNMC111/graphite cells at EOL, in two limiting cases: (b) graphiteand NMC111 perfectly matching each other when fully charged and (c)graphite in excess when NMC111 reaches the highest potential, causingNMC111 to be pushed to higher voltages.

49

the potential of the negative electrode is higher than 0 V vs. Li).At this point, Li plating could cease.

While a mild capacity fade can be observed at 25 C in Figure 4.14, thecells cycled at 40 C display a faster degradation, characterized by a sud-den increase of the ageing rate at ∼20 cycles. The unbalanced cells at 25C, though forced to suffer Li-plating due to the mismatched electrodes,do not show a substantial capacity fade within the first 60 cycles (∼ 4%),indicating that the Li plating is somewhat reversible in this case. At 40C, however, a substantial capacity fade occurs after the first 20 cycles,showing a much decreased stability and reversibility of the plated Li. Thefirst portion of this capacity fade (after 20 cycles) would correspond totransitioning from Figure 4.21a to 4.21b. Beyond ∼0.65 mA h cm−2 oflost capacity, the condition in Figure 4.21c is reached, which leads to anincrease in NMC111’s cut-off above +4.5 V vs. Li. Since a higher temper-ature increases the rate of LLI- and LAM-inducing mechanisms [99], theunbalanced cells at 40 C are expected to suffer of a more severe slippage,implying that a higher upper-voltage cut-off than +4.5 V vs. Li is reachedon NMC111. As such, the faster degradation would not be merely a conse-quence of a higher temperature, but also the effect of an increased voltagecut-off on the positive electrode. In this way, we show how lab-scaled cellscan still be used to represent the localized effects in a commercial LIBwhen specifically considering the uneven stoiochiometric drift occurringacross the jelly roll over cycling.

50

Chapter 5

Conclusions

In the present work, four common electrochemical techniques (CC cycling,GITT, EIS and CV) are used for investigating NMC111’s behaviour atBOL and EOL.

At BOL, the thermodynamic and dynamic properties of NMC111 areinvestigated both qualitatively and quantitatively. In such sense, GITTand EIS prove the most suitable techniques, as they allow to separate thekinetic contribution into charge transfer and diffusion, and to quantifykinetic parameters as the kinetic rate constants, and the effective solid-state diffusion coefficients. GITT in particular is the only technique ableto visually capture the slow relaxation occuring at BOL above +3.85 Vvs. Li. Moreover, GITT allows to build equilibrium curves; when com-pared with CC curves, for a visual separation of the thermodynamic anddynamic contributions can be performed, apt to study the polarization inNMC111. When the same analysis is attempted for CV measurements, onthe other hand, a varying sensitivity of the dynamic response is found inthe voltage window considered, strongly dependent on the current mea-sured: specifically, an ”amplification” effect is observed in the peak region,while no changes are registered above +3.9 V vs. Li, where the measure-ment displays an almost linear i vs. E profile. Overall, GITT proves tobe the most versatile and information-dense technique for investigatingNMC111 at BOL.

On the other hand, the different techniques display more of their non-concurrent nature at EOL, delivering complementary information about

51

the ageing phenomena in the material. CC cycling and CV both capturethe capacity fade, and a non-uniform current distribution in the material.EIS captures the impedance rise, from which the different ageing phenom-ena can be identified, and linked back to the capacity loss. On the otherhand, GITT captures the occurrence of an oxidative parasitic reaction atvoltages above +3.85 V vs. Li. In addition, using the same GITT pro-cedure employed at BOL reveals that aged NMC1111 cannot reach a fullrelaxation at EOL even below +3.85 V vs. Li, since the time constantof the kinetic processes has been slowed down by the degradation. As aconsequence, the OCP curve thus obtained can’t be considered at steady-state: this underlines the importance of updating such testing protocol asthe cycling proceeds, in order to avoid errors in SOC estimation.

From the electrochemical characterization at BOL, a negligible tem-perature dependency is observed at steady-state. When the system isperturbed from equilibrium, on the other hand, the dynamic response istemperature-dependent, and overall symmetric between charge and dis-charge (with the only exception at high DOD, due to re-lithiation hin-drance). The slow relaxation observed above +3.85 V vs. Li could bequantitatively captured by including the effects of mechanical stress intoalready developed electrochemical descriptions. Furthermore, this alsoreveals how the dynamic response of NMC111 varies depending on the de-gree of lithiation: specifically, the kinetic rate constants and the diffusioncoefficients display opposite trends below and above +3.85 V vs. Li, adetail to be taken into account for an accurate physics-based descriptionof NMC111, and similar materials.

When NMC111 reaches the EOL criterion after high operation, a con-siderable, partially reversible capacity loss is observed, not often reportedin the literature, and due to LAM. This LAM is linked to the impedancerise registered in both semicircles of the Nyquist plot, indicating that thedegradation occurs at different interfaces in the electrode. Specifically, themeasured LAM and impedance rise are connected, since the first would becaused by the formation of insulating layers on NMC111’s surface. Theselayers are formed due to the oxidative decomposition of the electrolyte onNMC111’s surface. Overall, it is revealed that under high voltage opera-tion NMC111 contributes to the overall degradation both in the form ofimpedance rise (as reported in the literature) and capacity fade; the two

52

modes are interconnected by the degradation of the electrolyte, and theconsequent formation of insulating layers on NMC111’s surface.

Some of the properties inferred from NMC111’s characterization atBOL (namely, its steady-state behaviour, the assumption of semi-infinitelinear diffusion and quasi-reversibility) are employed to create a semi-empirical model for predicting CC voltage curves of LIBs, to be used inlarger energy systems and for on-line estimation. Although the model wasdesigned mostly based on NMC111’s thermodynamic and dynamic prop-erties, it can generalize to commercial LIBs with different layered oxidepositive materials, and it delivers high-accuracy results when compared tosimilar approaches. The evolution of the fitted parameters roughly indi-cates the limiting processes occurring across cycling in the different LIBsconsidered; the addition of specific terms accounting for different ageingphenomena is suggested for improving the physical validity of the model.Together with a model for predicting CC curves, the importance of collect-ing such data with relevance for commercial set-ups and applications is alsodiscussed. Specifically, it is shown how high voltage operation, performedin lab-scaled pouch-cells, can in fact be referred to commercial LIBs withwound configuration, if the localized geometry-induced effects are prop-erly captured. For targeting stationary applications, something not oftenaddressed through standardized protocols, a testing protocol is proposedto mimic the low-current operating conditions of off-grid, PV-connectedLIBs. In order to maintain the relatability to real-usage conditions, thetesting is performed over a time span of two years, without employingaccelerated ageing procedure. The results allow to identify the protocolwhich impacts the least the overall battery lifetime, an input needed fordesigning optimal operational strategies which minimize the cost of sys-tems in which LIBs are included.

53

Chapter 6

Acknowledgements

The Swedish Energy Agency (Energimyndigheten) is gratefully acknowl-edged for funding the project.

Due acknowledgements need to be paid to my supervisory team: Prof.Goran Lindbergh, Matilda Klett, and Pontus Svens. Goran, your supportmade this all possible, particularly in the last (and most difficult) phaseof the PhD. Matilda, your sharp and inquisitive gaze always pushed meto dig deeper, and to deliver a higher quality in my work. I wouldn’tbe as proud of it as I am, if it was not for you. Pontus, your positiveattitude, your thinking out of the box, and your vast technical knowledgehave brought a great contribution to my projects. You were such a goodaddition to the supervisory team! I would also like to acknowledge theco-workers I had the privilege to work with, first and foremost Jing YingKo, whom I shared the project with. It has been really pleasant, and atrue privilege, to work with someone as talented as you. Henrik Ekstrom,the silent overseer behind my manuscripts: you were my answerer forany theoretical doubt. Somehow, your explanations always worked forme. Pietro Elia Campana: I don’t even know how to put it in words.Your unending hunger for learning, your positivity and resilience, and thepassion for your work, have been a huge inspiration for me. I was luckyto meet you at the right moment: you have been the sparkle I needed.Andrzej Nowak: when I just arrived at KTH, you taught me everythingI needed to know about batteries. Mussa, it has been such an honourto work with, and learn from someone so brilliant, and so humble at the

54

same time. Ulriika, Hyeyun, and Yasemin: you have not only been greatcolleagues, but also true friends. You have made the difference. I wouldalso like to acknowledge Prof. Annick Hubin, Prof. Herman Terryn, andDr. Xinhua Zhu at Vrije Universiteit Brussels (VUB) for giving me thechance to spend 2 weeks in their lab, and learn about their approachtowards batteries. It was a great experience to meet and work with yourresearch team! Speaking of opportunities, I cannot avoid thanking fromthe bottom of my heart Prof. Pierluigi Bonora, my mentor, who was therein the very beginning, and is here at the end. It is fair to say that withouthim, my whole journey would have never started. Prof. Christina Divne,thanks for your patient and steady support in all sorts of matters, andyour guidance in moments of doubts.

I would like to thank the crew in Sweden and the Netherlands: Kasra,Maria Letizia & Enrique, Lisa, Anna & Fabrizio (+ Samuele and Alessia),Mladena & Branko (and Luka!), Ennery & Amarelis (and Elizabeth!),Shoshan (and Rafael!), Lisette, Karen & Augusto, Jiayi & Wenquin (andSiska!). Thanks for your support and cheering across the years!

Ik wil ook graag de Kramer-Kea familie bedanken: Joke & Jaap,Brenda & Teun (+ Lieke en...), Erik & Timna. Toen de eerste dag dieik jullie ontmoette, voelde ik als ik een van jullie was. Ik nooit voeldeafgekeurd omdat ik een buitenlander was (en dat is helaas veel keer aanmij gebeurd): voor mij, dit is de grootse cadeau die jullie kon mij geven.Jullie voortdurende steun was een mooie extra!

Ringraziamenti anche alla famiglia Varini-Zanoni, che mi e’ stata ac-canto in questo calvario! Sono contenta di essere arrivata a scrivere iringraziamenti, e potervi avere tutti qui.

There is one more person to thank: Koen, mijn lief. You walkedalongside me the entire time, always holding my hand, never letting mego, even if it meant going through approximately 1460 Skype calls, and atotal of 100000 km of travel. If this is not love, then I don’t know what itis.

Finally, thanks to you, reader. Go through my thesis. Might you findwhat you were looking for. If what you will find here will help you movefurther in your path of even a millimetre, then I would have done what Icame for.

55

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