Phenomenologically modeling the formation and evolution of the solid electrolyte interface on the graphite electrode for lithium-ion batteries

The formation and evolution of the solid electrolyte interface (SEI) film during the first electrochemical intercalation of lithium into graphite were modeled as a special precipitation process including a nucleation phase of the SEI film's solid deposition, and followed by a growth phase involving the precipitation of new solids on previously formed solid nuclei. It was shown that the solid species can nucleate in the electrolyte solution, directly on the graphite surface, or adjacent to an already present particle on the graphite surface when precipitating from the electrolyte solution. Within the framework of classical nucleation theory (CNT), we can qualitatively explain the origin of the two-layer structure of SEI films, which consists of a thin, compact polycrystalline or heteromicrophase layer rich in inorganic species (e.g., LiF, Li₂O) close to the electrode, and a thicker porous and amorphous layer composed mainly of organic compounds (e.g., ROLi, ROCO₂Li) that is farther from the graphite.     

Novel SEI formation of maleimide-based additives and its improvement of capability and cyclicability in lithium ion batteries

This investigation elucidates three maleimide (MI)-based aromatic molecules as additives in electrolyte that is used in lithium ion batteries. The 1.1 M LiPF₆ in ethylene carbonate (EC):propylene carbonate (PC):diethylene carbonate (DEC) (3:2:5 in volume) containing MI-based additives can prompt the formation of a solid electrolyte interface (SEI); and inhibit the entering into the irreversible state during lithium intercalation and co-intercalation. The reduction potential is 0.71-0.98 V versus Li/Li⁺ as determined by cyclic voltammetry (CV). The morphology and element analysis of the positive and negative electrode after the 100th charge-discharge cycle are examined by scanning electron microscopy (SEM), energy dispersive spectrometry (EDS) and X-ray photoelectron spectroscopy (XPS). Moreover, the MI was used in lithium ion batteries and provided 4.9% capacity increase and 16.7% capacity retention increase when cycled at 1C/1C. The MI-based additive also ensures respectable cycle-ability of lithium ion batteries. MI is decomposed electrochemically to form a long winding narrow SEI strip on the graphite surface. This novel SEI strip not only prevents exfoliation on the graphite electrode but also stabilizes the electrolyte. The MI-based additive also ensures respectable cycle-ability of lithium ion batteries.     

Micromechanisms of solid electrolyte interphase formation on electrochemically cycled graphite electrodes in lithium-ion cells

The microstructural and compositional changes that occurred in the solid electrolyte interphase (SEI) formed on graphite electrodes subjected to voltammetry tests (vs. Li/Li⁺) at different voltage scan rates were investigated. The microstructure of the SEI layer, characterized using high-resolution transmission electron microscopy, consisted of an amorphous structure incorporating crystalline domains of ～5–20 nm in size. Evidence of lithium compounds, namely Li₂CO₃ and Li₂O₂, and nano-sized graphite fragments was found within these crystalline domains. The morphology and thickness of the SEI depended on the applied voltage scan rate (dV/dt). The variations in the Li⁺ diffusion coefficient (D_Li⁺) at the electrode/electrolyte interface during the SEI formation process were measured and two regimes were identified depending on the scan rate; for dV/dt ≥ 3.00 mV s^?1, D_Li⁺ was 3.13 × 10^?8 cm² s^?1. At lower scan rates where D_Li⁺ was low, 0.57 × 10^?8 cm² s^?1, a uniform and continuous SEI layer with a tubular morphology was formed whereas at high dV/dt, the SEI formed had a columnar morphology and did not provide a uniform coverage.     

Surface chemistry of intermetallic AlSb-anodes for Li-ion batteries

The solid electrolyte interphase (SEI) layer on AlSb electrodes has been studied in Li/AlSb cells containing a LiPF₆ EC/DEC electrolyte using X-ray photoelectron spectroscopy (XPS). Data were collected before SEI-formation, during formation, and after formation at 0.01 V versus Li⁰/Li⁺, and at full delithiation in cycled cells at 1.20 V. The thickness of the SEI layer increases during lithiation and decreases during delithiation. This dynamic behaviour occurs continuously on cycling the cells. The growth of the SEI layer can be attributed predominantly to the deposition of carbonaceous species below 0.50 V versus Li⁰/Li⁺; these species disappear almost completely during delithiation. The extra surface-layer formation is a consequence of the additional charge that is needed to lithiate the remaining Sb component of the micrometer-sized AlSb particles at low potentials as seen by synchrotron-based X-ray diffraction. Aluminium is not reactive to lithium alloying in this electrolyte. Relatively small amounts of LiF were detected in the AlSb SEI layers compared to that commonly found in the SEI layers on graphite electrodes.     

Electrochemical intercalation of lithium into a natural graphite anode in quaternary ammonium-based ionic liquid electrolytes

Electrochemical intercalation of lithium into a natural graphite anode was investigated in electrolytes based on a room temperature ionic liquid consisting of trimethyl-n-hexylammonium (TMHA) cation and bis(trifluoromethanesulfone) imide (TFSI) anion. Graphite electrode was less prone to forming effective passivation film in 1 M LiTFSI/TMHA-TFSI ionic electrolyte. Reversible intercalation/de-intercalation of TMHA cations into/from the graphene interlayer was confirmed by using cyclic voltammetry, galvanostatic measurements, and ex situ X-ray diffraction technique. Addition of 20 vol% chloroethylenene carbonate (Cl-EC), ethylene carbonate (EC), vinyl carbonate (VC), or ethylene sulfite (ES) into the ionic electrolyte resulted in the formation of solid electrolyte interface (SEI) film prior to TMHA intercalation and allowed the formation of Li-C₆ graphite interlayer compound. In the ionic electrolyte containing 20 vol% Cl-EC, the natural graphite anode exhibited excellent electrochemical behavior with 352.9 mAh/g discharge capacity and 87.1% coulombic efficiency at the first cycle. A stable reversible capacity of around 360 mAh/g was obtained in the initial 20 cycles without any noticeable capacity loss. Mechanisms concerning the significant electrochemical improvement of the graphite anode were discussed. Ac impedance and SEM studies demonstrated the formation of a thin, homogenous, compact and more conductive SEI layer on the graphite electrode surface.     

Study of the formation of a solid electrolyte interphase (SEI) in ionically crosslinked polyampholytic gel electrolytes

An ionic complex of anionic and cationic monomers was obtained by protonation of (N,N-diethylamino)ethylmethacrylate with acrylic acid. A novel ionically crosslinked polyampholytic gel electrolyte was prepared through the free radical copolymerization of the ionic complex and acrylamide in a solvent mixture of ethylene carbonate, dimethyl carbonate and ethyl methyl carbonate (1:1:1, v/v) containing 1 mol/L of LiPF₆. The impedance analysis indicated that the ionic conductivity of the polyampholytic gel electrolyte was rather close to that of solution electrolytes in the absence of a polymer at the same temperature. The temperature dependence of the conductivity was found to be well in accord with the Arrhenius behavior. The formation processes of the solid electrolyte interphase (SEI) formed in both gel and solution electrolytes during the cycles of charge-discharge were investigated by cyclic voltammetry and electrochemical impedance spectroscopy. The cyclic voltammetry curves show a strong peak at a potential of 0.68 V and an increase of the interfacial resistance from 17.2 Ω to 35.8 Ω after the first cycle of charge-discharge. The results indicate that the formation process of SEI formed in both gel and solution electrolytes was similar which could effectively prevent the organic electrolyte from further decomposition and inserting into the graphite electrode. The morphologies of SEI formed in both gel and solution electrolytes were analyzed by field emission scanning electron microscopy. The results indicate that the SEI formed in the gel electrolyte showed a rough surface consisting of smaller solid depositions. Moreover, the SEI formed in the gel electrolyte became more compact and thicker as the cycling increased.     

Triethyl orthoformate as a new film-forming electrolytes solvent for lithium-ion batteries with graphite anodes

Triethyl orthoformate (TEOF) as a new solvent used in propylene carbonate (PC)-based electrolytes together with graphitic anodes in lithium-ion batteries has been investigated. It can be observed that TEOF was capable of suppressing the co-intercalation of PC solvated lithium-ions into the graphite layer during the first lithiation process and the irreversible discharge capacity of the first cycle is the smallest when using 1.0 M LiPF₆ in PC and TEOF at solvent ratio of 1:1 as the electrolytes. The CV, FTIR, EIS, SEM results show that the PC-based electrolytes containing the solvent TEOF can generate an effective solid electrolytes interphase (SEI) film during the first cycling process, and the film is probably mainly composed of ROCO₂Li, ROLi, Li₂CO₃, etc. The formation of a stable passivating film on the graphite surface is believed to be the reason for the improved cell performance. All these results show that TEOF possesses a promising performance for use as an effective film-forming electrolytes solvent in lithium-ion batteries with graphitic anodes.     

Properties of Li-graphite and LiFePO4 electrodes in LiPF6–sulfolane electrolyte

Sulfolane (also referred to as tetramethylene sulfone, TMS) containing LiPF₆ and vinylene carbonate (VC) was tested as a non-flammable electrolyte for a graphite |LiFePO₄ lithium-ion battery. Charging/discharging capacity of the LiFePO₄ electrode was ca. 150 mAh g⁻¹ (VC content 5 wt%). The capacity of the graphite electrode after 10 cycles establishes at the level of ca. 350 mAh g⁻¹ (C/10 rate). In the case of the full graphite |1 M LiPF₆ + TMS + VC 10 wt% |LiFePO₄ cell, both charging and discharging capacity (referred to cathode mass) stabilized at a value of ca. 120 mAh g⁻¹. Exchange current density for Li⁺ reduction on metallic lithium, estimated from electrochemical impedance spectroscopy (EIS) experiments, was j_o(Li/Li⁺) = 8.15 × 10⁻⁴ A cm⁻². Moreover, EIS suggests formation of the solid electrolyte interface (SEI) on lithium, lithiated graphite and LiFePO₄ electrodes, protecting them from further corrosion in contact with the liquid electrolyte. Scanning electron microscopy (SEM) images of pristine electrodes and those taken after electrochemical cycling showed changes which may be interpreted as a result of SEI formation. No graphite exfoliation was observed. The main decomposition peak of the LiPF₆ + TMS + VC electrolyte (TG/DTA experiment) was present at ca. 275 °C. The LiFePO₄(solid) + 1 M LiPF₆ + TMS + 10 wt% VC system shows a flash point of ca. 150 °C. This was much higher in comparison to that characteristic of a classical LiFePO₄ (solid) + 1 M LiPF₆ + 50 wt% EC + 50 wt% DMC system (T_f ≈ 37 °C).     

Characterisation of the SEI formed on natural graphite in PC-based electrolytes

The origin of the different Li⁺ intercalation behaviour of raw and jet-milled natural graphite has been investigated. Jet-milled graphite is found to cycle reversibly in equal solvent mixture of propylene carbonate (PC) and ethylene carbonate (EC), whereas raw graphite does not. Using both Al Kα and synchrotron radiation (SR) Photoelectron Spectroscopy, new insight is obtained into the formation of the solid electrolyte interphase (SEI) on the two different graphite materials during electrochemical cycling in 1 M LiPF₆ in either PC:EC (1:1) or in PC with 5% vinylene carbonate (VC) as additive. Solvent reduction products are found at the surface of both raw and jet-milled graphite cycled in PC:EC (1:1), but differed in composition. The addition of VC reduces primarily the quantities of salt reaction products (LiF and Li_xPF_y compounds) and produces a mainly organic SEI layer. Electron diffraction from the edges for raw and jet-milled graphite particles shows a more disordered surface structure in the jet-milled particles than in the raw graphite. The more disordered surface structure can serve as a physical barrier hindering PC co-intercalation and facilitating the formation of a stable SEI layer.     

Impedance study of protecting film formation on lithium and lithiated graphite induced by bis(fluorosulfonyl) imide anion

The process of Li⁺ reduction from room temperature ionic liquids consisting of N-methyl-N-propylpyrrolidinium cation (MPPyr⁺) and bis(fluorosulfonyl) imide (FSI⁻) or bis(trifluoromethanesulfonyl) imide (TFSI⁻) anions was studied with the use of impedance spectroscopy. Reduction was carried out on both metallic lithium (Li) and graphite (G) electrodes. It has been found that the FSI anion in high amounts is able to form a protective film on both graphite and metallic lithium. The Li⁺/Li couple should rather be represented by a Li⁺/SEI/Li system. The SEI structure depends on the manner of its formation (chemical or electrochemical) and is not stable with time. The rate constant for the Li⁺ + e⁻ → Li process at the Li/SEI/Li⁺ (in MPPyrFSI) interface is k_o = 4.2 × 10⁻⁵ cm/s. In the case of carbon electrodes (G/SEI/Li⁺ interface), lithium diffusion in solid graphite is the rate determining step, reducing current by ca. two orders of magnitude, from ca. 10⁻⁴ A/cm², characteristic of the Li/SEI/Li⁺ electrode, to ca. 10⁻⁶ A/cm².     

Interfacial reactions at electrode/electrolyte boundary in all solid-state lithium battery using inorganic solid electrolyte, thio-LISICON

Electrode/electrolyte interface was studied for all solid-state batteries using inorganic solid electrolyte with the crystalline thio-LISICON and glassy Li-Si-P-S-O systems. The formation of the interfacial phase depends on the electrolyte. The thio-LISICON (Li_3.25Ge_0.25P_0.75S₄) and the Li-Al negative electrode provided the best electrode/electrolyte interface for fast charge-discharge characteristics, while the SEI phase formed at the Li-Al/Li₃PO₄-Li₂S-SiS₂ glass boundary caused high interfacial resistance. The formation of the SEI phase is general behavior at the electrode/electrolyte interface of solid-state batteries, and the fast electrochemical reaction is attained as a result of optimization of the electrode/electrolyte combination.     

Interfacial structural stabilization on amorphous silicon anode for improved cycling performance in lithium-ion batteries

Interfacial structures of electrode-current collector and electrode-electrolyte have been designed to be stabilized for improved cycling performance of amorphous silicon (Si) that is considered as an alternative anode material to graphite for lithium-ion batteries. Interfacial structural stabilization involves the interdigitation of Si electrode-Cu current collector substrate by anodic Cu etching with thiol-induced self-assembly, and the formation of self-assembled siloxane on the surface of Si electrode using silane. The novel interfacial architecture possesses promoted interfacial contact area between Si and Cu, and a surface protective layer of siloxane that suppresses interfacial reactions with the electrolyte of 1 M LiPF₆/ethylene carbonate (EC):diethylene carbondate (DEC). FTIR spectroscopic analyses revealed that a stable solid electrolyte interphase (SEI) layer composed of lithium carbonate, organic compounds with carboxylate metal salt and ester functionalities, and PF-containing species formed when having siloxane on Si electrode. Interfacially stabilized Si electrode exhibited a high capacity retention 80% of the maximum discharge capacity after 200 cycles between 0.1 and 1.5 V vs. Li/Li⁺. The data contribute to a basic understanding of interfacial structural causes responsible for the cycling performance of Si-based alloy anodes in lithium-ion batteries.     

Stabilisation of lithiated graphite in an electrolyte based on ionic liquids: an electrochemical and scanning electron microscopy study

1-Ethyl-3-methylimidazolium-bis(trifluoromethylsulfonyl)imide (EMI-TFSI) is shown to reversibly permit lithium intercalation into standard TIMREX^® SFG44 graphite when vinylene carbonate (VC) is used in small amounts as additive. The best performance was obtained when 5% of VC was added to a 1 M solution of LiPF₆ in EMI-TFSI. Intercalation of lithium in the SFG44 graphite host was demonstrated over 100 cycles without noticeable capacity fading. The reversible charge capacity was around 350 mA h g⁻¹ and an only small irreversible capacity loss per cycle could be observed. Li₄Ti₅O₁₂ was used as counter electrode material. Scanning electron microscopy indicates the reduction of the electrolyte without graphite exfoliation in the neat electrolyte and the formation of a passivation film in the case of a VC-containing electrolyte. Other additives that were tested comprise ethylene sulphite and acrylonitrile which show also a positive effect, but a smaller one than vinylene carbonate. LiCoO₂ positive electrodes were cycled in a 1 M solution of LiPF₆ in EMI-TFSI with good charge capacity retention over more than 300 cycles, when Li₄Ti₅O₁₂ was used as counter electrode. The formation of a passivation film is proven on the LiCoO₂-electrodes, when the electrolyte contained VC, but not in the neat ionic liquid. Finally, the stable cycling of a full cell configuration is proven in this electrolyte system. An ammonium-containing ionic liquid (methyltrioctylammonium-bis(trifluoromethylsulfonyl)-imide, MTO-TFSI) is shown to permit the cycling of both, graphite and lithium cobalt oxide when VC is used as additive in small amounts, but at slightly elevated temperatures.     

Comparisons of graphite and spinel Li1.33Ti1.67O4 as anode materials for rechargeable lithium-ion batteries

The aim of this work was to compare the electrochemical behaviors and safety performance of graphite and the lithium titanate spinel Li_1.33Ti_1.67O₄ with half-cells versus Li metal. Their electrochemical properties in 1 M LiPF₆/EC + DEC (1:1 w/w) or 1 M LiPF₆/PC + DEC (1:1 w/w) at room and elevated temperatures (30 and 60 °C) have been studied using galvanostatic cycling. At 30 °C graphite has higher reversible capacity than Li_1.33Ti_1.67O₄ when using the LiPF₆/EC + DEC as electrolyte. At 60 °C graphite declines in cell capacity yet Li_1.33Ti_1.67O₄ remains almost unchanged. In a propylene carbonate (PC) containing electrolyte, graphite electrode exfoliates and loses its mechanical integrity while Li_1.33Ti_1.67O₄ electrode is very stable. An accelerating rate calorimeter (ARC) and microcalorimeter have been used to compare the thermal stability of lithiated lithium titanate spinel and graphite. Results show that Li_1.33Ti_1.67O₄ may be used as an alternative anode material offering good battery performance and higher safety.     

Compatibility of quaternary ammonium-based ionic liquid electrolytes with electrodes in lithium ion batteries

Electrochemical intercalation/deintercalation behavior of lithium into/from electrodes of lithium ion batteries was comparatively investigated in 1 mol/L LiClO₄ ethylene carbonate-diethyl carbonate (EC-DEC) electrolyte and a quaternary ammonium-based ionic liquid electrolyte. The natural graphite anode exhibited satisfactory electrochemical performance in the ionic liquid electrolyte containing 20 vol.% chloroethylenene carbonate (Cl-EC). This is attributed to the mild reduction of solvated Cl-EC molecules at the graphite/ionic electrolyte interface resulting in the formation of a thin and homogenous SEI on the graphite surface. However, rate capability of the graphite anode is poor due to the higher interfacial resistance than that obtained in 1 mol/L LiClO₄/EC-DEC organic electrolyte. Spinel LiMn₂O₄ cathode was also electrochemically cycled in the ionic electrolyte showing satisfactory capacity and reversibility. The ionic electrolyte system is thus promising for 4 V lithium ion batteries based on the concept of “greenness and safety”.     

Electrolyte additives for enhanced thermal stability of the graphite anode interface in a Li-ion battery

The influence of electrolyte additives on the thermal stability of graphite anodes in a Li-ion battery has been investigated. The selected additives are: ethyltriacetoxysilane, 1,3-benzoldioxole, tetra(ethylene glycol)dimethylether and vinylene carbonate. These compounds were added in 4% to an electrolyte consisting of 1M LiBF₄ ethylene carbonate (EC)/diethyl carbonate (DEC) solvent mixture. Differential scanning calorimetry (DSC) was used to investigate the thermal stability. The electrochemical performance was investigated by galvanostatic cycling and the formed solid electrolyte interphase (SEI) was characterised by photoelectron spectroscopy (PES) using Al Kα and synchrotron radiation (SR). The onset temperature for the thermally activated reactions was found to increase for all electrodes cycled with additives compared to electrodes cycled without additives. The onset temperature increased in the order: no additive < tetra(ethylene glycol)dimethyl ether < 1,3-benzoldioxole < ethyl-triacetoxysilane < vinylene carbonate. Features in the PES spectra found to be associated with high onset temperatures for thermally activated reactions are: (i) no discernible graphite peak, (ii) small amount of salt species of the type LiF and Li_xBF_yO_z and (iii) larger amounts of organic compounds preferably with a high oxygen content.     

Kinetic analysis of Li|Li+ interphase in an ionic liquid electrolyte

Kinetic analysis of the Li|Li⁺ interphase in an electrolyte based on N-metyl-N-propylpyrrolidinium bis(trifluoromethanesulfon)imide ionic liquid (MPPyrrTFSI) and lithium bis(trifluoromethanesulfon)imide salt (LiTFSI) was performed. Li|electrolyte|Li and LiC₆|electrolyte|Li cells were galvanostatically charged/discharged in order to form solid electrolyte interphase (SEI) protecting layer. SEM images showed that the surface of both Li and LiC₆ anodes was covered with small particles. The fitting procedure of electrochemical impedance data taken at different temperatures gave three resistances (R _el, R _SEI, R _ct) and hence, three lnR = f(T ^?1) straight lines of different slopes. Specific conductivity and activation energy of the conduction process of the liquid electrolyte, were ca. σ = 2.5 mS cm^?1 (at T = 25.0 °C) and $ E_{\text{el}}^{\# } $  = 15 kJ mol^?1. Activation energy for the conduction process in the SEI layer was ca. 56 kJ mol^?1 in the case of the metallic lithium and 62 kJ mol^?1 for the graphite anode. Activation energy of the charge transfer process, $ E_{\text{ct}}^{\# } $ , for Li and LiC₆ anodes was 71 and 65 kJ mol^?1, respectively. Analysis of literature data for different electrolytes suggests that the $ E_{\text{ct}}^{\# } $ value for Li⁺ reduction may be approximated by 57 ± 5 kJ mol^?1. Activation energy for the diffusion processes in the graphite electrode, detected from the Warburg coefficient, was ca 74 kJ mol^?1.     

The influence of lithium salt on the interfacial reactions controlling the thermal stability of graphite anodes

The thermal stability of graphite anodes used in Li-ion batteries has been investigated, with the influence of electrolyte salt under special scrutiny, LiPF₆, LiBF₄, LiCF₃SO₃ and LiN(SO₂CF₃)₂ in an ethylene carbonate (EC)/dimethyl carbonate (DMC) solvent mixture. Differential scanning calorimetry (DSC) showed exothermic reactions in the temperature range 60-200 °C for all electrolyte systems. The reactions were coupled to decomposition of the solid electrolyte interphase (SEI) and reactions involving intercalated lithium. The onset temperature of the exothermic reactions increased with type of salt in the order: LiBF₄<LiPF₆<LiCF₃SO₃<LiN(SO₂CF₃)₂. X-ray photoelectron spectroscopy (XPS) was used to identify surface species formed prior to and after the exothermic reactions, to clarify different thermal behaviour for different salts. The decomposed SEI's in LiCF₃SO₃ and LiN(SO₂CF₃)₂ electrolytes were found to be mainly solvent-based, including lithium alkyl carbonate decomposition to stable Li₂CO₃ and the formation of poly(ethylene oxide) (PEO)-type polymers. In the LiBF₄ and LiPF₆ systems, decomposition was governed by salt reactions, which decomposed the salts and resulted in the main product LiF.     

The function of vinylene carbonate as a thermal additive to electrolyte in lithium batteries

The role of vinylene carbonate (VC) as a thermal additive to electrolytes in lithium ion batteries is studied in two aspects: the protection of liquid electrolyte species and the thermal stability of the solid electrolyte interphase (SEI) formed from VC on graphite electrodes at elevated temperatures. The nuclear magnetic resonance (NMR) spectra indicate that VC can not protect LiPF₆ salt from thermal decomposition. However, the function of VC on SEI can be observed via impedance and electron spectroscopy for chemical analysis (ESCA). These results clearly show VC-induced SEI comprises polymeric species and is sufficiently stable to resist thermal damage. It has been confirmed that VC can suppress the formation of resistive LiF, and thus reduce the interfacial resistance.     

The behaviour of graphite, carbon black, and Li4Ti5O12 in LiBOB-based electrolytes

The film formation behaviour of lithium bis(oxalato)borate (LiBOB), a new electrolyte salt for lithium batteries, on graphite, carbon black and lithium titanate is reported. LiBOB is actively involved in the formation of the solid electrolyte interphase (SEI) at the anode. Part of this formation is an irreversible reductive reaction which takes place at potentials of around 1.75 V vs Li/Li⁺ and contributes to the irreversible capacity of anode materials in the first cycle. Carbon black interacts strongly with LiBOB-based electrolytes, which results in strong film formation and loss of electronic conductivity within the composite electrode. In LiBOB-based electrolytes the electrode kinetics increase in the order: carbon black << fine particulate graphite ~ metal powder, due to decreased film formation of the conductive additive. The influence of various solvents, surfactant additives, and potential impurities was also studied.