Mikrostrukturrekonstruktion und FEM-Mikrostrukturmodelle für Lithium-Ionen Batterien

Transcription

1 Modellbildung elektrochemischer Systeme Mikrostrukturrekonstruktion und FEM-Mikrostrukturmodelle für Lithium-Ionen Batterien André Weber - IAM-WET Adenauerring 20b, Geb (FZU), Raum 314 phone: 0721/ , fax: 0721/ andre.weber@kit.edu KIT Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft

2 Microstructure Reconstruction and Parameter Evaluation electrolyte Li + 1 Charge transfer at the interface between active material and electrolyte Li electrochemically active surface active material 2 Solid state diffusion into particles particle size carbon black e - 3 ionic and electronic transport in porous structure tortuosity of transport paths Quantification of a cathode microstructure FIB tomography using new preparation method microstructure parameter determination Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 2,

3 LiFePO 4 Cathode cathode composition LiFePO 4 (70% by weight) carbon black (24% by weight) PVDF binder (6% by weight) Slurry (mixed with NMP) was coated on aluminum current collector Z / Ω LiFePO 4 /Li cell (SOC 100%, T=20 C) Z / Ω Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 3,

4 FIB/SEM Reconstruction of LiB Electrodes Zeiss 1540XB CrossBeam SEM imaging FIB milling 200 consecutive images (24 million voxels) slice to slice spacing: 25nm current collector infiltrated cathode silicon resin 5 µm [1] B. Rüger, J. Joos, T. Carraro, A. Weber and E. Ivers-Tiffée, ECS Trans., 25 (2), p (2009) [2] J. Joos, T. Carraro, A. Weber and E. Ivers-Tiffée, J. Power Sources (2010), in press 15 µm Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 4,

5 Sample Preparation No infiltration Common infiltration (epoxy resin) New infiltration (silicon resin) LiFePO 4 carbon black porosity 1 µm LiFePO 4 carbon black & porosity 1 µm LiFePO 4 carbon black porosity 1 µm BUT: more complex preparation caused by elastic nature of the silicon resin Schematic assembly Finished sample porous electrode on current collector epoxy resin silicon resin M. Ender, J. Joos, T. Carraro and E. Ivers-Tiffée, Electrochemistry Communications 13, pp (2011). Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 5,

6 Image Preprocessing SEM raw frame raw image adjusted image 1 cropping & Alignment adjustment of relative positions 2 resampling change of pixel size ( nm) 3 4 stretching of histogram noise filtering y x Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 6,

7 Image Preprocessing SEM raw frame raw image adjusted image 1 cropping & Alignment adjustment of relative positions 2 resampling change of pixel size ( nm) 3 4 stretching of histogram noise filtering y x Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 7,

8 Segmentation Threshold Calculation histogram of whole reconstructed volume probability density functions p(t) p pore p CB p LiFePO grayscale value t different algorithms available when a minimum is present Minimum algorithm Otsu s algorithm fitting of normal distributions to grayscale values Maximum likelihood: calculation of probabilities P i, that a grayscale value t is caused by material of phase i Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 8,

9 Segmentation Threshold Calculation histogram of whole reconstructed volume probability density functions p(t) p CB grayscale value t p pore t 1 t 2 p LiFePO4 fitting of normal distributions to grayscale values Maximum likelihood: calculation of probabilities P i, that a grayscale value t is caused by material of phase i probability P i (t) probabilities P i P CB P pore P LiFePO4 t 1 t grayscale value t Best threshold: Value of t where the adjacent phases have the same probability: P i (t)=p j (t) t 1 = 61, t 2 = 138 Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 9,

10 Segmentation Improved Threshold Calculation Local Threshold Technique What if luminosity and contrast are not constant over the whole volume? Partitioning of the volume into = 192 cubes (consisting of voxel each) y x z p(t) entire volume indicated cube Threshold determination for all cubes t t 2 local threshold z 3 x a 0 a 1 a 2 a 3 t t Fitting of a linear function to get a local threshold Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 10,

11 Filtering of Reconstruction Data comparison of volume fractions Global threshold [1] Local threshold Local threshold (filtered) LiFePO Carbon black Pores Small corrections due to filtering three demands can be made: [1] M. Ender, J. Joos, T. Carraro and E. Ivers-Tiffée, Electrochemistry Communications, 13 (2), p. 166 (2011). exampel: island removal filter pore volume is completely connected active material has a minimum particle size (particles with less than 5 voxel are noise) No floating particles (active material and carbon black are connected) Application on pores & carbon black Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 11,

12 Spatial Material Distribution 3D material distribution 24 Million Voxel! 2 µm carbon black LiFePO 4 representative volume element??? (RVE) porosity (semi transparent) µm 3 parameter determination for quantification of the electrode s microstructure electrochemically active surface A active particle size d LiFePO4 tortuosity of transport paths τ pore, CB, Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 12,

13 Representative Volume Element full height (15 µm) full base area (5 5 µm 2 ) volume fraction volume fraction volume / µm volume / µm 3 pores carbon black LiFePO 4 Half base area leads to a difference of up to 3.5% in the volume fractions Half height leads to a difference of up to 15.5% in the volume fractions Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 13,

14 Necessary Volume Element - Loss and Benefit Reduction of the volume Half of the base area Half of the number of frames Half of the milling time Half of the base area leads to a change in the volume fractions of up to 3.5% Calculation of the microstructure parameters from the whole reconstructed volume Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 14,

15 Tortuosity of Transport Paths definition of tortuosity σ eff examples x = σi τ x=0.5 τ=1 l x=0.5 τ= d d τ tortuosity x volume fraction x=0.5 τ=1.12 x=? τ=? l? l d d ( σ φ) = 0 bulk Φ / V Φ=1V Φ=0V Transport equation solved by own parallel FEM software [1] results for τ porosity 1.31 carbon black 5.52 LiFePO 4 + carbon black 3.16 calculation by FEM simulation [1] J. Joos, B. Rüger, T. Carraro, A. Weber and E. Ivers-Tiffée, ECS Trans., 28 (11), p. 81 (2010). Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 15,

16 Electrochemically Active Surface Marching cube algorithm The method active LiFePO LiFePO possibilities 15 fundamental cases 1 Marching through the volume and selecting cubes of eight voxel each Calculation of the electrochemically active surface becomes 2 now possible: A assigning the vertices to material or pore 3 selecting the corresponding case from a lookup table (15 fundamental cases) 4CBcounting Apore of the = frequency 3.56 of occurrence for each case and multiplying it with the corresponding surface 1 = A µm 4 2 ( ) 1 A + A specific surface / µm -1 LiFePO carbon black porosity Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 16,

17 Other Reconstructions Tomography of a complete Cell 65 mm 18 mm Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 17,

18 Reconstruction ~350 µm Quelle: Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 18,

19 Microstructure Parameters graphite anode (Sony) glas fibre separator (EL-Cell) LiFePO 4 cathode (Sony) x Graphit = x Pore = a Graphit = µm -1 a Pore = µm -1 d Graphit = 2.31 µm d Pore = 1.10 µm τ Pore = 2.2 (Bruggemann) x Glasfaser = x Pore = a Pore = µm -1 d Glasfaser = 0.78 µm d Pore = 2.41 µm τ Pore = 1.16 x LiFePO4 = x carbon = x Pore = a LiFePO4 = µm -1 a carbon = µm -1 a Pore = µm -1 d LiFePO4 = 205 nm d agglomerat = 1.15 µm d carbon = 112 nm d Pore = 125 nm τ Pore = 1.9 Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 19,

20 Homogenized Model Graphite Anode model geometry simulations and measurements of anode y x z measurement simulation r z ε cat τ cat a spec ε sep τ sep D cell voltage U / V C 0.5 C OCV 1C C x in Li x C 6 The homogenized model parameterized with geometrical parameters from reconstruction is able to describe the principle electrode behavior. Further improvements:, Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 20,

21 Model Extension Two Particle Diameters model geometry influence on charge/discharge curves,!," µm 1µm & 10µm (1:1 by vol.) r z cell voltage U / V C OCV 1C 0.5 C 2C 0.1 x cat,1 a spec,1 1 x cat,2 a spec, x in Li x C 6 coupling of two particle diameters leads to a smoothing of the charge/discharge curves real particle size distributions, arbitrary particle shapes and dual-scale electrode structures require 3D space-resolved models Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 21,

22 Gradierte Elektroden Prozessbedingter Gradient: Gezielter Gradient: Nasser Film Fall 1 Fall 2 Zweischichtiger Elektrodenaufbau Sedimentierung Sedimentierung Trocknung Trocknung Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 22,

23 Erweiterung Gradierte Elektroden / 2-Schichtaufbau r z ε cat τ cat a spec ε cat τ cat a spec Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 23,

24 Gradierte Elektroden / 2-Schichtaufbau Simulation Elektrodenpotential / V LiFePO 4 Kathode 1C Entladung Gradiert 1 Normal Gradiert 2 20 µm 20 µm r = 4.1µm ε = 0.35 r = 5µm ε = 0.3 r = 3µm ε = 0.4 r = 4.1µm ε = 0.35 r = 3µm ε = 0.4 r = 5µm ε = C/C theo Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 24,

25 Blendelektroden Kokam 2 µm Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 25,

26 Blendelektroden Kokam Co Al Ni C 2 µm Kathode ist ein Blend aus: LiCoO2 LiNi0.8Co0.18Al0.02O2 Graphit/Kohlenstoff Leitruß Kombination verschiedener Materialien um möglichst gutes Gesamtverhalten zu erzielen. Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 26,

27 Erweiterung Blendelektroden,!," r z Φ OCV1 LiMn 2 O 4 Φ OCV2 ε cat τ cat a spec ε cat τ cat a spec LiNi x Co y Al z O 2 Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 27,

28 Blendelektroden LiMn 2 O 4 / LiNi x Co y Al 1-x-y O 2 Simulation 4.2 Entladung mit 1C LiMn 2 O 4 NCA Blend (1:1) Φ / V Q / mah g -1 Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 28,

29 Grenzen homogenisierter Modelle? LiFePO 4 Kathode (kommerziell, AJ02) Zweiskaliger Aufbau? 2µm 3D Simulationen Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 29,

30 Entwicklung des Mikrostrukturmodells Was soll modelliert werden? Lade-/EntladeVorgänge in der Li-Batterie: Ionentransport im Elektrolyten Ladungstransfer Elektrolyt/Aktivmaterial Li-Diffusion im Festkörper (Phasenseparation) Elektronischer Transport in der Elektroden Anforderungen Zeitabhängige Simulation Beliebige Geometrien (real und künstlich) Einfache Variation der Materialparameter Verschiedene Randbedingungen (Lade-/Entladeraten, Relaxation, CV???) Konstante Li- Konzentration Ladungstransfer (Butler-Vollmer) Kontaktwiderstand Laststrom Diffusion Diffusion Elektr. Leitung Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 30,

31 Graphit Ladevorgang Simulierter Ladevorgang (1C und 5C) E / V OCV 5C 1C Li-Konzentration Austauschstrom (t =1200 =3600 s) C cat / mol m -3 j ct / A m x in Li x C 6 Entladerate: 1C D El = 10-6 m/s 2 c max,cat = mol/m D(c/c max ) k ct = m/s 10-9 cat Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 31,

32 Mikrostrukturmodelle Ansätze 3D Modell (Graphitanode) C/10 Ladevorgang (t = 0 8,9 h) Mikrostruktur - Rekonstruktion % 1 Parameterbestimmung homogenisiertes Modell 3D-Modell % 0 makroskopisches Verhalten mikroskopisches Verhalten µm 3 Lithiumverteilung im Aktivmaterial 2.5 Tage Rechenzeit Quelle: IWE Vorlesung MES 09 - Mikrostrukturrekonstruktion LiB - Zellen.pptx, Folie: 32,