Quantifying slow diffusion in high capacity, multi-phase electrode materials

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https://doi.org/10.4224/40002048

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Quantifying slow diffusion in high capacity, multi-phase electrode

materials

Early, Sara; Feygin, E.; Ghavidel, M. Z.; Ding, S.; Sendetskyi, O.;

Fleischauer, M. D.

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NRC.CANADA.CA

Quantifying slow diffusion in high capacity,

multi-phase electrode materials

Sara Early,1,2 _{E. Feygin,}1,3 _{M.Z. Ghavidel,}4 _{S. Ding,}1

O. Sendetskyi,4 _{and M.D. Fleischauer}1,4

1 - National Research Council - Nanotechnology Research Centre 2 - Department of Chemistry, University of Waterloo

3 - Department of Physics, University of Waterloo 4 - Department of Physics, University of Alberta

michael.fleischauer@nrc.ca PRiME 2020 (A02-0406)

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Role of Solid-State Diffusion

• _{Batteries store and release energy via phase transitions}

• _{Phase transitions have thermodynamic and kinetic constraints}

• Our goal: estimate diffusion rates within each phase to separate thermodynamic and kinetic effects

• _{Modeling of cell capacity and voltage}

• _{Compare to (non) diffusion-limited experimental data}

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Lithium-Aluminum as example system

Metal alloy negative electrodes

• high capacities at lower costs Four phases of Lithium-Aluminum

• β-LiAl, Li3Al2, Li2−xAl, Li9Al4

• _{Phases with a higher percent}

composition of Lithium are less common

• _{Slow diffusion may be the reason why}

these phases are not regularly observed

Potential / capacity data:

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Experimental Setup - 1D diffusion in to planar sample

Galvanostatic insertion of lithium into aluminum at defined current and temperature; continues until the specified potential is reached.

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Our expectation of 1D diffusion

Lithiation proceeds until all phases have formed in sequence.

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Simulation - fast 1D Fickian diffusion

Electrodes are treated as a series of distinct layers.

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Simulation - slow 1D Fickian diffusion

The overall capacity (and thickness) is significantly reduced by slow diffusion.

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Simulation - 1D Fickian diffusion

• _{Variation of temperature and current density to produce multiple conditions} • _{Compare results (potential, capacity, surface concentration) to ∼ 90}

experimental data sets

• _{13 µm thick, 1.3 cm}2 _{area, 4.5 mg 1100-series aluminum disks}

• _{Cycling at fixed temperature: 30}◦_{C - 150}◦_C

• _{Very low to moderate current densities}

µA 40 160 320 640 1280

C rate∗ C/280 C/70 C/35 C/18 C/9

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Computational Process - Flux

Flux Between =⇒ Layer / Surface =⇒ Potential

Layers Concentration

J → Flux w

[flux into electrode] t → Time

x → Displacement

Capacity T → Temperature

C → Concentration D → Diffusion φ →Potential

• Fick’s 1st _{Law of Diffusion}

• Nernst-Planck

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Computational Process - Flux

Fick’s 1st _Law J(x , t) = −D(C, T ) ∗ ∂C(x ,t)_∂t Nernst-Planck J(x , t) = −D(C, T ) ∗ ∂C(x ,t) ∂t + zF RTC(x , t) ∂φ ∂x 10

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Computational Process - Concentration

J → Flux w

x → Displacement Capacity T → Temperature C → Concentration D → Diffusion φ →Potential Integration of Flux

• Cartesian or Spherical Coordinates

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Computational Process - Potential

J → Flux w

x → Displacement Capacity T → Temperature C → Concentration D → Diffusion φ →Potential • Nernst Equation 12

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Computational Process - Potential

Nernst Equation E = E0+ RT_nF ln 1−xi xi

where xi = _{max phase concentration}surface concentration

E₀˜_βLiAl ∼ 0.35 V E₀˜ Li3Al2 ∼ 0.15 V E₀˜ Li2−x Al ∼ 0.05 V E₀˜ Li9Al4 ∼ 0.005 V 13

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Computational Process

J → Flux w

x → Displacement

Capacity T → Temperature

C → Concentration D → Diffusion φ →Potential

• Plot potential as a function of capacity

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Results - 320 µA (C/35), 135

◦

C

The measured plateau is flatter than predicted by the Nernst equation.

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Results - 320 µA (C/35)

The measured ‘plateau’ in fact has features. Diffusion pathways may be changing.

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Results - 640 µA (C/18)

Higher rates exaggerate transitions between pathways (e.g. bulk, pores, grain

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Results - 160 µA (C/70)

Changes in potential may be very temperature-dependant when diffusion-limited.

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Conclusions and Next steps

• _{Diffusion-limited potential-capacity data has many unexpected features.}

The Nernst equation may not be sufficient.

• Our nominally planar samples have some porosity, and grain boundaries. We need improved model samples.

• _{Single crystal planar foil, spheres}

• _{Compare model results to diffusion rates estimated with alternate techniques.} • _{Verify model by quantifying diffusion in other material systems.}