Experimental phase diagram of lithium-intercalated graphite

Woo, K. C.; Mertwoy, H.; Fischer, J. E.; Kamitakahara, W. A.; Robinson, Douglas S.

doi:10.1103/physrevb.27.7831

Cited by 53 publications

(26 citation statements)

References 15 publications

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“…Comparing these diagrams to that of the near-room temperature LiC 6 system [21,72,90], we see again that the model cannot capture the details of the low average filling (high stage number) phases. Also, neither model captures the details of the top line of the phase diagram including the high-temperature stable stage 2 region [72,91,92], although the case with Ω c = 0 more closely approximates the temperature values at which order disappears (top line of the diagram). Although neither model accurately captures the phase diagram, the result highlights the value of free energy based models as starting points to make predictive temperature-dependent models to capture electrochemical behavior in non-isothermal systems [93].…”

Section: Phase Diagrammentioning

confidence: 99%

Intercalation Kinetics in Multiphase-Layered Materials

2017

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Many intercalation compounds possess layered structures or inter-penetrating lattices that enable phase separation into three or more stable phases, or "stages," driven by competing intra-layer and inter-layer forces. While these structures are often well characterized in equilibrium, their effects on intercalation kinetics and transport far from equilibrium are typically neglected or approximated by empirical solid solution models. Here, we formulate a general phase-field model with thermodynamically consistent reaction kinetics and cooperative transport to capture the dynamics of intercalation in layered materials. As an important case for Li-ion batteries, we model single particles of lithium intercalated graphite as having a periodic two-layer structure with three stable phases, corresponding to zero, one, or two layers full of lithium. The electrochemical intercalation reaction is described by a generalized Butler-Volmer equation with thermodynamic factors to account for the flexible structure of the graphene planes. The model naturally captures the "voltage staircase" discharge curves as a result of staging dynamics with internal "checkerboard" domains, which cannot be described by solid-solution models based on Fickian diffusion. On the other hand, the two-layer model is computationally expensive and excludes low-density stable phases with longer-range periodicity, so we also present a reduced model for graphite, which captures the high-density stages while fitting the low-density voltage profile as an effective solid solution. The two models illustrate the general tradeoff between the explicit modeling of periodic layers or lattices and the needs for computational efficiency and accurate fitting of experimental data.

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Section: Phase Diagrammentioning

confidence: 99%

Intercalation Kinetics in Multiphase-Layered Materials

2017

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“…At higher rates, when the entire edge plane is assumed to be covered with a pure phase, only the diffusion through the solid-solution of each phase governs the kinetics. But both the diffusion coefficient and the solid-solution miscibility regime depend on temperature, as shown in the binary phase diagram of the lithium-graphite system [19]. Therefore, when the temperature is decreased the flux per area J = -D dc/dr is reduced significantly due to a decrease in the permissible Δc for the miscibility regime and a lower diffusion coefficient.…”

Section: Proposed Diffusion Pathwaymentioning

confidence: 99%

Shrinking annuli mechanism and stage-dependent rate capability of thin-layer graphite electrodes for lithium-ion batteries

Heß

Novák

2013

Electrochimica Acta

123

118

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The kinetic performance of graphite particles is difficult to deconvolute from half-cell experiments, where the influences of the working electrode porosity and the counter electrode contribute nonlinearly to the electrochemical response. Therefore, thin-layer electrodes of circa 1 µm thickness were prepared with standard, highly crystalline graphite particles to evaluate their rate capability. The performance was evaluated based on the different stage transitions. We found that the transitions towards the dense stages 1 and 2 with LiC 6 in-plane density are one of the main rate limitations for charge and discharge. But surprisingly, the transitions towards the dilute stages 2L, 3L, 4L, and 1L progress very fast and can even compensate for the initial diffusion limitations of the dense stage transitions during discharge. We show the existence of a substantial difference between the diffusion coefficients of the liquid-like stages and the dense stages. We also demonstrate that graphite can be charged at a rate of ~6C (10 min) and discharged at 600C (6 s) while maintaining 80 % of the total specific charge for particles of 3.3 µm median diameter. Based on these findings, we propose a shrinking annuli mechanism which describes the propagation of the different stages in the particle at medium and high rates.Besides the limited applicable overpotential during charge, this mechanism can explain the long-known but as yet unexplained asymmetry between the charge and discharge rate performance of lithium intercalation in graphite.

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“…The intercalation of lithium atoms into graphite and the structural feature have been well investigated so far. [15][16][17][18] Lithium atoms form a superstructure in interlayers of graphite, and the stacking of graphene and lithium layers has periodicity, which is called staging. The staging phenomenon is characterized by a periodic sequence of intercalant layers, and the stage number n refers to the number of host layers separating two intercalant layers.…”

Section: A Diffusion Of LI Atoms In Licmentioning

confidence: 99%

First-principles approach to chemical diffusion of lithium atoms in a graphite intercalation compound

et al. 2008

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We evaluate mean frequencies for atomic jumps in a crystal from first principles based on transition state theory, taking lithium diffusion by the interstitial and vacancy mechanisms in LiC 6 as a model case. The mean jump frequencies are quantitatively evaluated from the potential barriers and the phonon frequencies for both initial and saddle-point states of the jumps under the harmonic approximation. The lattice vibrations are treated within quantum statistics, not using the conventional treatment by Vineyard corresponding to the classical limit, and the discrepancy between the two treatments is quantitatively discussed. The apparent activation energies and the vibrational prefactors of the mean jump frequencies essentially depend on temperature, unlike in the case of the classical approximation. The discrepancies of the activation energies correspond to the changes in zero-point vibrational energy at 0 K, and there remains the effect even at 1000 K. With regard to the vibrational prefactors, the classical approximation extremely overestimates the prefactors at low temperatures while the discrepancies rapidly decrease with increasing temperature, e.g., by 30% at room temperature and by 5% at 1000 K. The calculated chemical diffusion coefficients of lithium atoms by the interstitial and vacancy mechanisms are 1 ϫ 10 −11 and 1 ϫ 10 −10 cm 2 / s, respectively.

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Experimental phase diagram of lithium-intercalated graphite

Cited by 53 publications

References 15 publications

Intercalation Kinetics in Multiphase-Layered Materials

Intercalation Kinetics in Multiphase-Layered Materials

Shrinking annuli mechanism and stage-dependent rate capability of thin-layer graphite electrodes for lithium-ion batteries

First-principles approach to chemical diffusion of lithium atoms in a graphite intercalation compound

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