Entropy of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Li</mml:mi></mml:mrow></mml:math>intercalation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Li</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">CoO</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:math>

Reynier, Yvan; Graetz, Jason; Swan-Wood, T.; Rez, Peter; Yazami, Rachid; Fultz, B.

doi:10.1103/physrevb.70.174304

Cited by 120 publications

(123 citation statements)

References 17 publications

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“…This is because the first delithiation of LiCoO 2 contains a significant amount of irreversible capacity from the electro-oxidative decomposition of electrolyte species, which makes it difficult to determine the exact value of x at a given nominal capacity. However, the entropy data in Figure 2c can be superimposed upon and match up closely with those of Reynier et al 11 and Thomas and Newman. 26 The only quantitative difference is in the order-disorder transition region, where the tilde shapes from the two other studies are more pronounced, to differing degrees, than that in the present work.…”

Section: Resultssupporting

confidence: 79%

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Cycling-Induced Changes in the Entropy Profiles of Lithium Cobalt Oxide Electrodes

Hudak

Davis

Nagasubramanian

2014

J. Electrochem. Soc.

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Entropy profiles of lithium cobalt oxide (LiCoO 2 ) electrodes were measured at various stages in their cycle life to examine performance degradation and cycling-induced changes, or lack thereof, in thermodynamics. LiCoO 2 electrodes were cycled at C/2 rate in half-cells (vs. lithium anodes) up to 20 cycles or C/5 rate in full cells (vs. MCMB anodes) up to 500 cycles. The electrodes were then subjected to entropy measurements (∂E/∂T, where E is open-circuit potential and T is temperature) in half-cells at regular intervals over the approximate range 0.5 ≤ x ≤ 1 in Li x CoO 2 . Despite significant losses in capacity, the cycling did not result in any change to the overall shape of the entropy profile, indicating retention of the LiCoO 2 structure, lithium insertion mechanism, and thermodynamics. This confirms that cycling-induced performance degradation in LiCoO 2 electrodes is primarily caused by kinetic barriers that increase with cycling. Electrodes cycled at C/5 exhibited a subtle, quantitative, and gradual change in the entropy profile in the narrow potential range of the hexagonal-to-monoclinic phase transition. The observed change is indicative of a decrease in the intralayer lithium ordering that occurs at these potentials, and it demonstrates that a cycling-induced structural disorder accompanies the kinetic degradation mechanisms. Lithium-ion batteries (LIB) are the most common power sources for portable electronic devices and emerging electric vehicles. Fundamental understanding of the electrode reactions and degradation mechanisms of such batteries will help lead to improvements in shelf life and operational life (also known as cycle life), which are necessary for the widespread commercialization of LIB-powered electric vehicles.1 To this end, many in situ characterization methods 2 have been developed to characterize LIB electrode reactions during lithiation or delithiation, including X-ray diffraction, 3 synchrotron X-ray techniques, 4 atomic force microscopy, 5 Raman spectroscopy, 6 and transmission electron microscopy.7 Most of these methods require electrochemical cells that are specially designed and electrode materials that are nanostructured or immobilized in a particular fashion. A simple and often overlooked method of battery characterization is the electrochemical measurement of thermodynamic quantities for individual electrode reactions or full electrochemical cells.8 Thermodynamic studies provide fundamental insight into electrode reactions, which can lead to performance improvements, and quantitative information for thermo-electrochemical models of cells and batteries, which are essential for predicting heat generation and preventing thermal runaway. The electrochemical measurement of thermodynamic quantities can be performed as an in situ diagnostic tool for cells or batteries of any form factor, including commercial cells, or as an ex situ evaluation of composite electrodes before or after cycling.The three major thermodynamic quantities for an electrochemical cell are the Gibbs free e...

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Section: Resultssupporting

confidence: 79%

“…11 The electronic contribution to partial molar entropy was found to be negligible compared to the total observed values. The vibrational contribution from the Li x CoO 2 cathode in Figure 2c), the monotonic increase in dE/dT follows a lattice gas model for random lithium insertion into a host lattice.…”

Section: Resultsmentioning

confidence: 84%

Cycling-Induced Changes in the Entropy Profiles of Lithium Cobalt Oxide Electrodes

Hudak

Davis

Nagasubramanian

2014

J. Electrochem. Soc.

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“…Phonon DOS measurements were performed on samples of Li x CoO 2 for various values of x in the O3 structure, including x = 0.62 and x = 1.0 [233]. Perhaps surprisingly, there was little difference in the DOS or the vibrational entropy of these two compositions.…”

Section: Lithium Insertion In LI X Coomentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

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570

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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“…5(b). Phonon entropy accounts for much of the negative entropy of lithiation because the phonons in Li x CoO 2 have much higher frequen-cies than those of Li metal [82]. On the other hand, the change of phonon entropy with lithium concentration was found to be small.…”

Section: Entropy and Enthalpy Of Lithium Intercalation Into Licoomentioning

confidence: 98%

The Science of Electrode Materials for Lithium Batteries

Fultz¹

2007

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Entropy ofLiintercalation inLixCoO2

Cited by 120 publications

References 17 publications

Cycling-Induced Changes in the Entropy Profiles of Lithium Cobalt Oxide Electrodes

Cycling-Induced Changes in the Entropy Profiles of Lithium Cobalt Oxide Electrodes

Vibrational thermodynamics of materials

The Science of Electrode Materials for Lithium Batteries

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