Higher Stage Graphite Intercalation Compounds Research Articles

Out-of-Plane Electron Transport in Graphite Intercalation Compounds with Applications in Battery Anodes

Graphite intercalation compounds (GICs) are commonly used as anode materials for alkali metal-ion batteries, such as Li-ion and K-ion batteries. Although typically prepared as a low-stage intercalation compound (with a high concentration of the intercalating metal), over several electrochemical cycles, the distribution of intercalate within the graphite sample is expected to be non-uniform with domains of high-stage regions where the intercalant fraction is low [1]. The mechanism of interlayer electron transport in GICs strongly depends on the intercalation staging and temperature, and is expected to vary over the lifetime of a battery.High-stage GICs and highly oriented pyrolytic graphite (HOPG), which is the upper limit of infinite-stage GIC, have an out-of-plane electrical conductivity that exponentially increases with temperature, whereas low-stage GICs have a conductivity that decreases as a function of temperature [2, 3, 4]. Although out-of-plane electron transport in low-stage GICs can be described by a metallic conduction model, the mechanism of out-of-plane electron transport in HOPG and high-stage GICs is a hitherto unresolved problem [5]. Out-of-plane electrical conductivity for HOPG and high-stage GICs increases exponentially with temperature, which cannot be described by metallic conduction, nor by conventional impurity or defect hopping mechanisms [6].We propose a new mechanism of electron transport that takes place in HOPG and high-stage GICs at temperatures relevant to battery operation. Electrons are transferred between graphite and intercalant layers through tunneling that is enhanced by large amplitude out-of-plane phonon modes in graphite layers. Due to weak interlayer interactions in adjacent graphite layers, GICs can accommodate large amplitude phonon modes in the out-of-plane direction that locally enhance the interlayer electron tunneling probability. The tunneling enhancement is temperature dependent, and exponentially depends on the population of out-of-plane phonon modes excited at a given temperature. The expression for the conductivity 𝜎 for the phonon amplitude-driven tunneling mechanism as a function of temperature T is shown in Eq. 1; the exponential dependence of conductivity with temperature qualitatively agrees with experimental observations in HOPG and high-stage GICs. On a quantitative level, we also observe from Fig.1 that the theory agrees with experimental values for out-of-plane conductivity in HOPG.The phonon amplitude-driven tunneling mechanism of electron transport is relevant in describing the kinetic over-potential in batteries that employ layered materials as anodes in ambient temperature operating conditions, and optimally sizing the anode accounting for both electron transport and ion diffusion rates.

C-Axis Conduction in Lamellar Solids: High Stage Graphite Intercalation Compounds

We have examined the c axis electrical resistivity ρC of high stage (5 ≤ s ≤ 12) GaCl3 intercalated graphite from 4.2 ≤ T ≤ 295 K. All materials are highly anisotropic. There is a progressive change from “metallic” behaviour with dρc/dT > 0 over the full T range to semiconductor-like (dρc/dT < 0) as s rises. It is shown that interstratification and intercalate layer crystallization strongly influence ρC (T).

Orientational ordering of a cesium monolayer on graphite.

Orientational ordering has been observed by low-energy electron diffraction for structures close to (2\ifmmode\times\else\texttimes\fi{}2) in an overlayer of cesium absorbed on the graphite (0001) surface at liquid-nitrogen temperature. The relative orientation of the Cs overlayer to the graphite substrate varies from about 5\ifmmode^\circ\else\textdegree\fi{} to 0\ifmmode^\circ\else\textdegree\fi{} and the lattice misfit changes from about 27.6% to 0% as the coverage of Cs on the graphite surface is increased. For the same lattice-parameter misfit the rotation angles in the structure are almost half of those in the rare-gas physisorbed systems on graphite (0001), the Na chemisorbed on Ru(001), and the Cs planar layer intercalated in the high-stage graphite intercalation compounds. The (2\ifmmode\times\else\texttimes\fi{}2) family of structures for the Cs-chemisorption-on-graphite system is consistent with the Novaco-McTague theory of orientational ordering, but there is a stronger bond strength between adatoms in the Cs/C overlayer than in the above other three systems.

High stage graphite intercalation compounds of rare earth metals and alkali-metal vapor-transport technique

We present a new technique to synthesize high stage graphite intercalation compounds of low vapor-pressure elements such as rare earth metals (RE). The technique consists of two processes, (1) the co-intercalation of alkali-metal (AM) and RE, in which the stage is mainly controlled by vapor pressure of AM, and (2) the following de-intercalation of AM from the compound, in which the preferential removal of AM results in a high stage RE_GIC. We first obtained stages 2, 3 and 4 Eu- and stage 2 Sm-GICs. However an intercalant layer is composed of a mixture of RE and residual AM; i.e. the in-plane composition x in Eu xK 1−x-GIC was less than 0.75. The temperature dependence of magnetization of stage 3 Eu 0.75K 0.25-GIC shows two anomalies at T c1 = 30 K and T c2 = 80 K. While at T > T c2 it obeys the Curie-Weiss law with ⊗ = −15K, the magnetization process at T < T c1 shows remarkable metamagnetism which resembles that of stage 1 EuC 6. The magnetic anomaly at T c2 is unique to high stage Eu compounds.

Nuclear magnetic resonance in higher-stage graphite intercalation compounds.

The theoretical results of $^{13}\mathrm{C}$ nuclear magnetic resonance shifts of higher-stage graphite intercalation compounds (GIC's) are presented. In this calculation a new formalism for calculating the chemical shifts and Knight shifts for a metallic energy-band system is proposed. In this formalism the overall feature of graphite \ensuremath{\pi} bands and \ensuremath{\sigma} bands which are mixed due to the inhomogeneous c-axis charge distribution is taken into account. The calculated results show several resonant lines with different values of scalar and dipolar Knight shifts which can be assigned to the inequivalent carbon atoms due to A-B stacking and inhomogeneous c-axis charge distribution of the graphite layers. The theoretical results of the NMR shifts on the basis of the first-principles band calculations of the higher-stage GIC's are in good agreement with the observed ones.

Electronic structures of higher stage graphite intercalation compounds

Self-consistent non-empirical calculations of the band structures of higher stage graphite intercalation compounds up to the 6-th stage were performed by the local density functional formalism. It was clarified that the charge distribution along the c-axis is extremely inhomogeneous, and that the orbital contribution to magnetic susceptibility, which is paramagnetic, reaches a maximum at about stage 6 in the case of f=1.0. Finally, the stage dependence of the total energy was determined.

Band Structures and Charge Distributions along the c-Axis of Higher Stage Graphite Intercalation Compounds

Self-consistent non-empirical calculations of band structures of higher stage graphite intercalation compounds have been performed up to the 6-th stage by using the numerical-basis-set LCAO method. The calculations are carried out for a thin film of n contiguous graphite layers bounded by two ionized intercalant layers. From these calculations, the charge distribution along the c -axis and the stage dependence of the Fermi-level density of states are determined. It is clarified that the c -axis charge distribution is extremely inhomogeneous and that the effect of the σ bands is essentially important in determining the charge distribution along the c -axis. The measured stage dependence of the orbital contribution in the total magnetic susceptibility of alkali-metal compounds is discussed on the basis of the calculated results of the c -axis charge distribution.

Relaxed incommensurate structure of the intercalant layer in higher-stage graphite intercalation compounds

Relaxed incommensurate structure of the intercalant layer in higher-stage graphite intercalation compounds

Self-consistent band structures of higher stage graphite intercalation compounds

Self-consistent non-empirical band structures of third and fourth stage graphite intercalation compounds have been calculated by using the numerical-basis-set LCAO method within the local density functional formalism. The calculations are carried out for a thin film model consisting of n contiguous graphite layers bounded by two partially ionized intercalant layers. The calculated band structures show that most of electrons transferred from the intercalant layers occupy the states in the lowest two conduction π bands mainly localized on the bounding graphite layers. The low-energy optical transitions of higher stage GICs are discussed in terms of the obtained band structures.

High-pressure x-ray and Raman studies of rubidium and cesium graphite intercalation compounds

Systematic pressure-dependence studies have been performed on $M{\mathrm{C}}_{8}$ and $M{\mathrm{C}}_{12n}$ ($M=\mathrm{R}\mathrm{b},\phantom{\rule{0ex}{0ex}}\mathrm{C}\mathrm{s}$ and $n=2, 3, 4$) graphite intercalation compounds. Pressure-induced staging phase transitions similar to that which had been previously reported for K${\mathrm{C}}_{24}$ by Clarke et al. were found in these high-stage graphite intercalation compounds ($n\ensuremath{\ge}2$). The $\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{\perp}c$ x-ray experiments revealed the formation of a 2\ifmmode\times\else\texttimes\fi{}2 superlattice under hydrostatic pressure from the disordered intercalant layers at ambient conditions. The Raman spectra from $\mathrm{Rb}{\mathrm{C}}_{12n}$ ($n=2, 3, 4$) gave clear evidence for the pressure-induced staging transition by showing a change in the Raman intensities of the bounding (1605 ${\mathrm{cm}}^{\ensuremath{-}1}$) and interior (1582 ${\mathrm{cm}}^{\ensuremath{-}1}$) ${E}_{2g}$-like phonon peaks with pressure. In addition, the compressibilities ${k}_{d}$ of Cs${\mathrm{C}}_{8}$ and Rb${\mathrm{C}}_{8}$ were measured as (1.56\ifmmode\pm\else\textpm\fi{}0.05) and (2.42\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$/dyn, respectively. The compressibility results indicate that the interlayer-coupling strength varies drastically among alkali-graphite intercalation compounds. The pressure-dependent Raman spectra of Rb${\mathrm{C}}_{8}$ showed an appreciable change in the Fano resonance shape at \ensuremath{\sim} 580 ${\mathrm{cm}}^{\ensuremath{-}1}$ with pressure. The mode-Gr\uneisen constant ${\ensuremath{\gamma}}_{0\ensuremath{\perp}}$ of pristine graphite for the for the interlayer mode ${E}_{2g}$ was found to be 1.66\ifmmode\pm\else\textpm\fi{}0.13. The rates of Raman frequency shifts with respect to pressure, $\frac{\ensuremath{\partial}{\ensuremath{\omega}}_{0}}{\ensuremath{\partial}P}$, were measured to be (0.70\ifmmode\pm\else\textpm\fi{}0.12), (0.51\ifmmode\pm\else\textpm\fi{}0.09), (0.44\ifmmode\pm\else\textpm\fi{}0.05), (0.54\ifmmode\pm\else\textpm\fi{}0.08) ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{kbar}}^{\ensuremath{-}1}$ for the bounding modes of Cs${\mathrm{C}}_{24}$ and $\mathrm{Rb}{\mathrm{C}}_{12n}$ ($n=2, 3, 4$), and (0.78\ifmmode\pm\else\textpm\fi{}0.08), (0.32\ifmmode\pm\else\textpm\fi{}0.12) ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{kbar}}^{\ensuremath{-}1}$ for the interior modes of $\mathrm{Rb}{\mathrm{C}}_{12n}$ ($n=3, 4$), respectively.

Electrical resistivity of higher stage graphite intercalation compounds

Remarkable features of observed resistivity in higher stage graphite intercalation compounds are discussed by the theory recently developed by Inoshita and Kamimura. It is shown that the existence of two inequivalent electron pockets of cylindrical Fermi surface gives rise to the T 2-like temperature dependence in the resistivity. The calculated room temperature resistivity is 8.6 × 10 −6Ω cm for C 24K which is of the order of copper, and it can be ascribed to high Fermi velocity. Finally, it is suggested that the existence of a minimum in the observed resistivity-versus-stage curve is due to a variation of the charge distribution from layer to layer.

Theory of phonon-limited resistivity and electron-phonon interaction in higher-stage graphite intercalation compounds

The first principle calculations of the basal-plane resistivity and of the electron-phonon coupling constant are presented for higher stage graphite intercalation compounds using a pseudopotential method. On account of the intra- and inter-pocket scatterings in two inequivalent cylindrical Fermi surfaces, the temperature dependence of total resistivity deviates from the ordinary T linear law and follows the T 2 law in the high temperature region, which is consistent with experimental results. It is shown that the present theory also explains other observed characteristics of resistivity such as the existence of a minimum in the resistivity vs. stage curve, and higher mobility compared with those of ordinary metals. Finally, the electron-phonon coupling constant is calculated as a first step towards understanding the mechanism of superconductivity in first stage compounds. It is shown that the electron-phonon coupling constant is fairly large even for second stage compounds and it is comparable with those of weak coupling superconducting metals.