${}^{13}\mathrm{C}$ NMR study of the electronic structure of lithiated graphite

The change in the electronic structure of graphite during electrochemical lithiation was investigated using solid-state NMR. The ${}^{13}\mathrm{C}$ NMR peak positions for the lithiated graphite compounds stages 3L - 1 were assigned. The dense stage ${\mathrm{LiC}}_{12}$ and ${\mathrm{LiC}}_6$ compounds were shown via ${}^{13}\mathrm{C}$ and ${}^7\mathrm{Li}$ to be metallic in nature, with Korringa relaxation being the dominant relaxation mechanism for both nuclei. The ${}^7\mathrm{Li}$ NMR shifts in graphite can be described by a direct Fermi-contact Knight shift, while the ${}^{13}\mathrm{C}$ NMR shifts can be described by the spin-dipolar Knight shift and isotropic Knight shift. The isotropic ${}^{13}\mathrm{C}$ NMR Knight shift of ${\mathrm{LiC}}_6$ was smaller than expected for a Knight shift caused purely by the core polarization of $1s$ orbitals. This showed that there must be a contribution of $2s$ orbitals at the Fermi level. The density of states at the Fermi level $\rho \left(E_F\right)$ for ${\mathrm{LiC}}_6$ was estimated and the values, which are dependent on the Stoner enhancement factor $\alpha$, agree reasonably well with those found in literature.

Figure 1

(a) When the magnetic field, $B_0=0$, the energy levels of the spin-up and spin-down electrons are equal and there is no net population difference. (b) In the presence of a magnetic field, the energy of spin-up ($m_s=+1/2$) electrons is increased and lowered for spin-down ($m_s=-1/2$) electrons. Since the Fermi level must be equal for both spins, some spin-up electrons will flip leading to a net spin-down population, which results in an increase of the magnetic field at the nucleus due to the negative gyromagnetic ratio of an electron. Here the straight arrows indicate the direction of the magnetic moment. The curved arrow indicates the direction of electron flow on application of the magnetic field.

Figure 2

The core polarization effect depicted for a system such as lithiated graphite where the conduction band lies in the $2p_z$ orbital. (a) When $B_0=0$, there is no net spin density at the nucleus. (b) In the presence of a magnetic field, the magnetic moment of the spin-down electrons in the $p_z$ orbital will align with the magnetic field. The spatial extent of the spin-down electrons in the $1s$ orbitals will then expand slightly due to the exchange interaction. This results in a net spin-up density at the nucleus generating a negative magnetic moment, resulting in a smaller local magnetic field at the nucleus. Here up and down refer to the spin of the electron, which has a negative gyromagnetic ratio.

Figure 3

(a) Potential profile as function of capacity $x$, in ${\mathrm{Li}}_{\mathrm{x}}{\mathrm{C}}_6$. The irreversible capacity due to SEI formation has been accounted for (see main text). (b) Differential capacity plot as a function of voltage. The points in a and b represent the potentials at which cells were stopped for ex-situ XRD and NMR characterization. Square “points” represent samples that were only measured in 1.3 mm rotors using MAS NMR whilst circles represent those that were measured in a 4-mm rotor with VT, static and MAS NMR spectroscopy.

Figure 4

(a) ${}^7\mathrm{Li}$ and (b) ${}^{13}\mathrm{C}$ MAS NMR spectra of the ${\mathrm{LiC}}_6, {\mathrm{LiC}}_{12}$, and ${\mathrm{LiC}}_{31}\mathrm{a}$ compounds. Samples were measured in a 4-mm rotor with a MAS frequency of 10 kHz and a recycle delay that was at least five times $T_1$. Intensities are normalized by sample mass.

Figure 5

Static ${}^{13}\mathrm{C}$ CPMG NMR spectra of the pure Hitachi Mage 3 graphite.

Figure 6

The ${}^{13}\mathrm{C}$ NMR $T_{1}s$ multiplied by temperature T as a function of temperature for the three lithiated graphite compounds.

Figure 7

Experimental static ${}^{13}\mathrm{C}$ NMR powder pattern (blue trace) and simulated spectrum (red trace) for ${\mathrm{LiC}}_6$. The relaxation rate $1/T_1$ as a function of chemical shift (black squares) is overlayed on top of the spectrum.

Figure 8

Experimental static ${}^{13}\mathrm{C}$ NMR powder pattern (blue trace) and simulated spectrum (red trace) for (a) ${\mathrm{LiC}}_{12}$ and (b) ${\mathrm{LiC}}_{31}\mathrm{a}$.

Figure 9

(a) ${}^{13}\mathrm{C}$ and (b) ${}^7\mathrm{Li}$ NMR of the dilute stage samples ${\mathrm{LiC}}_{24}, {\mathrm{LiC}}_{31}$, and ${\mathrm{LiC}}_{43}$ acquired using a CPMG pulse sequence in a 1.3-mm rotor with a MAS of 50 kHz. The intensity of the ${}^{13}\mathrm{C}$ NMR peaks were normalized so that the peak heights were the same.