Formation Dynamics of Potassium-Based Graphite Intercalation Compounds: An Ab Initio Study

This paper is a contribution to the Physical Review Applied collection in memory of Mildred S. Dresselhaus.

We use ab initio molecular dynamics simulations to study the microscopic dynamics of potassium intercalation in graphite. Upon adsorbing on graphite from the vapor phase, K atoms transfer their valence charge to the substrate. K atoms adsorbed on the surface diffuse rapidly along the graphene basal plane and eventually enter the interlayer region following a “$\mathsf{U}$-turn” across the edge, gaining additional energy. This process is promoted at higher coverages associated with higher K pressure, leading to the formation of a stable intercalation compound. We find that the functionalization of graphene edges is an essential prerequisite for intercalation since bare edges reconstruct and reconnect, closing off the entry channels for the atoms.

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Figure 1

Initial geometry of the $AA$-stacked graphene bilayer ${\mathrm{C}}_{128}{\mathrm{H}}_{16}$ unit cell with eight K atoms in the molecular dynamics simulations, presented in (a) a top and (b) a perspective view. Potassium atoms are represented by the labeled large yellow balls, hydrogen atoms by small white balls, and carbon atoms by cyan balls. Of the eight K atoms per unit cell, four—shown in light yellow—are above the surface and the other four—shown in dark yellow—are near the interlayer region. (c) The geometry and (d) the binding energy of a K atom interacting with the graphene bilayer surface.

Figure 2

Diffusion behavior of K atoms interacting with a graphene bilayer. (a) Perspective view of the K-graphite system, with $d$ defining the horizontal distance outside the closest of the two edges, highlighted by the solid red lines. (b) Diffusion characteristic of the four K atoms, labeled 1–4 in Figs. 1 and 1, which are initially placed above the strip. (c) Diffusion characteristic of the other four K atoms, labeled 5–8 in Figs. 1 and 1, which are initially placed near the interlayer region. (d) Change in the diffusion characteristics of atoms in (c) induced by an increase of K vapor pressure at $t=1470\mathrm{fs}$, modeled by placing four additional alkali atoms near the interlayer region. (e) Change in the diffusion characteristics of atoms in (d) induced by a further increase of K vapor pressure at $t=2340\mathrm{fs}$, modeled by placing two additional alkali atoms near the interlayer region.

Figure 3

Microscopic kinetics of K intercalation in graphite. (a) Geometry of the $\mathsf{U}$-turn process. The horizontal graphene plane is shown in light blue, with its edge enhanced by the red line. Another plane, shown in orange, contains a K atom, and the graphene edge is shown in red. The dihedral angle $\alpha$ is the angle between these planes. $\mathrm{\Delta }z$ is the distance between the K atom and the graphene layer. (b) Snapshot of atomic positions at $t=1470\mathrm{fs}$ during the intercalation process, superposed with a representation of the charge flow due to the insertion of a K atom into the interlayer region. The entry of K increases the interlayer distance by $\lesssim 70\%$. The charge density difference $\mathrm{\Delta }\rho ={\rho }_{\mathrm{tot}}({\mathrm{C}}_{128}{\mathrm{H}}_{16}+8\mathrm{K})-{\rho }_{\mathrm{tot}}(\mathrm{K})-{\rho }_{\mathrm{tot}}({\mathrm{C}}_{128}{\mathrm{H}}_{16}+7\mathrm{K})$ is presented by the isosurfaces of the excess negative charge at $\mathrm{\Delta }\rho =+{10}^{-3}e/{\AA }^3$, shown in blue, and the negative charge deficit at $\mathrm{\Delta }\rho =-{10}^{-3}e/{\AA }^3$, shown in red. The potassium atom in the center of the red cloud loses 0.531 electrons. (c) Time dependence of the dihedral angle $\alpha$ during the $\mathsf{U}$-turn of a K atom from the surface region, across the edge, to the area between the graphene layers. (d) Time dependence of the vertical position $\mathrm{\Delta }z$ of a K atom during the intercalation process. $\alpha <180°$ and $\mathrm{\Delta }z>0$ indicate that the K atom is above the graphitic surface. $\alpha >180°$ and $\mathrm{\Delta }z<0$ indicate that the K atom is between the graphene layers.