Mobile metal adatoms on single layer, bilayer, and trilayer graphene: An ab initio DFT study with van der Waals corrections correlated with electron microscopy data

The plane-wave density functional theory code CASTEP was used with the Tkatchenko-Scheffler van der Waals correction scheme and the generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA PBE) to calculate the binding energy of Au, Cr, and Al atoms on the armchair and zigzag edge binding sites of monolayer graphene, and at the high-symmetry adsorption sites of single layer, bilayer, and trilayer graphene. All edge site binding energies were found to be substantially higher than the adsorption energies for all metals. The adatom migration activation barriers for the lowest energy migration paths on pristine monolayer, bilayer, and trilayer graphene were then calculated and found to be smaller than or within an order of magnitude of $k_{B}T$ at room temperature, implying very high mobility for all adatoms studied. This suggests that metal atoms evaporated onto graphene samples quickly migrate across the lattice and bind to the energetically favorable edge sites before being characterized in the microscope. We then prove this notion for Al and Au on graphene with scanning transmission electron microscopy (STEM) images showing that these atoms are observed exclusively at edge sites, and also hydrocarbon-contaminated regions, where the pristine regions of the lattice are completely devoid of adatoms. Additionally, we review the issue of fixing selected atomic positions during geometry optimization calculations for graphene/adatom systems and suggest a guiding principle for future studies.

Figure 1

STEM HAADF images at 60 keV showing preferential binding of metal atoms to edge defects, hydrocarbon-contaminated regions, and metal clusters. (a) Monolayer graphene sheet with hole, onto which a 2 Å layer of Al was evaporated. Al atoms are seen only at edge sites and in clusters near the hole.[35] (b) Monolayer graphene sheet with bilayer and trilayer regions onto which a 5 Å layer of Au gold was evaporated. Individual Au atoms and Si contaminants (of less bright contrast) clearly bind preferentially to edge sites. The pristine regions of the lattice are completely devoid of adatoms in both cases.

Figure 2

Symmetry breaking caused by fixing atoms on the supercell perimeter without appealing to lattice symmetries. (a) The lattice environment experienced by the adatom along directions ${\stackrel{\rightharpoonup }{r}}_3$ is different to that along ${\stackrel{\rightharpoonup }{r}}_1$ and ${\stackrel{\rightharpoonup }{r}}_2$, despite these directions being crystallographically equivalent. (b) The resulting twofold rotational symmetry of the unfixed carbon sublattice and (c) the twofold rotational symmetry of the fixed carbon sublattice about the axis passing through the adsorption site.

Figure 3

The high symmetry adsorption sites located at the vertices of the symmetry-reduced Wigner Seitz cell boundaries for (a) single layer graphene and (b) 2$+$ layer graphene, for which AB stacking is assumed. In the multilayer case, the top layer is represented by small black balls and sticks and the sublayer is represented by large grey balls and sticks. (c) and (d) The high symmetry binding sites of the monolayer armchair edge and zigzag edge considered in this work.

Figure 4

Example supercells used for metal binding to monolayer edges with accompanying unit cells. $|{\stackrel{\rightharpoonup }{A}}_{1l,\mathrm{zigzag}}|=8|{\stackrel{\rightharpoonup }{a}}_{1l}|\AA$, $|{\stackrel{\rightharpoonup }{B}}_{1l,\mathrm{zigzag}}|=5\sqrt{3}\left|{\stackrel{\rightharpoonup }{a}}_{1l}\right|+20\AA$, $|{\stackrel{\rightharpoonup }{A}}_{1l,\mathrm{armchair}}|=5\sqrt{3}\left|{\stackrel{\rightharpoonup }{a}}_{1l}\right|\AA$, and $|{\stackrel{\rightharpoonup }{B}}_{1l,\mathrm{armchair}}|=7|{\stackrel{\rightharpoonup }{a}}_{1l}|+20\AA$.

Figure 5

Example supercells used for migration activation barrier calculations. (a) $\mathrm{H}\to \mathrm{B}\to \mathrm{H}$ trajectory used for Cr and Al on the monolayer and (b) ${\mathrm{A}}_1\to \mathrm{B}\to {\mathrm{A}}_2$ trajectory used for Au.

Figure 6

The calculated binding energy for metal atoms adsorbed on the pristine substrates and bound at monolayer edge sites. The energetic ordering of the adsorption sites is seen to remain the same for increasing thicknesses. See Fig. 3 for nomenclature of binding sites.

Figure 7

Electron density images showing the difference in bonding character between adsorption and edge sites for Au. (a) Cross section of the total electron density field shown in color units of electrons $/{\AA }^3$ for Au at adsorption site A for the fully relaxed monolayer. (b) Corresponding trilayer image, showing Au at site A${}_1$. The cross sections shown intersect the graphene along the “armchair” direction, thus showing the carbon-carbon bonds for comparison. The bonding character is seen to be consistent with physisorption in both cases, though a slightly more substantial bond is evident for the trilayer case. Au atom binding to the edge sites (c) Z${}_1$ (d) Z${}_2$ (e) C${}_1$, and (f) C${}_2$. Clear and substantial regions of electron density are observable in all four cases, consistent with a stronger metal carbide bond. See Fig. 3 for nomenclature of binding sites.

Figure 8

(a) Fully optimized graphene unit cell with relaxed lattice parameters in red. Atoms and bonds are represented by balls and sticks, respectively. (b) Fully optimized multilayer graphene unit cell, as in (a). To aid visualization, the atoms and bonds of the first sublayer are represented with large gray balls and sticks, and those of the top layer with small black balls and sticks. The second sublayer is not indicated owing to the assumed AB stacking structure. (c) Isolated metal atom cubic supercell. The lattice parameters shown indicate the smallest supercell size required to decouple all intercellular metal-metal interactions. (d) Graphene $+$ metal supercell spanning $2\times 2$ unit cells. The lattice parameters shown indicate the vacuum thicknesses required to decouple intercellular interactions along the vacuum direction only.

Figure 9

The three single layer supercells before geometry optimization used for the adatom $+$ graphene systems for (a) site A, (b) site B, and (c) site H. In all cases, carbon atoms whose positions are fixed are represented in blue and those whose positions are relaxed are represented in black. The corresponding unfixed and fixed sublattices are displayed to the right of their corresponding supercells, in which the green lines show boundaries between segments of the lattice which are equivalent by virtue of rotational symmetry about the axis passing through the adsorption site represented by the green dot in the center. The red cross denotes the initial adatom location. $|{\stackrel{\rightharpoonup }{a}}_{1l}|=|{\stackrel{\rightharpoonup }{b}}_{1l}|=2.459\AA$ (3 d.p.), $|{\stackrel{\rightharpoonup }{A}}_{1l}|=|{\stackrel{\rightharpoonup }{B}}_{1l}|=5|{\stackrel{\rightharpoonup }{a}}_{1l}|=12.293\AA$ (3 d.p.), and $|{\stackrel{\rightharpoonup }{C}}_{1l}|=|{\stackrel{\rightharpoonup }{c}}_{1l}|=20\AA$. See Fig. 3 for nomenclature on adsorption sites.

Figure 10

The multilayer input supercells for (a) site A${}_1$, (b) site A${}_2$, (c) site B, and (d) site H. The top carbon layer is represented by small balls and sticks, and the first sublayer is represented by large balls and sticks. No further sublayers are indicated owing to the assumed AB stacking structure. Fixed top layer and sublayer C atoms are blue and light green, respectively. Unfixed top layer and sublayer C atoms are colored black and gray, respectively. As in Fig. 9, the red cross denotes the initial adatom location. As in Fig. 9, the unfixed and fixed sublattices are shown on the right of their corresponding supercell, divided into segments which are equivalent by rotational symmetry about the axis passing through the adsorption site. $|{\stackrel{\rightharpoonup }{a}}_{2l}|=|{\stackrel{\rightharpoonup }{b}}_{2l}|=2.457\AA$ (3 d.p.), $|{\stackrel{\rightharpoonup }{A}}_{2l}|=|{\stackrel{\rightharpoonup }{B}}_{2l}|=5|{\stackrel{\rightharpoonup }{a}}_{2l}|=12.283\AA$ (3 d.p.), $|{\stackrel{\rightharpoonup }{C}}_{2l}|=|{\stackrel{\rightharpoonup }{c}}_{2l}|=24\AA$, $|{\stackrel{\rightharpoonup }{a}}_{3l}|=|{\stackrel{\rightharpoonup }{b}}_{3l}|=2.456\AA$ (3 d.p.), $|{\stackrel{\rightharpoonup }{A}}_{3l}|=|{\stackrel{\rightharpoonup }{B}}_{3l}|=5|{\stackrel{\rightharpoonup }{a}}_{3l}|=12.280\AA$ (3 d.p.), and $|{\stackrel{\rightharpoonup }{C}}_{3l}|=|{\stackrel{\rightharpoonup }{c}}_{3l}|=27\AA$. ${}^{*}$The B site in (c) is the only site for which the rotational symmetry of the first sublayer (and also therefore the complete lattice) is onefold. For this case, C positions were fixed on the supercell perimeter on the first sublayer in preference to some other arbitrary selection resulting in onefold symmetry, resulting in the twofold fixed sublattice rotational symmetry shown. See Fig. 3 for nomenclature on adsorption sites.