First-principles calculations of the initial incorporation of carbon into flat and stepped Pd surfaces

We employ density-functional-theory calculations to examine carbon adsorption and diffusion in Pd bulk, and on Pd(111) and Pd(211) surfaces. Different possible subsurface and on-surface structures are explored and the most stable structures are analyzed. We calculate various diffusion paths: lateral diffusion on a surface, migration to a subsurface region, and within the first interlayer. Our calculations show in accordance with the earlier theoretical results that on Pd(111) carbon prefers to adsorb on octahedral interstitial sites. On Pd(211) the fourfold hollow site under the step is energetically the most favorable one and the second best sites are the octahedral sites. The calculations indicate that migration into the first interlayer is more favorable than diffusion on the Pd(111) surface and migration into the second interlayer is already highly activated with barrier height close to those obtained in bulk. Nearly nonactivated diffusion paths into the first interlayer are found at the step edge of bare Pd(211) but carbon is found to diffuse easily from the first interlayer to the fourfold hollow site on Pd(211) thus leading to the decoration of step edges with carbon. Preadsorbed carbon increases the surface-subsurface diffusion barrier but it remains smaller than the corresponding value on bare Pd(111). At higher carbon concentration the mixed surface-subsurface structures are the most stable ones and carbon atoms tend to sit as far away from each other as possible.

Figure 1

(Color online) The relevant on-surface adsorption sites of fcc(211) slab (fcc, hcp, and Ffh) and subsurface sites in fcc lattice (Oct, Tet1, and Tet2). Surface atoms of different terraces are of different color. fcc and hcp sites are identical to the ones on Pd(111). In subsurface structures the carbon is presented in gray and the palladium atoms in ochre. Oct is an abbreviation for octahedral and Tet is for tetrahedral.

Figure 2

(Color online) Side views of Pd(111) and Pd(211) slabs. Surface and subsurface sites are depicted with gray dots and corresponding adsorption energies are given for C in electron volt. These pictures are projections of the Pd lattices and adsorption sites to a plane perpendicular to the surface (and the steps). The actual lattice points and adsorption sites do not reside in a plane.

Figure 3

(Color online) The atom projected density-of-states plots of a clean Pd(111) surface, a Pd surface with $25\text{at}\text{.}\mathrm{\%}$ C adsorbed to on-surface sites and a Pd surface with $25\text{at}\text{.}\mathrm{\%}$ C in subsurface layer. For the Pd surfaces the $d$ bands of the two topmost atomic layers are plotted and for the C atoms the $s$ and $p$ bands. The dashed orange and green lines are the DOS of Pd and C, respectively, of the model with on-surface C. The blue solid line and the red dot and dash line are the DOS of Pd and C, respectively, of the model with subsurface C. The light blue area is the DOS of the clean Pd surface.

Figure 4

(Color online) Charge-density difference figures of C adsorbed to Oct, hcp, and Ffh sites when viewed from the top (A to C, respectively) and from the side (D to E, respectively). The red (blue) color indicates the increase (decrease) in the electron density. In the top views the contours $\pm \left(0.01,0.015,0.02\right)e{a}_0^{-3}$ of the electron density are presented. In the side views the contours $\pm 0.01$, $\pm 0.02$, and $\pm 0.015e{a}_0^{-3}$ are presented for D, E, and F, respectively.

Figure 5

(Color online) A schematic representation of the studied diffusion path ways from the (111) surface to the first and second interlayers.

Figure 6

(Color online) Schematic representation of the studied diffusion paths from on-surface sites to the first and second interlayers.

Figure 7

(Color online) Top views of the most stable model systems with (1) all C atoms at subsurface positions for 25, 31, 36, and $40\text{at}\text{.}\mathrm{\%}$ of C (A, B, C, and F, respectively), (2) both on-surface and subsurface carbon 25, 31, 36, and $40\text{at}\text{.}\mathrm{\%}$ of C (A, D, E, and I, respectively), and (3) different distributions of C between on-surface and subsurface layers at $40\text{at}\text{.}\mathrm{\%}$ of C (F–L). The light yellow spheres are Pd atoms, the blue ones are subsurface C, and the orange ones are on-surface C. The black rhombus depicts the supercell.

Figure 8

(Color online) Averaged adsorption energies of C on 111 surfaces containing C both on and below surface. The energies are given as a function of C atoms on surface divided by the total number of C atoms $\left[N_{\text{C},s}/\left(N_{\text{C},s}+N_{\text{C},ss}\right)\right]$. Some points in the plot are accompanied with a letter and the structures of those systems are presented in Fig. 7. The circled points represent energy minimums of the different C concentrations.

Figure 9

(Color online) The work functions of Pd(111) surfaces containing different amounts of C are plotted against the distribution between subsurface and on-surface sites. On the $x$ axis the zero value corresponds to all atoms being located at the subsurface layer and the infinity corresponds to all atoms being on the surface. Work function of the clean surface is presented with the dashed horizontal line.

Figure 10

(Color online) The energetics of diffusion from an hcp site to the second interlayer on 111 (red, solid line) and 211 surface (orange, dashed line) presented with potential-energy surfaces. Each diffusion step is accompanied with an illustration of the transition state structure and a number referring to the paths in Figs. 5, 6. In the structures the black (white) spheres are carbon (palladium) atoms and only relevant atoms are shown.