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Structure and chemical reactivity of the polar three-fold surfaces of GaPd: A density-functional study
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10.1063/1.4795435
/content/aip/journal/jcp/138/12/10.1063/1.4795435
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795435

Figures

Image of FIG. 1.
FIG. 1.

The B20 structure can be interpreted as a packing of prolate and oblate rhombohedra. Along the Cartesian directions the B20 structure is formed by a sequence of alternating prolate and oblate (with dashed diagonal) rhombohedra. The length of the lattice constant a is marked explicitly (blue line segment at the bottom). The elementary cell consists of 4 prolate and 4 oblate rhombohedra. Dark spheres represent transition metal atoms.

Image of FIG. 2.
FIG. 2.

The layered structure of GaPd along the polar [111] direction. A view of two elementary cells along horizontal direction are presented. This side view along of enantiomorph A can be alternatively understood as a mirror image of enantiomorph B rotated by 180°. Positions of atoms are shown by circles: Ga – light-blue, Pd – violet. In one period perpendicular to [111] there are nine atomic layers: three flat occupied by Pd only (P), three flat Ga layers (G), and three layers with mixed Ga-Pd occupancy (M).

Image of FIG. 3.
FIG. 3.

Side views of cleaved B20 structures for the three possible locations of a (111) cleavage plane, leading to the exposure of different pairs of threefold surfaces: (a) GP and MP, (b) MG and PG, (c) PM and GM. These side views along of enantiomorph A can be alternatively understood as mirror images of enantiomorph B rotated by 180°. The inter-planar distances between the four near-surface layer marked 1 to 4 given in Table IV . The violet circles mark positions of Pd atoms, the light-blue circles are Ga atoms.

Image of FIG. 4.
FIG. 4.

Top view of the relaxed threefold surfaces of GaPd terminated by (a) A(111) GP and (b) A MP bi-layers. A surface area of 8 hexagonal surface cells is shown. The violet circles mark the positions of Pd atoms, the light-blue circles are Ga atoms. Atoms in the sub-surface layers are darker. The diameters of the circles are 2.8 Å for both Ga and Pd atoms.

Image of FIG. 5.
FIG. 5.

Top view of threefold surfaces of GaPd on both side of a possible cleavage plane: (a) A(111) MG termination, (b) A PG termination, cf. Fig. 4 .

Image of FIG. 6.
FIG. 6.

Top view of the threefold surfaces of GaPd on both sides of a possible cleavage plane: (a) PM, (b) GM surface, cf. Fig. 4 .

Image of FIG. 7.
FIG. 7.

Mutual dependencies of the surface energies for the threefold surfaces of GaPd: (a) Variation of the surface energies γ for the MP, MG, and PG surfaces with the assumed value of γ(GP). (b) Variation of the surface energy of the PM surface with the assumed value of γ(GM). The absolute values of the surface energies estimated according to Eq. (1) , , are given by the intersections with the vertical dashed line, cf. text.

Image of FIG. 8.
FIG. 8.

Differential surface energies Δγ as a function of the chemical potential μGa: (a) Difference of the surface energies of the A(111) terminations GP, MG, gG, and pG with respect to the PM surface. (b) Difference of the surface energies of the A( ) terminations PG, MP, gP, and pP with respect to the GM surface. Difference of the surface energies Δγ as a function of the chemical potential μAl for AlPd surface terminations: (c) the A(111) terminations AP, MA, aA, and pA with respect to the PM surface, (d) the A( ) terminations PA, MP, aP, and pP with respect to the AM surface, cf. text. The vertical lines mark the value of the chemical potential consistent with the values of the surface energies estimated using approximation [Eq. (1) ].

Image of FIG. 9.
FIG. 9.

Top view of the surfaces obtained from the A(111) MG termination after partial desorption of atoms: (a) gG, (b) pG surface. The violet circles mark the positions of Pd atoms, the light-blue circles are Ga atoms. Atoms in the sub-surface layers are darker.

Image of FIG. 10.
FIG. 10.

The surface density of states of (a) the A(111) terminations GP (black line), gG (red dashed line), and pG (blue chain line), and (b) the A terminations GM (black line) and PG (red dashed line).

Image of FIG. 11.
FIG. 11.

Simulated STM images of the A(111) gG (a), pG (b), and GP (c) surface terminations.

Image of FIG. 12.
FIG. 12.

Simulated STM images of the A GM (a) and PG (b) surface terminations.

Image of FIG. 13.
FIG. 13.

Top-view of the A(111) gG surface. An area of two hexagonal surface cells is shown. Part (a) shows the possible adsorption sites, part (b) the positions of adsorbed CO molecules at maximum coverage on the relaxed surface. Atoms are represented by circles: Ga – light blue, Pd – violet, C – black, O – red.

Image of FIG. 14.
FIG. 14.

Top-view of the A(111) pG surface. An area of two hexagonal surface cells is shown. Part (a) shows the possible adsorption sites, part (b) the positions of adsorbed CO molecules at maximum coverage on the relaxed surface. Atoms are represented by circles: Ga - light blue, Pd – violet, C – black, O – red.

Image of FIG. 15.
FIG. 15.

Top-view of the A(111) GP surface. An area of two hexagonal surface cells is shown. Part (a) shows the possible adsorption sites, part (b) the positions of adsorbed CO molecules at maximum coverage on the relaxed surface. Atoms are represented by circles: Ga – light blue, Pd – violet, C – black, and O – red.

Image of FIG. 16.
FIG. 16.

Top-view of the A GM surface. An area of two hexagonal surface cells is shown. Part (a) shows the possible adsorption sites, part (b) the positions of adsorbed CO molecules at maximum coverage on the relaxed surface. Atoms are represented by circles: Ga – light blue, Pd – violet, C – black, and O – red.

Image of FIG. 17.
FIG. 17.

Top-view of the A PG surface. An area of two hexagonal surface cells is shown. Part (a) shows the possible adsorption sites, part (b) the positions of adsorbed CO molecules at maximum coverage on the relaxed surface. Atoms are represented by circles: Ga – light blue, Pd – violet, C – black, and O – red.

Image of FIG. 18.
FIG. 18.

(a) Front view, (b) side view of equilibrium shape of a GaPd crystallite, and (c) side view of a AlPd crystallite. Facets: {100} – green, {210} – red, A{111} – yellow, A – blue.

Tables

Generic image for table
Table I.

Calculated lattice constant a and internal coordinates u for considered B20 structures, compared to experiment.

Generic image for table
Table II.

Calculated surface energies γ of the (100) and (210) surfaces of AlPd and GaPd compared with the surface energies of low-index surfaces of the constituent elements Al, Ga, and Pd. The energy of the Ga(111)* surface has been calculated for the threefold surface of hypothetical fcc Ga.

Generic image for table
Table III.

Correspondence between our notation for the surface terminations and that used by Rosenthal et al. 21 and Prinz et al. 22

Generic image for table
Table IV.

Stoichiometries, interlayer distances, and surface energies of the threefold surfaces of GaPd. N Ga and N Pd are number of atoms in the surface bilayer per hexagonal surface cell, d 12, d 23, and d 34 are inter-planar distances between the four topmost atomic planes for the relaxed surfaces and their bulk values (in parentheses). The last column lists the estimated values of the surface energies, see Sec. III D .

Generic image for table
Table V.

Average surface energies for the surfaces on both sides of stoichiometric slabs, cf. text.

Generic image for table
Table VI.

Average surface energies for the surfaces on both sides of non-stoichiometric slabs, calculated for the limiting values of the chemical potential μGa, cf. text.

Generic image for table
Table VII.

Adsorption energies E b of CO molecules on the A(111) gG, pG, and GP surfaces. The coverage is expressed as the number of CO molecules per hexagonal surface cell. The adsorption energy at maximum coverage given as the average adsorption energy per CO molecule.

Generic image for table
Table VIII.

Adsorption energies E b of CO molecules on the A GM and PG surfaces. The coverage is expressed as the number of CO molecules per hexagonal surface cell. The adsorption energy at maximum coverage is given as the average adsorption energy per CO molecule.

Generic image for table
Table IX.

Calculated surface energies and relative surface areas occupied by different facets for GaPd crystallites.

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/content/aip/journal/jcp/138/12/10.1063/1.4795435
2013-03-26
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Structure and chemical reactivity of the polar three-fold surfaces of GaPd: A density-functional study
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795435
10.1063/1.4795435
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