4.4 Surface Alloying
133
character [64]. In addition, in the case where the radius of the adsorbate B atom
is larger than that of the substrate A atom, the interatomic distance d B−A in the
surface alloy is shorter than that in the corresponding bulk alloy, which has been
confirmed by the density functional theory (DFT) calculations [74]. For example,
d Sn−Ni = 0.253 nm in the surface alloy of Ni (111)
√
3 ×
√
3
R30
◦ -Sn [67] is
shorter than d Sn−Ni = 0.261 ∼ 0.264 nm in the bulk Ni 3 Sn alloy [64]. Furthermore,
the DFT calculations [75] for the surface structure and surface stress of a series of
different surface alloy phases confirmed that the effective radius of adsorbate atom
is reduced by alloying for the systems with larger adsorbate atoms, and showed that
the tensile stress is reduced by alloying and the surface stress becomes compressive
for some systems in which the radius of adsorbate atom is significantly larger than
that of substrate atom. By contrast, the tensile stress is increased by alloying for the
surface phase of W (100)c(2 × 2)-Cu in which the adsorbate Cu atom is smaller than
the substrate W atom.
Figure 4.16 shows (a) the changes in surface stress g due to alloying and (b) the
surface stress g of surface alloy, plotted versus the calculated difference in atomic
radius r between adsorbate and substrate atoms for the surface alloys in which the
radius of adsorbate atom is larger than that of the substrate atom [75]. In Fig. 4.16,
it is reminded that the results for the surface alloys in which the radius of adsorbate
atom is smaller than that of substrate atom are excluded from the original figure in
ref [75] to avoid the complexity. The value of g in Fig. 4.16a was obtained by
subtracting the absolute value of surface stress, calculated for the respective clean
substrate metal surface from the absolute value of surface stress g, calculated for
the respective surface alloy in Fig. 4.16b. It is clear from Fig. 4.16a that the changes
in surface stress due to alloying tend to shift toward more compressive direction
(g < 0) with increasing r . It is noticed that the unit of the abscissa in Fig. 4.16a
and b is expressed by Ångström (Å = 0.1 nm).
On a clean metal surface, because of the missing bond, the electronic charge
accumulates between the surface atoms to cause the contraction of the equilibrium
bond distance between surface atoms, by which the tensile stress arises on the clean
metal surface [50]. If the electronic charge accumulated between surface atoms is
removed due to the bonding of surface atoms with adsorbate atoms, the surface
stress varies toward compressive direction. Besides, in the case where the radius of
the adsorbate atom is significantly larger than that of the substrate atom, the substitution of the substrate atoms in the surface layer by the adsorbate atoms, followed
by the surface alloy formation, induces the large changes in surface stress toward
compressive direction due to the large difference in atomic radius between adsorbate
and substrate atoms. However, the compressive surface stress may be released to
some extent by achieving shorter interatomic distance (i.e., significant reduction in
the effective radius of adsorbate atom) in the resulting surface alloy phase, which
may be energetically favorable for the formation of the surface alloy in such systems.
By contrast, in the case where the radius of the adsorbate atom is smaller than
that of the substrate atom such as W (100) c(2 × 2)-Cu, the surface alloy formation
increases the tensile surface stress. Unfortunately, there have been no reports of the
133
character [64]. In addition, in the case where the radius of the adsorbate B atom
is larger than that of the substrate A atom, the interatomic distance d B−A in the
surface alloy is shorter than that in the corresponding bulk alloy, which has been
confirmed by the density functional theory (DFT) calculations [74]. For example,
d Sn−Ni = 0.253 nm in the surface alloy of Ni (111)
√
3 ×
√
3
R30
◦ -Sn [67] is
shorter than d Sn−Ni = 0.261 ∼ 0.264 nm in the bulk Ni 3 Sn alloy [64]. Furthermore,
the DFT calculations [75] for the surface structure and surface stress of a series of
different surface alloy phases confirmed that the effective radius of adsorbate atom
is reduced by alloying for the systems with larger adsorbate atoms, and showed that
the tensile stress is reduced by alloying and the surface stress becomes compressive
for some systems in which the radius of adsorbate atom is significantly larger than
that of substrate atom. By contrast, the tensile stress is increased by alloying for the
surface phase of W (100)c(2 × 2)-Cu in which the adsorbate Cu atom is smaller than
the substrate W atom.
Figure 4.16 shows (a) the changes in surface stress g due to alloying and (b) the
surface stress g of surface alloy, plotted versus the calculated difference in atomic
radius r between adsorbate and substrate atoms for the surface alloys in which the
radius of adsorbate atom is larger than that of the substrate atom [75]. In Fig. 4.16,
it is reminded that the results for the surface alloys in which the radius of adsorbate
atom is smaller than that of substrate atom are excluded from the original figure in
ref [75] to avoid the complexity. The value of g in Fig. 4.16a was obtained by
subtracting the absolute value of surface stress, calculated for the respective clean
substrate metal surface from the absolute value of surface stress g, calculated for
the respective surface alloy in Fig. 4.16b. It is clear from Fig. 4.16a that the changes
in surface stress due to alloying tend to shift toward more compressive direction
(g < 0) with increasing r . It is noticed that the unit of the abscissa in Fig. 4.16a
and b is expressed by Ångström (Å = 0.1 nm).
On a clean metal surface, because of the missing bond, the electronic charge
accumulates between the surface atoms to cause the contraction of the equilibrium
bond distance between surface atoms, by which the tensile stress arises on the clean
metal surface [50]. If the electronic charge accumulated between surface atoms is
removed due to the bonding of surface atoms with adsorbate atoms, the surface
stress varies toward compressive direction. Besides, in the case where the radius of
the adsorbate atom is significantly larger than that of the substrate atom, the substitution of the substrate atoms in the surface layer by the adsorbate atoms, followed
by the surface alloy formation, induces the large changes in surface stress toward
compressive direction due to the large difference in atomic radius between adsorbate
and substrate atoms. However, the compressive surface stress may be released to
some extent by achieving shorter interatomic distance (i.e., significant reduction in
the effective radius of adsorbate atom) in the resulting surface alloy phase, which
may be energetically favorable for the formation of the surface alloy in such systems.
By contrast, in the case where the radius of the adsorbate atom is smaller than
that of the substrate atom such as W (100) c(2 × 2)-Cu, the surface alloy formation
increases the tensile surface stress. Unfortunately, there have been no reports of the