Chemistry Reference
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energies near steps or island edges. From bond energy, bond order, bond length
reasoning [
46
], one can expect such atoms - which lack their full complement of
near-neighbor bonds, to move closer to the remaining neighbors to partially compen-
sate for the loss. Persson showed that relaxation in the form of adsorption away from
high-symmetry sites can lead to effective trio interactions, and attendant effects, in
systems with ostensibly only pair interactions [
2
,
34
]. Our goal here is to show that
these relaxation effects are especially significant for multisite interactions, where
the relaxations are not along the bond directions. Furthermore, multisite interac-
tions, in general, have a large elastic component; hence, a careful consideration of
relaxation effects is needed while computing them. We discuss in particular how
strain-related effects are important when calculating the step stiffness on Cu(100).
Because of adatom relaxation near steps, the inclusion of non-pairwise, quarto inter-
action between four adatoms is required on this square-lattice surface in order to
preserve a lattice-gas description.
2.5.1 Multisite Interactions in Step-Stiffness Asymmetry
Step stiffness (which earlier served as the mass in the 1D fermion model of steps)
underlies how steps respond. It is one of the three parameters of the step-continuum
model [
47
], which has proved a powerful way to describe step behavior on a coarse-
grained level, without recourse to a myriad of microscopic energies and rates. In the
analogy between 2D configurations of steps and worldlines of spinless fermions in
(1
β
plays the role of the mass of the fermion. As the inertial
term, stiffness determines how a step responds to fluctuations, to driving forces, and
to interactions with other steps.
We summarize our lattice-gas-based computations of the orientation dependence
of step stiffness for the (001) and (111) faces of Cu [
48
,
49
]. This work illustrates
both successes and some shortcomings of using a lattice-gas model with just NN
interactions: whereas the step stiffness on Cu(111) is well described by NN interac-
tions alone, the step stiffness on Cu(001) requires the inclusion of NNN and perhaps
even trio interactions. We discuss only the latter.
The step stiffness
+
1)D, step stiffness
β(θ)
≡
β(θ)
+
β
(θ)
weights deviations from straightness in
the step Hamiltonian, where
is conventional designation of the azimuthal misori-
entation angle; it measured from the close-packed direction. Here
θ
is the step-free
energy per length (or, equivalently, the line tension, since the surface is maintained
at constant [zero] charge [
50
]). The stiffness is inversely proportional to the step
diffusivity, which measures the degree of wandering of a step perpendicular to its
mean direction. This diffusivity can be readily written down in terms of the energies
ε
k
of kinks along steps with a mean orientation
β
θ
=
0: in this case, all kinks are
thermally excited. Conversely, experimental measurements of the low-temperature
diffusivity (via the scale factor of the spatial correlation function) can be used to
deduce the kink energy. A more subtle question is how this stiffness depends on
θ
.
Even for temperatures much below
ε
k
, there are always a non-vanishing number
