[1] The process can generally be thought of in terms of particles jumping between adjacent adsorption sites on a surface, as in figure 1.
[3] While in principle the process can occur on a variety of materials, most experiments are performed on crystalline metal surfaces.
Due to experimental constraints most studies of surface diffusion are limited to well below the melting point of the substrate, and much has yet to be discovered regarding how these processes take place at higher temperatures.
Real-world applications relying heavily on these phenomena include catalytic converters, integrated circuits used in electronic devices, and silver halide salts used in photographic film.
For cases where more than one diffusion mechanism is present (see below), there may be more than one Ediff such that the relative distribution between the different processes would change with temperature.
For a given crystalline material each Miller Index plane may display unique diffusion phenomena.
The manner in which they diffuse is important as it may dictate the kinetics of movement, temperature dependence, and overall mobility of surface species, among other parameters.
With increased temperature adsorbed molecules, molecular fragments, atoms, and clusters tend to have much greater mobility (see equation 1).
However, with increased temperature the lifetime of adsorption decreases as the factor kBT becomes large enough for the adsorbed species to overcome the barrier to desorption, Q (see figure 2).
Surface diffusion may be studied by a variety of techniques, including both direct and indirect observations.
In order to study surface diffusion on the atomistic scale it is unfortunately necessary to perform studies on rigorously clean surfaces and in ultra high vacuum (UHV) conditions or in the presence of small amounts of inert gas, as is the case when using He or Ne as imaging gas in field-ion microscopy experiments.
Figure 1. Model of a single
adatom
diffusing across a square surface lattice. Note the frequency of vibration of the adatom is greater than the jump rate to nearby sites. Also, the model displays examples of both nearest-neighbor jumps (straight) and next-nearest-neighbor jumps (diagonal). Not to
scale
on a spatial or temporal basis.
Figure 2. Diagram of the energy landscape for diffusion in one dimension.
x
is displacement;
E(x)
is energy;
Q
is the heat of adsorption or binding energy;
a
is the spacing between adjacent adsorption sites;
E
diff
is the barrier to diffusion.
Figure 3. Model of six adatoms diffusing across a square surface lattice. The adatoms block each other from moving to adjacent sites. As per
Fick’s law
, flux is in the opposite direction of the concentration gradient, a purely statistical effect. The model is not intended to show repulsion or attraction, and is not to scale on a spatial or temporal basis.
Figure 4. Model of an atomic exchange mechanism occurring between an adatom (pink) and surface atom (silver) at a square surface lattice (blue). The surface atom becomes an adatom. Not to scale on a spatial or temporal basis.
Figure 5. Model of surface diffusion occurring via the vacancy mechanism. When surface coverage is nearly complete the vacancy mechanism dominates. Not to scale on a spatial or temporal basis.
Figure 6. Surface diffusion jump mechanisms. Diagram of various jumps that may take place on a square lattice such as the fcc (100) plane. 1) Pink atom shown making jumps of various length to locations 2-5; 6) Green atom makes diagonal jump to location 7; 8) Grey atom makes rebound jump (atom ends up in same place it started). Non-nearest-neighbor jumps typically take place with greater frequency at higher temperatures. Not to scale.
Figure 7. Graph showing relative probability distribution for adatom displacement,Δx, upon diffusion in one dimension. Blue: single jumps only; Pink: double jumps occur, with ratio of single:double jumps = 1. Statistical analysis of data may yield information regarding diffusion mechanism.
Figure 8. Cross-channel diffusion involving an adatom (grey) on a channeled surface (such as fcc (110), blue plus highlighted green atom). 1) Initial configuration; 2) "Dumbbell" intermediate configuration. Final displacement may include 3, 4, 5, or even a return to the initial configuration. Not to scale.
Figure 9. Long range atomic exchange mechanism for surface diffusion at a square lattice. Adatom (pink), resting at surface (1), inserts into lattice disturbing neighboring atoms (2), ultimately causing one of the original substrate atoms emerge as an adatom (green) (3). Not to scale.
Figure 10. Individual mechanisms for surface diffusion of clusters. (1) Sequential displacement; (2) Edge diffusion; (3) Evaporation-condensation. In this model all three mechanisms lead to the same final cluster displacement. Not to scale.
