Surface diffusion is a key process in surface science, involving the movement of atoms and molecules across surfaces. It's driven by thermal energy and influenced by the surface's potential energy landscape, with atoms preferring low-energy paths like channels or step edges.

Temperature plays a crucial role in surface diffusion, following the Arrhenius equation. Surface defects like steps, kinks, and vacancies can enhance diffusion by providing low-energy sites. Understanding these mechanisms is vital for controlling surface processes in various applications.

Surface diffusion processes

Movement of atoms and molecules on surfaces

• Surface diffusion involves the movement of atoms, molecules, or clusters across a surface
• Adatoms, which are atoms adsorbed on a surface and not part of the regular crystal lattice, can move across the surface
• Diffusion occurs through a series of jumps between adjacent adsorption sites (hollow sites, bridge sites, or top sites)
• The rate of diffusion is determined by the activation energy barrier for each jump

Influence of surface potential energy landscape

• The potential energy landscape of the surface influences the diffusion pathways and rates
• Atoms preferentially move along low-energy paths, such as surface channels or step edges
• Surface reconstructions can create anisotropic diffusion barriers, leading to directional diffusion
• Interactions between adatoms and the surface, as well as adatom-adatom interactions, can modify the potential energy landscape

Thermally activated process

• Surface diffusion is a thermally activated process, with the rate increasing exponentially with temperature
• The temperature dependence follows the Arrhenius equation: $D = D_0 \exp(-E_a/k_BT)$, where $D$ is the diffusion coefficient, $D_0$ is the pre-exponential factor, $E_a$ is the activation energy, $k_B$ is the Boltzmann constant, and $T$ is the absolute temperature
• Higher temperatures provide more thermal energy for adatoms to overcome diffusion barriers
• The activation energy for surface diffusion is typically lower than that for bulk diffusion, leading to faster diffusion rates on surfaces

Surface defects in diffusion

Role of steps and kinks

• Surface steps are one-dimensional defects that can act as preferential adsorption sites for diffusing species
• Steps lower the activation energy barrier for diffusion jumps, leading to faster diffusion rates along step edges compared to flat terraces
• Kinks are zero-dimensional defects at step edges that provide additional low-energy sites for adatom attachment and detachment during diffusion
• Kink sites have a higher coordination number than step sites, making them more stable and reducing the diffusion barrier

Influence of vacancies and other point defects

• Vacancies are point defects on the surface that can facilitate diffusion by providing empty sites for adatoms to jump into
• The presence of vacancies lowers the activation energy for diffusion, as adatoms can move into the vacant sites more easily
• Other point defects, such as interstitials or substitutional impurities, can also influence surface diffusion by modifying the local potential energy landscape
• Defect-mediated diffusion mechanisms, such as vacancy-assisted diffusion or interstitialcy diffusion, can become dominant at certain temperatures or defect concentrations

Enhanced diffusion at grain boundaries and dislocations

• Grain boundaries are interfaces between crystalline domains with different orientations, and they can act as fast diffusion pathways
• The disordered structure and higher energy of grain boundaries lead to increased adatom mobility compared to the bulk crystal
• Dislocations are line defects that can also enhance surface diffusion by providing low-energy sites and fast diffusion channels
• The strain field around dislocations can modify the local potential energy landscape, affecting the diffusion barriers and pathways

Temperature dependence of diffusion

Arrhenius behavior and activation energy

• The diffusion coefficient, $D$, quantifies the rate of surface diffusion and follows an Arrhenius temperature dependence: $D = D_0 \exp(-E_a/k_BT)$
• $D_0$ is the pre-exponential factor, which depends on the attempt frequency for diffusion jumps and the lattice geometry
• $E_a$ is the activation energy for diffusion, representing the energy barrier that an adatom must overcome to move from one adsorption site to another
• The activation energy depends on the surface material, crystal orientation, and the specific diffusion mechanism

Experimental techniques to study temperature dependence

• Field ion microscopy (FIM) can be used to directly observe the motion of individual adatoms on a surface as a function of temperature
• Scanning tunneling microscopy (STM) allows for imaging of surface diffusion processes with atomic resolution and can measure diffusion rates at different temperatures
• Helium atom scattering (HAS) can probe the dynamics of surface diffusion by measuring the changes in the helium atom beam intensity scattered from the surface
• Other techniques, such as low-energy electron diffraction (LEED) and reflection high-energy electron diffraction (RHEED), can provide information on the temperature-dependent surface structure and diffusion processes

Deviations from Arrhenius behavior

• In some cases, surface diffusion may exhibit non-Arrhenius behavior, where the diffusion coefficient does not follow a simple exponential dependence on temperature
• Deviations can arise from changes in the diffusion mechanism at different temperature regimes, such as a transition from hopping to exchange diffusion
• Interactions between adatoms, such as attractive or repulsive forces, can lead to coverage-dependent diffusion rates and non-Arrhenius behavior
• Quantum effects, such as tunneling or zero-point energy, can become significant at low temperatures and cause deviations from classical Arrhenius behavior

Diffusion mechanisms on surfaces

Hopping and exchange diffusion

• Hopping is the most common surface diffusion mechanism, involving adatoms jumping between adjacent adsorption sites on the surface
• The hopping rate depends on the activation energy barrier between the initial and final adsorption sites, as well as the attempt frequency
• Exchange diffusion occurs when an adatom replaces a surface atom, which then becomes a new adatom, leading to a net displacement of the adatom
• Exchange diffusion typically has a higher activation energy than hopping due to the additional energy required to displace a surface atom

Tunneling and quantum effects

• Tunneling diffusion is a quantum mechanical process where adatoms move through the potential energy barrier instead of over it
• Tunneling can be significant at low temperatures, where classical hopping is suppressed due to insufficient thermal energy
• Quantum effects, such as zero-point energy and delocalization of the adatom wavefunction, can modify the effective diffusion barrier and rates
• Isotope effects in surface diffusion can arise from differences in the quantum behavior of different atomic masses

Collective and correlated diffusion

• Collective diffusion involves the concerted motion of multiple adatoms or clusters, leading to faster diffusion rates than individual adatom hopping
• Correlated diffusion occurs when the motion of adatoms is influenced by their mutual interactions, such as attractive or repulsive forces
• Surface crowding and high adatom coverages can lead to modified diffusion mechanisms, such as the formation of diffusing clusters or the occurrence of multi-atom exchange processes
• Collective diffusion can play a role in surface phase transitions, such as the formation of ordered overlayers or the growth of self-assembled structures