Overlayer

Short description: Layer of adatoms adsorbed onto a surface

An overlayer is a layer of adatoms adsorbed onto a surface, for instance onto the surface of a single crystal.[1]

## Contents

* 1 On single crystals
* 2 Types
* 3 Notation
* 3.1 Wood's notation
* 3.2 Matrix notation
* 4 See also
* 5 Citations
* 6 References
* 6.1 Textbooks
* 6.2 Websites

## On single crystals

Adsorbed species on single crystal surfaces are frequently found to exhibit long-range ordering; that is to say that the adsorbed species form a well-defined overlayer structure. Each particular structure may only exist over a limited coverage range of the adsorbate, and in some adsorbate/substrate systems a whole progression of adsorbate structure are formed as the surface coverage is gradually increased.[2]

The periodicity of the overlayer (which often is larger than that of the substrate unit cell) can be determined by low-energy electron diffraction (LEED), because there will be additional diffraction beams associated with the overlayer.[3]

## Types

There are two types of overlayers: commensurate and incommensurate. In the former the substrate-adsorbate interaction tends to dominate over any lateral adsorbate-adsorbate interaction, while in the latter the adsorbate-adsorbate interactions are of similar magnitude to those between adsorbate and substrate.[4]

## Notation

An overlayer on a substrate can be notated in either Wood's notation or matrix notation.[5]

### Wood's notation

Wood's notation takes the form

[math]\displaystyle{ \text{M}(hk\ell) - \left( \tfrac{|\textbf{a}_0|}{|\textbf{a}_s|} \times \tfrac{|\textbf{b}_0|}{|\textbf{b}_s|} \right) - \text{R}\alpha^\circ - \text{A} }[/math]

where M is the chemical symbol of the substrate, A is the chemical symbol of the overlayer, [math]\displaystyle{ (hk\ell) }[/math] are the Miller indices of the surface plane, R and [math]\displaystyle{ \alpha }[/math] correspond to the rotational difference between the substrate and overlayer vectors, and the vector magnitudes shown are those of the substrate ([math]\displaystyle{ s }[/math] subscripts) and of the overlayer ([math]\displaystyle{ 0 }[/math] subscripts). This notation can only describe commensurate overlayers however, while matrix notation can describe both.

### Matrix notation

Matrix notation differs from Wood's notation in the second term, which is replaced by the [math]\displaystyle{ G }[/math] matrix that describes the overlayer primitive vectors in terms of the substrate primitive vectors:

[math]\displaystyle{ \begin{pmatrix} \textbf{a}_0\\\ \textbf{b}_0 \end{pmatrix}= G \begin{pmatrix} \textbf{a}_s\\\ \textbf{b}_s \end{pmatrix} }[/math], where [math]\displaystyle{ G=\begin{pmatrix} G_{11} & G_{12}\\\ G_{21}& G_{22}\\\ \end{pmatrix} }[/math]

and so hence matrix notation has the form

[math]\displaystyle{ \text{M}(hk\ell) - G - \text{R}\alpha^\circ - \text{A} }[/math]

## See also

* Surface reconstruction
* Superstructure
* LEED#Superstructures

## Citations

1. ↑ Kolasinski 2012, p. 10.
2. ↑ Classification of Overlayer Structures.
3. ↑ Attard & Barnes 1998, p. 53.
4. ↑ Attard & Barnes 1998, p. 33.
5. ↑ Attard & Barnes 1998, p. 34,35,36,53,54.

## References

### Textbooks

* Kolasinski, Kurt W. (2012). Surface Science: Foundations of Catalysis and Nanoscience (3 ed.). Wiley. ISBN 978-1119990352.
* Attard, Gary; Barnes, Colin (1998). Surfaces. Oxford Chemistry Primers. ISBN 978-0198556862.

### Websites

* "6.1: Classification of Overlayer Structures". 11 February 2015. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Surface_Science/6:_Overlayer_Structures_and_Surface_Diffraction/6.1:_Classification_of_Overlayer_Structures.

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