**surface superstructure**(rus. суперструктура поверхности) — the term is used to denote a specific structure of the top atomic layer (or several layers) of a crystal.

### Description

The term "superstructure" has evolved because the structure of the surface layer can differ much from the structure of a crystal’s underlying layers, and this holds good even for an atomically clean surface, in the absence of any tramp adsorbates.

The notation to denote a certain superstructure relates its two-dimensional lattice with a lattice of a substrate’s ideal plane. This is usually done in one of the two ways below.

The notation proposed by Park and Madden is the definition of the matrix, which establishes a relationship between the vectors of primitive surface translations and the vectors of primitive ideal plane translations of a substrate. If , and , are the translation vectors of a superstructure and the substrate plane, respectively, then they can be described by the relationships as follows

The notation to denote a certain superstructure relates its two-dimensional lattice with a lattice of a substrate’s ideal plane. This is usually done in one of the two ways below.

The notation proposed by Park and Madden is the definition of the matrix, which establishes a relationship between the vectors of primitive surface translations and the vectors of primitive ideal plane translations of a substrate. If , and , are the translation vectors of a superstructure and the substrate plane, respectively, then they can be described by the relationships as follows

_{}

_{}

and the superstructure can be described by the matrix

Sometimes the notation used is as follows .

A more vivid but not that universal notation was proposed by Elizabeth Wood. This notation indicates the ratio of the primitive translation vector lengths of the superstructure and the substrate plane. If necessary, it can indicate the angle by which the surface unit cell must be rotated in order for its axes to be aligned with the primitive translation vectors of the substrate. Thus, if the substrate surface has formed a superstructure with primitive translations vectors

If the axes of the unit cell match the substrate axes, i.e. = 0, there is no need to specify the zero angle (for example, . To denote a centred lattice the letter c is used (for example, . If the superstructure is formed due to the adsorbate, the notation shall have the chemical symbol of the adsorbate at the end (for example, .

Sometimes the notation used is as follows .

A more vivid but not that universal notation was proposed by Elizabeth Wood. This notation indicates the ratio of the primitive translation vector lengths of the superstructure and the substrate plane. If necessary, it can indicate the angle by which the surface unit cell must be rotated in order for its axes to be aligned with the primitive translation vectors of the substrate. Thus, if the substrate surface has formed a superstructure with primitive translations vectors

_{}and the angle of , then the superstructure is described by .

If the axes of the unit cell match the substrate axes, i.e. = 0, there is no need to specify the zero angle (for example, . To denote a centred lattice the letter c is used (for example, . If the superstructure is formed due to the adsorbate, the notation shall have the chemical symbol of the adsorbate at the end (for example, .

#### Authors

- Zotov Andrey V.
- Saranin Alexander A.

#### Sources

- Park R. L., Madden H.H. Annealing changes on the (100) surface of palladium and their effect on CO adsorption // Surface Science. 1968. V. 11, №2. P. 188–202.
- Wood E. A. Vocabulary of surface crystallography // J. Appl. Phys. 1964. V. 35, №4. P. 1306–1312.
- Oura K. et al. Surface Science: An Introduction // Springer, 2010 - 452 pp.