Gold crystallizes as a face-centered cubic crystal....

Gold crystallizes as a face-centered cubic crystal. Calculate the surface number density of gold atoms in the 100 planes. Take the length of the unit cell (Figure $29.3$ ) to be $407.9 \mathrm{pm}$.

Key Concepts

Face-Centered Cubic (FCC) Crystal Structure

The face-centered cubic structure is a common crystal arrangement where atoms are situated at each of the eight corners of a cube along with one atom centered on each of the six faces. This highly symmetric configuration results in an efficient packing and influences many physical properties such as density and surface structure.

Crystallographic Planes (Miller Indices)

Crystallographic planes are denoted by Miller indices, which provide a shorthand notation for identifying the orientation of planes within a crystal lattice. The notation helps in analyzing the atomic arrangement on different surfaces, such as the (100) plane in cubic crystals, which is critical for understanding and calculating surface properties.

Surface Number Density

Surface number density is defined as the number of atoms per unit area on a particular crystallographic face. This measure is essential when studying surface properties, including catalysis and adsorption, as it quantifies how packed the atoms are on a given plane of the material.

Unit Cell Dimensions

The unit cell of a crystal is the smallest repetitive volume that fully describes the structure of the material, with its dimensions directly linked to physical properties such as area and volume. Using the unit cell edge length allows one to relate the lattice parameters to properties like surface number density, which depends on the geometry of the cell face.

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