Explain the structure of a hexagonal close-packed lattice in metals.

A hexagonal close-packed (HCP) lattice in metals is a tightly packed structure with a repeating pattern of hexagonal layers.

In more detail, the hexagonal close-packed structure is one of the two simple types of atomic packing with the highest density, the other being the face-centred cubic (FCC). This structure is referred to as 'close-packed' because it allows the maximum number of atoms to occupy a given volume.

The HCP structure consists of layers of atoms arranged in a hexagonal pattern, with a third layer nestled into the depressions of the first two, and so on. This creates a repeating ABAB pattern, where each letter represents a different layer. The atoms in each layer are in contact with three atoms in the layer below and three atoms in the layer above.

Each atom in a hexagonal close-packed structure has 12 nearest neighbours, which means it has a coordination number of 12. The coordination number is a measure of how many neighbouring atoms a particular atom is directly touching.

The packing efficiency of HCP structures is approximately 74%, meaning that 74% of the total volume is occupied by atoms. This is the same packing efficiency as the face-centred cubic structure. The remaining 26% is empty space, which can have significant effects on the properties of the metal, such as its density and its ability to deform.

The HCP structure is found in many metals including magnesium, zinc, and titanium. These metals exhibit certain characteristics due to their HCP structure. For example, they typically have lower ductility (ability to deform without breaking) compared to metals with a face-centred cubic structure. This is because the HCP structure has fewer slip systems (directions in which atoms can easily move) which makes it harder for the atoms to slide past each other under stress.

Understanding the structure of a hexagonal close-packed lattice is crucial in the study of materials science and solid-state chemistry, as it helps to explain the physical properties of many metals.