# What is the packing fraction for a hexagonal structure?

## What is the packing fraction for a hexagonal structure?

HCP has a packing fraction of 74% assuming a hard sphere packing. This packing also implies an ideal c/a ratio (see below).

### What is the packing factor of spheres?

approximately 74%
For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 63.5%.

What is meant by hexagonal close packing of spheres?

Hexagonal close packed (hcp) refers to layers of spheres packed so that spheres in alternating layers overlie one another. Hexagonal close packed is a slip system, which is close-packed structure. The hcp structure is very common for elemental metals, including: Beryllium.

How do you solve hexagonal packing?

The area of the hexagon can be found by splitting it into six equilateral triangles and the total area is 6\times (1/\sqrt{3}) \times 1 = 2\sqrt{3} square units. To get the proportion of the plane covered by the circles we must divide by pi by 2\sqrt{3} to get 0.90689\ldots or 90.7\% to 3 significant figures.

## How do you find the hcp packing factor?

HCP has 6 atoms per unit cell, lattice constant a = 2r and c = (4√6r)/3 (or c/a ratio = 1.633), coordination number CN = 12, and Atomic Packing Factor APF = 74%.

### What is the atomic packing factor of the hexagonal close packing unit cell?

0.74
For fcc and hcp structures, the atomic packing factor is 0.74, which is the maximum packing possible for spheres all having the same diameter.

How do you calculate packing factor?

Another parameter that we need to define is the atomic packing factor (APF). This is the fraction of the volume occupied by the hard spheres in the unit cell. It can be calculated as the sum of the volume of the atoms divided by the volume of the unit cell, and it indicates the maximum possible packing of hard spheres.

What is hexagonal unit cell?

The hexagonal closest-packed structure is described by a hexagonal unit cell, which has a diamond shaped or hexagonal base with sides of equal length (a = b). The base is perpendicular to the longest side (length c)) of the unit cell. An atom is centered on each corner of the unit cell.

## What is the formula of hexagonal packing?

### What is the formula of packing efficiency?

Packing efficiency = Volume occupied by 6 spheres ×100 / Total volume of unit cells.