Crystal Packing

Introduction

When molecules pack together and form solids, they can either pack into a disordered, amorphous solid, or they can pack into a more ordered, crystalline form. The choice whether to pack into an amorphous or a crystal form depends on the molecules involved and the rates at which they solidify. If solids are allowed to form slowly, they will generally arrange into a crystal.

Crystals are a solid in which the atoms are spaced into a regular array known as a crystal lattice. Within the crystal lattice, the atoms are spaced in a repeating pattern. The smallest repeating unit is called the unit cell.

The seven classes of unit cells

There are seven classes of unit cells. They are seen in the diagram to the left with their degrees of freedom shown.

Packing arrangement variations exist in each of the classes, yet here we will only explore the cubic and the hexagonal classes because they are the simplest. All the packing arrangements we will see in the cubic and hexagonal classes can be extended to the other five unit cell classes.

Cubic unit cells

The simplest unit cells are known as cubic unit cells.

Simple cubic

The most simple unit cell is known as a simple cubic unit cell. This is where one atom occupies each of the eight corners of a cube. The distance from atom to atom along the lattice is the same in every direction, and the angle between each of axes is 90°.

Explore the simple cubic unit cell in the screen on the left.

Body-centered cubic

The next unit cell is known as the body-centered cubic. It has the same properties as the simple cubic cell, except there is an additional atom in the center of the cube. This packing can fit more atoms into less space than the simple cubic unit cell.

Face-centered cubic

A slightly more tightly packed unit cell is the face-centered cubic unit cell. In this form of crystal, there is an atom at each vertex of the unit cell. And there is an atom at the center of each of the six faces of the cubic unit cell. This crystal packing form has an even higher density than the body-centered cubic unit cell.

Hexagonal unit cells

As atoms attempt to pack even tighter, the cubic unit cell will yield and a hexagonal form arises. A hexagonal arrangement is more space-efficient than a cube. This can also be seen in the honeycomb of bees.

Simple hexagonal

The first of the different types of hexagonal unit cells is the simple hexagonal unit cell. The hexagons form sheets, and they stack on top of each other so a line perpendicular to the hexagonal sheet will go straight from atom to atom in the next sheet down.

Explore the simple cubic unit cell in the screen on the left.

Hexagonal closest packing

To achieve even higher densities, every other sheet of hexagons can be translated so the atoms of each sheet lie in the middle of the triangles of the adjacent sheets.

These two hexagonal forms conclude the hexagonal unit cells.

Review Question 1:

Load the structure below by selecting "Display."

What is the type of unit cell displayed on the screen?