Crystal lattices and unit cells

In the field of solid state chemistry, understanding the nature of crystal lattices and unit cells is crucial to understanding the structure and properties of solids. These concepts are key to understanding how atoms and molecules arrange in space to form the substances we encounter in everyday life, from table salt to diamonds. In this lesson, we will explore the detailed nature of crystal lattices and unit cells using simple language and illustrative examples.

What is a crystal lattice?

A crystal lattice is the three-dimensional arrangement of atoms or molecules in a crystalline solid. Imagine it as a grid where each point on the grid represents the position of an atom or group of atoms. The entire lattice is a repetitive, orderly pattern that extends in all directions.

Imagine the crystal lattice of a simple structure like sodium chloride (NaCl). In NaCl, each sodium ion (Na⁺) is surrounded by six chlorine ions (Cl⁻), and vice versa, arranged in a cubic structure. We can represent this arrangement as follows:

In this illustration, the green squares represent sodium ions, and the yellow squares represent chlorine ions in the crystal lattice.

Basic terminology

Before delving deeper, it is important to be familiar with some terminology related to crystal lattices:

• Point lattice: A three-dimensional arrangement of points that corresponds to the positions of atoms in a crystal.
• Basis: The atom or group of atoms associated with each point in the lattice.
• Coordination number: The number of nearest neighbouring atoms around a given atom.
• Lattice parameters: Definitions such as edge lengths and angles between the sides of a unit cell.

Unit cell: the building block of a crystal

The unit cell is the smallest repeating unit of a crystal lattice which, when put together in all directions, recreates the complete lattice. It contains all the structural information about the lattice and can be repeated indefinitely to form a complete structure.

There are seven unique crystal systems that define distinct unit cells based on their geometrical property. These systems are:

1. Cube
2. Square
3. Orthorhombic
4. Rhombic (or triangular)
5. Hexagonal
6. Monoclinic
7. Triclinic

Cubic crystal system

The cubic system is one of the simplest and most symmetrical. It consists of cells where all sides (edges) are the same length and all angles are 90 degrees. Examples include NaCl, where the sodium and chlorine atoms form a face-centered cubic (FCC) pattern.

Let's look at a simple cubic unit cell:

Here, the lines represent the edges of the cube, and the vertices (corners) are the specific locations of the lattice points.

Types of unit cell

Unit cells can exist in different types depending upon the arrangement and location of atoms with respect to the edges and faces of the cell. The main types are:

Simple cube (SC)

In the simple cubic structure, atoms are located only at the corners of the cube. The coordination number is 6, which means that each atom touches six others. Examples include the structure of polonium.

Body-centered cubic (BCC)

The body-centered cubic arrangement has one atom at each corner of the cube and an additional atom at the center of the cube. The coordination number is 8. Metals such as iron and tungsten are common examples.

In this representation, the red circles represent the corner atoms, and the blue circle represents the additional atom at the center of the cell.

Face-centered cubic (FCC)

In the face-centered cubic structure, atoms reside at each corner of the cube and at the center of each face. The coordination number is 12, which provides high packing efficiency. This configuration is common in metals such as aluminum, copper, and gold.

Here, the red circles represent the corner atoms, while the blue circles represent the atoms at the center of each face.

Importance of crystal lattices and unit cells

The study of crystal lattices and unit cells is fundamental in understanding the properties of matter. Here are some reasons for this:

• Durability and strength: The strength of a material can often be linked to its crystal structure. For example, the FCC structure usually provides a good balance of ductility and strength.
• Electrical conductivity: Metallic bonding in densely-packed structures like FCC helps in excellent electrical conductivity.
• Thermal expansion: Some structures expand more when heated because the arrangement and bonding of atoms are different.
• Reactivity and catalysis: Surface structure plays an important role in catalytic activity, which is often related to how the unit cells expose atoms.

Cubic structures are generally easy to theoretically analyze because of their regular, symmetrical shape. However, it is important to understand less symmetrical structures, such as monoclinic or triclinic systems in materials such as crystals and minerals.

Conclusion

Crystals are a beautiful expression of order in the natural world. Studying their lattices and unit cells is not just a theoretical exercise, but a practical necessity for understanding and developing new materials. As our knowledge of crystal structures grows, so does our ability to customize materials for specific applications in technology, engineering, and medicine.

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