 # Crystal Lattices and Unit Cell

The imaginary, three-dimensional representation of atoms and molecules present in any solid crystal is known as crystal lattice. The definition of the crystal lattice is the symmetrical three-dimensional arrangement of atoms, ions of the crystalline solid as spatial points. You can picture many cricket balls arranged in an orderly fashion inside a box to understand the structure. Now for getting it organized correctly, the best way is to form layers of cricket balls inside the container, placing one above the other (see the picture below for reference). There are a total of fourteen possible three-dimensional lattices with six basic shapes.

### Characteristics of Crystal Lattice

The fourteen crystal lattice show similar characteristics, and they are:

• The lattice is made up of many points, and these represent one part of the crystal and therefore known as lattice point in the crystal lattice.

• Each point represents a part of the crystal, made up of building particles, which may be an atom or a molecule or ions.

• Once these lattice points are joined, one can derive the shape of the crystal.

• Each of the fourteen Bravais Lattices has a unique shape.

### Unit Cell

The building block of a crystal lattice that gets repeated multiple times at different directions in the crystal structure is called a unit cell. These cells have the least volume and can come together to form the shape of the crystal lattice. A unit cell holds a geometric shape in itself, having three edges at three respective angles.

### Characteristics of a unit cell

• The three edges of the unit cell are a, b, and c that can be represented in the vectors.

• The three edges a, b, and c doesn’t necessarily have to be at 90° to each other.

• The angle forming between edges b and c is called α, the angle formed between edges a and c is β, and the angle between a and b is known as γ.

### Types of Unit Cell

1. Primitive Unit Cells

The primitive unit cell has atoms, ions, or molecules at the lattice corners, and no other position. Therefore, primitive unit cells have a singular lattice point.

2. Non - Primitive Unit Cells

Here, the particles are not just at the lattice corners but also in other crystal lattice positions, including that of being on either face and inside the unit cell. Therefore, a non-primitive unit cell has more than one lattice point. The three types of non-primitive unit cells are:

a. Body Centred: In such an arrangement, a unit cell comprises only one building block, an atom, ion, or molecule located in the centre of its body, while others are across the corners. There's a relationship established between the atomic radius and unit cell based on the formed cube diagonal. The diagonal has one radius from each corner and one more at the central atom. The representation of the length of one side would be:

$a = \frac{4r}{\sqrt{3}}$

b. Face Centred: An unit cell that contains constituent elements like atoms, ions, or molecules on each of its face, and other elements at its corners. Since in such types of unit cells, there's no atom present in the centre, therefore the atoms present in the centre of the face share two cells; i.e. each of the six faces share one and half of an atom = three atoms. The relationship between the length of the unit cell to that of the diagonal is that four atomic radii and therefore can be represented as:

$a = \frac{4r}{\sqrt{2}}$

c. End Centred: An unit cell with a single constituent particle of atom, molecules, or ions located in the centre of the opposite faces, apart from that present in the corners.

### Difference between Crystal Lattice and Unit Cell

What is a Crystal Lattice?

The crystal lattice is the arrangement of the constituent particles like atoms, molecules, or ions in a three-dimensional surface. The constituent particles form the dots when they are arranged on the crystal lattice. The lattice in itself represents the imaginary array of all lattice points that are known to be infinite, located in the space - periodic and regular.

What is a Unit Cell?

On the other hand, the unit cell is known to be the building blocks of the crystal lattice, as they get repeated in three-dimensional space to yield shape to the crystal. Unlike crystal lattice, a unit cell has a definite volume and a specific number of points.  Therefore a crystal lattice and unit cell coexist in a three-dimensional representation of atoms, ions or molecules in a crystal.

### Ionic Lattice and Covalent Lattice

When any crystal is made up of constituent ions, the formed compound is known as an ionic lattice. Some of the more popular ionic lattices are the crystals of potassium permanganate, copper sulfate.

Similarly, when any crystal gets formed with the help of covalent bonds between the constituent atoms, it is called the covalent lattice. Examples of such infinite covalent lattices could be that of a diamond, silicon, quartz, and more.

1. What are Lattice Defects?

In theory, the ionic lattice only shows the representation of a solid crystal, where the atoms or ions get repeated at regular intervals (also known as unit cells). However, in reality, crystals often exhibit lattice defects, where an atom or many atoms can be missing from its estimated position into particular sites. Such crystals could be examples of lattice defects that can lead to having better conducting abilities in compounds. Some of the more popular defects are Frenkel defect, Schottky defects, etc.

2. Give the Significance of a Lattice Point.

The following are the significance of a lattice point:

• Also known as the lattice side, each point in a crystal lattice represents a constituent particle known as an atom, molecule, or an ion.

• Each lattice point comes from a similar surrounding, except those present on the surface or corner of a crystal.

• When a line is drawn between two lattice points, it would have to pass multiple identical locations at regular intervals.

• When joined on straight lines, the lattice points can bring out the lattice geometry, which does not show any chemical bondings.