A Brief Overview of Crystal Lattices

Solid substances are divided into two categories:

1. Amorphous solids: Amorphous solids have no definite order or arrangement of atoms, molecules, and ions. They follow a short-range order.

2. Crystals: A crystal has a well-defined arrangement of the particles in the space. They follow a long-range order.

A crystal lattice is a three-dimensional depiction of atoms and molecules organised in a specific order or pattern. A crystal lattice may be described as the spatial arrangement of constituent particles of matter (atoms, ions, or molecules) as points in space. Each point represents a different element of the crystal. Auguste Bravais, a french chemist, discovered that there are only 14 three-dimensional lattices that may be constructed, known as the Bravais lattice.

The following are the names of the crystal lattice systems:

1. Primitive cubic (a = b = c, 𝛂 = 𝞫 = 𝝲 = 90o )

2. Body-centred cubic (a = b = c, 𝛂 = 𝞫 = 𝝲 = 90o )

3. Face-centred cubic (a = b = c, 𝛂 = 𝞫 = 𝝲 = 90o )

4. Primitive tetragonal (a = b ≠ c, 𝛂 = 𝞫 = 𝝲 = 90o )

5. Body-centred tetragonal (a = b ≠ c, 𝛂 = 𝞫 = 𝝲 = 90o )

6. Primitive Orthorhombic (a ≠ b ≠ c, 𝛂 = 𝞫 = 𝝲 = 90o )

7. Base-centred Orthorhombic (a ≠ b ≠ c, 𝛂 = 𝞫 = 𝝲 = 90o )

8. Body-centred Orthorhombic (a ≠ b ≠ c, 𝛂 = 𝞫 = 𝝲 = 90o )

9. Face-centred Orthorhombic (a ≠ b ≠ c, 𝛂 = 𝞫 = 𝝲 = 90o )

10. Primitive monoclinic (a ≠ b ≠ c, 𝞫 = 𝝲 = 90o ,𝛂 ≠ 90o )

11. Base-centred monoclinic  (a ≠ b ≠ c, 𝞫 = 𝝲 = 90o ,𝛂 ≠ 90o )

12. Triclinic (a ≠ b ≠ c, 𝛂 ≠ 𝞫 ≠ 𝝲 ≠ 90o )

13. Rhombohedral (a = b = c, 𝛂 = 𝞫 = 𝝲 ≠ 90o )

14. Hexagonal (a = b ≠ c, 𝛂 = 𝞫 =90o, 𝝲 = 120o )

 Properties of Crystal lattice

• Each atom, molecule, or ion (constituent particle) in a crystal lattice is represented by a single point in the crystal lattice.

• The term “lattice site” or “lattice point” refers to these sites occupied by particles.

• In a crystal lattice, lattice sites or points are connected by a straight line that connects them together.

• As a result of connecting these straight lines, we may get a three-dimensional representation of the structure. The term for this 3D structure is Crystal Lattice, which is also known as Bravais Lattices. 

• There are 14 types of Crystal lattices present, also known as Bravais Lattices. Each lattice has its unique crystal structure.

Unit Cell

A unit cell is the smallest part in the crystal lattice whose repetition in space in different directions generates the entire crystal lattices. It gives the maximum idea about the nature of crystals.

A unit cell has six parameters that define the nature of crystal lattice – three edges a, b, c, and three angles α, β, γ. These parameters can be identical and different depending on the type of lattice. 

There are two types of unit cells present:

1. Primitive Unit cell 

2. Centred Unit cell

 Primitive Unit Cell

When the constituent particles (atoms, molecules, and ions) occupy only the corner position of the unit cell, it is called the primitive unit cell. It is also known as the simple cubic unit cell because it is the simplest unit cell present in nature.

Centred Unit Cell

When the constituent particles (atoms, molecules, and ions) occupy other positions along with the corner position as well, the unit cell is called a centred unit cell. A centred unit cell has three types:

1. Body-centred: The unit cell in which constituent particles occupy all the eight corners, as well as one at the centre of the body, is called a body-centred unit cell.

2. Face-centred: The unit cell in which constituent particles occupy all the eight corners, as well as the centre of each face of the unit cell, is called a face-centred unit cell.

3. End-centred: The unit cell in which constituent particles occupy all the eight corners, as well as the centre of the two opposite faces, is called an end-centred unit cell.

Number of Atoms in a Unit Cell

1. Primitive Cubic Unit Cell

A primitive cubic unit cell contains atoms only at the corners of the unit cell. There are a total of 8 corners present in a cubic unit cell, so 8 atoms are present at the corners, and those corner atoms contribute only 1/8th of the original volume to the unit cell. 

Total number of atoms in a primitive cubic unit cell = 18 x 8 = 1 atom

So, only one atom is present in the primitive unit cell.

2. Body-centred Cubic Unit Cell

A body-centred cubic unit cell contains atoms at the corners of the unit cell and one atom at the centre of the unit cell. There are a total of 8 corners in a body-centred cubic unit cell, so 8 atoms are present at the corners, and one corner atom contributes only 1/8th of the original volume to the unit cell; and one atom contributes fully because it is present at the centre of the unit cell.

 Total number of atoms in a body-centred cubic unit cell =18 x 8 + 1 = 2 atoms

Lattice Defects

The calculated tensile strength of a crystal based on a mathematically perfect ionic lattice would be significantly larger than what is observed. Lattice faults are causes of weakness in real crystals. Lattice defects include ions that are absent from their predicted places and ions that occupy unexpected coordination sites. Lattice faults may also be advantageous, as they improve the conductivity of some semiconductor materials.

Conclusion

After discussing crystal lattice, including its properties and various types, we now understand that the pattern generated by the constituent particles is known as the ‘crystal lattice,’ and it is used to indicate the placements of these recurring structural components. We also know that a lattice is the best way to explain the repeating pattern of an ideal crystal.