Crystal Lattice and Unit Cells

A crystal lattice is a three-dimensional arrangement of atoms, ions, or molecules in a crystalline solid. A unit cell is the basic repeating structural unit that forms the three-dimensional lattice of a crystalline solid. It is the smallest portion of the crystal lattice that, when repeated in all three dimensions, generates the entire crystalline structure.

Lattice Parameter

Different crystal lattice can be classified on the basis of lattice parameters. There are two main lattice parameters mentioned below:

• Lattice Constants (a, b, c): The lengths of the edges of the unit cell along the three axes are denoted as a, b, and c. These lengths are measured in units such as angstroms (Å) or picometers (pm).
• Angles Between Edges (α, β, γ): The angles between the edges of the unit cell, typically denoted as α, β, and γ. These angles define the orientation of the edges relative to each other and are measured in degrees.

Coordination Number

Coordination number is the number of atoms or ions directly adjacent to a central atom or ion in a crystal lattice. It indicates how many other particles are in direct contact with the central particle. The value of coordination number ranges from 2 to 12, the most common are 4, 6 and 8.

Types of Unit Cell

Unit cell can be classified as Primitive and Non-Primitive. No-Primitive Unit cell can be further classified as face centered, base centered and edge centered.

• Primitive Cubic Unit Cell
• Non-Primitive Unit Cell
  • Body-centered Cubic Unit Cell
  • Face centered cubic unit cell
  • Edge Centered

Primitive Cubic Unit Cell

In Primitive Cubic unit cell the atoms are present only at the corners. The properties of primitive unit cell is discussed below:

• Coordination Number: It has a coordination number of six which means every atom in a primitive cubic unit cell is directly joined to six other atoms.
• Atoms per Unit Cell: Each cube’s corner has a single atom. The eight nearby unit cells share these corner atoms. Hence, effective number of atoms per unit cell is 1.
• Edge Length Relationship: The equation a = 2r describes the relationship between the atomic radius (r) and the edge length (a) of the cubic unit cell.

Non-Primitive Unit Cell

Non-Primitive Unit Cells have atoms at corners of the unit cell as well as other places of the unit cell such as body center, face center or edge center. Based on this Non-Primitive unit cells are classified as follows

• Body-centered Cubic Unit Cell
• Face centered cubic unit cell

Body-Centered Cubic Unit Cell

In BCC unit cell, an atom is present in each cube corner and an extra atom is present in the center of a body-centered cubic arrangement. A body-centered cubic unit cell has the following essential characteristics:

• Coordination Number: Because it is physically related to eight nearby atoms, every atom in a body-centered cubic unit cell has a coordination number of eight.
• Atoms per Unit Cell: In a body-centered cubic lattice, a cube has two atoms per unit cell: one at each corner and one in the center.
• Connection between Atomic Radius and Edge Length: The equation a = 4r/√3 relates the atomic radius (r) to the edge length (a) of the cubic unit cell.

Face Centered Cubic Unit Cell

In FCC, there is extra atoms at the center of each face and atoms at each cube’s corner. A face-centered cubic unit cell has the following essential characteristics:

• Coordination Number: Because it is physically coupled to twelve nearby atoms, every atom in a face-centered cubic unit cell has a coordination number of twelve.
• Atoms per Unit Cell: The number of atoms in a face-centered cubic lattice is four per unit cell, with one atom located at each corner and one at the center of each face.
• Volume Occupied: The atoms in a face-centered cubic unit cell fill the whole volume of the unit cell and occupy the cube’s faces and corners.
• Edge Length Relationship: The equation a = 2√2 r describes the relationship between the atomic radius (r) and the edge length (a) of the cubic unit cell.

Solid State is a state of matter in which the shape and volume of matter remain unchanged irrespective of the container they are kept in. Solid state materials are of huge importance due to their wide ranging applications in daily lives. This versatility of solid state lead to formation of a separate field under the domain of chemistry named as Solid State chemistry.

In this article, we will lean in detail about solid state, its properties, types. We will also cover complete solid state chemistry to cover all the points related to solid state that would help in last minute revision for our exams.