What Is a Unit Cell Definition Types and Lattice Parameters Explained
An ordered arrangement of atoms, ions and molecules described in a Crystalline material is termed as Crystal structure. Ordered structures happen where the nature of particles shape up in a pattern that is symmetrical which repeats with the principle direction of matter in three-dimensional space.
The unit cell mirrors the structure and symmetry of the whole crystal that is created by the unit cell’s repetitive translation with its principal axis.
The principal axes’ length and the angles of the unit cell are known as lattice constants. They are known as cell parameters or lattice parameters.
The crystal’s properties of symmetry are defined by the space group’s concept.
The structure and symmetry of crystals play a vital role in defining multiple physical properties like cleavage, optical transparency and electronic band structure.
A unit cell is said to be the smallest repeating unit of the crystal lattice in the living organism, which is also said to be the building block of the crystal. That’s how life started to exist on earth. Atoms are arranged in a three-dimensional symmetry within a crystal structure.
A crystal structure is defined as the arrangement of particles in a unit cell in terms of geometry. The unit cell’s geometry is known as a parallelepiped.
It provides six lattice parameters marked as the cell edge’s length and their angles.
The particle's position in the unit cell is shown by fractional coordinates. They are measured by a reference point, with the edges of the cell. It is important to report the coordinates of particles of the smallest asymmetric subset. To occupy the smallest physical space, these particles are chosen, which proves that it’s not necessary for all the particles to be located physically inside the boundaries provided by lattice parameters.
Unit cell’s other particles are created by the symmetry operations which describe the unit cell’s symmetry. The collection of unit cell’s symmetry operations is defined as the Crystal structure’s space group.
The Group of atoms of the Crystal structure is the same, the basis, they are stationed around each and every lattice point.
There are three types of unit cells present in nature, primitive cubic, body-centered cubic, and face-centered cubic.
Types of Unit Cell
As we have already mentioned earlier, there are three types of unit cells, and we will discuss them in brief in this section.
Primitive Cubic Unit Cell
If you look at the primitive cubic unit cell, you will find out that only at the corners, you are going to find the atoms. Every single atom which is present in the unit cell is shared with the other adjacent cell. Meaning each unit cell shares its atoms with 8 other primitive cubic unit cells. Thus, a particular unit cell contains only ⅛ of an atom. On the other hand, 4 unit cells are present in the same layer, and there are 2 layers. The upper and the lower layer makes a particular unit cell be 1/8th of the atom that is present inside it.
(Image will be Uploaded Soon)
The total number of atoms present in the single primitive cubic unit cell can be counted by taking eight atoms present in the corner. Thus, ⅛ X 8 = 1 atom.
Body-Centered Cubic Unit Cell
The BCC is almost the same as a simple cubic unit cell, meaning it has eight atoms present in each corner of the cube and one atom in the center of the cube. BCC has an open structure. The atom which is present at the center solely belongs to the unit cell in which it is present.
(Image will be Uploaded Soon)
To find the number of atoms present in BCC, you need to consider two things.
First, 8 corners will make ⅛ per corner atom = 8 x ⅛ = 1 atom
One atom present at the center of the body = 1 atom
Thus, the body-centered cubic unit cell has two atoms.
Face-Centered Cubic Unit Cell (FCC)
A face-centered cubic unit cell is the most densely populated unit cell. In addition to this, at the center of the cube's faces, you will find out one atom. These face-centered atoms are shared between 2 adjacent unit cells, and only ½ of each atom is a part of the individual cell.
To find out the number of atoms present in the FCC, you need to know this in the first place.
There are 8 corners x 18 per corner atom = 8 x 18 = 1 atom
6 face-centered atoms x 12 atoms per unit cell = 3 atoms
Thus, we have 4 atoms in a Face centered cubic unit cell.
What is the Basic Unit of Life?
What distinguishes a living organism from a non-living object? Well, the answer is a living being will have self-sustaining biological processes. A cell is the smallest and the most basic form in which life exists on earth. The new cells made in the living organism came into existence from the division of the preexisting cells into two.
Classification of Crystal Structure by Symmetry
The property that is used to define Crystal structure is in its symmetry only. When some symmetry operations are performed on the Crystal lattice, it remains unchanged. All the crystals consist of translational symmetry in three types but it’s possible that some contain other elements of symmetry.
Lettice System:
When Crystal structures are grouped by the axial system which is used to define their lattice, it is known as lattice system.
Each lattice system has a set of axes that are arranged geometrically.
All the crystals come under the seven lattice system. They seem similar but they are not the same as the seven Crystal systems.
FAQs on Unit Cell in Crystallography and Solid State Chemistry
1. What is a unit cell in chemistry?
A unit cell is the smallest repeating three-dimensional portion of a crystal lattice that represents the entire crystal structure. It contains the arrangement of atoms, ions, or molecules in a crystalline solid and, when repeated in space, builds the whole crystal. Key points about a unit cell include:
- It is defined by its edge lengths (a, b, c) and interaxial angles (α, β, γ).
- It reflects the symmetry and geometry of the crystal.
- Repeating the unit cell in all directions forms the complete crystal lattice.
2. What are the types of unit cells?
The types of unit cells are primitive and centered unit cells, classified based on the arrangement of lattice points. The main types include:
- Primitive (simple): Atoms only at the eight corners.
- Body-centered (BCC): Atoms at corners and one at the center of the cube.
- Face-centered (FCC): Atoms at corners and at the center of each face.
- End-centered: Atoms at corners and at the centers of two opposite faces.
These classifications are used to describe crystal structures in solid-state chemistry.
3. What is the difference between a primitive and a body-centered unit cell?
The main difference is that a primitive unit cell has lattice points only at the corners, while a body-centered unit cell (BCC) has an additional lattice point at the center. In detail:
- Primitive (simple cubic): 8 corner atoms × 1/8 each = 1 atom per unit cell.
- Body-centered cubic (BCC): 8 corners (1 atom total) + 1 center atom = 2 atoms per unit cell.
This difference affects packing efficiency, density, and coordination number.
4. How do you calculate the number of atoms in a unit cell?
The number of atoms in a unit cell is calculated by adding the fractional contributions of atoms at corners, faces, edges, and the body center. The contributions are:
- Corner atom = 1/8 (shared by 8 cells)
- Face-centered atom = 1/2 (shared by 2 cells)
- Edge-centered atom = 1/4 (shared by 4 cells)
- Body-centered atom = 1 (fully inside)
For example, in an FCC unit cell: (8 × 1/8) + (6 × 1/2) = 1 + 3 = 4 atoms per unit cell.
5. What is the coordination number in a unit cell?
The coordination number is the number of nearest neighboring atoms surrounding a single atom in a crystal lattice. It depends on the type of unit cell:
- Simple cubic (SC): 6
- Body-centered cubic (BCC): 8
- Face-centered cubic (FCC): 12
A higher coordination number generally indicates closer packing and greater stability of the crystal structure.
6. What is the packing efficiency of different unit cells?
The packing efficiency is the percentage of space occupied by atoms in a unit cell. The common values are:
- Simple cubic (SC): 52%
- Body-centered cubic (BCC): 68%
- Face-centered cubic (FCC): 74%
FCC has the highest packing efficiency among cubic unit cells, meaning atoms are packed most closely in this structure.
7. How do you calculate the density of a unit cell?
The density of a unit cell is calculated using the formula ρ = (Z × M) / (a3 × NA). Here:
- ρ = density
- Z = number of atoms per unit cell
- M = molar mass
- a = edge length of the cubic cell
- NA = Avogadro constant (6.022 × 1023 mol-1)
This formula links crystal structure with measurable physical properties like density.
8. What is the relationship between edge length and atomic radius in cubic unit cells?
The relationship between edge length (a) and atomic radius (r) depends on the cubic structure type. The standard relations are:
- Simple cubic (SC): a = 2r
- Body-centered cubic (BCC): a = 4r / √3
- Face-centered cubic (FCC): a = 2√2 r
These relationships are derived from the geometry of atoms touching along edges, body diagonals, or face diagonals.
9. What are the seven crystal systems in crystallography?
The seven crystal systems classify crystals based on their unit cell dimensions and angles. They are:
- Cubic
- Tetragonal
- Orthorhombic
- Monoclinic
- Triclinic
- Hexagonal
- Rhombohedral (Trigonal)
Each system has characteristic edge lengths and interaxial angles that define its unit cell geometry.
10. Why is the unit cell important in solid-state chemistry?
The unit cell is important because it determines the physical and chemical properties of crystalline solids. It helps in:
- Calculating density and packing efficiency
- Determining coordination number
- Understanding crystal symmetry and structure
- Predicting properties like hardness, melting point, and conductivity
By studying the unit cell, chemists can relate microscopic atomic arrangement to macroscopic material properties.
