What is a Unit Cell?
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.
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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.
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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
1. What exactly is a unit cell in chemistry?
Think of a large, patterned wall made of identical tiles. A unit cell is like a single one of those tiles. It is the smallest repeating structural unit of a crystalline solid. When this single unit is repeated over and over in three dimensions, it forms the entire crystal structure, also known as the crystal lattice.
2. What are the main types of cubic unit cells studied in the CBSE syllabus?
In a cubic system where all sides are equal and all angles are 90°, there are three main types of unit cells:
- Simple Cubic (SC): Has particles only at the eight corners of the cube.
- Body-Centred Cubic (BCC): Has particles at the eight corners and one particle in the very centre of the cube's body.
- Face-Centred Cubic (FCC): Has particles at the eight corners and one particle in the centre of each of the six faces.
3. How do you calculate the number of atoms in a unit cell?
To find the total number of atoms, you must consider how atoms are shared between adjacent cells. The contribution is calculated as follows:
- An atom at a corner is shared by 8 unit cells, so its contribution is 1/8.
- An atom at a face centre is shared by 2 unit cells, so its contribution is 1/2.
- An atom at the body centre is not shared and belongs entirely to that unit cell, so its contribution is 1.
Using this, a Simple Cubic cell has 1 atom, a BCC has 2 atoms, and an FCC has 4 atoms in total.
4. What is the difference between a primitive and a non-primitive unit cell?
A primitive unit cell is the simplest type, where the constituent particles (atoms, ions, or molecules) are located only at the corners. A Simple Cubic (SC) cell is an example of a primitive unit cell. In contrast, a non-primitive unit cell contains particles at the corners as well as at other positions, such as the face centres (in FCC) or the body centre (in BCC).
5. How is a crystal lattice different from a unit cell?
A crystal lattice is a conceptual framework; it's an array of imaginary points in space that shows the arrangement of particles. The unit cell is the actual, physical building block containing the particles that is repeated at these lattice points to build the entire crystal. In simple terms, the lattice is the blueprint, and the unit cell is the brick used to build according to the blueprint.
6. Why is understanding the unit cell important for real-world materials?
The arrangement of atoms within a unit cell directly determines a material's physical and chemical properties. For example, the packing efficiency (how tightly atoms are packed) in FCC structures makes metals like copper and aluminium highly dense and ductile. The specific structure also influences a material's melting point, hardness, and electrical conductivity, which is crucial for engineering and technology.
7. Do unit cells always have to be perfect cubes?
No, they do not. While the cubic system is common, a unit cell's shape is defined by its edge lengths (a, b, c) and the angles between them (α, β, γ). Based on these parameters, unit cells are classified into seven crystal systems, which include cubic, tetragonal, orthorhombic, monoclinic, triclinic, rhombohedral, and hexagonal. The cubic system is just one where all sides are equal and all angles are 90°.
8. Are the perfect crystal structures shown in textbooks realistic?
The structures shown in textbooks represent an ideal, perfect crystal. In reality, all crystals contain defects or imperfections. These can be point defects (like a missing atom, called a vacancy) or line defects (dislocations). These defects are not always bad; they significantly influence the material's mechanical strength, electrical properties, and reactivity.
