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Understanding Unit Cell - Types, Structure & FAQs
IMPORTANT LINKS
The Solid State
Defining a Unit Cell
A unit cell is the fundamental, repeating building block that constitutes a crystal lattice. It is the smallest repeatable unit in a crystal.
A unit cell is the fundamental, repeating building block that constitutes a crystal lattice. It is the smallest repeatable unit in a crystal.
The unit cells, identical in nature, are arranged in such a way that they fill up space without any overlaps. The crystal lattice, a three-dimensional arrangement of atoms, molecules, or ions, is composed of numerous unit cells. Each lattice point is occupied by one of the constituent particles.
Unit cells can be classified into three types: primitive cubic, body-centred cubic (BCC), or face-centred cubic (FCC). In this section, we will explore these types in more detail.
Primitive Cubic Unit Cell
The primitive cubic unit cell is characterized by atoms that are only present at the corners. Every atom at the corner is shared among eight adjacent unit cells, with four unit cells in the same layer and four in the upper (or lower) layer. As a result, a specific unit cell only contains 1/8th of an atom. The following figure illustrates this open structure, with each small sphere representing the center of a particle occupying that particular position.
Each cubic unit cell contains eight atoms at the corners, meaning the total number of atoms in one unit cell is 1.
Body-centred Cubic Unit Cell (BCC)
A BCC unit cell is characterized by atoms at all corners of the cube and one atom at the center of the structure. The atom at the center of the body belongs entirely to the unit cell it is present in.
Number of Atoms in BCC Cell:
The total number of atoms in a BCC cell is calculated as follows:
- 8 corners × 1/8 per corner atom = 1 atom
- 1 body center atom = 1 atom
Therefore, the total number of atoms per unit cell is 2 atoms.
Face-centred Cubic Unit Cell (FCC)
An FCC unit cell contains atoms at all corners of the crystal lattice and at the centers of all the cube faces. The atom at the center of each face is shared between two adjacent unit cells, and only half of each atom belongs to an individual cell.
Number of Atoms in FCC Cell
In an FCC cell, the total number of atoms is calculated as follows:
- 8 corners × 1/8 per corner atom = 1 atom
- 6 face-centered atoms × 1/2 atom per unit cell = 3 atoms
Therefore, the total number of atoms per unit cell is 4 atoms.
Volume of Hexagonal Close Packed (HCP) Unit Cell
A unit cell is the smallest representation of an entire crystal. The HCP unit cell has a coordination number of 12 and contains 6 atoms per unit cell. The face-centered cubic (FCC) unit cell also has a coordination number of 12, but it contains 4 atoms per unit cell.
The volume of an HCP unit cell can be calculated using the formula: Volume = area of base × height
Frequently Asked Questions
What is unit cell and its types?
The smallest replicating portion of a crystal lattice is a unit cell. Unit cells exist in many types. The cubic crystal structure, for example, consists of three distinct unit cell types : (1) plain cubic, (2) face-centered cubic, and (3) body-centered cubic.
What is meant by unit cell of crystal?
The unit cell is defined as the smallest repeated unit with full crystal structure symmetry. The unit cell geometry is known as a parallelepiped, providing six lattice parameters taken as the lengths of the edges of the cells (a, b , c) and the angles between them (α, β, ÿ).
How many kinds of primitive unit cells are possible?
Seven simple crystal structures exist; cubic, tetragonal, orthorhombic, hexagonal, monoclinic, triclinic, and rhombohedral. They differ in the way their crystallographic axes and angles are arranged. Bravis defined 14 possible crystal systems according to the above seven.
What do you mean by primitive unit cell?
A primitive cell (also known as a primitive unit cell) is a minimum-volume unit cell in mathematics, biology, mineralogy (especially crystallography), and solid state physics, referring to a single lattice point of a structure with discrete translation symmetry. The main cell is simple.
What is hcp unit cell?
In a unit cell, the number of coordinates of an atom is the number of atoms that it touches. The closest hexagonal packed (hcp) has a coordinating number of 12 and contains six atoms per unit cell. The face-centered cubic (fcc) has a total of 12 coordinates and contains 4 atoms per unit cell.