Dimension of a unit cell: Overview, Questions, Preparation

Unit cells are divided into two categories, namely primitive and centred unit cells.

Primitive Unit Cells: When constituent particles are present only on the corner positions of a unit cell, it is called a primitive unit cell. 

Centred Unit Cells: When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. 

The Centred unit cells are of three types: 

Body-Centred Unit Cells: This unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners. 

Face-Centred Unit Cells: This unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.

End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.

Here's a brief note on the topic of "Dimensions of a Unit Cell": In the study of crystalline solids, a fundamental concept is the "unit cell." A unit cell can be defined as the smallest repeating structural unit of a crystal lattice. The arrangement of particles in a crystal lattice can be described by specifying the dimensions of the unit cell.

• To fully describe the dimension of a unit cell, three parameters are commonly used: a, b, and c. These parameters represent the lengths of the unit cell edges along the three perpendicular axes, typically referred to as the x, y, and z axes.
• The angles between these edges are denoted as α, β, and γ.
• Therefore, the dimensions of a unit cell are determined by the lengths a, b, and c, as well as the angles α, β, and γ between them.

There are several types of unit cells based on their dimensions and angles:

Cubic Unit Cell: In a cubic unit cell, all the edges are of equal length (a = b = c) and all angles are 90 degrees (α = β = γ = 90°).

Tetragonal Unit Cell: In a tetragonal unit cell, two edges (a and b) have the same length (a = b), while the third edge (c) is of a different length, and all angles are 90 degrees.

Orthorhombic Unit Cell: In an orthorhombic unit cell, all three edges (a, b, and c) have different lengths, and all angles are 90 degrees.

Rhombic Unit Cell: In a rhombic unit cell, all three edges (a, b, and c) have different lengths, and all angles are not equal (α ≠ β ≠ γ).

Monoclinic Unit Cell: In a monoclinic unit cell, all three edges (a, b, and c) have different lengths, and only one angle (β) is not equal to 90 degrees.

Triclinic Unit Cell: In a triclinic unit cell, all three edges (a, b, and c) have different lengths, and all three angles (α, β, and γ) are not equal and not equal to 90 degrees.

We can find the volume of the unit cell using the  geometry and attributes of unit cells. Using volume and mass of atoms, we can calculate the density of the unit cell. A crystal lattice is represented in terms of unit cells. we can evaluate the density of crystal lattices by evaluating the density of unit cells.

Density of unit cell = mass of unit cell/volume of unit cell

The knowledge of unit cell parameters is important for determining the density of a crystal, understanding its symmetry, and predicting its physical properties.These parameters help in identifying and classifying different crystal systems, which are important in various fields, including materials science, mineralogy, and solid-state chemistry.

In conclusion, understanding the dimensions of a unit cell is fundamental when studying crystalline solids. These parameters provide essential information about the internal structure of crystals and are instrumental in unraveling their properties and behavior. In Class 12 NCERT Chemistry, the topic Dimensions of a Unit Cell is an important concept within the study of solid state. This topic is particularly relevant when discussing the arrangement of particles in crystalline solids, which are characterised by their highly ordered and repeating three-dimensional structures.