Question

What is the relation between the edge lengths in body centered orthorhombic unit cells?

Answer 1

Hint There are 7 types of crystal systems possible and an orthorhombic crystal system is one of them. Here ortho is a greek word that means upright which suggests that all three axes will intersect each-other at ${{90}^{0}}$ that suggests that only its edges can be different in length.

Complete Step by step Solution:
As in orthorhombic crystal system all the axial angles are equal and $90{}^{0}$ So, lets search all the possibilities in edge length variations:
In the first situation all edge lengths a, b and c can be equal. Now when all edge lengths are equal and all the axial angles are equal and $90{}^{0}$ then these will be dimensions of the cube. So, this represents cubic crystal system
In the second situation two edge lengths (a, b) can be equal and c can be different. Now when only two edge lengths are equal and all the axial angles are equal and $90{}^{0}$ then this will resemble the dimensions of the tetragonal crystal system.
In third and last possibility all edge lengths a, b and c can be unequal. Now when all edge lengths are unequal and system all the axial angles are equal and $90{}^{0}$ then these dimensions are definitely going to represent an orthorhombic crystal system.

So, for a body centered orthorhombic crystal a, b and c, all three edge lengths will be unequal.

Additional information:
Rhombic sulfur, potassium sulfate, potassium nitrate, Barium Sulfate etc. are Solids that possess orthorhombic crystal systems.

Note: In orthorhombic crystal system there are four types of Bravais lattices are possible and there are: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.