1. Anandh Subramaniam & Kantesh Balani
Defect in a Defect
&
Hierarchy of Defects
MATERIALS SCIENCE
&
ENGINEERING
Anandh Subramaniam & Kantesh Balani
Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur
URL: home.iitk.ac.in/~anandh
AN INTRODUCTORY E-BOOK
Part of
A Learner’s Guide

2. Defect in a Defect! This is an interesting concept to explore.
We will consider some examples to explore this concept.
0D ◘ Vacancy is a point defect. Vacancies can get ordered to form Vacancy Ordered Phases. ◘ There could be point defect in the Vacancy sublattice → an atom present where a vacancy should have been there (Atom is a defect in the vacancy sublattice!) → this is a defect in a defect!
1D ◘ Dislocation is a defect. ◘ A kink or a jog is a defect in the dislocation line → a defect in a defect.
2D ◘ Surface is a defect. ◘ Defect in a defect → Steps in a surface is a defect in the surface. ◘ Defect in a defect in a defect → Steps in these steps is a defect in the steps

3. 0D Perfect Ordered Crystal Vacancy Ordered Phase Schematics
In a Vacancy Ordered Phase (VOP) there could be a vacancy in the ‘vacancy sublattice’ → this is an atom!  we can conceive such a hierarchy of ‘higher order’ defects!
Vacancy in the vacancy sublattice → i.e. an atom!
Perfect Ordered Crystal
Vacancy Ordered Phase
Schematics

4. We can even further visualize things like a kink in the jog!1D
We can even further visualize things like a kink in the jog!

5. 2D
Defect in the surface
Defect in the Ledges

6. Hierarchy of Defects This is another interesting concept
We will try to understand this using the example of VOP
We have seen that an atom is a defect in the vacancy sublattice of the VOP.
These atoms could be randomly present in the vacancy sublattice or be ordered in the sublattice to give a sub-sublattice
A defect in this atom sub-sublattice of the vacancy sublattice is again a vacancy!
This process of formation of defects in ‘sub’, ‘sub-sub’ … can be carried forward and we can conceptualize this hierarchy of defects!