Defect in a Defect & Hierarchy of Defects

1. MATERIALS SCIENCE & ENGINEERING Part of A Learner’s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email:anandh@iitk.ac.in, URL:home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm Defect in a Defect & Hierarchy of Defects

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 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. 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!