SIMULATIONS AT THE NANOSCALE TO UNDERSTAND STRUCTURES AND DEFECTS THEREIN

A rich trove of concepts emerges by exploration into the nanoscale. Computational techniques have paved way for new results and discoveries and have set a vision for experiments to follow. Examples cited below highlight new methodologies developed and discoveries made in the Symmetry Lab of the Department of Materials Science and Engineering, IITK.

Discovery of a new class:

NEUTRAL EQUILIBRIUM MATERIAL-STRUCTURES [1]

A ball on a plane represents a rigid body in neutral equilibrium. A limited number of structures like Anglepoise lamps and certain tensegrities have been identified to exist in a state of neutral equilibrium with respect to change in configurations and have been classified as zero-stiffness structures (i.e. the energy of the system does not change with configurations). Defining a super-class of material-structures (which lie in-between materials and structures), the authors discover a non-trivial new class: 'the zero-stiffness material-structures' (in these like 'ball on a plane' or a neutral equilibrium structure, the energy of the system does not change with respect to configurations). Eshelby's classic work from 1951 is taken forward in making this discovery. Eshelby had considered an edge dislocation in a thin 'bendable plate'. Hence, now we can have rigid bodies, structures and material-structures in a state of neutral equilibrium.
This work also introduces a new concept: "Reversible Plastic Deformation due to Elasticity". This implies that with the motion of the dislocation along the length of the plate (the direction of which can be reversed) there is permanent deformation (plastic deformation), arising out of elastic stress fields.

The above discovery is based on the following fundamental work.

SIXTY YEAR OLD THEORY OF IMAGE FORCES ON EDGE DISLOCATIONS CHALLENGED [2]

Dislocations can feel forces either due to (i) externally applied forces or (ii) due to the presence of interfaces in the material. The configurational force experienced by a dislocation towards a free surface is termed as the 'image force' (i.e. this can arise without an application of external forces). The usual technique of calculation of the image force involves the construction of a negative image (or a sequence of images…; which can extend to infinity!) on the other side of the free surface. Developing a simple new methodology to calculate image forces on edge dislocations without using any fictitious images; the authors have shown that the 60 year old theory (A.K. Head, Proc. Phys. Soc. B 66 (1953) p.793) usually found in textbooks, breaks down when image forces become relevant. It is to be noted that image forces become relevant when a dislocation is positioned close to a free-surface. The technique is applicable to structural dislocations as well (e.g interfacial misfit edge dislocations in epitaxial systems). A new concept of positive images is also introduced (i.e. It is shown that an ‘image’ can be negative (attractive), zero or even positive (repulsive)).

For details please consult:
[1] Materials analogue of zero-stiffness structures
Arun Kumar and Anandh Subramaniam
Philosophical Magazine Letters, Vol. 91, No. 4, April 2011, 272–279.

[2] Image forces on edge dislocations: a revisit of the fundamental concept with special regard to nanocrystals
Prasenjit Khanikar, Arun Kumar and Anandh Subramaniam
Philosophical Magazine, Vol. 91, No. 5, 11 February 2011, 730–750.

(Philos. Mag. is a journal published since 1798)

Anandh Subramaniam
FB408, Department of Materials Science and Engineering (MSE)
Indian Institute of Technology, Kanpur- 208016
Phone : (+91) (512) 259 7215
Fax : (+91) (512) 259 7505
Email : anandh@iitk.ac.in, anandh333@rediffmail.com
URL : home.iitk.ac.in/~anandh