Abstract:
In this thesis, the author wishes to describe the development and subsequent use of a computational tool that can help analyse the defect-states
of the order parameter field that form near ferroelectric phase transitions,
within the purview of a generalized Landau Theory. Defect-states in the
order-parameter field are very important objects of study as they are manifestations of a very rich underlying physics that operate at multiple length
and time scales. The study of ferroelectrics as a class of materials is in itself
technologically promising as a backbone for devices that exhibit electrically
erasable memory. The use of a computational tool that helps validate the
energetic ease with which various defect-states can be formed in real ferroelectric materials such as BaTiO3 can serve as an invaluable step in the
design of memory devices such as FeRAM’s. We begin with an introduction to dislocation-mediated melting in 2D giving the example of KosterlitzThouless transition and thus motivate an investigation of topological defects.
