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Title: Martensitic transformation in TiNi based shape memory alloys : a first principles study
Author: Gandi, Appala Naidu
ISNI:       0000 0004 2732 1779
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2013
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The martensitic transformation in TiNi-based shape memory alloys has been investigated using various theoretical methods. The direct method for ab initio lattice dynamics is used for calculating phonon dispersion relations in austenite (B2) and martensites (B19, B19′). Normal mode symmetries in a B2 crystal are determined. Vibrational modes in the B2 crystal are labelled according to symmetry properties of their polarisation vector. Normal modes with imaginary frequencies are observed at the locations of experimentally observed soft modes. While labelling normal modes, the published mode symmetry label of a soft transverse acoustic (TA2) mode with a [Mathematical formula appears here. To view, please open pdf attachment] polarisation at [Mathematical formula appears here. To view, please open pdf attachment] is corrected to Σ2. Irreducible representations of the soft modes are used for determining the order parameters for various martensitic transformation paths experimentally observed using group theoretical methods. Accuracy of the interpolated frequencies in the phonon dispersion relations is assessed by using three different supercell sizes and by calculating the elastic constants from the slopes of the acoustic branches at the Brillouin zone. Born et al. derived a relation between the force constants and elastic constants for a general crystal. Further simplification of this relation is possible for a B2 crystal because of its symmetry. This simplification is derived by applying elementary group theory. Elastic constants calculated with the simplified relation are in agreement with the elastic constants calculated from the slopes of the dispersion relations. The self-consistent ab initio lattice dynamics (SCAILD) formulation is derived for an ordered compound. Precautions that need to be taken while practically implementing this formulation are discussed. The effect of Hf or Zr addition to a binary Ti-Ni system is studied by considering one configuration at each of five compositions from 0 to 25 at.% Hf or Zr. Elastic constants are calculated following a homogeneous deformation method. Selected normal mode frequencies are calculated using the direct method.
Supervisor: Dye, David ; Finnis, Mike Sponsor: UK-India Education and Research Initiative (UKIERI)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral