Martensitic transformation in TiNi based shape memory alloys – a first principles study

摘要

The martensitic transformation in TiNi-based shape memory alloysudhas been investigated using various theoretical methods. The directudmethod for ab initio lattice dynamics is used for calculating phononuddispersion relations in austenite (B2) and martensites (B19, B19′).udNormal mode symmetries in a B2 crystal are determined. Vibrationaludmodes in the B2 crystal are labelled according to symmetryudproperties of their polarisation vector. Normal modes with imaginaryudfrequencies are observed at the locations of experimentally observedudsoft modes. While labelling normal modes, the published mode symmetryudlabel of a soft transverse acoustic (TA2) mode with a [Mathematical formula appears here. To view, please open pdf attachment]udpolarisation at [Mathematical formula appears here. To view, please open pdf attachment] is corrected to Σ2. Irreducible representationsudof the soft modes are used for determining the order parametersudfor various martensitic transformation paths experimentally observedudusing group theoretical methods. Accuracy of the interpolated frequenciesudin the phonon dispersion relations is assessed by using threeuddifferent supercell sizes and by calculating the elastic constants fromudthe slopes of the acoustic branches at the Brillouin zone.udBorn et al. derived a relation between the force constants andudelastic constants for a general crystal. Further simplification of thisudrelation is possible for a B2 crystal because of its symmetry. Thisudsimplification is derived by applying elementary group theory. Elasticudconstants calculated with the simplified relation are in agreementudwith the elastic constants calculated from the slopes of the dispersionudrelations.udThe self-consistent ab initio lattice dynamics (SCAILD) formulationudis derived for an ordered compound. Precautions that need to beudtaken while practically implementing this formulation are discussed.udThe effect of Hf or Zr addition to a binary Ti-Ni system is studiedudby considering one configuration at each of five compositions from 0udto 25 at.% Hf or Zr. Elastic constants are calculated following audhomogeneous deformation method. Selected normal mode frequenciesudare calculated using the direct method.