Towards a continuum theory for phase transformations using atomistic calculations

M. G.A. Tijssens, R. D. James

Research output: Chapter in Book/Report/Conference proceedingChapter


We develop a continuum theory for martensitic phase transformations in which explicit use is made of atomistic calculations based on density functional theory. Following the work of Rabe and coworkers, branches of the phonondispersion relation with imaginary frequencies are selected to construct a localized basis tailored to the symmetry of the crystal lattice. This so-called Wannier basis helps to construct an effective Hamiltonian of a particularly simple form. We extend the methodology by incorporating finite deformations and passing the effective Hamiltonian fully to continuum level. The developments so far are implemented on a one-dimensional unstable di-atomic chain.

Original languageEnglish (US)
Title of host publicationComputational Fluid and Solid Mechanics 2003
PublisherElsevier Inc.
Number of pages3
ISBN (Electronic)9780080529479
ISBN (Print)9780080440460
StatePublished - Jun 2 2003

Bibliographical note

Publisher Copyright:
© 2003 Elsevier Science Ltd. All rights reserved.


  • Continuum free energy
  • Effective Hamiltonian
  • Martensitic phase transformation
  • Phonon-dispersion relation
  • Phonons
  • Wannier basis


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