On Landau theory and symmetric energy landscapes for phase transitions

Kai Hormann, Johannes Zimmer

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The aim of this presentation is the development of a general approach for modelling the global complex energy landscapes of phase transitions. For the sake of clarity and brevity the exposition is restricted to martensitic phase transition (i.e., diffusionless phase transitions in crystalline solids). The methods, however, are more broadly applicable. Explicit energy functions are derived for the cubic-to-tetragonal phase transition, where data are fitted for InTl. Another example is given for the cubic-to-monoclinic transition in CuZnAl. The resulting energies are defined globally, in a piecewise manner. We use splines that are twice continuously differentiable to ensure sufficient smoothness. The modular (piecewise) technique advocated here allows for modelling elastic moduli, energy barriers and other characteristics independent of each other.

Original languageEnglish
Pages (from-to)1385-1409
Number of pages25
JournalJournal of the Mechanics and Physics of Solids
Issue number7
StatePublished - Jul 2007
Externally publishedYes


  • A. Microstructures
  • A. Phase transformations
  • B. Elastic material
  • C. Optimization
  • C. Stability and bifurcation


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