Numerical study of transverse lattice waves connected with martensitic transformation

Abstract

The behavior of the transverse lattice wave connected with the nucleation process of martensite is studied, taking into account the anharmonicity, by use of one-dimensional model for the crystal. The key factor which determines the behavior of the transverse lattice waves according to the model is its amplitudeA with respect to the critical amplitudeA c. As far asA < A c, the presence of the transverse lattice wave does not lead to the initiation of the martensite. Depending on the variation ofA andA c with temperature, the model suggests two alternative processes for the initiation of the martensitic transformation. 1) In case the variation ofA c with temperature is larger than the variation ofA with temperature, the transverse lattice wave develops into the stable nuclei of the martensite, as soon asA c becomes smaller thanA with decrease of temperature. 2) In case the variation ofA with temperature is larger than the variation ofA c with temperature, the transverse lattice wave represents the heterophase fluctuation whenA « A c. The stable martensite is formed with the reduction ofA as temperature is reduced. The presently available experimental data suggest the process 1) as the nucleation mechanism of the martensite. The prominent role of the interface energy between the martensite and the austenite in determining both the structure of the martensite and the dispersion relationship of the transverse lattice wave in the austenite is pointed out.