J. Phys. IV France 112 (2003) 119
DOI: 10.1051/jp4:2003847

An application of a polytope (4D-polyhedron) concept for the description of polymorphic transitions: Iron martensite and solid oxygen

V.S. Kraposhin¹, M.N. Pankova¹, A.L. Talis² and Yu.A. Freiman<sup>3

1</sup>  I.P. Bardin State Science Center for Ferrous Metallurgy, 2${\rm nd}$ Baumanskaya Ul. 9/23, 107005 Moscow, Russia
²  Institute for the Mineral Synthesis, lnstitutskaya Ut. 1, 601650 Alexandrov, Russia
³  B. Verkin lnstitute for Low Temperature Physics and Engineering, National Academy of Science, 310164 Kharkiv, Ukraine

Abstract
A polymorphic transformation between BCC and FCC phases can be described in the framework of the root lattice E ₈ in a 8D-space as the hypothetical praphase with symmetry group playing a role of the supergroup for both participants of the transformation. The special subset of vectors of the E ₈ and coinciding topologically with the unit cell of the A15 structure (Cr ₃Si-type) in the 3D Euclidian space was found, this subset can be regarded as an intermediate configuration during transformation between FCC and BCC structures. The proposed description of the polymorphic transformation is supported by experimentally observed habite planes of martensite in iron based alloys and by the existence ofthe A15-phase in the solid oxygen.

© EDP Sciences 2003