Analysis of the tetragonality of the crystal lattice of martensite of Fe-C alloys in the hard-sphere model

The model of packaging solid atoms-spheres was used in the article to clarify a number of issues affecting martensitic transformation in carbon steels. The deformation that occurs when a spherical carbon atom with a radius of 0.77 Å is placed in the octahedral pore of the z-sublattice of iron incorporation is considered. It is shown that the displacements of iron atoms lying on the oz axis are so significant that they block the next two octahedral pores from possible filling. They will be released only when four carbon atoms occupy similar pores on the edges of the unit cell and again remove iron atoms from the blocked pores. The calculation was made of the number of carbon atoms in the unit cell, depending on the carbon content in the steel. It turned out that the number of carbon atoms in the cell equal to 0.5 is achieved at a carbon concentration of 5.13 wt. %. Consequently, almost all hardened structural and tool steels on average do not fill even one octahedral pore in the center of the face. Within the framework of this model, the lattice parameters a and c are calculated, which are compared with the experimental data obtained by academician G.V. Kurdyumov. Their very good agreement is shown for parameter c and less accurate for parameter a, which, from our point of view, is due to the lack of information about the Poisson ratio for processes on the atomic scale. A method has been developed for determining the lattice parameters of an ideal martensite, in which all z-pores are occupied by carbon atoms.