" Nanoobjects microscopy"

Method of matrix description of orientational relations of austenite-ferrite-cementite in steels
Sukhomlyn V. I.
Department of Condensed State Physics, State Higher Educational Institution. "DnIprovskiy State Technical University", DGTU, vul. Dniprostroevska, 2, 51918, Kam'yanske Ukraine, tel. +38 (0569) 53-02-62 E-mail: v_suhomlyn@ukr.net, ORCID ID: 0000-0002-3673-1353

The orientation of a surface or a crystal plane may be defined by considering how the plane (or indeed any parallel plane) intersects the main crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices , (hkl) ; a set of numbers which quantify the intercepts and thus may be used to uniquely identify the plane or surface.
The values of Miller's indices were used to determine the orientational relations between the phases in steel by the method of matrices of orientational and dimensional correspondence [1]. In this paper, the matrix elements were used up to the second sign, which made it impossible to determine the parameters of the orientation relations with an accuracy greater than half the angular degree.
The application of the proposed technique made it possible to improve the accuracy of determining the basic orientational relationships between the austenite, ferrite, and cementite phases during the transformation of austenite in low-carbon steels [2]. The matrices of the orientational and dimensional correspondence between phases are obtained with an accuracy of 0.2 angular degrees.
By this method, the matrices of the Kurdyumov-Sachs orientation relations (between austenite and martensite), Arbuzov-Kurdyumov (between austenite and cementite), Isaychev (between ferritic and cementite) were refined.
The author thanks the professor G.D. Sukhomlyn for help in discussing the article.

1.	Utevskiy L.M. Difraktsionnaya elektronnaya mikroskopiya v metallovedenii – M.: Metallurgiya. 1973. – 584 s.
2.	Bolshakov V. I. Kristallograficheskie svyazi tsementit–austenit–ferrit pri diffuzionnom raspade austenita / V. I. Bolshakov, G. D. Suhomlin, V. I. Suhomlin // VIsnik PridnIprovskoYi derzhavnoYi akademIYi budIvnitstva ta arhItekturi. - 2016. - # 5. - S. 79-87.