| Summary: | We derived the chemical compositions and the micro hardness of the two studied steels Fe20Mn5Cr and Fe9S28Mn. The contamination of these two compounds by oxygen gives the series M2O3 (M = Fe, Cr, Al). Rhombohedral crystal structure of these compounds was determined by means of the X-rays diffraction. First principles calculations were performed to investigate structural, elastic and mechanical properties of M2O3 (M = Fe, Cr, Al) compounds at equilibrium pressure. Fe2O3 and Cr2O3 are classified as ductile materials, while Al2O3 is brittle. The Debye temperature, the elastic wave velocities and the integration of elastic wave velocities in various directions of the single crystal were obtained. All these compounds are elastically and chemically stable. The calculated elastic constants are in good agreement with the experiment values in the approximation of the gradient generalized for the correlation and exchange potential. We calculated the partial and total densities of states PDOD and TDOS for M2O3 (M = Fe, Cr, Al) compounds. As a result, electronic bands, DOS at the Fermi level, were obtained for the first time especially for Fe2O3 and Cr2O3. Keywords: Band structure, Bulk moduli, Electronic properties
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