REVIEWS OF TOPICAL PROBLEMS

Anisotropy of elasticity of strongly nonstoichiometric disordered cubic carbides MC$_y$ (M = Ti, Zr, Hf, Nb, Ta) and monoxides MO$_y$ (M = Ti, V, Nb)

S. I. Sadovnikov, A. I. Gusev

Institute of Solid State Chemistry, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: In recent years, significant progress has been achieved in the study of the anisotropy of elastic properties of nonstoichiometric cubic carbides MC$_y$ (M = Ti, Zr, Hf, Nb, Ta) and monoxides MO$_y$ (M = Ti, V, Nb). The composition of nonstoichiometric cubic compounds MX$_y$ (X = C, O) determines their electronic structure, mechanical (elastic) properties and possible fields of application in modern engineering. This critical review summarizes recent achievements in the semi-empirical evaluation of elastic characteristics of nonstoichiometric cubic compounds. The main results on the dependences of elastic constants c$_{ij}$ on the composition of disordered nonstoichiometric cubic carbides MC$_y$ (M = Ti, Zr, Hf, Nb, Ta) and monoxides MO$_y$ (M = Ti, Nb) are systematized for the first time. The effect of nonstoichiometry on the elastic anisotropy of carbides and monoxides is considered. It is shown that the maxima and minima of the spatial three-dimensional distributions of elastic moduli of the discussed nonstoichiometric cubic compounds are observed in the equivalent directions [$\pm$100], [0$\pm$10], [00$\pm$1] or directions [$\pm$1 $\pm$1 $\pm$1], respectively. It is shown that among the considered nonstoichiometric compounds, cubic titanium monoxide TiO$_y$ has the largest anisotropy of elastic properties, which is a plastic material in terms of the ratio of shear and bulk moduli. An empirical relationship between the elastic stiffness constants c$_{ij}$ of nonstoichiometric cubic carbides MC$_y$ and their melting temperature is proposed.

Keywords: nonstoichiometry, nonmetal sublattice defectivity, elastic properties anisotropy, melting temperature

PACS: 46.25.-y, 46.35.+z, 62.20.D-, 62.20.de

Received: May 23, 2025
Revised: July 9, 2025
Accepted: August 5, 2025

DOI: 10.3367/UFNr.2025.08.039994

 English version: DOI: 10.3367/UFNe.2025.08.039994