Issues »  Volume 47, Issue 9

Coefficients of the Hall–Petch Equation for Multicomponent Solid Solutions with an F.C.C. Crystal Lattice

S. O. Firstov, T. H. Rohul’, V. F. Horban’

I. M. Frantsevych Institute for Problems in Materials Science, N.A.S. of Ukraine, 3 Omeljan Pritsak Str., UA-03142 Kyiv, Ukraine

Received: 17.01.2025; final version - 21.05.2025. Download: PDF

The results of a comparative analysis of the coefficients σ0 (or H0) and ky (or kh) of the Hall−Petch relation between the yield strength and the grain size for medium- and high-entropy alloys (MEA and HEA) and pure metals with an f.c.c. crystal lattice are presented. As shown, the values of the indicated coefficients for MEA and HEA exceed significantly their values for pure metals, while the coefficients σ0 grow much more slowly than ky. An influence of crystal-lattice distortions, electron concentration, and pair-interatomic-interaction enthalpy on the values of σ0 and ky is discussed. The factors determining the high values of σ0 and ky for multicomponent solid solutions are determined. As shown, the sharp increase in the grain-boundary-strengthening coefficient ky, in addition to the mechanisms inherent to f.c.c. metals, can be caused by unusual phenomena of boundary strengthening inherent only to multicomponent solid solutions: a decrease in the energy of grain boundaries due to additional doping of multicomponent alloys with the so-called ‘useful impurity’, which, when interacting with an atom of an element of the multicomponent alloy at the boundary, forms a strong chemical bond (atoms have a high pair-interatomic-interaction enthalpy), and as a result of the appearance of segregation of one of the elements of the multicomponent solid solution at the grain boundaries due to the redistribution of atoms due to peak-level shifts. Some models of solid-solution softening of multicomponent solid solutions are analysed, which causes an increase in the coefficient σ0 and is determined by the averaged resistance to the movement of dislocations caused by the presence of peak-level distortions of the crystal lattice, which are created by the atoms of the alloy components due to their moduli-size mismatch.

Key words: medium- and high-entropy alloys, yield strength, hardness, crystal-lattice distortions, grain-boundary strengthening.

URL: https://mfint.imp.kiev.ua/en/abstract/v47/i09/0957.html

DOI: https://doi.org/10.15407/mfint.47.09.0957

PACS: 61.72.Hh, 61.72.Mm, 62.20.fg, 62.20.Qp, 81.07.Wx, 81.40.Cd, 83.60.La

Citation: S. O. Firstov, T. H. Rohul’, and V. F. Horban’, Coefficients of the Hall–Petch Equation for Multicomponent Solid Solutions with an F.C.C. Crystal Lattice, Metallofiz. Noveishie Tekhnol., 47, No. 9: 957–972 (2025) (in Ukrainian)

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