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Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41 Page 5 of 45

Four core effects
Despite their relatively short history, HEAs have already shown great potential for practical applications.
Their properties are already competitive with and even exceed those of state-of-the-art materials. This
potential is highlighted in Figure 2B, which illustrates the exceptional combination of high toughness and
[5]
yield strength of HEAs compared to traditional structural materials . The origin of these outstanding
properties is often attributed to four core effects associated with HEAs: the high entropy effect, severe lattice
[48]
distortion, sluggish diffusion, and cocktail effect . Figure 3 presents a schematic illustration of the four
core effects associated with HEAs. Each of these effects contributes to the unique properties observed in
HEAs, and these contributions will be discussed below.

High entropy effect
Traditional alloying strategies suggest that alloys with multi-principal elements form multi-phase, brittle
[51]
intermetallic systems . However, many works on HEAs show they could achieve metastable and stable
single-phase solid solutions [53-55] . Even in HEAs that show multiple phases, the number of phases is much
lower than the maximum number predicted by the Gibbs phase rule [56-58] . These results suggest that the high
mixing entropy leads to increased mutual solubility of elements in HEA systems. The effect of high mixing
entropy is described by the equation for Gibbs free energy of formation, which implies that phases with high
[59]
entropy will have a lower Gibbs free energy and thus be more stable . Thus, the high mixing entropy aids
in stabilizing single-phase solid solutions as long as this contribution overcomes the enthalpy of formation
of possible intermetallic phases, especially at elevated temperatures. Additionally, this relationship also
implies that the contribution of the mixing entropy to the Gibbs free energy decreases at lower temperatures
and suggests that HEAs in the form of solid solutions at high temperatures may become metastable and
decompose at low temperatures. For example, Stepanov et al. showed that Cantor alloy exhibits a typical
single-phase face-centered cubic (FCC) structure upon quenching; however, it can decompose with the
[60]
precipitation of a secondary Cr-rich σ-phase after prolonged annealing at 600 °C . This representative
finding again underscores the importance of processing history in the phase selection of HEAs, which will
be discussed in later sections.

Sever lattice distortion
In HEA systems, various atoms with different atomic sizes lead to varying bond configurations and local
[61,62]
lattice energies. These bond configurations create a high lattice distortion within the crystal structure .
The severe lattice distortion has been experimentally confirmed in many HEA systems via X-ray diffraction
(XRD), neutron diffraction, and TEM [62-66] . Such severe lattice distortion leads to more diffuse scattering
through the lattice and causes the broadening of diffraction peaks with a decrease in the peak intensities
compared to traditional dilute alloy systems. The increase in lattice distortion also impedes the motion of
dislocations through the matrix, which leads to solid solution strengthening. Traditional solid solution
strengthening models typically involve the contributions of solute atoms to a matrix of solvent atoms. Still,
these models are challenging to apply to HEAs as the solvent and solute atoms cannot be clearly
[59]
distinguished . To that end, new solid solution hardening models have been developed by accounting for
[61,67]
the lattice and shear modulus distortion in the local environment near each constituent atom . The
lattice distortion within HEA systems has also been shown to correlate strongly with the stability of various
phases. For example, single-phase solid solutions tend to be more stable in systems with low lattice
distortions. In contrast, intermetallic and multi-phase structures are more likely to form in systems with
high lattice distortions. This effect can sometimes outweigh the effect of high configurational entropy in
phase selection [55,68,69] .