Quantum mechanics

Entropy of mixing

Solid solution

High entropy alloys

Metallurgy

Materials science

Enthalpy

Entropy (arrow of time)

Component (thermodynamics)

Atomic radius

Statistical physics

Thermodynamics

Physics

Alloy

Mathematics

Optics

Lattice constant

Superalloy

Composite material

Surface energy

Diffraction

Elastic energy

Binary number

Arithmetic

Scripta Materialia

The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model. By surveying the dependence of the elastic energy on the chemical composition and lattice misfit, we derive a lattice strain coefficient λ*. Studying several high-entropy alloys and superalloys, we propose that most solid solution multi-component alloys are stable when λ*<0.16, generalizing the Hume-Rothery atomic-size rule for binary alloys. We also reveal that the polydispersity index δ, frequently used for describing strain in multi-component alloys, directly represents the elastic energy (e) with e=qδ2, q being an elastic constant. Furthermore, the effects of (i) the number and (ii) the atomic-size distribution of constituting elements on the phase stability of high-entropy alloys were quantified. The present derivations and discussions open for richer considerations of elastic effects in high-entropy alloys, offering immediate support for quantitative assessments of their thermodynamic properties and studying related strengthening mechanisms.

Elastic energy of multi-component solid solutions and strain origins of phase stability in high-entropy alloys