Phase formation rules
Kapitel i bok, 2016

This chapter gives an overview of existing active phase formation rules for high-entropy alloys (HEAs). A parametric approach using physiochemical parameters including enthalpy of mixing, entropy of mixing, melting points, atomic size difference, and valence electron concentration is used to delineate phase formation rules for HEAs, with a reference to other multicomponent alloys like bulk metallic glasses (BMGs). Specifically, rules on forming solid solutions, intermetallic compounds, and the amorphous phase are described in detail; formation rules of solid solutions with the face-centered cubic (fcc) or body-centered cubic (bcc) structure are also discussed. Some remaining issues and future prospects on phase formation rules for HEAs are also addressed at the end. © Springer International Publishing Switzerland 2016.

Empirical rules

Valence electron concentration e/a ratio

Atomic size difference

High-entropy alloys (HEAs)

Hexagonal close-packed (hcp)

Hume-Rothery rules


Entropy of mixing

Face-centered cubic (fcc)

Single phase

Enthalpy of mixing

Solid solution

Body-centered cubic (bcc)

Electronegativity difference

Bulk metallic glasses


Yong Zhang

University of Science and Technology Beijing

Sheng Guo

Chalmers, Material- och tillverkningsteknik, Yt- och mikrostrukturteknik

C. T. Liu

City University of Hong Kong

Xiao Yang

University of Science and Technology Beijing

High-Entropy Alloys: Fundamentals and Applications