Empirical design of single phase high-entropy alloys with high hardness

Fuyang Tian, Lajos K. Varga, Nanxian Chen, Jiang Shen, Levente Vitos

Research output: Contribution to journalArticle

63 Citations (Scopus)


We collect the available basic properties of nearly 100 high-entropy alloys (HEAs) with a single face centered cubic (fcc) or body centered cubic (bcc) phase. HEAs crystallizing in the fcc structure are mainly composed of the late 3d elements (LTM-HEAs), whereas HEAs consisting of the early (refractory) transition elements and the LTM-HEAs containing an increased level of bcc stabilizer form the bcc structure. Guided by the solid solution theory, we investigate the structure and hardness of HEAs as a function of the valence electron concentration (VEC) and the atomic size difference (δ). The fcc structure is found for VEC between 7.80 and 9.50, whereas the structure is bcc for VEC between 4.33 and 7.55. High strength is obtained for an average valence electron number VEC ∼ 6.80 and for an average atomic size difference δ ∼ 6%. Based on these empirical correlations, one can design the high-entropy alloys with desired hardness.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
Publication statusPublished - Mar 2015


  • A. High-entropy alloys
  • B. Valence electron concentration
  • C. Atomic size difference
  • D. Hardness

ASJC Scopus subject areas

  • Chemistry(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Metals and Alloys
  • Materials Chemistry

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