skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys

Abstract

High-entropy alloys constitute a new class of materials that provide an excellent combination of strength, ductility, thermal stability, and oxidation resistance. Although they have attracted extensive attention due to their potential applications, little is known about why these compounds are stable or how to predict which combination of elements will form a single phase. Here, we present a review of the latest research done on these alloys focusing on the theoretical models devised during the last decade. We discuss semiempirical methods based on the Hume-Rothery rules and stability criteria based on enthalpies of mixing and size mismatch. To provide insights into the electronic and magnetic properties of high-entropy alloys, we show the results of first-principles calculations of the electronic structure of the disordered solid-solution phase based on both Korringa Kohn Rostoker coherent potential approximation and large supercell models of example face-centered cubic and body-centered cubic systems. Furthermore, we discuss in detail a model based on enthalpy considerations that can predict which elemental combinations are most likely to form a single-phase high-entropy alloy. The enthalpies are evaluated via first-principles high-throughput density functional theory calculations of the energies of formation of binary compounds, and therefore it requires no experimental or empirically derivedmore » input. Finally, the model correctly accounts for the specific combinations of metallic elements that are known to form single-phase alloys while rejecting similar combinations that have been tried and shown not to be single phase.« less

Authors:
 [1];  [2];  [3];  [4];  [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science and Technology Division
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science and Technology Division; Univ. of Tennessee, Knoxville, TN (United States). Dept. of Materials Science and Engineering
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physical and Life Sciences
  4. Carnegie Mellon Univ., Pittsburgh, PA (United States). Pittsburgh Supercomputing Center
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1265832
Grant/Contract Number:  
AC05-00OR22725; AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
JOM. Journal of the Minerals, Metals & Materials Society
Additional Journal Information:
Journal Volume: 67; Journal Issue: 10; Journal ID: ISSN 1047-4838
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Density Functional Theory; local density approximation; binary compound; multicomponent alloy; coherent potential approximation

Citation Formats

Troparevsky, M. Claudia, Morris, James R., Daene, Markus, Wang, Yang, Lupini, Andrew R., and Stocks, G. Malcolm. Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys. United States: N. p., 2015. Web. doi:10.1007/s11837-015-1594-2.
Troparevsky, M. Claudia, Morris, James R., Daene, Markus, Wang, Yang, Lupini, Andrew R., & Stocks, G. Malcolm. Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys. United States. doi:10.1007/s11837-015-1594-2.
Troparevsky, M. Claudia, Morris, James R., Daene, Markus, Wang, Yang, Lupini, Andrew R., and Stocks, G. Malcolm. Thu . "Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys". United States. doi:10.1007/s11837-015-1594-2. https://www.osti.gov/servlets/purl/1265832.
@article{osti_1265832,
title = {Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys},
author = {Troparevsky, M. Claudia and Morris, James R. and Daene, Markus and Wang, Yang and Lupini, Andrew R. and Stocks, G. Malcolm},
abstractNote = {High-entropy alloys constitute a new class of materials that provide an excellent combination of strength, ductility, thermal stability, and oxidation resistance. Although they have attracted extensive attention due to their potential applications, little is known about why these compounds are stable or how to predict which combination of elements will form a single phase. Here, we present a review of the latest research done on these alloys focusing on the theoretical models devised during the last decade. We discuss semiempirical methods based on the Hume-Rothery rules and stability criteria based on enthalpies of mixing and size mismatch. To provide insights into the electronic and magnetic properties of high-entropy alloys, we show the results of first-principles calculations of the electronic structure of the disordered solid-solution phase based on both Korringa Kohn Rostoker coherent potential approximation and large supercell models of example face-centered cubic and body-centered cubic systems. Furthermore, we discuss in detail a model based on enthalpy considerations that can predict which elemental combinations are most likely to form a single-phase high-entropy alloy. The enthalpies are evaluated via first-principles high-throughput density functional theory calculations of the energies of formation of binary compounds, and therefore it requires no experimental or empirically derived input. Finally, the model correctly accounts for the specific combinations of metallic elements that are known to form single-phase alloys while rejecting similar combinations that have been tried and shown not to be single phase.},
doi = {10.1007/s11837-015-1594-2},
journal = {JOM. Journal of the Minerals, Metals & Materials Society},
number = 10,
volume = 67,
place = {United States},
year = {2015},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 18 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Complete Solution of the Korringa-Kohn-Rostoker Coherent-Potential-Approximation Equations: Cu-Ni Alloys
journal, July 1978


Microstructure and Mechanical Properties of New AlCo x CrFeMo 0.5 Ni High-Entropy Alloys
journal, February 2010

  • Hsu, Chin-You; Wang, Woei-Ren; Tang, Wei-Yeh
  • Advanced Engineering Materials, Vol. 12, Issue 1-2
  • DOI: 10.1002/adem.200900171

Libxc: A library of exchange and correlation functionals for density functional theory
journal, October 2012

  • Marques, Miguel A. L.; Oliveira, Micael J. T.; Burnus, Tobias
  • Computer Physics Communications, Vol. 183, Issue 10
  • DOI: 10.1016/j.cpc.2012.05.007

Gradient-corrected density functionals: Full-potential calculations for iron
journal, May 1991


Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys
journal, May 2011


Solid Solution or Intermetallics in a High-Entropy Alloy
journal, August 2009

  • Wang, Yan Ping; Li, Bang Sheng; Fu, Heng Zhi
  • Advanced Engineering Materials, Vol. 11, Issue 8
  • DOI: 10.1002/adem.200900057

Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems
journal, August 2014


Microstructural development in equiatomic multicomponent alloys
journal, July 2004


The microstructure and phase equilibrium of new high performance high-entropy alloys
journal, August 2009


More than entropy in high-entropy alloys: Forming solid solutions or amorphous phase
journal, October 2013


Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys
journal, August 2013


Accelerated exploration of multi-principal element alloys for structural applications
journal, September 2015


Deviation from high-entropy configurations in the atomic distributions of a multi-principal-element alloy
journal, January 2015

  • Santodonato, Louis J.; Zhang, Yang; Feygenson, Mikhail
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms6964

Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes
journal, May 2004

  • Yeh, J.-W.; Chen, S.-K.; Lin, S.-J.
  • Advanced Engineering Materials, Vol. 6, Issue 5, p. 299-303
  • DOI: 10.1002/adem.200300567

First-principles pseudopotential calculations of magnetic iron
journal, April 1992


Adhesive wear behavior of AlxCoCrCuFeNi high-entropy alloys as a function of aluminum content
journal, September 2006


Microstructures and properties of high-entropy alloys
journal, April 2014


Theory of Magnetic and Structural Ordering in Iron
journal, April 1985


Solid-Solution Phase Formation Rules for Multi-component Alloys
journal, June 2008

  • Zhang, Y.; Zhou, Y. J.; Lin, J. P.
  • Advanced Engineering Materials, Vol. 10, Issue 6, p. 534-538
  • DOI: 10.1002/adem.200700240

Inhomogeneous Electron Gas
journal, November 1964


Hybrid Monte Carlo/Molecular Dynamics Simulation of a Refractory Metal High Entropy Alloy
journal, October 2013

  • Widom, Michael; Huhn, W. P.; Maiti, S.
  • Metallurgical and Materials Transactions A, Vol. 45, Issue 1
  • DOI: 10.1007/s11661-013-2000-8

The high-throughput highway to computational materials design
journal, February 2013

  • Curtarolo, Stefano; Hart, Gus L. W.; Nardelli, Marco Buongiorno
  • Nature Materials, Vol. 12, Issue 3
  • DOI: 10.1038/nmat3568

Calculating properties with the coherent-potential approximation
journal, April 1980


AFLOWLIB.ORG: A distributed materials properties repository from high-throughput ab initio calculations
journal, June 2012


Phase separation in equiatomic AlCoCrFeNi high-entropy alloy
journal, September 2013


High-entropy Alloys with High Saturation Magnetization, Electrical Resistivity and Malleability
journal, March 2013

  • Zhang, Yong; Zuo, TingTing; Cheng, YongQiang
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep01455

Mechanical performance of the Al x CoCrCuFeNi high-entropy alloy system with multiprincipal elements
journal, May 2005

  • Tong, Chung-Jin; Chen, Min-Rui; Yeh, Jien-Wei
  • Metallurgical and Materials Transactions A, Vol. 36, Issue 5
  • DOI: 10.1007/s11661-005-0218-9

Low-density, refractory multi-principal element alloys of the Cr–Nb–Ti–V–Zr system: Microstructure and phase analysis
journal, March 2013


Predicting Crystal Structures with Data Mining of Quantum Calculations
journal, September 2003


Searching for Next Single-Phase High-Entropy Alloy Compositions
journal, October 2013


Prediction of high-entropy stabilized solid-solution in multi-component alloys
journal, February 2012


Thermal Stability and Performance of NbSiTaTiZr High-Entropy Alloy Barrier for Copper Metallization
journal, January 2011

  • Tsai, Ming-Hung; Wang, Chun-Wen; Tsai, Che-Wei
  • Journal of The Electrochemical Society, Vol. 158, Issue 11
  • DOI: 10.1149/2.056111jes

Microstructure and electrochemical properties of high entropy alloys—a comparison with type-304 stainless steel
journal, September 2005


Magnetic and vibrational properties of high-entropy alloys
journal, April 2011

  • Lucas, M. S.; Mauger, L.; Muñoz, J. A.
  • Journal of Applied Physics, Vol. 109, Issue 7
  • DOI: 10.1063/1.3538936

Coherent-Potential Model of Substitutional Disordered Alloys
journal, April 1967


Fatigue behavior of Al0.5CoCrCuFeNi high entropy alloys
journal, September 2012


Order- N Multiple Scattering Approach to Electronic Structure Calculations
journal, October 1995


Wear resistance and high-temperature compression strength of Fcc CuCoNiCrAl0.5Fe alloy with boron addition
journal, May 2004

  • Hsu, Chin-You; Yeh, Jien-Wei; Chen, Swe-Kai
  • Metallurgical and Materials Transactions A, Vol. 35, Issue 5
  • DOI: 10.1007/s11661-004-0254-x

Korringa-Kohn-Rostoker nonlocal coherent-potential approximation
journal, March 2003


A fracture-resistant high-entropy alloy for cryogenic applications
journal, September 2014


Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys
journal, April 2013


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


Density-Functional Theory for Random Alloys: Total Energy within the Coherent-Potential Approximation
journal, May 1986