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Title: Thermodynamics of concentrated solid solution alloys

Abstract

This study reviews the three main approaches for predicting the formation of concentrated solid solution alloys (CSSA) and for modeling their thermodynamic properties, in particular, utilizing the methodologies of empirical thermo-physical parameters, CALPHAD method, and first-principles calculations combined with hybrid Monte Carlo/Molecular Dynamics (MC/MD) simulations. In order to speed up CSSA development, a variety of empirical parameters based on Hume-Rothery rules have been developed. Herein, these parameters have been systematically and critically evaluated for their efficiency in predicting solid solution formation. The phase stability of representative CSSA systems is then illustrated from the perspectives of phase diagrams and nucleation driving force plots of the σ phase using CALPHAD method. The temperature-dependent total entropies of the FCC, BCC, HCP, and σ phases in equimolar compositions of various systems are presented next, followed by the thermodynamic properties of mixing of the BCC phase in Al-containing and Ti-containing refractory metal systems. First-principles calculations on model FCC, BCC and HCP CSSA reveal the presence of both positive and negative vibrational entropies of mixing, while the calculated electronic entropies of mixing are negligible. Temperature dependent configurational entropy is determined from the atomic structures obtained from MC/MD simulations. Current status and challenges in using these methodologiesmore » as they pertain to thermodynamic property analysis and CSSA design are discussed.« less

Authors:
 [1];  [2];  [3];  [2];  [3];  [4];  [5]
  1. National Energy Technology Lab. (NETL), Albany, OR (United States); AECOM, Albany, OR (United States)
  2. CompuTherm LLC, Middleton, WI (United States)
  3. Tennessee State Univ., Nashville, TN (United States)
  4. Carnegie Mellon Univ., Pittsburgh, PA (United States)
  5. National Energy Technology Lab. (NETL), Albany, OR (United States)
Publication Date:
Research Org.:
National Energy Technology Lab. (NETL), Albany, OR (United States)
Sponsoring Org.:
USDOE Office of Fossil Energy (FE)
OSTI Identifier:
1439969
Report Number(s):
CONTR-PUB-247
Journal ID: ISSN 1359-0286; PII: S1359028616302029
Grant/Contract Number:  
FE0004000
Resource Type:
Accepted Manuscript
Journal Name:
Current Opinion in Solid State and Materials Science
Additional Journal Information:
Journal Volume: 21; Journal Issue: 5; Journal ID: ISSN 1359-0286
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Gao, Michael C., Zhang, C., Gao, P., Zhang, F., Ouyang, L. Z., Widom, M., and Hawk, J. A. Thermodynamics of concentrated solid solution alloys. United States: N. p., 2017. Web. doi:10.1016/j.cossms.2017.08.001.
Gao, Michael C., Zhang, C., Gao, P., Zhang, F., Ouyang, L. Z., Widom, M., & Hawk, J. A. Thermodynamics of concentrated solid solution alloys. United States. https://doi.org/10.1016/j.cossms.2017.08.001
Gao, Michael C., Zhang, C., Gao, P., Zhang, F., Ouyang, L. Z., Widom, M., and Hawk, J. A. Thu . "Thermodynamics of concentrated solid solution alloys". United States. https://doi.org/10.1016/j.cossms.2017.08.001. https://www.osti.gov/servlets/purl/1439969.
@article{osti_1439969,
title = {Thermodynamics of concentrated solid solution alloys},
author = {Gao, Michael C. and Zhang, C. and Gao, P. and Zhang, F. and Ouyang, L. Z. and Widom, M. and Hawk, J. A.},
abstractNote = {This study reviews the three main approaches for predicting the formation of concentrated solid solution alloys (CSSA) and for modeling their thermodynamic properties, in particular, utilizing the methodologies of empirical thermo-physical parameters, CALPHAD method, and first-principles calculations combined with hybrid Monte Carlo/Molecular Dynamics (MC/MD) simulations. In order to speed up CSSA development, a variety of empirical parameters based on Hume-Rothery rules have been developed. Herein, these parameters have been systematically and critically evaluated for their efficiency in predicting solid solution formation. The phase stability of representative CSSA systems is then illustrated from the perspectives of phase diagrams and nucleation driving force plots of the σ phase using CALPHAD method. The temperature-dependent total entropies of the FCC, BCC, HCP, and σ phases in equimolar compositions of various systems are presented next, followed by the thermodynamic properties of mixing of the BCC phase in Al-containing and Ti-containing refractory metal systems. First-principles calculations on model FCC, BCC and HCP CSSA reveal the presence of both positive and negative vibrational entropies of mixing, while the calculated electronic entropies of mixing are negligible. Temperature dependent configurational entropy is determined from the atomic structures obtained from MC/MD simulations. Current status and challenges in using these methodologies as they pertain to thermodynamic property analysis and CSSA design are discussed.},
doi = {10.1016/j.cossms.2017.08.001},
journal = {Current Opinion in Solid State and Materials Science},
number = 5,
volume = 21,
place = {United States},
year = {Thu Oct 12 00:00:00 EDT 2017},
month = {Thu Oct 12 00:00:00 EDT 2017}
}

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Works referenced in this record:

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

Microstructural development in equiatomic multicomponent alloys
journal, July 2004


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


A critical review of high entropy alloys and related concepts
journal, January 2017


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


Guidelines in predicting phase formation of high-entropy alloys
journal, April 2014


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


High-Entropy Alloys in Hexagonal Close-Packed Structure
journal, August 2015

  • Gao, M. C.; Zhang, B.; Guo, S. M.
  • Metallurgical and Materials Transactions A, Vol. 47, Issue 7
  • DOI: 10.1007/s11661-015-3091-1

Refractory high-entropy alloys
journal, September 2010


Design of Refractory High-Entropy Alloys
journal, September 2015


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

Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys
journal, May 2011

  • Guo, Sheng; Ng, Chun; Lu, Jian
  • Journal of Applied Physics, Vol. 109, Issue 10
  • DOI: 10.1063/1.3587228

Relationship between the widths of supercooled liquid regions and bond parameters of Mg-based bulk metallic glasses
journal, June 2003


Design of high entropy alloys: A single-parameter thermodynamic rule
journal, July 2015


A geometric model for intrinsic residual strain and phase stability in high entropy alloys
journal, August 2015


Atomic-size and lattice-distortion effects in newly developed high-entropy alloys with multiple principal elements
journal, September 2015


Predicting the formation and stability of single phase high-entropy alloys
journal, February 2016


A new thermodynamic parameter to predict formation of solid solution or intermetallic phases in high entropy alloys
journal, February 2016


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


A criterion for the formation of high entropy alloys based on lattice distortion
journal, April 2016


The Crystal Chemistry and Physics of Metals and Alloys
journal, April 1973

  • Pearson, W. B.; Weaire, Denis
  • Physics Today, Vol. 26, Issue 4
  • DOI: 10.1063/1.3128023

Phase diagram calculation: past, present and future
journal, January 2004


Computational Thermodynamics Aided High-Entropy Alloy Design
journal, June 2012


An understanding of high entropy alloys from phase diagram calculations
journal, June 2014


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


Understanding phase stability of Al-Co-Cr-Fe-Ni high entropy alloys
journal, November 2016


High-Temperature Tensile Strength of Al10Co25Cr8Fe15Ni36Ti6 Compositionally Complex Alloy (High-Entropy Alloy)
journal, June 2015


Ab initio investigation of high-entropy alloys of 3 d elements
journal, February 2013


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

Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys
journal, October 2015

  • Zhang, Yanwen; Stocks, G. Malcolm; Jin, Ke
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms9736

Atomic scale modelling of hexagonal structured metallic fission product alloys
journal, April 2015

  • Middleburgh, S. C.; King, D. M.; Lumpkin, G. R.
  • Royal Society Open Science, Vol. 2, Issue 4
  • DOI: 10.1098/rsos.140292

Calculating elastic constants in high-entropy alloys using the coherent potential approximation: Current issues and errors
journal, January 2016


Model predictions for the enthalpy of formation of transition metal alloys
journal, January 1977


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


Absence of long-range chemical ordering in equimolar FeCoCrNi
journal, June 2012

  • Lucas, M. S.; Wilks, G. B.; Mauger, L.
  • Applied Physics Letters, Vol. 100, Issue 25
  • DOI: 10.1063/1.4730327

Microstructure characterization of Al x CoCrCuFeNi high-entropy alloy system with multiprincipal elements
journal, April 2005

  • Tong, Chung-Jin; Chen, Yu-Liang; Yeh, Jien-Wei
  • Metallurgical and Materials Transactions A, Vol. 36, Issue 4
  • DOI: 10.1007/s11661-005-0283-0

Decomposition in multi-component AlCoCrCuFeNi high-entropy alloy
journal, January 2011


Microstructure and wear behavior of AlxCo1.5CrFeNi1.5Tiy high-entropy alloys
journal, September 2011


Microstructure and mechanical property of as-cast, -homogenized, and -deformed AlxCoCrFeNi (0≤x≤2) high-entropy alloys
journal, November 2009


Phases, microstructure and mechanical properties of AlxCoCrFeNi high-entropy alloys at elevated temperatures
journal, March 2014


Recrystallization Behavior of CoCrCuFeNi High-Entropy Alloy
journal, October 2014

  • Park, Nokeun; Watanabe, Ikuto; Terada, Daisuke
  • Metallurgical and Materials Transactions A, Vol. 46, Issue 4
  • DOI: 10.1007/s11661-014-2594-5

Ductile CoCrFeNiMox high entropy alloys strengthened by hard intermetallic phases
journal, September 2016


Effect of V content on microstructure and mechanical properties of the CoCrFeMnNiVx high entropy alloys
journal, April 2015


Structure of some CoCrFeNi and CoCrFeNiPd multicomponent HEA alloys by diffraction techniques
journal, October 2016


Microstructures and mechanical properties of multiprincipal component CoCrFeNiTix alloys
journal, October 2012


Aluminum Alloying Effects on Lattice Types, Microstructures, and Mechanical Behavior of High-Entropy Alloys Systems
journal, October 2013


Vibrational thermodynamics of materials
journal, May 2010


Design of Light-Weight High-Entropy Alloys
journal, September 2016

  • Feng, Rui; Gao, Michael; Lee, Chanho
  • Entropy, Vol. 18, Issue 9
  • DOI: 10.3390/e18090333

Ab initiomolecular dynamics for liquid metals
journal, January 1993


Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


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

Thermomagnetic analysis of FeCoCr x Ni alloys: Magnetic entropy of high-entropy alloys
journal, May 2013

  • Lucas, M. S.; Belyea, D.; Bauer, C.
  • Journal of Applied Physics, Vol. 113, Issue 17
  • DOI: 10.1063/1.4798340

Prediction of A2 to B2 Phase Transition in the High-Entropy Alloy Mo-Nb-Ta-W
journal, October 2013


Entropy and Diffuse Scattering: Comparison of NbTiVZr and CrMoNbV
journal, September 2015


Tetrahedron approximation of the cluster variation method for b.c.c. alloys
journal, January 1989


Differences in vibrational entropy of disordered and ordered Cu 3 Au
journal, December 1995


Senary refractory high entropy alloy MoNbTaTiVW
journal, March 2015


Senary refractory high-entropy alloy Cr MoNbTaVW
journal, December 2015


Senary Refractory High-Entropy Alloy HfNbTaTiVZr
journal, September 2015

  • Gao, M. C.; Zhang, B.; Yang, S.
  • Metallurgical and Materials Transactions A, Vol. 47, Issue 7
  • DOI: 10.1007/s11661-015-3105-z

NbTaV-(Ti,W) refractory high-entropy alloys: Experiments and modeling
journal, September 2016


MoNbTaV Medium-Entropy Alloy
journal, May 2016

  • Yao, Hongwei; Qiao, Jun-Wei; Gao, Michael
  • Entropy, Vol. 18, Issue 5
  • DOI: 10.3390/e18050189

Accelerated exploration of multi-principal element alloys with solid solution phases
journal, March 2015

  • Senkov, O. N.; Miller, J. D.; Miracle, D. B.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms7529

Tensile ductility of an AlCoCrFeNi multi-phase high-entropy alloy through hot isostatic pressing (HIP) and homogenization
journal, October 2015


A Study of Ternary Geometrical Models
journal, June 1989

  • Chou, Kuo-Chih; Austin Chang, Y.
  • Berichte der Bunsengesellschaft für physikalische Chemie, Vol. 93, Issue 6
  • DOI: 10.1002/bbpc.19890930615

Precipitation in the equiatomic high-entropy alloy CrMnFeCoNi
journal, March 2016


Ab initio calculations of cohesive energies of Fe -based glass-forming alloys
journal, October 2004


Reassessment of Al-Ce and Al-Nd binary systems supported by critical experiments and first-principles energy calculations
journal, December 2005

  • Gao, Michael C.; Ünlü, Necip; Shiflet, G. J.
  • Metallurgical and Materials Transactions A, Vol. 36, Issue 12, p. 3269-3279
  • DOI: 10.1007/s11661-005-0001-y

First-principles calculation of structural energetics of Al–TM (TM=Ti, Zr, Hf) intermetallics
journal, June 2005


Ab initio lattice stabilities of some elemental complex structures
journal, December 2006


First-principles calculation of lattice stability of C15–M2R and their hypothetical C15 variants (M=Al, Co, Ni; R=Ca, Ce, Nd, Y)
journal, September 2006


AFLOW: An automatic framework for high-throughput materials discovery
journal, June 2012


Lattice stability of aluminum-rare earth binary systems: A first-principles approach
journal, May 2007


Manufacturing of High Entropy Alloys
journal, July 2015


Works referencing / citing this record:

High-Entropy Alloys
book, January 2016


First-principles prediction of high-entropy-alloy stability
journal, November 2017


Effect of Molybdenum on the Corrosion Behavior of High-Entropy Alloys CoCrFeNi 2 and CoCrFeNi 2 Mo 0.25 under Sodium Chloride Aqueous Conditions
journal, January 2018

  • Rodriguez, Alvaro A.; Tylczak, Joseph H.; Gao, Michael C.
  • Advances in Materials Science and Engineering, Vol. 2018
  • DOI: 10.1155/2018/3016304

A cobalt-rich eutectic high-entropy alloy in the system Al–Co–Cr–Fe–Ni
journal, October 2019


Size effects on plasticity in high-entropy alloys
journal, August 2018

  • Basu, Indranil; Ocelík, Václav; De Hosson, Jeff Th. M.
  • Journal of Materials Research, Vol. 33, Issue 19
  • DOI: 10.1557/jmr.2018.282

High-entropy high-hardness metal carbides discovered by entropy descriptors
journal, November 2018


Current and emerging practices of CALPHAD toward the development of high entropy alloys and complex concentrated alloys
journal, June 2018

  • Gorsse, Stéphane; Tancret, Franck
  • Journal of Materials Research, Vol. 33, Issue 19
  • DOI: 10.1557/jmr.2018.152

Design, Microstructure and Mechanical Properties of Cast Medium Entropy Aluminium Alloys
journal, May 2019


On Nb Silicide Based Alloys: Alloy Design and Selection
journal, May 2018


Rare-earth high entropy alloys with hexagonal close-packed structure
journal, November 2018

  • Qiao, J. W.; Bao, M. L.; Zhao, Y. J.
  • Journal of Applied Physics, Vol. 124, Issue 19
  • DOI: 10.1063/1.5051514

Influence of compositional complexity on interdiffusion in Ni-containing concentrated solid-solution alloys
journal, March 2018


Modeling the structure and thermodynamics of high-entropy alloys
journal, July 2018


Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways
journal, August 2019


High-entropy functional materials
journal, September 2018

  • Gao, Michael C.; Miracle, Daniel B.; Maurice, David
  • Journal of Materials Research, Vol. 33, Issue 19
  • DOI: 10.1557/jmr.2018.323

Review of high entropy ceramics: design, synthesis, structure and properties
journal, January 2019

  • Zhang, Rui-Zhi; Reece, Michael J.
  • Journal of Materials Chemistry A, Vol. 7, Issue 39
  • DOI: 10.1039/c9ta05698j

Microstructural Characterization of Mechanically Alloyed FeCoNiMnV High Entropy Alloy Consolidated by Spark Plasma Sintering
journal, December 2019

  • Alijani, Fatemeh; Reihanian, Mohsen; Gheisari, Khalil
  • Advanced Engineering Materials, Vol. 22, Issue 4
  • DOI: 10.1002/adem.201901311

Transition from high-entropy to Cu-based (TiZrNbNi) 1− x Cu x metallic glasses
journal, October 2019

  • Ristić, Ramir; Figueroa, Ignacio A.; Lachová, Andrea
  • Journal of Applied Physics, Vol. 126, Issue 15
  • DOI: 10.1063/1.5119373

Hexagonal close-packed high-entropy alloy formation under extreme processing conditions
journal, January 2019

  • Devanathan, Ram; Jiang, Weilin; Kruska, Karen
  • Journal of Materials Research, Vol. 34, Issue 5
  • DOI: 10.1557/jmr.2018.438

Influence of compositional complexity on interdiffusion in Ni-containing concentrated solid-solution alloys [Supplemental Data]
dataset, March 2018

  • Jin, Ke; Zhang, Chuan; Zhang, Fan
  • figshare-Supplementary information for journal article at DOI: 10.1080/21663831.2018.1446466, 1 DOCX file (49.53 kB)
  • DOI: 10.6084/m9.figshare.5956360

High-entropy alloys
journal, June 2019


First-principles prediction of high-entropy-alloy stability
preprint, January 2017


High-entropy high-hardness metal carbides discovered by entropy descriptors
text, January 2018


Predictive multiphase evolution in Al-containing high-entropy alloys
journal, October 2018


Design, Microstructure and Mechanical Properties of Cast Medium Entropy Aluminium Alloys
journal, May 2019


High Entropy Alloys Mined From Binary Phase Diagrams
journal, October 2019


On Nb Silicide Based Alloys: Alloy Design and Selection
journal, May 2018