First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM = Ti, Zr and Hf) systems: A comparison of cluster expansion and supercell methods

G. Ghosh; A. van de Walle; M. Asta

doi:10.1016/j.actamat.2008.03.006

First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM = Ti, Zr and Hf) systems: A comparison of cluster expansion and supercell methods

G. Ghosh^*, A. van de Walle, M. Asta

^*Corresponding author for this work

Materials Science and Engineering

Research output: Contribution to journal › Article › peer-review

152 Scopus citations

Abstract

The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al-TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (Δ_mE) calculated by CE and dilute supercells agree very well. In the concentrated region, the Δ_mE values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of Δ_mE for hcp Al-Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al-TM-based alloys.

Original language	English (US)
Pages (from-to)	3202-3221
Number of pages	20
Journal	Acta Materialia
Volume	56
Issue number	13
DOIs	https://doi.org/10.1016/j.actamat.2008.03.006
State	Published - Aug 2008

Funding

This research was supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract Nos. DE-FG02-02ER45997 (G.G.) and DE-FG02-01ER45910 (A.v.d.W. and M.A.) at Northwestern, and DE-FG02-06ER46282 (M.A.) at UC Davis. In addition, this material is based upon work supported by the National Science Foundation under the following NSF programs: Partnerships for Advanced Computational Infrastructure, Distributed Terascale Facility (DTF) and Terascale Extensions: Enhancements to the Extensible Terascale Facility. Specific to NSF programs, two of us (G.G. and A.v.d.W.) have utilized Itanium clusters as a part of TeraGrid sites at the University of Illinois at Urbana-Champaign and at San Diego Supercomputing Center. One of us (G.G.) would like to thank Prof. I.A. Abrikosov, Linköping University, Sweden, for fruitful discussions. The authors thank Prof. M. Widom, Carnegie Mellon University, for sharing his partial correlation function calculation code.

Keywords

Ab initio electron theory
Cluster expansion
Phase stability
Special quasirandom structure (SQS)
Thermodynamics

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Ceramics and Composites
Polymers and Plastics
Metals and Alloys

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title = "First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM = Ti, Zr and Hf) systems: A comparison of cluster expansion and supercell methods",

abstract = "The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al-TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (ΔmE) calculated by CE and dilute supercells agree very well. In the concentrated region, the ΔmE values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of ΔmE for hcp Al-Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al-TM-based alloys.",

keywords = "Ab initio electron theory, Cluster expansion, Phase stability, Special quasirandom structure (SQS), Thermodynamics",

author = "G. Ghosh and {van de Walle}, A. and M. Asta",

note = "Funding Information: This research was supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract Nos. DE-FG02-02ER45997 (G.G.) and DE-FG02-01ER45910 (A.v.d.W. and M.A.) at Northwestern, and DE-FG02-06ER46282 (M.A.) at UC Davis. In addition, this material is based upon work supported by the National Science Foundation under the following NSF programs: Partnerships for Advanced Computational Infrastructure, Distributed Terascale Facility (DTF) and Terascale Extensions: Enhancements to the Extensible Terascale Facility. Specific to NSF programs, two of us (G.G. and A.v.d.W.) have utilized Itanium clusters as a part of TeraGrid sites at the University of Illinois at Urbana-Champaign and at San Diego Supercomputing Center. One of us (G.G.) would like to thank Prof. I.A. Abrikosov, Link{\"o}ping University, Sweden, for fruitful discussions. The authors thank Prof. M. Widom, Carnegie Mellon University, for sharing his partial correlation function calculation code. ",

year = "2008",

month = aug,

doi = "10.1016/j.actamat.2008.03.006",

language = "English (US)",

volume = "56",

pages = "3202--3221",

journal = "Acta Materialia",

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publisher = "Acta Materialia Inc",

number = "13",

}

First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM = Ti, Zr and Hf) systems: A comparison of cluster expansion and supercell methods. / Ghosh, G.; van de Walle, A.; Asta, M.
In: Acta Materialia, Vol. 56, No. 13, 08.2008, p. 3202-3221.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM = Ti, Zr and Hf) systems

T2 - A comparison of cluster expansion and supercell methods

AU - Ghosh, G.

AU - van de Walle, A.

AU - Asta, M.

N1 - Funding Information: This research was supported by the US Department of Energy, Office of Basic Energy Sciences, under Contract Nos. DE-FG02-02ER45997 (G.G.) and DE-FG02-01ER45910 (A.v.d.W. and M.A.) at Northwestern, and DE-FG02-06ER46282 (M.A.) at UC Davis. In addition, this material is based upon work supported by the National Science Foundation under the following NSF programs: Partnerships for Advanced Computational Infrastructure, Distributed Terascale Facility (DTF) and Terascale Extensions: Enhancements to the Extensible Terascale Facility. Specific to NSF programs, two of us (G.G. and A.v.d.W.) have utilized Itanium clusters as a part of TeraGrid sites at the University of Illinois at Urbana-Champaign and at San Diego Supercomputing Center. One of us (G.G.) would like to thank Prof. I.A. Abrikosov, Linköping University, Sweden, for fruitful discussions. The authors thank Prof. M. Widom, Carnegie Mellon University, for sharing his partial correlation function calculation code.

PY - 2008/8

Y1 - 2008/8

N2 - The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al-TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (ΔmE) calculated by CE and dilute supercells agree very well. In the concentrated region, the ΔmE values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of ΔmE for hcp Al-Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al-TM-based alloys.

AB - The thermodynamic properties of solid solutions with body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in the Al-TM (TM = Ti, Zr and Hf) systems are calculated from first-principles using cluster expansion (CE), Monte-Carlo simulation and supercell methods. The 32-atom special quasirandom structure (SQS) supercells are employed to compute properties at 25, 50 and 75 at.% TM compositions, and 64-atom supercells have been employed to compute properties of alloys in the dilute concentration limit (one solute and 63 solvent atoms). In general, the energy of mixing (ΔmE) calculated by CE and dilute supercells agree very well. In the concentrated region, the ΔmE values calculated by CE and SQS methods also agree well in many cases; however, noteworthy discrepancies are found in some cases, which we argue originate from inherent elastic and dynamic instabilities of the relevant parent lattice structures. The importance of short-range order on the calculated values of ΔmE for hcp Al-Ti alloys is demonstrated. We also present calculated results for the composition dependence of the atomic volumes in random solid solutions with bcc, fcc and hcp structures. The properties of solid solutions reported here may be integrated within the CALPHAD formalism to develop reliable thermodynamic databases in order to facilitate: (i) calculations of stable and metastable phase diagrams of binary and multicomponent systems, (ii) alloy design, and (iii) processing of Al-TM-based alloys.

KW - Ab initio electron theory

KW - Cluster expansion

KW - Phase stability

KW - Special quasirandom structure (SQS)

KW - Thermodynamics

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UR - http://www.scopus.com/inward/citedby.url?scp=45849123164&partnerID=8YFLogxK

U2 - 10.1016/j.actamat.2008.03.006

DO - 10.1016/j.actamat.2008.03.006

M3 - Article

AN - SCOPUS:45849123164

SN - 1359-6454

VL - 56

SP - 3202

EP - 3221

JO - Acta Materialia

JF - Acta Materialia

IS - 13

ER -

First-principles calculations of the structural and thermodynamic properties of bcc, fcc and hcp solid solutions in the Al-TM (TM = Ti, Zr and Hf) systems: A comparison of cluster expansion and supercell methods

Abstract

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