First-Principles Calculations, Experimental Study, and Thermodynamic Modeling of the Al-Co-Cr System

Liu, Xuan L.; Gheno, Thomas; Lindahl, Bonnie B.; Lindwall, Greta; Gleeson, Brian; Liu, Zi-Kui

doi:10.1371/journal.pone.0121386

First-Principles Calculations, Experimental Study, and Thermodynamic Modeling of the Al-Co-Cr System

Journal Article · Mon Apr 13 00:00:00 EDT 2015 · PLoS ONE

DOI:https://doi.org/10.1371/journal.pone.0121386· OSTI ID:1904847

Liu, Xuan L. ^[1]; Gheno, Thomas ^[2]; Lindahl, Bonnie B. ^[3]; Lindwall, Greta ^[4]; Gleeson, Brian ^[2]; Liu, Zi-Kui ^[4]

Pennsylvania State University, University Park, PA (United States); OSTI
University of Pittsburgh, PA (United States)
KTH Royal Institute of Technology, Stockholm (Sweden)
Pennsylvania State University, University Park, PA (United States)

The phase relations and thermodynamic properties of the condensed Al-Co-Cr ternary alloy system are investigated using first-principles calculations based on density functional theory (DFT) and phase-equilibria experiments that led to X-ray diffraction (XRD) and electron probe micro-analysis (EPMA) measurements. A thermodynamic description is developed by means of the calculations of phase diagrams (CALPHAD) method using experimental and computational data from the present work and the literature. Emphasis is placed on modeling the bcc-A2, B2, fcc-γ, and tetragonal-σ phases in the temperature range of 1173 to 1623 K. Liquid, bcc-A2 and fcc-γ phases are modeled using substitutional solution descriptions. First-principles special quasirandom structures (SQS) calculations predict a large bcc-A2 (disordered)/B2 (ordered) miscibility gap, in agreement with experiments. A partitioning model is then used for the A2/B2 phase to effectively describe the order-disorder transitions. The critically assessed thermodynamic description describes all phase equilibria data well. A2/B2 transitions are also shown to agree well with previous experimental findings.

View Accepted Manuscript (DOE)

Research Organization:: Pennsylvania State University, University Park, PA (United States); University of Pittsburgh, PA (United States)

Sponsoring Organization:: European Research Fund for Coal and Steel (RFCS); National Science Foundation (NSF); Office of Naval Research (ONR); USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0007271

OSTI ID:: 1904847

Journal Information:: PLoS ONE, Journal Name: PLoS ONE Journal Issue: 4 Vol. 10; ISSN 1932-6203

Publisher:: Public Library of ScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (69)

Enthalpies of formation of (cobalt + chromium) alloys at 473 K Downie, D. B.; Arslan, F. The Journal of Chemical Thermodynamics, Vol. 15, Issue 7 https://doi.org/10.1016/0021-9614(83)90078-2	journal	July 1983
A model for alloying in ferromagnetic metals Hillert, Mats; Jarl, Magnus Calphad, Vol. 2, Issue 3 https://doi.org/10.1016/0364-5916(78)90011-1	journal	January 1978
The role of magnetism in the calculation of phase diagrams Inden, G. Physica B+C, Vol. 103, Issue 1 https://doi.org/10.1016/0378-4363(81)91004-4	journal	January 1981
Calculations of thermophysical properties of cubic carbides and nitrides using the Debye–Grüneisen model Lu, Xiao-Gang; Selleby, Malin; Sundman, Bo Acta Materialia, Vol. 55, Issue 4 https://doi.org/10.1016/j.actamat.2006.05.054	journal	February 2007
Progress in coatings for gas turbine airfoils Goward, G. W. Surface and Coatings Technology, Vol. 108-109 https://doi.org/10.1016/s0257-8972(98)00667-7	journal	October 1998
The compound energy formalism Hillert, Mats Journal of Alloys and Compounds, Vol. 320, Issue 2 https://doi.org/10.1016/s0925-8388(00)01481-x	journal	May 2001
Algebraic Representation of Thermodynamic Properties and the Classification of Solutions Redlich, Otto; Kister, A. T. Industrial & Engineering Chemistry, Vol. 40, Issue 2 https://doi.org/10.1021/ie50458a036	journal	February 1948
High-precision sampling for Brillouin-zone integration in metals Methfessel, M.; Paxton, A. T. Physical Review B, Vol. 40, Issue 6 https://doi.org/10.1103/physrevb.40.3616	journal	August 1989
Structural properties of ordered high-melting-temperature intermetallic alloys from first-principles total-energy calculations Mehl, M. J.; Osburn, J. E.; Papaconstantopoulos, D. A. Physical Review B, Vol. 41, Issue 15 https://doi.org/10.1103/physrevb.41.10311	journal	May 1990
Antiferromagnetism in 3dtransition metals Moruzzi, V. L.; Marcus, P. M. Physical Review B, Vol. 42, Issue 13 https://doi.org/10.1103/physrevb.42.8361	journal	November 1990
Improved tetrahedron method for Brillouin-zone integrations Blöchl, Peter E.; Jepsen, O.; Andersen, O. K. Physical Review B, Vol. 49, Issue 23 https://doi.org/10.1103/physrevb.49.16223	journal	June 1994
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/physrevb.54.11169	journal	October 1996
Role ofCoantisite segregation in theCoAl(111)surface Hammer, L.; Blum, V.; Schmidt, Ch. Physical Review B, Vol. 71, Issue 7 https://doi.org/10.1103/physrevb.71.075413	journal	February 2005
Special quasirandom structures Zunger, Alex; Wei, S.-H.; Ferreira, L. G. Physical Review Letters, Vol. 65, Issue 3, p. 353-356 https://doi.org/10.1103/physrevlett.65.353	journal	July 1990
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/physrevlett.77.3865	journal	October 1996
60 years of IUCr journals Authier, André Acta Crystallographica Section A Foundations of Crystallography, Vol. 65, Issue 3 https://doi.org/10.1107/s0108767309007235	journal	April 2009
Phase equilibria and stability of the bcc aluminide in the Co-Cr-Al system Ishikawa, K.; Ise, M.; Ohnuma, I. Berichte der Bunsengesellschaft für physikalische Chemie, Vol. 102, Issue 9 https://doi.org/10.1002/bbpc.19981020924	journal	September 1998
First-Principles Calculations and CALPHAD Modeling of Thermodynamics Liu, Zi-Kui Journal of Phase Equilibria and Diffusion, Vol. 30, Issue 5 https://doi.org/10.1007/s11669-009-9570-6	journal	September 2009
Designing oxidation-resistant coatings Nicholls, J. R. JOM, Vol. 52, Issue 1 https://doi.org/10.1007/s11837-000-0112-2	journal	January 2000
Assessment of Co-Cr-Ni ternary system by CALPHAD technique Yang, Shuyu; Jiang, Min; Li, Hongxiao Rare Metals, Vol. 31, Issue 1 https://doi.org/10.1007/s12598-012-0466-y	journal	January 2012
SGTE data for pure elements Dinsdale, A. T. Calphad, Vol. 15, Issue 4 https://doi.org/10.1016/0364-5916(91)90030-N	journal	October 1991
Magnetic contribution to the bulk modulus of 3d transition metals and alloys Mōri, N. Physica B+C, Vol. 149, Issue 1-3 https://doi.org/10.1016/0378-4363(88)90246-X	journal	March 1988
Use of Sound Velocity Measurements in Determining the Debye Temperature of Solids Alers, George A. Lattice Dynamics https://doi.org/10.1016/B978-0-12-395669-9.50008-4	book	January 1965
Mechanisms controlling the durability of thermal barrier coatings Evans, A. G.; Mumm, D. R.; Hutchinson, J. W. Progress in Materials Science, Vol. 46, Issue 5 https://doi.org/10.1016/S0079-6425(00)00020-7	journal	January 2001
Progress in coatings for gas turbine airfoils Goward, G. W. Surface and Coatings Technology, Vol. 108-109 https://doi.org/10.1016/S0257-8972(98)00667-7	journal	October 1998
Thermodynamic re-assessment of the ternary system Al-Cr-Ni Dupin, N.; Ansara, I.; Sundman, B. Calphad, Vol. 25, Issue 2 https://doi.org/10.1016/S0364-5916(01)00049-9	journal	June 2001
Thermo-Calc & DICTRA, computational tools for materials science Andersson, J-O; Helander, Thomas; Höglund, Lars Calphad, Vol. 26, Issue 2 https://doi.org/10.1016/S0364-5916(02)00037-8	journal	June 2002
The compound energy formalism Hillert, Mats Journal of Alloys and Compounds, Vol. 320, Issue 2 https://doi.org/10.1016/S0925-8388(00)01481-X	journal	May 2001
Calculation of debye temperature for crystalline structures—a case study on Ti, Zr, and Hf Chen, Q.; Sundman, B. Acta Materialia, Vol. 49, Issue 6 https://doi.org/10.1016/S1359-6454(01)00002-7	journal	April 2001
Direct evidence of magnetically induced phase separation in the fcc phase and thermodynamic calculations of phase equilibria of the Co–Cr system Oikawa, Katsunari; Qin, Gao-Wu; Ikeshoji, Tamio Acta Materialia, Vol. 50, Issue 9 https://doi.org/10.1016/S1359-6454(01)00433-5	journal	May 2002
Thermodynamic properties of Al, Ni, NiAl, and Ni3Al from first-principles calculations Wang, Y.; Liu, Z. -K.; Chen, L. -Q. Acta Materialia, Vol. 52, Issue 9 https://doi.org/10.1016/j.actamat.2004.02.014	journal	May 2004
First-principles study of constitutional point defects in B2 NiAl using special quasirandom structures Jiang, Chao; Chen, Long-Qing; Liu, Zi-Kui Acta Materialia, Vol. 53, Issue 9 https://doi.org/10.1016/j.actamat.2005.02.026	journal	May 2005
An assessment of the entire Al–Fe system including D03 ordering Sundman, Bo; Ohnuma, Ikuo; Dupin, Nathalie Acta Materialia, Vol. 57, Issue 10 https://doi.org/10.1016/j.actamat.2009.02.046	journal	June 2009
First-principles study of ternary bcc alloys using special quasi-random structures Jiang, Chao Acta Materialia, Vol. 57, Issue 16 https://doi.org/10.1016/j.actamat.2009.06.026	journal	September 2009
Ab initio lattice stability in comparison with CALPHAD lattice stability Wang, Y.; Curtarolo, S.; Jiang, C. Calphad, Vol. 28, Issue 1 https://doi.org/10.1016/j.calphad.2004.05.002	journal	March 2004
First-principles calculations and thermodynamic re-modeling of the Hf–W system Lieser, Alyson C.; Zacherl, Chelsey L.; Saengdeejing, Arkapol Calphad, Vol. 38 https://doi.org/10.1016/j.calphad.2012.04.005	journal	September 2012
Phase stability and thermodynamic modeling of the Re–Ti system supplemented by first-principles calculations Zacherl, Chelsey L.; Shang, Shun-Li; Saengdeejing, Arkapol Calphad, Vol. 38 https://doi.org/10.1016/j.calphad.2012.05.001	journal	September 2012
First-principles aided thermodynamic modeling of the Nb–Re system Liu, Xuan L.; Hargather, Chelsey Z.; Liu, Zi-Kui Calphad, Vol. 41 https://doi.org/10.1016/j.calphad.2013.02.006	journal	June 2013
First-principles thermodynamics from phonon and Debye model: Application to Ni and Ni3Al Shang, Shun-Li; Wang, Yi; Kim, DongEung Computational Materials Science, Vol. 47, Issue 4 https://doi.org/10.1016/j.commatsci.2009.12.006	journal	February 2010
First-principles calculations of pure elements: Equations of state and elastic stiffness constants Shang, S. L.; Saengdeejing, A.; Mei, Z. G. Computational Materials Science, Vol. 48, Issue 4 https://doi.org/10.1016/j.commatsci.2010.03.041	journal	June 2010
On the scaling factor in Debye–Grüneisen model: A case study of the Mg–Zn binary system Liu, Xuan L.; VanLeeuwen, Brian K.; Shang, Shun-Li Computational Materials Science, Vol. 98 https://doi.org/10.1016/j.commatsci.2014.10.056	journal	February 2015
Recent developments in gas turbine materials and technology and their implications for syngas firing Wright, I.; Gibbons, T. International Journal of Hydrogen Energy, Vol. 32, Issue 16 https://doi.org/10.1016/j.ijhydene.2006.08.049	journal	November 2007
Ab initio study of formation energy and magnetism of sigma phase in Cr–Fe and Cr–Co systems Pavlů, J.; Vřešťál, J.; Šob, M. Intermetallics, Vol. 18, Issue 2 https://doi.org/10.1016/j.intermet.2009.07.018	journal	February 2010
Melting behaviour and homogeneity range of B2 CoAl and updated thermodynamic description of the Al–Co system Stein, F.; He, C.; Dupin, N. Intermetallics, Vol. 39 https://doi.org/10.1016/j.intermet.2013.03.011	journal	August 2013
Crystal chemistry and Calphad modeling of the σ phase Joubert, J. -M. Progress in Materials Science, Vol. 53, Issue 3 https://doi.org/10.1016/j.pmatsci.2007.04.001	journal	March 2008
Modelling of phase equilibria in MCrAlY coating systems Achar, D. R. G.; Munoz-Arroyo, R.; Singheiser, L. Surface and Coatings Technology, Vol. 187, Issue 2-3 https://doi.org/10.1016/j.surfcoat.2004.02.018	journal	October 2004
Temperature dependence of phase relationships in different types of MCrAlY-coatings Toscano, J.; Gil, A.; Hüttel, T. Surface and Coatings Technology, Vol. 202, Issue 4-7 https://doi.org/10.1016/j.surfcoat.2007.06.044	journal	December 2007
The Superalloys Reed, Roger C. Cambridge University Press https://doi.org/10.1017/CBO9780511541285	book	January 2006
Évaluation thermodynamique du système Al-Co Dupin, N.; Ansara, I. Revue de Métallurgie, Vol. 95, Issue 9 https://doi.org/10.1051/metal/199895091121	journal	September 1998
Low‐Temperature Elastic Moduli of Aluminum Kamm, G. N.; Alers, G. A. Journal of Applied Physics, Vol. 35, Issue 2 https://doi.org/10.1063/1.1713309	journal	February 1964
First-principles elastic constants of α- and θ-Al2O3 Shang, Shunli; Wang, Yi; Liu, Zi-Kui Applied Physics Letters, Vol. 90, Issue 10 https://doi.org/10.1063/1.2711762	journal	March 2007
Finite Elastic Strain of Cubic Crystals Birch, Francis Physical Review, Vol. 71, Issue 11 https://doi.org/10.1103/PhysRev.71.809	journal	June 1947
High-precision sampling for Brillouin-zone integration in metals Methfessel, M.; Paxton, A. T. Physical Review B, Vol. 40, Issue 6 https://doi.org/10.1103/PhysRevB.40.3616	journal	August 1989
Structural properties of ordered high-melting-temperature intermetallic alloys from first-principles total-energy calculations Mehl, M. J.; Osburn, J. E.; Papaconstantopoulos, D. A. Physical Review B, Vol. 41, Issue 15 https://doi.org/10.1103/PhysRevB.41.10311	journal	May 1990
Antiferromagnetism in 3dtransition metals Moruzzi, V. L.; Marcus, P. M. Physical Review B, Vol. 42, Issue 13 https://doi.org/10.1103/PhysRevB.42.8361	journal	November 1990
Improved tetrahedron method for Brillouin-zone integrations Blöchl, Peter E.; Jepsen, O.; Andersen, O. K. Physical Review B, Vol. 49, Issue 23 https://doi.org/10.1103/PhysRevB.49.16223	journal	June 1994
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/PhysRevB.59.1758	journal	January 1999
Magnetic ground state of Cr in density-functional theory Hafner, R.; Spišák, D.; Lorenz, R. Physical Review B, Vol. 65, Issue 18 https://doi.org/10.1103/PhysRevB.65.184432	journal	May 2002
First-principles study of binary bcc alloys using special quasirandom structures Jiang, Chao; Wolverton, C.; Sofo, Jorge Physical Review B, Vol. 69, Issue 21 https://doi.org/10.1103/PhysRevB.69.214202	journal	June 2004
Role ofCoantisite segregation in theCoAl(111)surface Hammer, L.; Blum, V.; Schmidt, Ch. Physical Review B, Vol. 71, Issue 7 https://doi.org/10.1103/PhysRevB.71.075413	journal	February 2005
Special quasirandom structures Zunger, Alex; Wei, S.-H.; Ferreira, L. G. Physical Review Letters, Vol. 65, Issue 3, p. 353-356 https://doi.org/10.1103/PhysRevLett.65.353	journal	July 1990
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
The crystal structure of the Co–Cr σ phase Dickins, G. J.; Douglas, A. M. B.; Taylor, W. H. Acta Crystallographica, Vol. 9, Issue 3 https://doi.org/10.1107/S0365110X56000826	journal	March 1956
Materials Design for the Next Generation Thermal Barrier Coatings Clarke, D. R.; Levi, C. G. Annual Review of Materials Research, Vol. 33, Issue 1 https://doi.org/10.1146/annurev.matsci.33.011403.113718	journal	August 2003
The Determination of the Thermodynamic Properties of Cobalt–Chromium Alloys Using Solid-Electrolyte EMF and High-Temperature Calorimetric Techniques Bell, H. B.; Hajra, J. P.; Putland, F. H. Metal Science Journal, Vol. 7, Issue 1 https://doi.org/10.1179/030634573790445442	journal	January 1973
Thermal barrier coatings technology: critical review, progress update, remaining challenges and prospects Darolia, R. International Materials Reviews, Vol. 58, Issue 6 https://doi.org/10.1179/1743280413Y.0000000019	journal	August 2013
An experimental investigation of possible B2-ordering in the Al-Cr system Helander, T.; Tolochko, O. Journal of Phase Equilibria, Vol. 20, Issue 1 https://doi.org/10.1361/105497199770335947	journal	January 1999

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First-Principles Calculations, Experimental Study, and Thermodynamic Modeling of the Al-Co-Cr System

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