Abstract
A new thermodynamic assessment of the binary Cr-Nb system was performed using the CALPHAD method based on a review of the available literature and ab initio calculations for the hypothetical end members of the C15 Laves phase. Recent experiments reported in the literature revealed that there is no C14 type high temperature phase in this system, which is in contrast to most of the literature. A thorough analysis of these reports, however, showed that the C14 phase has never been directly observed and that its presence had been derived from ternary phase diagram data, twinning of the C15 low temperature phase and erroneous interpretations of x-ray diffractograms. Due to the lack of clear evidence in favor of its existence, the C14 phase was not considered a thermodynamically stable compound in the present evaluation.
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J. Quadakkers, L. Niewolak, and P. Ennis, PCT/DE2007/000166, WO2007093148-A1, DE102006007598-A1, Germany, 2006
J. Froitzheim, G.H. Meier, L. Niewolak, P. Ennis, H. Hattendorf, L. Singheiser, and W.J. Quadakkers, Development of High Strength Ferritic Steel for Interconnect Application in SOFCs, J. Power Sources, 2008, 178, p 163-173
M. Venkatraman and J.P. Neumann, The Cr-Nb (Chromium-Niobium) System, Bull. Alloy Phase Diagr., 1986, 7(5), p 462-466
T.B. Massalski, H. Okamoto, P.R. Subramanian, and L. Kacprzak, Binary Alloy Phase Diagrams, 2nd ed., Materials-Park, OH, ASM International, 1990, p 1298-1299
J.G. Costa Neto, S.G. Fries, H.L.Lukas, S. Gama, and G. Effenberg, Thermodynamic Optimisation of the Nb-Cr System, CALPHAD, 1993, 17, p 219-228
J.G. Costa Neto, Master Thesis, 1991, Faculdade de Engenharia Mecinica, Universidade de Campinas, Brazil
D.J. Thoma and J.H. Perepezko, An experimental Evaluation of the Phase Relationships and Solubilities in the Nb-Cr System, Mater. Sci. Eng., 1992, 156A, p 97-108
J. Pavlu, J. Vrest’al, and P. Sob, Re-modeling of Laves Phases in the Cr-Nb and Cr-Ta Systems Using First-Principles Results, CALPHAD, 2009, 33, p 179-186
H.J. Goldschmidt and J.A. Brand, The Constitution of the Chromium-Niobium-Silicon System, J. Less Common Met., 1961, 3, p 44-61
H.J. Goldschmidt and J.A. Brand, The Constitution of the Chromium-Niobium-Molybdenum System, J. Less Common Met., 1961, 3, p 34-43
M.I. Zakharova and D.A. Proskoshin, An Investigation of the Niobium-Molybdenum-Chromium System, Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Metall. Topl., 1961, 4, p 59-67, in Russian
M. Takeyama and C.T. Liu, Microstructure and Mechanical Properties of Laves-Phase Alloys Based on Cr2Nb, Mater. Sci. Eng., 1991, 132A, p 61-66
V.M. Pan, Polymorphic Transformation in NbCr2, Fiz. Met. Metalloved., 1961, 12(3), p 455-457
V.M. Pan, Definition of Equilibrium Diagrams for Cr-Nb and NbCr2-Ni3Nb Systems, Dopov. Akad. Nauk Ukr. RSR, 1961, 4, p 332-334
K.S. Kumar and P.M. Hazzledine, Polytypic Transformations in Laves Phases, Intermetallics, 2004, 12, p 763-770
J. Aufrecht, A. Leineweber, and E.J. Mittemeijer, Metastable Hexagonal Modifications of the NbCr 2 Laves Phase as Function of Cooling Rate, MRS Fall Meeting, Boston, MA, 2008
J. Aufrecht, A. Leineweber, A. Senyshyn, and E.J. Mittemeijer, The Absence of a Stable Hexagonal Laves Phase Modification (NbCr2) in the Nb-Cr System, Scr. Mater., 2010, 62(5), p 227-230
X.-W. Nie, Comments on “The absence of a stable hexagonal Laves phase modification (NbCr2) in the Nb-Cr system”, Scr. Mater., 2011, 64, p 990-993
J.H. Zhu, C.T. Liu, and P.K. Liaw, Phase Stability and Mechanical Behavior of NbCr2-Based Laves Phases, Intermetallics, 1999, 7, p 1011-1016
F. Stein, M. Palm, and G. Sauthoff, Structure and Stability of Laves Phases. Part I. Critical Assessment of Factors Controlling Laves Phase Stability, Intermetallics, 2004, 12, p 713-720
F. Stein, M. Palm, and G. Sauthoff, Structure and Stability of Laves Phases Part II—Structure Type Variations in Binary and Ternary Systems, Intermetallics, 2005, 13, p 1056-1074
J.H. Zhu, P.K. Liaw, and C.T. Liu, Effect of Electron Concentration on the Phase Stability of NbCr2-Based Laves Phase Alloys, Mater. Sci. Eng., 1997, A239-240, p 260-264
X.W. Nie, S.Q. Lu, and K.L. Wang, Phase Transformation of NbCr2 Intermetallics Produced by Mechanical Alloying Followed by Hot-Pressing Consolidation, Mater. Charact., 2008, 59, p 816-819
K. Korniyenko, Chromium-Iron-Niobium, Landolt Börnstein New Series, 2008, IV/11D3
K.S. Kumar and C.T. Liu, Precipitation in a Cr-Cr2Nb Alloy, Acta Mater., 1997, 45(9), p 3671-3686
K.S. Kumar, L. Pang, J.A. Horton, and C.T. Liu, Structure and Composition of Laves Phases in Binary Cr-Nb, Cr-Zr and Ternary Cr-(Nb, Zr) Alloys, Intermetallics, 2003, 11, p 677-685
T. Takasugi, K.S. Kumar, C.T. Liu, and E.H. Lee, Microstructure and Mechanical Properties of Two-Phase Cr-Cr2Nb, Cr-Cr2Zr and Cr-Cr2(Nb, Zr) Alloys, Mater. Sci. Eng., 1999, 260A, p 108-123
B.P. Bewlay, J.A. Sutliff, M.R. Jackson, and H.A. Lipsitt, Microstructural and Crystallographic Relationships in Directionally Solidified Nb-Cr2Nb and Cr-Cr2Nb eutectics, Acta Metall. Mater., 1994, 42(8), p 2869-2878
L.N. Guseva, Phase Transformations in Chromium-Tantalum and Chromium-Niobium Alloys, Izv. Akad. Nauk. SSSR Neorg. Mater., 1965, 1(10), p 1743-1747
A. Leineweber, J. Aufrecht, A. Senyshyn, and E.J. Mittemeijer, Reply to Comments on the Absence of a Stable Hexagonal Laves Phase Modification (NbCr2) in the Nb-Cr System, Scr. Mater., 2011, 64, p 994-997
V.P. Elyutin and V.F. Funke, Some Data for the Chromium-Niobium Phase Diagram, Izvest. Acad. Nauk SSSR Otd. Tekh. Nauk, 1956, 3, p 68-76
I.I. Kornilov, K.I. Shakhova, P.B. Budberg, and N.A. Nedumov, Phase Diagrams in the System TiCr2-NbCr2, Dokl. Akad. Nauk SSSR, 1963, 149(6), p 1340-1342
J. Aufrecht, A. Leineweber, V. Duppel, and E.J. Mittemeijer, Transformation-Dislocation Dipoles in Laves Phases: A High-Resolution Transmission Electron Microscopy Analysis, J. Mater. Res., 2010, 25(10), p 1983-1991
J. Aufrecht, W. Baumann, A. Leineweber, V. Duppel, and E.J. Mittemeijer, Layer-Stacking Irregularities in C36-Type Nb-Cr and Ti-Cr Laves Phases and Their Relation with Polytypic Phase Transformations, Philos. Mag., 2010, 90(23), p 3149-3175
V.N. Eremenko, G.V. Zudilova, and L.A. Gaevskaya, About the Phase Diagram of the Chromium-Niobium System, Metalloved. I, Obrabotka Met., 1958, 1, p 11-16
E. Rudy, Compendium of Phase Diagram Data, Part V, Technical Report AFML-TR-65-2, 1969, 21, p 127-130
J.F. Martin, F. Müller, and O. Kubaschewski, Thermodynamic Properties of TaCr2 and NbCr2, Trans. Faraday Soc., 1970, 66, p 1065-1072
S. Hong and C.L. Fu, Phase Stability and Elastic Moduli of Cr2Nb by First-Principles Calculations, Intermetallics, 1999, 7, p 5-9
Q. Yao, J. Sun, Y. Zhang, and B. Jiang, First-Principles Studies of Ternary Site Occupancy in the C15 NbCr2 Laves Phase, Acta Mater., 2006, 54(13), p 3585-3591
A. Ormeci, F. Chu, J. Wills, T. Mitchell, R. Albers, D. Thoma, and S. Chen, Total-Energy Study of Electronic Structure and Mechanical Behavior of C15 Laves Phase Compounds: NbCr2 and HfV2, Phys. Rev. B, 1996, 54(18), p 12753-12762
A. Kellou, T. Grosdidier, C. Coddet, and H. Aourag, Theoretical Study of Structural, Electronic, and Thermal Properties of Cr(Zr, Nb) Laves Alloys, Acta Mater., 2005, 53(5), p 1459-1466
P.E.N. De Souza, L.M. De Oliveira, W.A. Ortiz, P.C. De Camargo, and A.J.A. De Oliveira, Local Magnetic Moments in Dilute Cr-Nb Alloys: the Effects of Applied Magnetic Field and Nb Concentration, J. Phys. Condens. Matter, 2005, 17, p 2191-2196
G. te Velde and E.J. Baerends, Precise Density-Functional Method for Periodic Structures, Phys. Rev. B, 1991, 44(15), p 7888-7903
G. Wiesenekker and E.J. Baerends, Quadratic Integration Over the Three-Dimensional Brillouin Zone, J. Phys., 1991, 3, p 6721-6742
J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77, p 3865-3868
E. van Lenthe, A.E. Ehlers, and E.J. Baerends, Geometry Optimization in the Zero Order Regular Approximation for Relativistic Effects, J. Chem. Phys., 1999, 110, p 8943-8953
K. Hari Kumar and P. Wollants, Wollants, Some Guidelines for Thermodynamic Optimisation of Phase Diagrams, J. Alloys Compd., 2001, 320, p 189-198
R. Schmid-Fetzer, D. Andersson, P. Chevalier, L. Eleno, O. Fabrichnaya, U. Kattner, B. Sundman, C. Wang, A. Watson, L. Zabdyr, and M. Zinkevich, Assessment Techniques, Database Design and Software Facilities for Thermodynamics and Diffusion, CALPHAD, 2007, 31(1), p 38-52
N. Saunders and A.P. Miodownik, CALPHAD (A Comprehensive Guide), Elsevier, London, 1998
H.L. Lukas, S.G. Fries, and B. Sundman, Computational Thermodynamics, Cambridge University Press, Cambridge, UK, 2007
J.O. Andersson, T. Helander, L. Höglund, P.F. Shi, and B. Sundman, Thermo-Calc & DICTRA, Computational Tools for Materials Science, CALPHAD, 2002, 26(2), p 273-312
A.T. Dinsdale, SGTE Data for Pure Elements, CALPHAD, 1991, 15, p 317-425
J.H. Zhu, L.M. Pike, C.T. Liu, and P.K. Liaw, Point Defects in Binary NbCr2 Laves-Phase Alloy, Scr. Mater., 1998, 39(7), p 833-838
Y.J. Bhatt, L. Kumar, R.V. Patil, G.B. Kale, and S.P. Garg, Diffusion Studies in Hf-Mo, Zr-Mo, Cr-Nb, Cr-Ta and Th-Re Systems Above 1900 K, J. Alloy. Compd., 2000, 302, p 177-186
M.H.F. Sluiter, Ab Initio Lattice Stabilities of Some Elemental Complex Structures, CALPHAD, 2006, 30, p 357-366
R.G. Ross and W. Hume-Rothery, High Temperature x-ray Metallography: I. A New Debye-Scherrer Camera for Use at Very High Temperatures II. A New Parafocusing Camera III. Applications to the Study of Chromium, Hafnium, Molybdenum, Rhodium, Ruthenium and Tungsten, J. Less Common Met., 1963, 5, p 258-270
Z. Blazina and R. Trojko, Structural Investigations of the Nb1−x Si x T2 and Nb1−x Al x T2 (T = Cr, Mn, Fe Co, Ni) Systems, J. Less-Common Met., 1986, 119, p 297-305
M.E. Straumanis and S. Zyszczynski, Lattice Parameters, Thermal Expansion Coefficients and Densities of Nb, and of Solid Solutions Nb-O and Nb-N-O and Their Defect Structure, J. Appl. Cryst., 1970, 3, p 1-6
Acknowledgments
The authors would like to express their thanks to Jülich Supercomputing Centre (JSC) for granting computing time for this work on the supercomputer JUROPA. Financial support through the Portfolio Project “Materials Research for Future Energy Supply” funded by the Helmholtz Association and by RFBR Project No. 14-08-31522 мoл_a is gratefully acknowledged.
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Schmetterer, C., Khvan, A., Jacob, A. et al. A New Theoretical Study of the Cr-Nb System. J. Phase Equilib. Diffus. 35, 434–444 (2014). https://doi.org/10.1007/s11669-014-0313-y
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DOI: https://doi.org/10.1007/s11669-014-0313-y