journal article·2021-03Open access

Laves phases: a review of their functional and structural applications and an improved fundamental understanding of stability and properties

Frank Stein, Andreas Leineweber

Journal of Materials Science· Volume 56· Issue 9

Abstract

Abstract Laves phases with their comparably simple crystal structure are very common intermetallic phases and can be formed from element combinations all over the periodic table resulting in a huge number of known examples. Even though this type of phases is known for almost 100 years, and although a lot of information on stability, structure, and properties has accumulated especially during the last about 20 years, systematic evaluation and rationalization of this information in particular as a function of the involved elements is often lacking. It is one of the two main goals of this review to summarize the knowledge for some selected respective topics with a certain focus on non-stoichiometric, i.e., non-ideal Laves phases. The second, central goal of the review is to give a systematic overview about the role of Laves phases in all kinds of materials for functional and structural applications. There is a surprisingly broad range of successful utilization of Laves phases in functional applications comprising Laves phases as hydrogen storage material (Hydraloy), as magneto-mechanical sensors and actuators (Terfenol), or for wear- and corrosion-resistant coatings in corrosive atmospheres and at high temperatures (Tribaloy), to name but a few. Regarding structural applications, there is a renewed interest in using Laves phases for creep-strengthening of high-temperature steels and new respective alloy design concepts were developed and successfully tested. Apart from steels, Laves phases also occur in various other kinds of structural materials sometimes effectively improving properties, but often also acting in a detrimental way.
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Research context

OpenAlex topics: Intermetallics and Advanced Alloy Properties · Metal and Thin Film Mechanics · Metallurgical and Alloy Processes

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References (100+)

Show source-provided references
1. Laves F, Löhberg K (1934) Die Kristallstruktur von intermetallischen Verbindungen der Formel AB2 (The crystal structure of intermetallic compounds with formula AB2; in German). Nachr Ges Wiss Göttingen, Math-Phys Kl IV, Neue Folge 1(6):59–66
2. Laves F, Witte H (1935) Die Kristallstruktur des MgNi2 und seine Beziehungen zu den Typen des MgCu2 und MgZn2 (The crystal structure of MgNi2 and its relations to the MgCu2 and MgZn2 types; in German). Metallwirtsch Metallwiss Metalltech 14:645–649
3. Schulze GER (1939) Zur Kristallchemie der intermetallischen AB2-Verbindungen (Laves-Phasen) (About the crystal chemistry of the intermetallic AB2 compounds (Laves phases); in German). Z Elektrochem 45:849–865. https://doi.org/10.1002/bbpc.1939045120210.1002/bbpc.19390451202 ↗
4. Paufler P, Gustav ER (2006) Schulze’s pioneering work on Laves phases. Z Kristallogr 221:311–318. https://doi.org/10.1524/zkri.2006.221.5-7.31110.1524/zkri.2006.221.5-7.311 ↗
5. Paufler P (2011) Early work on Laves phases in East Germany. Intermetallics 19:599–612. https://doi.org/10.1016/j.intermet.2010.11.03210.1016/j.intermet.2010.11.032 ↗
6. Villars P, Calvert LD (1991) Pearson’s handbook of crystallographic data for intermetallic phases, 2nd edn. ASM International, Materials Park
7. Ansara I, Chart TG, Fernández Guillermet A, Hayes FH, Kattner UR, Pettifor DG, Saunders N, Zeng K (1997) Thermodynamic modelling of selected topologically close-packed intermetallic compounds. Calphad 21:171–218. https://doi.org/10.1016/S0364-5916(97)00021-710.1016/S0364-5916(97)00021-7 ↗
8. Tsai M-H, Tsai R-C, Chang T, Huang W-F (2019) Intermetallic phases in high-entropy alloys: statistical analysis of their prevalence and structural inheritance. Metals 9:247. https://doi.org/10.3390/met902024710.3390/met9020247 ↗
9. Gorban’ VF, Krapivka NA, Firstov SA (2017) High-entropy alloys: interrelations between electron concentration, phase composition, lattice parameter, and properties. Phys Met Metallogr 118:970–981. https://doi.org/10.1134/S0031918X1708005110.1134/S0031918X17080051 ↗
10. Livingston JD (1992) Laves-phase superalloys? Phys Status Solidi A 131:415–423. https://doi.org/10.1002/pssa.221131021510.1002/pssa.2211310215 ↗
11. Lukas HL, Fries SG, Sundman B (2007) Computational thermodynamics: the calphad method. Cambridge University Press, Cambridge ISBN 978-052186811210.1017/CBO9780511804137 ↗
12. Thoma DJ (2001) Intermetallics: Laves phases. In: Buschow KHJ, Cahn RW, Flemmings MC, Ilschner B, Kramer EJ, Mahajan S (eds) Encyclopedia of materials: science and technology. Elsevier, Amsterdam, pp 4205–4213. https://doi.org/10.1016/B0-08-043152-6/00739-710.1016/B0-08-043152-6/00739-7 ↗
13. Westbrook JH, Fleischer RL (2002) Intermetallic compounds, Vol. 1 - Principles (1995), Vol. 2 - Practice (1995), Vol. 3 - Progress. Wiley, Chichester10.1002/0470845856 ↗
14. Kumar KS, Hazzledine PM (2004) Polytypic transformations in Laves phases. Intermetallics 12:763–770. https://doi.org/10.1016/j.intermet.2004.02.01710.1016/j.intermet.2004.02.017 ↗
15. Liu CT, Zhu JH, Brady MP, McKamey CG, Pike LM (2000) Physical metallurgy and mechanical properties of transition-metal Laves phase alloys. Intermetallics 8:1119–1129. https://doi.org/10.1016/S0966-9795(00)00109-610.1016/S0966-9795(00)00109-6 ↗
16. Stein F, Palm M, Sauthoff G (2004) Structure and stability of Laves phases Part I—Critical assessment of factors controlling Laves phase stability. Intermetallics 12:713–720. https://doi.org/10.1016/j.intermet.2004.02.01010.1016/j.intermet.2004.02.010 ↗
17. Stein F, Palm M, Sauthoff G (2005) Structure and stability of Laves phases Part II—Structure type variations in binary and ternary systems. Intermetallics 13:1056–1074. https://doi.org/10.1016/j.intermet.2004.11.00110.1016/j.intermet.2004.11.001 ↗
18. Ferro R, Saccone A (2008) Intermetallic chemistry. Elsevier, Amsterdam
19. Laves F (1942) Über den Einfluß geometrischer Faktoren auf die stöchiometrische Formel metallischer Verbindungen, gezeigt an der Kristallstruktur des KNa2 (About the effect of geometrical factors on the stoichiometric formula of metallic compounds, shown for the crystal structure of KNa2; in German). Z Anorg Allg Chem 250:110–120. https://doi.org/10.1002/zaac.1942250011010.1002/zaac.19422500110 ↗
20. Schulze GER (1961) Dichte und Raumerfüllung bei intermetallischen Verbindungen, insbesondere Laves-Phasen (Density and space filling in intermetallic compounds, especially Laves phases; in German). Z Kristallogr 115:261–268. https://doi.org/10.1524/zkri.1961.115.3-4.26110.1524/zkri.1961.115.3-4.261 ↗
21. Parthé E (1961) Space filling of crystal structures—a contribution to the graphical presentation of geometrical relationships in simple crystal structures. Z Kristallogr 115:52–79. https://doi.org/10.1524/zkri.1961.115.1-2.5210.1524/zkri.1961.115.1-2.52 ↗
22. Frank FC, Kasper JS (1958) Complex alloy structures regarded as sphere packings. I. Definitions and basic principles. Acta Crystallogr 11:184–190. https://doi.org/10.1107/S0365110X5800048710.1107/S0365110X58000487 ↗
23. Frank FC, Kasper JS (1959) Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures. Acta Crystallogr 12:483–499. https://doi.org/10.1107/S0365110X5900149910.1107/S0365110X59001499 ↗
24. Yarmolyuk YP, Kripyakevich PI (1974) Mean weighted coordination numbers and the origin of close-packed structures with atoms of unequal size but normal coordination polyhedra. Sov Phys Crystallogr 19:334–337
25. Shoemaker DP, Shoemaker CB (1986) Concerning the relative numbers of atomic coordination types in tetrahedrally close packed metal structures. Acta Crystallogr B 42:3–11. https://doi.org/10.1107/S010876818609867110.1107/S0108768186098671 ↗
26. Aroyo MI (ed) (2016) International tables for crystallography, volume A: space-group symmetry, 6th edn. Wiley, New York. https://doi.org/10.1107/9780955360206000011410.1107/97809553602060000114 ↗
27. Komura Y (1962) Stacking faults and two new modifications of the Laves phase in Mg-Cu-Al system. Acta Crystallogr 15:770–778. https://doi.org/10.1107/S0365110X6200201710.1107/S0365110X62002017 ↗
28. Komura Y, Tokunaga K (1980) Structural studies of stacking variants in Mg-base Friauf-Laves phases. Acta Crystallogr B 36:1548–1554. https://doi.org/10.1107/S056774088000656510.1107/S0567740880006565 ↗
29. Komura Y, Kitano Y (1977) Long-period stacking variants and electron-concentration dependence in the Mg-base Friauf-Laves phases. Acta Crystallogr B 33:2496–2501. https://doi.org/10.1107/S056774087700878410.1107/S0567740877008784 ↗
30. Zemp J, Celino M, Schönfeld B, Löffler JF (2015) Crystal-like rearrangements of icosahedra in simulated copper-zirconium metallic glasses and their effect on mechanical properties. Phys Rev Lett 115:165501. https://doi.org/10.1103/PhysRevLett.115.16550110.1103/PhysRevLett.115.165501 ↗
31. Zemp J, Celino M, Schönfeld B, Löffler JF (2014) Icosahedral superclusters in Cu64Zr36 metallic glass. Phys Rev B 90:144108. https://doi.org/10.1103/PhysRevB.90.14410810.1103/PhysRevB.90.144108 ↗
32. Yamamoto K, Kimura Y, Mishima Y (2004) Precipitation of the icosahedral quasicrystalline phase, R-phase and Laves phase in ferritic alloys. Mater Trans 45:357–360. https://doi.org/10.2320/matertrans.45.35710.2320/matertrans.45.357 ↗
33. Natarajan AR, Van der Ven A (2018) Connecting the simpler structures to topologically close-packed phases. Phys Rev Lett 121:255701. https://doi.org/10.1103/PhysRevLett.121.25570110.1103/PhysRevLett.121.255701 ↗
34. Hajiw S, Pansu B, Sadoc J-F (2015) Evidence for a C14 Frank–Kasper phase in one-size gold nanoparticle superlattices. ACS Nano 9:8116–8121. https://doi.org/10.1021/acsnano.5b0221610.1021/acsnano.5b02216 ↗
35. Ghosh S, Basu J, Ramachandran D, Mohandas E, Vijayalakshmi M (2012) A unified approach to phase and microstructural stability for Fe-ETM alloys through Miedema’s model. Intermetallics 23:148–157. https://doi.org/10.1016/j.intermet.2011.11.01610.1016/j.intermet.2011.11.016 ↗
36. Hasaka M, Nakashima H, Oki K (1984) Structure of the Laves phase observed in polystyrene latexes. Trans Jpn Inst Met 25:65–72. https://doi.org/10.2320/matertrans1960.25.6510.2320/matertrans1960.25.65 ↗
37. Marinica MC, Willaime F, Crocombette JP (2012) Irradiation-induced formation of nanocrystallites with C15 Laves phase structure in bcc iron. Phys Rev Lett 108:025501. https://doi.org/10.1103/PhysRevLett.108.02550110.1103/PhysRevLett.108.025501 ↗
38. Dézerald L, Marinica M-C, Ventelon L, Rodney D, Willaime F (2014) Stability of self-interstitial clusters with C15 Laves phase structure in iron. J Nucl Mater 449:219–224. https://doi.org/10.1016/j.jnucmat.2014.02.01210.1016/j.jnucmat.2014.02.012 ↗
39. Alexander R, Marinica MC, Proville L, Willaime F, Arakawa K, Gilbert MR, Dudarev SL (2016) Ab initio scaling laws for the formation energy of nanosized interstitial defect clusters in iron, tungsten, and vanadium. Phys Rev B 94:024103. https://doi.org/10.1103/PhysRevB.94.02410310.1103/PhysRevB.94.024103 ↗
40. Zhang Y, Bai X-M, Tonks MR, Biner SB (2015) Formation of prismatic loops from C15 Laves phase interstitial clusters in body-centered cubic iron. Scr Mater 98:5–8. https://doi.org/10.1016/j.scriptamat.2014.10.03310.1016/j.scriptamat.2014.10.033 ↗
41. Chartier A, Marinica MC (2019) Rearrangement of interstitial defects in alpha-Fe under extreme condition. Acta Mater 180:141–148. https://doi.org/10.1016/j.actamat.2019.09.00710.1016/j.actamat.2019.09.007 ↗
42. Loubeyre P, Jean-Louis M, LeToullec R, Charon-Gérard L (1993) High pressure measurements of the He-Ne binary phase diagram at 296 K: evidence for the stability of a stoichiometric Ne(He)2 solid. Phys Rev Lett 70:178–181. https://doi.org/10.1103/PhysRevLett.70.17810.1103/PhysRevLett.70.178 ↗
43. Dewaele A, Rosa AD, Guignot N (2019) Argon-neon binary diagram and ArNe2 Laves phase. J Chem Phys 151:124708. https://doi.org/10.1063/1.511941910.1063/1.5119419 ↗
44. Yan XZ, Chen YM, Geng HY (2019) Prediction of the reactivity of argon with xenon under high pressures. ACS Omega 4:13640–13644. https://doi.org/10.1021/acsomega.9b0063810.1021/acsomega.9b00638 ↗
45. Loubeyre P, Letoullec R, Pinceaux J-P (1994) Compression of Ar(H2)2 up to 175 GPa: a new path for the dissociation of molecular hydrogen? Phys Rev Lett 72:1360–1363. https://doi.org/10.1103/PhysRevLett.72.136010.1103/PhysRevLett.72.1360 ↗
46. Weck G, Dewaele A, Loubeyre P (2010) Oxygen/noble gas binary phase diagrams at 296 K and high pressures. Phys Rev B 82:014112. https://doi.org/10.1103/PhysRevB.82.01411210.1103/PhysRevB.82.014112 ↗
47. Laniel D, Weck G, Loubeyre P (2016) Xe(N2)2 compound to 150 GPa: reluctance to the formation of a xenon nitride. Phys Rev B 94:174109. https://doi.org/10.1103/PhysRevB.94.17410910.1103/PhysRevB.94.174109 ↗
48. Somayazulu MS, Finger LW, Hemley RJ, Mao HK (1996) High-pressure compounds in methane-hydrogen mixtures. Science 271:1400–1402. https://doi.org/10.1126/science.271.5254.140010.1126/science.271.5254.1400 ↗
49. Cazorla C, Errandonea D, Sola E (2009) High-pressure phases, vibrational properties, and electronic structure of Ne(He)2 and Ar(He)2: a first-principles study. Phys Rev B 80:064105. https://doi.org/10.1103/PhysRevB.80.06410510.1103/PhysRevB.80.064105 ↗
50. Hynninen A-P, Filion L, Dijkstra M (2009) Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres. J Chem Phys 131:064902. https://doi.org/10.1063/1.318272410.1063/1.3182724 ↗
51. Schaertl N, Botin D, Palberg T, Bartsch E (2018) Formation of Laves phases in buoyancy matched hard sphere suspensions. Soft Matter 14:5130–5139. https://doi.org/10.1039/C7SM02348K10.1039/C7SM02348K ↗
52. Lindquist BA, Jadrich RB, Truskett TM (2018) Communication: from close-packed to topologically close-packed: formation of Laves phases in moderately polydisperse hard-sphere mixtures. J Chem Phys 148:191101. https://doi.org/10.1063/1.502827910.1063/1.5028279 ↗
53. van der Meer B, Smallenburg F, Dijkstra M, Filion L (2020) High antisite defect concentrations in hard-sphere colloidal Laves phases. Soft Matter 16:4155–4161. https://doi.org/10.1039/D0SM00335B10.1039/D0SM00335B ↗
54. Hynninen A-P, Thijssen JHJ, Vermolen ECM, Dijkstra M, van Blaaderen A (2007) Self-assembly route for photonic crystals with a bandgap in the visible region. Nat Mater 6:202. https://doi.org/10.1038/nmat184110.1038/nmat1841 ↗
55. Vermolen ECM, Thijssen JHJ, Moroz A, Megens M, Av Blaaderen (2009) Comparing photonic band structure calculation methods for diamond and pyrochlore crystals. Opt Express 17:6952–6961. https://doi.org/10.1364/OE.17.00695210.1364/OE.17.006952 ↗
56. Avvisati G, Dijkstra M (2016) Colloidal Laves phases as precursors of photonic crystals. arXiv:160307591v1 1–5
57. Avvisati G, Dasgupta T, Dijkstra M (2017) Fabrication of colloidal Laves phases via hard tetramers and hard spheres: bulk phase diagram and sedimentation behavior. ACS Nano 11:7702–7709. https://doi.org/10.1021/acsnano.7b0050510.1021/acsnano.7b00505 ↗
58. Dasgupta T, Dijkstra M (2018) Towards the colloidal Laves phase from binary hard-sphere mixtures via sedimentation. Soft Matter 14:2465–2475. https://doi.org/10.1039/C8SM00237A10.1039/C8SM00237A ↗
59. Yoshimura S, Hachisu S (1983) Order formation in binary mixtures of monodisperse latices. Prog Colloid Polym Sci 68:59–7010.1007/BFb0114141 ↗
60. Ma GH, Fukutomi T, Morone N (1994) Preparation and analysis of ordered structure of binary mixtures composed of poly(4-vinylpyridine) and polystyrene microgels. J Colloid Interface Sci 168:393–401. https://doi.org/10.1006/jcis.1994.143510.1006/jcis.1994.1435 ↗
61. Cabane B, Li J, Artzner F, Botet R, Labbez C, Bareigts G, Sztucki M, Goehring L (2016) Hiding in plain view: colloidal self-assembly from polydisperse populations. Phys Rev Lett 116:208001. https://doi.org/10.1103/PhysRevLett.116.20800110.1103/PhysRevLett.116.208001 ↗
62. Kim K, Schulze MW, Arora A, Lewis RM, Hillmyer MA, Dorfman KD, Bates FS (2017) Thermal processing of diblock copolymer melts mimics metallurgy. Science 356:520–523. https://doi.org/10.1126/science.aam721210.1126/science.aam7212 ↗
63. Kim K, Arora A, Lewis RM, Liu M, Li W, Shi A-C, Dorfman KD, Bates FS (2018) Origins of low-symmetry phases in asymmetric diblock copolymer melts. Proc Natl Acad Sci 115:847–854. https://doi.org/10.1073/pnas.171785011510.1073/pnas.1717850115 ↗
64. Mueller AJ, Lindsay AP, Jayaraman A, Lodge TP, Mahanthappa MK, Bates FS (2020) Emergence of a C15 Laves phase in diblock polymer/homopolymer blends. ACS Macro Lett 9:576–582. https://doi.org/10.1021/acsmacrolett.0c0012410.1021/acsmacrolett.0c00124 ↗
65. Ducrot É, He M, Yi G-R, Pine DJ (2017) Colloidal alloys with preassembled clusters and spheres. Nature Mater 16:652–657. https://doi.org/10.1038/nmat486910.1038/nmat4869 ↗
66. Baez-Cotto CM, Mahanthappa MK (2018) Micellar mimicry of intermetallic C14 and C15 Laves phases by aqueous lyotropic self-assembly. ACS Nano 12:3226–3234. https://doi.org/10.1021/acsnano.7b0747510.1021/acsnano.7b07475 ↗
67. Filion L, Dijkstra M (2009) Prediction of binary hard-sphere crystal structures. Phys Rev E 79:046714. https://doi.org/10.1103/PhysRevE.79.04671410.1103/PhysRevE.79.046714 ↗
68. Seiser B, Drautz R, Pettifor DG (2011) TCP phase predictions in Ni-based superalloys: structure maps revisited. Acta Mater 59:749–763. https://doi.org/10.1016/j.actamat.2010.10.01310.1016/j.actamat.2010.10.013 ↗
69. Seiser B, Hammerschmidt T, Kolmogorov AN, Drautz R, Pettifor DG (2011) Theory of structural trends within 4d and 5d transition metal topologically close-packed phases. Phys Rev B 83:224116. https://doi.org/10.1103/PhysRevB.83.22411610.1103/PhysRevB.83.224116 ↗
70. Demchyna R, Leoni S, Rosner H, Schwarz U (2006) High-pressure crystal chemistry of binary intermetallic compounds. Z Kristallogr 221:420–434. https://doi.org/10.1524/zkri.2006.221.5-7.42010.1524/zkri.2006.221.5-7.420 ↗
71. Kal S, Stoyanov E, Belieres JP, Groy TL, Norrestam R, Häussermann U (2008) High-pressure modifications of CaZn2, SrZn2, SrAl2, and BaAl2: implications for Laves phase structural trends. J Solid State Chem 181:3016–3023. https://doi.org/10.1016/j.jssc.2008.07.03610.1016/j.jssc.2008.07.036 ↗
72. Cordier G, Czech E, Schäfer H (1982) Über eine Hochdruckmodifikation des SrAl2 (About a high pressure modification of SrAl2; in German). Z Naturforsch B 37:1442–1445. https://doi.org/10.1515/znb-1982-111510.1515/znb-1982-1115 ↗
73. Cordier G, Czech E, Schäfer H (1984) Zur Kenntnis der Hochdruckphase BaAl2 (On BaAl2, a high pressure phase; in German). Z Naturforsch B 39:421–423. https://doi.org/10.1515/znb-1984-040310.1515/znb-1984-0403 ↗
74. Tsvyashchenko AV, Menushenkov AP, Sidorov VA, Petrova AE, Fomicheva LN, Chernysheva OV, Lebed YB, Axenov SN, Bud’ko SL, Sun L, Zhao Z (2015) High pressure synthesis of a new phase of YbAg2: structure, valence of Yb and properties. J Alloys Compd 650:295–298. https://doi.org/10.1016/j.jallcom.2015.06.20310.1016/j.jallcom.2015.06.203 ↗
75. Lindbaum A, Hafner J, Gratz E, Heathman S (1998) Structural stability of YM2 compounds (M = Al, Ni, Cu) studied by ab initio total-energy calculations and high-pressure X-ray diffraction. J Phys: Condens Matter 10:2933–2945. https://doi.org/10.1088/0953-8984/10/13/01110.1088/0953-8984/10/13/011 ↗
76. Cannon JF, Robertson DL, Hall HT (1972) Synthesis of lanthanide-iron Laves phases at high pressures and temperatures. Mater Res Bull 7:5–12. https://doi.org/10.1016/0025-5408(72)90063-310.1016/0025-5408(72)90063-3 ↗
77. Tsvyashchenko AV, Popova SV (1985) New phases melt quenched under high pressure in R-Fe systems (R ≡ Pr, Sm, Dy, Tb, Ho, Er, Tm, Yb, Lu). J Less-Common Met 108:115–121. https://doi.org/10.1016/0022-5088(85)90436-910.1016/0022-5088(85)90436-9 ↗
78. Tsvyashchenko AV, Fomicheva LN, Magnitskaya MV, Sidorov VA, Kuznetsov AV, Eremenko DV, Trofimov VN (1998) New ferromagnetic compound CaCo2 (C15) synthesized at high pressure. J Exp Theor Phys Lett 68:908–914. https://doi.org/10.1134/1.56795410.1134/1.567954 ↗
79. Hasegawa M, Atou T, Badding JV (1997) High-pressure synthesis of an alkali metal–transition metal Laves phase: KAg2. J Solid State Chem 130:311–315. https://doi.org/10.1006/jssc.1997.739110.1006/jssc.1997.7391 ↗
80. Kienast G, Verma J, Klemm W (1961) Das Verhalten der Alkalimetalle zu Kupfer, Silber und Gold (The behavior of alkali metals towards Cu, Ag, and Au; in German). Z Anorg Allg Chem 310:143–169. https://doi.org/10.1002/zaac.1961310030410.1002/zaac.19613100304 ↗
81. Thompson JB Jr (1969) Chemical reactions in crystals. Am Mineral 54:341–375
82. Watson RE, Bennett LH (1984) Transition-metal alloy formation. The occurrence of topologically close packed phases-I. Acta Metall 32:477–489. https://doi.org/10.1016/0001-6160(84)90058-010.1016/0001-6160(84)90058-0 ↗
83. Watson RE, Bennett LH (1984) Model predictions of volume contractions in transition-metal alloys and implications for Laves phase formation–II. Acta Metall 32:491–502. https://doi.org/10.1016/0001-6160(84)90059-210.1016/0001-6160(84)90059-2 ↗
84. Tsakiropoulos P (2018) Alloying and properties of C14–NbCr2 and A15–Nb3X (X = Al, Ge, Si, Sn) in Nb–silicide-based alloys. Materials 11:395. https://doi.org/10.3390/ma1103039510.3390/ma11030395 ↗
85. Yamanouchi T, Miura S (2018) Influence of atomic size factors on the phase stability of Laves phase in Nb-Cr-Ni-Al and Nb-V-Ni-Al phase diagrams. Mater Trans 59:546–555. https://doi.org/10.2320/matertrans.MJ20160410.2320/matertrans.MJ201604 ↗
86. Joubert J-M, Crivello J-C (2012) Non-stoichiometry and Calphad modeling of Frank–Kasper phases. Appl Sci 2:669–681. https://doi.org/10.3390/app203066910.3390/app2030669 ↗
87. Joubert J-M, Andasmas M, Crivello J-C (2015) Irregular homogeneity domains in ternary intermetallic systems. Appl Sci 5:1570. https://doi.org/10.3390/app504157010.3390/app5041570 ↗
88. Spence JCH, Taftø J (1983) ALCHEMI: a new technique for locating atoms in small crystals. J Microsc 130:147–154. https://doi.org/10.1111/j.1365-2818.1983.tb04213.x10.1111/j.1365-2818.1983.tb04213.x ↗
89. Thoma DJ, Nibur KA, Chen KC, Cooley JC, Dauelsberg LB, Hults WL, Kotula PG (2002) The effect of alloying on the properties of (Nb, Ti)Cr2 C15 Laves phases. Mater Sci Eng A 329–331:408–415. https://doi.org/10.1016/S0921-5093(01)01614-810.1016/S0921-5093(01)01614-8 ↗
90. Mahdouk K, Gachon JC (2001) A thermodynamic study of the Al-Cr-Nb ternary system. J Alloys Compd 321:232–236. https://doi.org/10.1016/S0925-8388(01)00961-610.1016/S0925-8388(01)00961-6 ↗
91. Zhao J-C, Jackson MR, Peluso LA (2004) Evaluation of phase relations in the Nb-Cr-Al system at 1000°C using a diffusion-multiple approach. J Phase Equilib 25:152–159. https://doi.org/10.1007/s11669-004-0008-x10.1007/s11669-004-0008-x ↗
92. He C, Stein F (2010) Thermodynamic assessment of the Cr-Al-Nb system. Int J Mater Res 101:1369–1375. https://doi.org/10.3139/146.11042010.3139/146.110420 ↗
93. Prymak O, Stein F (2012) The ternary Cr-Al-Nb phase diagram: experimental investigations of isothermal sections at 1150, 1300 and 1450°C. J Alloys Compd 513:378–386. https://doi.org/10.1016/j.jallcom.2011.10.05310.1016/j.jallcom.2011.10.053 ↗
94. Zhao J-C, Jackson MR, Peluso LA (2003) Determination of the Nb-Cr-Si phase diagram using diffusion multiples. Acta Mater 51:6395–6405. https://doi.org/10.1016/j.actamat.2003.08.00710.1016/j.actamat.2003.08.007 ↗
95. Prymak O, Stein F, Kerkau A, Ormeci A, Kreiner G, Frommeyer G, Raabe D (2009) Phase equilibria in the ternary Nb-Cr-Al system and site occupation in the hexagonal C14 Laves phase Nb(AlxCr1-x)2. Mater Res Soc Symp Proc 1128:499–504. https://doi.org/10.1557/PROC-1128-U08-1110.1557/PROC-1128-U08-11 ↗
96. Chu F, Thoma DJ, Kotula PG, Gerstl S, Mitchell TE, Anderson IM, Bentley J (1998) Phase stability and defect structure of the C15 Laves phase Nb(Cr, V)2. Acta Mater 46:1759–1769. https://doi.org/10.1016/S1359-6454(97)00291-710.1016/S1359-6454(97)00291-7 ↗
97. Chu F, Zhu Q, Thoma DJ, Mitchell TE (1998) Structural and defect analysis of V-alloyed C15 NbCr2 from high resolution synchrotron X-ray powder diffraction. Philos Mag A 78:551–565. https://doi.org/10.1080/0141861980824192210.1080/01418619808241922 ↗
98. Okaniwa H, Shindo D, Yoshida M, Takasugi T (1999) Determination of site occupancy of additives-X (X = V, Mo, W and Ti) in the Nb-Cr-X Laves phase by ALCHEMI. Acta Mater 47:1987–1992. https://doi.org/10.1016/S1359-6454(99)00065-810.1016/S1359-6454(99)00065-8 ↗
99. Jacob A, Schmetterer C, Grüner D, Wessel E, Hallstedt B, Singheiser L (2015) The Cr–Fe–Nb ternary system: experimental isothermal sections at 700 °C, 1050 °C and 1350 °C. J Alloys Compd 648:168–177. https://doi.org/10.1016/j.jallcom.2015.06.13710.1016/j.jallcom.2015.06.137 ↗
100. Putland F, Chart T, Dinsdale A (1980) Thermodynamically calculated phase diagrams for the Co-Cr-Ta and Co-Cr-Nb systems. Calphad 4:133–141. https://doi.org/10.1016/0364-5916(80)90030-910.1016/0364-5916(80)90030-9 ↗