Abstract：In this study, the most recently reported thermodynamic parameters for the Ni-Cr, Ni-W, and Cr-W binary systems were integrated with experimental data from the Ni-Cr-W ternary system. A thermodynamic assessment and optimization were conducted using the calculation of phase diagram (CALPHAD) method, resulting in a self-consistent set of thermodynamic parameters. The σ phase in the system was modeled using a sublattice model: (Cr,Ni,W)0.533(Cr,Ni,W)0.333(Cr,Ni,W)0.134. The calculated isothermal sections of the Ni-Cr-W system at 1 273, 1 473, 1 673, and 1 813 K, as well as the liquidus projection, demonstrate excellent agreement with experimental data, indicating that the thermodynamic database of this work can accurately reproduce experimental observations and provide critical insights for the design of advanced multicomponent alloys within this system.
[1] YEH J W, CHEN S K, LIN S J, et al.Nanostructured high‐entropy alloys with multiple principal elements: novel alloy design concepts and outcomes[J]. Advanced Engineering Materials, 2004, 6(5): 299-303. [2] 宫书林, 王永东, 李艳春, 等. 激光熔覆CoCrFeNiTix高熵合金涂层的组织与性能[J]. 粉末冶金材料科学与工程, 2024, 29(2): 118-124. GONG Shulin, WANG Yongdong, LI Yanchun, et al.Microstructure and properties of CoCrFeNiTix high-entropy alloy coating by laser cladding[J]. Materials Science and Engineering of Powder Metallurgy, 2024, 29(2): 118-124. [3] ZHANG Y, ZUO T T, TANG Z, et al.Microstructures and properties of high-entropy alloys[J]. Progress in Materials Science, 2014, 61: 1-93. [4] SHI P J, REN W L, ZHENG T X, et al.Enhanced strength-ductility synergy in ultrafine-grained eutectic high-entropy alloys by inheriting microstructural lamellae[J]. Nature Communications, 2019, 10: 489. [5] CANTOR B.Multicomponent high-entropy cantor alloys[J]. Progress in Materials Science, 2021, 120: 100754. [6] CANTOR B, CHANG I T H, KNIGHT P, et al. Microstructural development in equiatomic multicomponent alloys[J]. Materials Science and Engineering A, 2004, 375: 213-218. [7] HE M Y, JIA N, LIU X C, et al.Abnormal chemical composition fluctuations in multi-principal-element alloys induced by simple cyclic deformation[J]. Journal of Materials Science & Technology, 2022, 113: 287-295. [8] TARIQ N H, NAEEM M, HASAN B A, et al.Effect of W and Zr on structural, thermal and magnetic properties of AlCoCrCuFeNi high entropy alloy[J]. Journal of Alloys and Compounds, 2013, 556: 79-85. [9] DONG Y, LU Y P.Effects of tungsten addition on the microstructure and mechanical properties of near-eutectic AlCoCrFeNi2 high-entropy alloy[J]. Journal of Materials Engineering and Performance, 2018, 27(1): 109-115. [10] MALATJI N, LENGOPENG T, PITYANA S, et al.Microstructural, mechanical and electrochemical properties of AlCrFeCuNiWx high entropy alloys[J]. Journal of Materials Research and Technology, 2021, 11: 1594-1603. [11] ZHANG L, HUO X F, WANG A G, et al.A ductile high entropy alloy strengthened by nano sigma phase[J]. Intermetallics, 2020, 122: 106813. [12] TREITSCHKE W, TAMMANN G.LIII. Über die legierungen des eisens mit chrom[J]. Zeitschrift Für Anorganische Chemie, 1907, 55(1): 402-411. TREITSCHKE W, TAMMANN G.LIII. On the alloys of iron with chromium[J]. Journal for Inorganic Chemistry, 1907, 55(1): 402-411. [13] BERGMAN B G, SHOEMAKER D P.The space group of the σ‐FeCr crystal structure[J]. The Journal of Chemical Physics, 1951, 19(4): 515. [14] OSTROWSKA M, CACCIAMANI G.Thermodynamic modelling of the σ and μ phases in several ternary systems containing Co, Cr, Fe, Mo, Re and W[J]. Journal of Alloys and Compounds, 2020, 845: 156122. [15] KIM S H, KIM H, KIM N J.Brittle intermetallic compound makes ultrastrong low-density steel with large ductility[J]. Nature, 2015, 518(7537): 77-79. [16] LIU W H, LU Z P, HE J Y, et al.Ductile CoCrFeNiMox high entropy alloys strengthened by hard intermetallic phases[J]. Acta Materialia, 2016, 116: 332-342. [17] JOUBERT J M.Comment on the paper “experimental investigation of the Ni-V-W ternary phase diagram”, calphad: comput. coupling phase diagrams thermochem. 76 (2022) 102384[J]. Calphad, 2022, 77: 102424. [18] JACOB A, SCHMETTERER C, SINGHEISER L, et al.Modeling of Fe-W phase diagram using first principles and phonons calculations[J]. Calphad, 2015, 50: 92-104. [19] LEI H, CHEN C, YE X, et al.Synergistic effect of Nb and W alloying on the microstructure and mechanical properties of CoCrFeNi high entropy alloys[J]. Journal of Materials Research and Technology, 2024, 28: 3765-3774. [20] GAMBARO S, FENOCCHIO L, VALENZA F, et al.Combined experimental and CALPHAD investigation of equimolar AlCoCrFeNiX (X=Mo, Ta, W) high-entropy alloys[J]. Calphad, 2024, 85: 102702. [21] ZHANG F, ZHANG C, CHEN S L, et al.An understanding of high entropy alloys from phase diagram calculations[J]. Calphad, 2014, 45: 1-10. [22] WANG W, CHEN H L, LARSSON H, et al.Thermodynamic constitution of the Al-Cu-Ni system modeled by CALPHAD and ab initio methodology for designing high entropy alloys[J]. Calphad, 2019, 65: 346-369. [23] STEIN C, GRANT N J.Chromium-rich portion of the chromium-nickel phase diagram[J]. The Journal of the Minerals, Metals & Materials Society, 1955, 7(1): 127-134. [24] 鲁欣欣, 刘伟, 李林, 等. MgO-Y2O3-Re2O3添加对氮化硅陶瓷微观组织及性能的影响[J]. 粉末冶金材料科学与工程, 2019, 24(6): 536-541. LU Xinxin, LIU Wei, LI Lin, et al.Effects of MgO-Y2O3-Re2O3 on microstructure and properties of Si3N4 ceramics[J]. Materials Science and Engineering of Powder Metallurgy, 2019, 24(6): 536-541. [25] NASH P.The Cr-Ni (chromium-nickel) system[J]. Bulletin of Alloy Phase Diagrams, 1986, 7(5): 466-476. [26] GUSTAFSON P.A thermodynamic evaluation of the Cr-Ni-W system[J]. Calphad, 1988, 12(3): 277-292. [27] LEE B J.On the stability of Cr carbides[J]. Calphad, 1992, 16(2): 121-149. [28] XIONG W.Thermodynamic and kinetic investigation of the Fe-Cr-Ni system driven by engineering applications[D]. Sweden, Stockholm: KTH Royal Institute of Technology, 2012. [29] DEN BROEDER F J A. Interface reaction and a special form of grain boundary diffusion in the Cr-W system[J]. Acta Metallurgica, 1972, 20(3): 319-332. [30] MARGARIA T, ALLIBERT C, ANSARA I, et al.Étude du système W-Ni-Cr à haute température[J]. High Temperatures- High Pressures, 1976, 8: 451-459. MARGARIA T, ALLIBERT C, ANSARA I, et al.Study of the W-Ni-Cr system at high temperature[J]. High Temperatures-High Pressures, 1976, 8: 451-459. [31] GABRIEL A, LUKAS H L, ALLIBERT C H, et al.Experimental and calculated phase diagrams of the Ni-W Co-W and Co-Ni-W system[J]. International Journal of Materials Research, 1985, 76(9): 589-595. [32] POPOVIČ J, BROŽ P, BURŠÍK J. Microstructure and phase equilibria in the Ni-Al-W system[J]. Intermetallics, 2008, 16(7): 884-888. [33] CURY R, JOUBERT J M, TUSSEAU-NENEZ S, et al.On the existence and the crystal structure of Ni4W, NiW and NiW2 compounds[J]. Intermetallics, 2009, 17(3): 174-178. [34] ISOMÄKI I, HÄMÄLÄINEN M, BRAGA M H, et al. First principles, thermal stability and thermodynamic assessment of the binary Ni-W system[J]. International Journal of Materials Research, 2017, 108(12): 1025-1035. [35] KUO K.Ternary laves and sigma-phases of transition metals[J]. Acta Metallurgica, 1953, 1(6): 720-724. [36] LAUGEE C, ALLIBERT C H, ANSARA I.Phase eaquilibria of the Ni-W-Cr system in the composition and temperature ranges of the liquid phase sintering of heavy alloys[J]. International Journal of Materials Research, 1985, 76(2): 138-142. [37] KIKUCHI M, KAJIHARA M, KADOYA Y, et al.Experimental determination of isothermal section in a Ni-Cr-W ternary system at 1 000 ℃[J]. Tetsu-to-Hagane, 1984, 70(16): 2246-2253. KIKUCHI M, KAJIHARA M, KADOYA Y, et al.Experimental determination of isothermal section in a Ni-Cr-W ternary system at 1 000 ℃[J]. Steel and Iron, 1984, 70(16): 2246-2253. [38] KAJIHARA M, KADOYA Y, KIKUCHI M, et al.Experimental determination of isothermal sections in the Ni-Cr-W ternary system at 1 100 and 1 200 ℃[J]. Tetsu-to- Hagane, 1985, 71(15): 1773-1779. KAJIHARA M, KADOYA Y, KIKUCHI M, et al.Experimental determination of isothermal sections in the Ni-Cr-W ternary system at 1 100 and 1 200 ℃[J]. Steel and Iron, 1985, 71(15): 1773-1779. [39] DINSDALE A T.SGTE data for pure elements[J]. Calphad, 1991, 15(4): 317-425. [40] HILLERT M.Partial Gibbs energies from redlich-kister polynomials[J]. Thermochimica Acta, 1988, 129(1): 71-75. [41] ANSARA I, DUPIN N, LUKAS H L, et al.Thermodynamic assessment of the Al-Ni system[J]. Journal of Alloys and Compounds, 1997, 247(1/2): 20-30.
2025, Vol. 30 
