Three-dimensional ultrasounds modulated solidification microstructure and mechanical property of (FeCoNiCrMn)<sub>92</sub>Mo<sub>8</sub> high-entropy alloy

WU Hao; WANG Xu; WANG Jianyuan; ZHAI Wei; WEI Bingbo

doi:10.7498/aps.74.20250657

Abstract

Three-dimensional ultrasonic waves with amplitudes of 14, 18, and 22 μm, respectively, are used during the solidification of (FeCoNiCrMn)₉₂Mo₈ high-entropy alloy, and its microstructural evolution and mechanical property are investigated in this work. Under static condition, the solidification microstructure is composed of primary γ phase dendrites with FCC structure and stripe-shaped σ phase with tetragonal structure. As the ultrasonic amplitude increases, the mean transient cavitation intensity rises to trigger off a significant nucleation rate increase of the primary γ phase to 5.6 × 10¹² m^–3·s^–1, leading to the remarkable grain size reduction by two orders of magnitude. The maximum and the average acoustic streaming velocity increase simultaneously, which accelerates atomic diffusion at the liquid/solid interface, reducing Cr content in the primary γ phase from 18.6% to 13.1% and Mo content from 6.8% to 3.4% (atomic percent). This atomic redistribution subsequently causes the liquid composition to approach the eutectic point and facilitate the formation of (γ + σ) eutectic, which accounts for more than 50% volume fraction. The two eutectic phases exhibit a semi-coherent interface relationship characterized by [110]_γ//[110]_σ and $(1\bar1\bar 1) $_γ//$(\overline110) $_σ. Furthermore, due to the gradual enrichment of Cr atoms in the remaining liquid phase, a small quantity of metastable μ phases with Cr content up to 62.3% form in the final microstructure. The maximum compressive yield strength of the ultrasonically solidified microstructure reaches 876.2 MPa, almost twice that of static solidification microstructure, and the compressive strain reaches 33.2%. The formation of (γ + σ) eutectic is the main factor that increases the yield strength of alloy by 527.1 MPa.

Keywords:

Authors and contacts

School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding author: ZHAI Wei, zhaiwei322@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52130405, 52088101) and the Natural Science Basic Research Plan of Shaanxi Province, China (Grant No. 2023-JC-JQ-28).

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References

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[4]	Fang J Z, Li R, Yao S L, Chen J, Wang K 2024 J. Appl. Phys. 136 245901 Google Scholar
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[33]	Turnbull D, Cech R E 1950 J. Appl. Phys. 21 804 Google Scholar
[34]	Thompson C V, Greer A L, Spaepen F 1983 Acta Metall. 31 1883 Google Scholar
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Cited By

图 1 液态(FeCoNiCrMn)₉₂Mo₈合金中声场和流场特征　(a) 模拟过程中所使用的3D模型; (b) A_3D = 14 μm, (c) A_3D = 18 μm和(d) A_3D = 22 μm条件下声场分布; (e) P₁-P₂连线处的声场强度; (f) 稳态与瞬态空化平均强度; (g) A_3D = 14 μm, (h) A_3D = 18 μm和(i) A_3D = 22 μm条件下流场分布; (j) 平均与最大流速

Figure 1. Acoustic field and flow field characteristics in liquid (FeCoNiCrMn)₉₂Mo₈ alloy: (a) 3D model used in the simulation process; sound field distribution of (b) A_3D = 14 μm, (c) A_3D = 18 μm, and (d) A_3D = 22 μm; (e) sound field intensity at the P₁-P₂ connection line; (f) average intensities of stable and transient cavitation; flow field distribution of (g) A_3D = 14 μm, (h) A_3D = 18 μm, and (i) A_3D = 22 μm; (j) average and maximum flow velocities.

DownLoad: Full-Size Img PowerPoint

图 2 静态和超声凝固条件下(FeCoNiCrMn)₉₂Mo₈合金相组成与热分析　(a) XRD图谱; (b) DSC曲线

Figure 2. Phase constitution and thermal analysis of (FeCoNiCrMn)₉₂Mo₈ alloy under static and ultrasonic solidification conditions: (a) XRD patterns; (b) DSC curves.

DownLoad: Full-Size Img PowerPoint

图 3 超声场中(FeCoNiCrMn)₉₂Mo₈合金凝固组织形貌　(a) 静态; (b) A_3D =14 μm; (c) A_3D = 22 μm

Figure 3. Solidification microstructure of (FeCoNiCrMn)₉₂Mo₈ alloy within ultrasonic fields: (a) Static; (b) A_3D = 14 μm; (c) A_3D = 22 μm

DownLoad: Full-Size Img PowerPoint

图 4 凝固组织特征尺寸及其相体积分数随超声振幅的变化规律　(a) 初生γ相平均尺寸和形核率; (b) 初生γ相与(γ + σ)共晶体积分数

Figure 4. Scale length characteristics and phase volume fractions of solidification microstructure versus ultrasound amplitude: (a) Average size and nucleation rate of primary γ phase; (b) volume fractions of primary γ phase and (γ + σ) eutectic.

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图 5 (FeCoNiCrMn)₉₂Mo₈合金各相Cr和Mo元素含量随超声振幅的变化规律　(a) 初生γ相; (b) (γ + σ)共晶

Figure 5. Cr and Mo element contents in various phases of (FeCoNiCrMn)₉₂Mo₈ alloy versus ultrasound amplitude: (a) Primary γ phase; (b) (γ + σ) eutectic.

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图 6 超声振幅22 μm条件下共晶γ/σ界面晶体学分析　(a) HAADF图像; (b) HRTEM图像; (c) HRTEM图像的FFT; (d) SAED模拟图

Figure 6. Crystallographic analysis of eutectic γ/σ interface under 22 μm ultrasound amplitude: (a) HAADF image; (b) HRTEM image; (c) FFT of HRTEM image; (d) simulated SAED pattern.

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图 7 超声振幅22 μm条件下所形成的亚稳μ相结构特征　(a) HAADF图像; (b) [110]晶带轴下的SAED; (c) [100]晶带轴下的SAED; (d) HRTEM图像

Figure 7. Structural characterization of mestable μ phase formed under 22 μm ultrasound amplitude: (a) HAADF image; (b) SAED pattern under [110] zone axis; (c) SAED pattern under [100] zone axis; (d) HRTEM image.

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图 8 (FeCoNiCrMn)₉₂Mo₈合金凝固过程中的热力学计算　(a) 初生γ相吉布斯自由能随超声振幅的变化; (b) Fe₁₆Co₁₇Ni₁₇Cr₂₀Mn₁₉Mo₁₁相体积分数随温度的变化

Figure 8. Thermodynamic calculations during solidification process of (FeCoNiCrMn)₉₂Mo₈ alloy: (a) Gibbs free energy of primary γ phase versus ultrasonic amplitude; (b) phase volume fractions of Fe₁₆Co₂₀Ni₁₇Cr₂₀Mn₁₉Mo₁₁ versus temperature.

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图 9 (FeCoNiCrMn)₉₂Mo₈合金的力学性能及屈服强度贡献　(a) 压缩应力应变曲线; (b) 共晶组织、固溶以及细晶强化对于屈服强度的贡献度

Figure 9. Mechanical properties and calculation of yield strength contribution value of (FeCoNiCrMn)₉₂Mo₈ alloy: (a) Stress-strain curves; (b) the contribution of eutectic structure, solid solution and grain strengthening to yield strength.

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表 1 (FeCoNiCrMn)₉₂Mo₈合金声场计算使用的物理参数

Table 1. Physical parameters used for acoustic field calculations of (FeCoNiCrMn)₉₂Mo₈ alloy.

参数	数值	参考文献
初始气泡半径 R₀/μm	3	[5,31]
初始气泡密度 N/m^–3	1.9×10⁹	[5]
密度 ρ_L/(kg·m^–3)	8230	CALPHAD
黏度 η_L/(Pa·s)	8.2×10^–3	CALPHAD
声速 c_L/(m·s^–1)	5170	[5]
表面张力 σ_L/(N·m^–1)	1.5	CALPHAD
石墨铸模密度 ρ_m/(kg·m^–3)	1820	[5]
石墨铸模声速 c_m/(m·s^–1)	3000	[5]

DownLoad: CSV

表 2 形核率计算使用的物理参数

Table 2. Physical parameters used for nucleation rate calculations.

参数	数值	参考文献
合金体积变化 ∆V/(cm³·mol^–1)	0.26	[35]
合金熔化焓 ∆H/( J·mol^–1)	12982	CALPHAD
润湿角因子 f(θ)	0.0001	[36]
γ 相摩尔体积 V_m/(cm³·mol^–1)	7.80	[35]
γ 相摩尔焓变 ∆H_m/(J·mol^–1)	13297	CALPHAD

DownLoad: CSV

表 3 屈服强度贡献值计算所使用的参数

Table 3. Parameters used for calculating the contribution value of yield strength.

符号	数值	参考文献
剪切模量G₀/GPa	81.3	[42,45]
拟合系数Z	0.0074	[42]
γ 枝晶Hall-Petch系数 k_y/(MPa·μm^1/2)	497	[43,44,46]
共晶Hall-Petch系数 k_h/(MPa·μm^1/2)	750	[43,44,47–49]
共晶层片间距λ/μm	0.9	本文统计
γ 相体积分数f_γ/%	91.2, 77.4, 68.4, 35.4	本文统计
共晶体积分数f_eu/%	0, 22.6, 31.6, 58.8	本文统计
初生相平均尺寸d/μm	7622, 656, 537, 45	本文统计

DownLoad: CSV

表 4 (FeCoNiCrMn)₉₂Mo₈合金屈服强度的各项贡献值(单位: MPa)

Table 4. Strengthening contributions of (FeCoNiCrMn)₉₂Mo₈ alloy (in MPa).

	静态	A_3D = 14 μm	A_3D = 18 μm	A_3D = 22 μm
晶格摩擦	210.0	210.0	210.0	210.0
固溶强化	109.3	95.0	89.2	47.0
细晶强化	5.7	19.4	21.5	27.0
σ相强化	70.4	—	—	—
共晶强化	—	202.6	283.3.	527.1
理论计算屈服强度	415.4	547.0	624.0	831.1
实际屈服强度	442.6	605.6	677.4	876.2

DownLoad: CSV

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[4]	Fang J Z, Li R, Yao S L, Chen J, Wang K 2024 J. Appl. Phys. 136 245901 Google Scholar
[5]	Wang X, Zhai W, Li H, Wang J Y, Wei B B 2023 Acta Mater. 252 118900 Google Scholar
[6]	Song H Q, Feng C S, Guan Z, Zhang W, Yang H Y, Tang Y, Zeng K, Yuan X, Zhang J W, Liu J, Zhang F X 2025 Appl. Phys. Lett. 126 031903 Google Scholar
[7]	Yu Z H, Wang H Y, Sun L G, Li Z H, Zhu L L 2024 Chin. Phys. B 33 116201 Google Scholar
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[9]	Cantor B 2021 Prog. Mater. Sci. 120 100754 Google Scholar
[10]	Han D Z, Luan H W, Zhao S F, Chen N, Peng R X, Shao Y, Yao K F 2018 Chin. Phys. Lett. 35 036102 Google Scholar
[11]	Xing R L, Liu X P 2024 Chin. Phys. B 33 016202 Google Scholar
[12]	安敏荣, 李思澜, 宿梦嘉, 邓琼, 宋海洋 2022 物理学报 71 243101 Google Scholar An M R, Li S L, Su M J, Deng Q, Song H Y 2022 Acta Phys. Sin. 71 243101 Google Scholar
[13]	Qin G, Chen R R, Zheng H T, Fang H Z, Wang L, Su Y Q, Guo J J, Fu H Z 2019 J. Mater. Sci. Technol. 35 578 Google Scholar
[14]	Sathiyamoorthi P, Kim H S 2022 Prog. Mater. Sci. 123 100709 Google Scholar
[15]	Azhagarsamy P, Sekar K, Murali K P 2022 Mater. Sci. Technol. 137 88
[16]	Wang H, He Q F, Yang Y 2022 Rare Met. 41 6
[17]	Li T, Chen H, Ma H, Zhou Z, Xu N, Song C, Niu Y, Li R, Li S, Wang Y D 2024 J. Mater. Sci. Technol. 194 15
[18]	Wang W L, Meng L J, Li L H, Hu L, Zhou K, Kong Z H, Wei B B 2016 Chin. Phys. Lett. 33 116102 Google Scholar
[19]	Khosro Aghayani M, Niroumand B 2011 J. Alloys Compd. 509 114 Google Scholar
[20]	张心怡, 吴文华, 王建元, 张颖, 翟薇, 魏炳波 2024 物理学报 73 184301 Google Scholar Zhang X Y, Wu W H, Wang J Y, Zhang Y, Zhai W, Wei B B 2024 Acta Phys. Sin. 73 184301 Google Scholar
[21]	Lou B G, Lee D R, Kwon K 2006 Appl. Phys. Lett. 89 18
[22]	杜人君, 解文军 2011 物理学报 60 114302 Google Scholar Du R J, Xie W J 2011 Acta Phys. Sin. 60 114302 Google Scholar
[23]	El Ghani N, Miralles S, Botton V, Henry D, Ben Hadid H, Ter Ovanessian B, Marcelin S 2021 Int. J. Heat Mass Transfer 172 121090 Google Scholar
[24]	Xu N X, Yu Y, Zhai W, Wang J Y, Wei B B 2023 Ultrason. Sonochem. 94 106343 Google Scholar
[25]	马艳, 林书玉, 徐洁 2018 物理学报 67 034301 Google Scholar Ma Y, Lin S Y, Xu J 2018 Acta Phys. Sin. 67 034301 Google Scholar
[26]	Patel B, Chaudhari G P, Bhingole P P 2012 Mater. Lett. 66 1 Google Scholar
[27]	Zhao M M, Wang X, Zhai W, Wang J Y 2024 J. Alloys Compd. 1008 176619 Google Scholar
[28]	Jamshidi R, Brenner G 2013 Ultrasonics 53 842 Google Scholar
[29]	Keller J B, Miksis M 1980 J. Acoust. Soc. Am. 68 628 Google Scholar
[30]	Lebon G S B, Salloum-Abou-Jaoude G, Eskin D, Tzanakis I, Pericleous K, Jarry P 2019 Ultrason. Sonochem. 54 171 Google Scholar
[31]	Brenner M P, Hilgenfeldt S, Lohse D 2002 Rev. Mod. Phys. 74 425 Google Scholar
[32]	Kurz W, Fisher D J 1998 Fundamentals of Solidification (5th Ed.) (Baech: Trans Tech Publications
[33]	Turnbull D, Cech R E 1950 J. Appl. Phys. 21 804 Google Scholar
[34]	Thompson C V, Greer A L, Spaepen F 1983 Acta Metall. 31 1883 Google Scholar
[35]	Gale W F, Totemeier T C 1983 Smithells Metals Reference Book (8th Ed.) (Oxford: Butterworth-Heinemann
[36]	Lin M J, Hu L, Zhu X N, Yan P X, Wei B B 2023 J. Alloys Compd. 968 171912 Google Scholar
[37]	Tzanakis I, Xu W W, Eskin D G, Lee P D, Kotsovinos N 2015 Ultrason. Sonochem. 27 72 Google Scholar
[38]	Hsu W L, Tsai C W, Yeh A C, Yeh J W 2024 Nat. Rev. Chem. 8 471 Google Scholar
[39]	Komarov S V, Kuwabara M, Abramov O V 2005 ISIJ Int. 45 1765 Google Scholar
[40]	Eskin G I, Eskin D G 2014 Ultrasonic Treatment of Light Alloy Melts (Boca Raton: CRC Press
[41]	Labusch R 1970 Phys. Status. Solidi 41 659 Google Scholar
[42]	Wang S P, Xu J 2018 Intermetallics 95 59 Google Scholar
[43]	Meyers M A, Mishra A, Benson D J 2006 Prog. Mater. Sci. 51 427 Google Scholar
[44]	Ma K K, Wen H M, Hu T, Topping T D, Isheim D, Seidman D N, Lavernia E J, Schoenung J M 2014 Acta Mater. 62 141 Google Scholar
[45]	Čižek L, Kratochvíl P, Smola B 1974 J. Mater. Sci. 9 1517 Google Scholar
[46]	Sun S J, Tian Y Z, Lin H R, Dong X G, Wang Y H, Wang Z J, Zhan Z F 2019 J. Alloys Compd. 25 806
[47]	Kwon H, Asghari-Rad P, Park J M, Sathiyamoorthi P, Bae J W, Moon J, Zargaran A, Choi Y T, Son S, Kim H S 2021 Intermetallics 135 107212 Google Scholar
[48]	Li J X, Yamanaka K, Zhang Y J, Furuhara T, Cao G Q, Hu J H, Chiba A 2024 Mater. Res. Lett. 12 399 Google Scholar
[49]	Wu Z G, Gao Y F, Bei H B 2016 Acta Mater. 120 108 Google Scholar

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Three-dimensional ultrasounds modulated solidification microstructure and mechanical property of (FeCoNiCrMn)₉₂Mo₈ high-entropy alloy

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Three-dimensional ultrasounds modulated solidification microstructure and mechanical property of (FeCoNiCrMn)92Mo8 high-entropy alloy

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Three-dimensional ultrasounds modulated solidification microstructure and mechanical property of (FeCoNiCrMn)₉₂Mo₈ high-entropy alloy