Optimization of Mechanical Properties and High-pressure Strengthening Mechanism of FeCoNiCuSi x B1 - x High Entropy Alloys

doi:10.11901/1005.3093.2025.262

Chinese Journal of Materials Research

2026, Vol. 40

Issue (7): 481-496 DOI: 10.11901/1005.3093.2025.262

ARTICLES

Current Issue | Archive | Adv Search

Optimization of Mechanical Properties and High-pressure Strengthening Mechanism of FeCoNiCuSi _x B_{1 -}_x High Entropy Alloys

BAO Fangxuan¹^,², GONG Minglong¹^,²(

), LIU Enrui¹^,², LIU Fengfang², BAI Jing¹^,², GAO Qiuzhi¹^,²

^1.School of Materials Science and Engineering, Northeastern University, Shenyang 110819, China
^2.School of Resources and Materials, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Cite this article:

BAO Fangxuan, GONG Minglong, LIU Enrui, LIU Fengfang, BAI Jing, GAO Qiuzhi. Optimization of Mechanical Properties and High-pressure Strengthening Mechanism of FeCoNiCuSi _x B_{1 -}_x High Entropy Alloys. Chinese Journal of Materials Research, 2026, 40(7): 481-496.

Download:

HTML

PDF(6115KB)
Export: BibTeX | EndNote (RIS)

Abstract

First-principles calculations were used to investigate the effects of Si content and pressure on the phase structures and mechanical properties of FeCoNiCuSi _x B_{1 -}_x (x = 0, 0.25, 0.5, 0.75, 1) high entropy alloys. Structural stability was evaluated by calculating relevant parameters based on the multicomponent phase formation criteria for high entropy alloys. The results show that the alloys exhibit a multiphase structure consisting of an FCC solid solution and intermetallic compounds. With increasing Si content, the FeCoNiCuSi _x B_{1 -}_x high entropy alloys exhibit increased lattice constants, decreased density, and reduced elastic moduli (B, G, and E). The B/G ratio and Poisson's ratio initially decrease and then increase, indicating that the ductility initially decreases and subsequently improves with increasing Si content, while high Si contents reduce the tendency toward brittle fracture. Heat of formation analysis reveals that Si enhances the thermodynamic stability of the alloy system. Under pressures ranging from 0 to 100 GPa, FeCoNiCuSi_0.5B_0.5 high entropy alloy exhibits a reduced lattice constant, increased density, enhanced deformation resistance, and weakened pressure-induced elastic anisotropy approaching isotropic behavior. The yield strength increases with increasing pressure, and the alloy exhibits excellent comprehensive mechanical properties.

Key words: metallic materials high entropy alloy first-principles pressure crystal structure mechanical properties

Received: 28 August 2025

ZTFLH:

TG139

Fund: National Natural Science Foundation of China(52471004)

Corresponding Authors: GONG Minglong, Tel: 15230357760, E-mail: gongminglong@qhd.neu.edu.cn

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	BAO Fangxuan
	GONG Minglong
	LIU Enrui
	LIU Fengfang
	BAI Jing
	GAO Qiuzhi

URL:

https://www.cjmr.org/EN/10.11901/1005.3093.2025.262 OR https://www.cjmr.org/EN/Y2026/V40/I7/481

Fig.1 Structural model of FeCoNiCuSi _x B_{1 -}_x high entropy alloys was constructed based on the VCA method (a) conventional modeling, (b) virtual crystal approximation method modeling

Table 1 Composition design of FeCoNiCuSi _x B_{1 -}_x high entropy alloys

Fig.2 Convergence test of FeCoNiCuSi _x B_{1 -}_x high entropy alloys (a) energy cutoff, (b) k-point

Alloys	$δ$ / %	$Δ S m i x$ / J·K^-1·mol^-1	$Δ H m i x$ / kJ·mol^-1	$Ω$	$Δ χ$ / %	VEC	$γ$
x = 0	14.89	13.38	-8.64	2.79	6.969	8.2	1.575
x = 0.25	13.05	14.32	-11.38	2.23	6.321	8.25	1.571
x = 0.5	10.84	14.53	-13.84	1.82	5.51	8.3	1.566
x = 0.75	7.97	14.32	-16.02	1.52	4.449	8.35	1.562
x = 1	2.92	13.38	-17.92	1.25	2.871	8.4	1.101

Table 2 Phase formation determination parameters of FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Fig.3 Lattice constant and density in FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Fig.4 Ground-state total energy and heat of formation of FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Alloys	$C 11$	Variation / %	$C 12$	Variation / %	$C 44$	Variation / %	$C 11 - C 12$	$C 11 + 2 C 12$
x = 0	1372.9	0	688.2	0	244.6	0	684.7	2749.3
x = 0.25	1302.8	-5.10	647.5	-5.92	236.1	-3.47	655.3	2597.8
x = 0.5	1200	-12.59	589.2	-14.39	229.7	-6.09	610.8	2378.4
x = 0.75	1074.8	-21.71	555.5	-19.28	197.9	-19.09	519.3	2185.8
x = 1	927.9	-32.41	542.4	-21.20	134.7	-44.93	385.5	2012.7

Table 3 Elastic constants (C_ij, GPa) and their variation percentage in FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Fig.5 Elastic modulus and dislocation strain energy of FeCoNiCuSi _x B_{1 -}_x high entropy alloys at different Si contents (a) elastic modulus, (b) strain energy per unit length of a single dislocation

Alloys	$B V$ / GPa	$B R$ / GPa	$B H$ / GPa	$G V$ / GPa	$G R$ / GPa	$G H$ / GPa
x = 0	916.4	916.4	916.4	283.7	276.1	279.9
x = 0.25	866	866	866	272.7	265.8	269.2
x = 0.5	792.8	792.8	792.8	260	255	257.5
x = 0.75	728.6	728.6	728.6	222.6	218.7	220.6
x = 1	670.9	670.9	670.9	157.9	153.1	155.5

Table 4 Bulk modulus

B

and shear modulus

G

of FeCoNiCuSi _x B_{1 -}_x high entropy alloys calculated via VRH approximation with varying Si contents

Alloys	$C 12 - C 44$ / GPa	$ν$	B/G	Hardness / GPa	Yield strength / GPa
x = 0	443.6	0.361	3.27	12.9	4.3
x = 0.25	411.4	0.359	3.22	12.81	4.27
x = 0.5	359.5	0.353	3.08	13.04	4.35
x = 0.75	357.6	0.362	3.3	10.8	3.6
x = 1	407.7	0.392	4.31	6.22	2.07

Table 5 Cauchy pressure, Poisson's ratio

ν

, B/G, Hardness (Tian2012), and Yield strength of FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Alloys	$A U$	$A G$	$A Z$
x = 0	0.138	0.014	0.714
x = 0.25	0.13	0.013	0.721
x = 0.5	0.098	0.01	0.752
x = 0.75	0.089	0.009	0.762
x = 1	0.157	0.015	0.699

Table 6 Anisotropy coefficients (

A Z

A G

A U

) of FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Fig.6 Three-dimensional surface plot of Young's modulus for FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents (a) x = 0, (b) x = 0.25, (c) x = 0.5, (d) x = 0.75, (e) x = 1

Fig.7 Energy factor $K$ of FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents (a) screw dislocation ( $K S c r e w$ ) and edge dislocation ( $K e d g e$ ), (b) mixed dislocation ( $K m i x e d$ )

Fig.8 Total density of states of the FeCoNiCuSi _x B_{1 -}_x high entropy alloys with varying Si contents

Fig.9 Lattice constant and density of FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures

Fig.10 Ground-state total energy and heat of formation of FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures

Pressure / GPa	$C 11$	Variation / %	$C 12$	Variation / %	$C 44$	Variation / %	$C 11 - C 12$	$C 11 + 2 C 12$
0	1200	0	589.2	0	229.7	0	610.8	2378.4
20	1309.3	9.11	657.3	11.56	261.9	14.02	652	2623.9
40	1429.4	19.12	739.2	25.46	293.9	27.95	690.2	2907.8
60	1528.9	27.41	804.8	36.59	324	41.05	724.1	3138.5
80	1647.1	37.26	889.5	50.97	353.4	53.85	757.6	3426.1
100	1742.2	45.18	952.8	61.71	381.9	66.26	789.4	3647.8

Table 7 Elastic constants (C_ij, GPa) and their variation percentages (%) in FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures

Fig.11 Elastic modulus and dislocation strain energy of FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures (a) elastic modulus, (b) strain energy per unit length of a single dislocation

Pressure / GPa	$B V$ / GPa	$B R$ / GPa	$B H$ / GPa	$G V$ / GPa	$G R$ / GPa	$G H$ / GPa
0	792.8	792.8	792.8	260	255	257.5
20	874.6	874.6	874.6	287.6	284.3	285.9
40	969.3	969.3	969.3	314.4	312.4	313.4
60	1046.2	1046.2	1046.2	339.2	338.2	338.7
80	1142.0	1142.0	1142.0	363.6	363.1	363.4
100	1215.9	1215.9	1215.9	387	386.9	387

Table 8 Bulk modulus B and Shear modulus G of FeCoNiCuSi_0.5B_0.5 high entropy alloy calculated via VRH approximation under different pressures

Pressure / GPa	$C 12 - C 44$ / GPa	$ν$	B/G	Hardness / GPa	Yield strength / GPa
0	359.5	0.3535	3.079	13.04	4.35
20	395.35	0.3526	3.059	14.15	4.72
40	445.32	0.3541	3.093	14.91	4.97
60	480.83	0.3539	3.089	15.78	5.26
80	536.07	0.3562	3.143	16.26	5.42
100	570.91	0.3561	3.142	17	5.67

Table 9 Cauchy pressure, Poisson's ratio

ν

, B/G, Hardness (Tian2012), and Yield strength of FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures

Pressure / GPa	$A U$	$A G$	$A Z$
0	0.098	0.0097	0.7521
20	0.058	0.0057	0.8034
40	0.031	0.0031	0.8514
60	0.015	0.0015	0.8950
80	0.0058	0.00057	0.9330
100	0.00131	0.00013	0.9674

Table 10 Anisotropy coefficients (

A U

A G

A Z

) of FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures

Fig.12 Three-dimensional surface plot of Young's modulus for FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures (a) x = 0 GPa, (b) x = 20 GPa, (c) x = 40 GPa, (d) x = 60 GPa, (e) x = 80 GPa, (f) x = 100 GPa

Fig.13 Energy factor K of FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures (a) screw dislocation ( $K S c r e w$ ) and edge dislocation ( $K e d g e$ ), (b) mixed dislocation ( $K m i x e d$ )

Fig.14 Total density of states of the FeCoNiCuSi_0.5B_0.5 high entropy alloy under different pressures

[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]. Adv. Eng. Mater., 2004, 6: 299 doi: 10.1002/adem.v6:5
[2]	Cantor B, Chang I T H, Knight P, et al. Microstructural development in equiatomic multicomponent alloys [J]. Mater. Sci. Eng., 2004, 375-377A: 213
[3]	Kang B, Lee J, Ryu H J, et al. Ultra-high strength WNbMoTaV high-entropy alloys with fine grain structure fabricated by powder metallurgical process [J]. Mater. Sci. Eng., 2018, 712A: 616
[4]	Cheng H, Chen W, Liu X Q, et al. Effect of Ti and C additions on the microstructure and mechanical properties of the FeCoCrNiMn high-entropy alloy [J]. Mater. Sci. Eng., 2018, 719A: 192
[5]	Arun S, Radhika N, Saleh B. Effect of additional alloying elements on microstructure and properties of AlCoCrFeNi high entropy alloy system: a comprehensive review [J]. Met. Mater. Int., 2025, 31(2): 285 doi: 10.1007/s12540-024-01752-3
[6]	Li G, Wen Y, Yu Z M, et al. Effect of Al content on properties of CrFeNiAl _x Si high entropy alloy [J]. Chin. J. Mater. Res., 2021, 35: 712
	李刚, 温影, 于中民等. Al含量对CrFeNiAl _x Si系高熵合金性能的影响 [J]. 材料研究学报, 2021, 35: 712
[7]	Liu Q, Wang X Y, Huang Y B, et al. Effect of molybdenum content on microstructure and corrosion resistance of CoCrFeNiMo high entropy alloy [J]. Chin. J. Mater. Res., 2020, 34: 868 doi: 10.11901/1005.3093.2020.269
	刘谦, 王昕阳, 黄燕滨等. Mo含量对CoCrFeNiMo高熵合金组织及耐蚀性能的影响 [J]. 材料研究学报, 2020, 34: 868
[8]	Tian Z G, Li X M, Qin Z, et al. Microstructure and wear resistance of CoCrFeNiTi _x high entropy alloy coating [J]. Chin. J. Mater. Res., 2023, 37: 219
	田志刚, 李新梅, 秦忠等. CoCrFeNiTi _x 高熵合金涂层的显微组织和耐磨性能 [J]. 材料研究学报, 2023, 37: 219 doi: 10.11901/1005.3093.2021.428
[9]	Ham G S, Kim Y K, Na Y S, et al. Effect of Ti addition on the microstructure and high-temperature oxidation property of AlCoCrFeNi high-entropy alloy [J]. Met. Mater. Int., 2021, 27(1): 156 doi: 10.1007/s12540-020-00708-7
[10]	Chen J, Niu P Y, Liu Y Z, et al. Effect of Zr content on microstructure and mechanical properties of AlCoCrFeNi high entropy alloy [J]. Mater. Des., 2016, 94: 39 doi: 10.1016/j.matdes.2016.01.033
[11]	Munitz A, Kaufman M J, Nahmany M, et al. Microstructure and mechanical properties of heat treated Al_1.25CoCrCuFeNi high entropy alloys [J]. Mater. Sci. Eng., 2018, 714A: 146
[12]	Hassan M A, Yehia H M, Mohamed A S A, et al. Effect of copper addition on the AlCoCrFeNi high entropy alloys properties via the electroless plating and powder metallurgy technique [J]. Crystals, 2021, 11(5): 540 doi: 10.3390/cryst11050540
[13]	Yu Y, Shi P Y, Feng K, et al. Effects of Ti and Cu on the microstructure evolution of AlCoCrFeNi high-entropy alloy during heat treatment [J]. Acta Metall. Sin. (Engl. Lett.), 2020, 33(8): 1077 doi: 10.1007/s40195-020-01002-6
[14]	Oh M C, Sharma A, Lee H, et al. Phase separation and mechanical behavior of AlCoCrFeNi-X (X = Cu, Mn, Ti) high entropy alloys processed via powder metallurgy [J]. Intermetallics, 2021, 139: 107369 doi: 10.1016/j.intermet.2021.107369
[15]	Gao Y, Chong K, Liu C, et al. The improvement of room temperature plasticity of refractory high entropy alloy based on different first principles calculation models and experiment verification [J]. J. Mater. Res. Technol., 2023, 26: 3917 doi: 10.1016/j.jmrt.2023.08.149
[16]	Wu Y N, Han C X, Liu R, et al. First-principles calculations and experimental studies of phase structure and mechanical stability of Al _x CoCrFeNi series high-entropy alloys [J]. Chin. J. Rare Met., 2024, 48: 671
	吴亚楠, 韩春霞, 刘瑞等. Al _x CoCrFeNi系高熵合金物相结构及力学稳定性第一性原理计算和试验研究 [J]. 稀有金属, 2024, 48: 671
[17]	Jiang H L, Hu Z F, Song C Y, et al. First principal study of TiZrHfNbSc _x refractory high entropy alloys with different Sc content [J]. Chin. J. Rare Met., 2022, 46: 1383
	江洪林, 胡志方, 宋春燕等. 第一性原理计算Sc含量对TiZrHfNbSc _x 难熔高熵合金性能的影响 [J]. 稀有金属, 2022, 46: 1383
[18]	Li Y, Yang Z, Duan H B, et al. Effects of V on microstructure and properties of Al_0.4Co_0.5V _x FeNi high-entropy alloys: first-principles study [J]. Rare Met. Mater. Eng., 2024, 53: 95
	李远, 杨忠, 段洪波等. 基于第一性原理计算V元素对高熵合金Al_0.4Co_0.5V _x FeNi的组织及性能影响 [J]. 稀有金属材料与工程, 2024, 53: 95
[19]	Kumar A, Dhekne P, Swarnakar A K, et al. Analysis of Si addition on phase formation in AlCoCrCuFeNiSi_x high entropy alloys [J]. Mater. Lett., 2017, 188: 73 doi: 10.1016/j.matlet.2016.10.099
[20]	Kumar A, Dhekne P, Swarnakar A K, et al. Phase evolution of CoCrCuFeNiSi _x high-entropy alloys prepared by mechanical alloying and spark plasma sintering [J]. Mater. Res. Express, 2019, 6(2): 026532
[21]	Lee H, Sharma A, Ahn B. Exploring strengthening mechanism of FeCoNiAl high-entropy alloy by non-metallic silicon addition produced via powder metallurgy [J]. J. Alloy. Compd., 2023, 947: 169545 doi: 10.1016/j.jallcom.2023.169545
[22]	Hou L L, Liang X Y, Yao Y H, et al. Effect of B content on microstructure and mechanical properties of FeCrCoNiMn high-entropy alloy [J]. Rare Met. Mater. Eng., 2018, 47: 3203
	侯丽丽, 梁霄羽, 要玉宏等. B含量对FeCrCoNiMn高熵合金组织及力学性能的影响 [J]. 稀有金属材料与工程, 2018, 47: 3203
[23]	Shu F Y, Zhang X B, Wang H P, et al. Research on mechanical properties and corrosion behavior of (Co₃₄Fe₈Cr₂₉Ni₈Si₇)_100- _x B _x high entropy alloy coating [J]. J. Therm. Spray Technol., 2024, 33(5): 1630 doi: 10.1007/s11666-024-01765-9
[24]	Xu Z Q, Ma Z L, Tan Y, et al. Effects of Si additions on microstructures and mechanical properties of VNbTiTaSi _x refractory high-entropy alloys [J]. J. Alloy. Compd., 2022, 900: 163517 doi: 10.1016/j.jallcom.2021.163517
[25]	Qi Y L, Cao T H, Zong H X, et al. Enhancement of strength-ductility balance of heavy Ti and Al alloyed FeCoNiCr high-entropy alloys via boron doping [J]. J. Mater. Sci. Technol., 2021, 75: 154 doi: 10.1016/j.jmst.2020.10.023
[26]	Zhang Z J, Li X M. Wear and corrosion resistance of laser cladding CoCrFeNiSi _x high entropy alloy coating [J]. Chin. J. Mater. Res., 2024, 38: 741
	张泽疆, 李新梅. 激光熔覆CoCrFeNiSi _x 高熵合金涂层的耐磨和耐蚀性能 [J]. 材料研究学报, 2024, 38: 741 doi: 10.11901/1005.3093.2023.562
[27]	Mao J J, Fu T, Pan H C, et al. Kr ions irradiation damage behavior of AlNbMoZrB refractory high-entropy alloy [J]. Chin. J. Mater. Res., 2023, 37: 641 doi: 10.11901/1005.3093.2022.526
	毛建军, 富童, 潘虎成等. AlNbMoZrB系难熔高熵合金的Kr离子辐照损伤行为 [J]. 材料研究学报, 2023, 37: 641 doi: 10.11901/1005.3093.2022.526
[28]	Larkin J M, Mcgaughey A J H. Predicting alloy vibrational mode properties using lattice dynamics calculations, molecular dynamics simulations, and the virtual crystal approximation [J]. J. Appl. Phys., 2013, 114(2): 023507
[29]	Ramer N J, Rappe A M. Application of a new virtual crystal approach for the study of disordered perovskites [J]. J. Phys. Chem. Solids, 2000, 61(2): 315 doi: 10.1016/S0022-3697(99)00300-5
[30]	Winkler B, Pickard C, Milman V. Applicability of a quantum mechanical `virtual crystal approximation' to study Al/Si-disorder [J]. Chem. Phys. Lett., 2002, 362(3-4): 266 doi: 10.1016/S0009-2614(02)01029-1
[31]	Payne M C, Teter M P, Allan D C, et al. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients [J]. Rev. Mod. Phys., 1992, 64(4): 1045 doi: 10.1103/RevModPhys.64.1045
[32]	Segall M D, Lindan P J D, Probert M J, et al. First-principles simulation: ideas, illustrations and the CASTEP code [J]. J. Phys.: Condens. Matter, 2002, 14(11): 2717 doi: 10.1088/0953-8984/14/11/301
[33]	Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J]. Phys. Rev. Lett., 1996, 77(18): 3865 doi: 10.1103/PhysRevLett.77.3865 pmid: 10062328
[34]	Wang L X, Yao S, Wen B. First-principle studies of AlFe _x TiCrZnCu high entropy alloys with the different mole fractions of Fe [J]. Mater. Rep., 2019, 33: 356
	王兰馨, 姚山, 温斌. 第一性原理计算Fe含量对高熵合金AlFe _x TiCrZnCu力学性能的影响 [J]. 材料导报, 2019, 33: 356
[35]	Paakkari T. A determination of the Debye–Waller temperature factor and the X-ray Debye temperature for Ni, Cr, Fe, Mo and W [J]. Acta Crystallogr., 1974, 30A(1) : 83
[36]	Jong M, Chen W, Angsten T, et al. Charting the complete elastic properties of inorganic crystalline compounds [J]. Sci. Data, 2015, 2(1): 150009 doi: 10.1038/sdata.2015.9
[37]	Wu B Y. Microstructure and mechanical properties of FeNiCoCu system high entropy alloys and their composites [D]. Guangzhou: South China University of Technology, 2017
	吴炳勇. FeNiCoCu系高熵合金及其复合材料的微观组织与力学性能研究 [D]. 广州: 华南理工大学, 2017
[38]	Tsau C H, Lin S X, Fang C H. Microstructures and corrosion behaviors of FeCoNi and CrFeCoNi equimolar alloys [J]. Mater. Chem. Phys., 2017, 186: 534 doi: 10.1016/j.matchemphys.2016.11.033
[39]	Li X J, Sun K, Chen C, et al. Investigation on properties of (Ti/Zr/Hf/Sn/W)NbMoTaV high-entropy alloys using first-principles calculation and analysis method [J]. J. Xi'an Jiaotong Univ., 2022, 56: 180
	李雪洁, 孙琨, 陈诚等. (Ti/Zr/Hf/Sn/W)NbMoTaV高熵合金性能第一性原理计算分析方法 [J]. 西安交通大学学报, 2022, 56: 180
[40]	Chen S Y, Yang X, Dahmen K A, et al. Microstructures and crackling noise of Al _x NbTiMoV high entropy alloys [J]. Entropy, 2014, 16(2): 870 doi: 10.3390/e16020870
[41]	Nutor R K, Cao Q P, Wang X D, et al. Phase selection, lattice distortions, and mechanical properties in high‐entropy alloys [J]. Adv. Eng. Mater., 2020, 22(11): 2000466 doi: 10.1002/adem.v22.11
[42]	Senkov O N, Miller J D, Miracle D B, et al. Accelerated exploration of multi-principal element alloys with solid solution phases [J]. Nat. Commun., 2015, 6(1): 6529 doi: 10.1038/ncomms7529
[43]	Guo S, Ng C, Lu J, et al. Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys [J]. J. Appl. Phys., 2011, 109(10): 103505 doi: 10.1063/1.3587228
[44]	Peng C, Zhao Y, Zhang F, et al. First-principles calculations of properties of Ti _x NbMoTaW high entropy alloys [J]. Mater. Rep., 2024, 38: 23040229
	彭超, 赵勇, 张芳等. Ti _x NbMoTaW系高熵合金性能的第一性原理计算 [J]. 材料导报, 2024, 38: 23040229
[45]	Zhang Y, Zhou Y J, Lin J P, et al. Solid-solution phase formation rules for multi-component alloys [J]. Adv. Eng. Mater., 2008, 10(6): 534 doi: 10.1002/adem.v10:6
[46]	Lee C, Chou Y, Kim G, et al. Lattice-distortion-enhanced yield strength in a refractory high-entropy alloy [J]. Adv. Mater., 2020, 32(49): 2004029 doi: 10.1002/adma.v32.49
[47]	Lee C, Song G, Gao M C, et al. Lattice distortion in a strong and ductile refractory high-entropy alloy [J]. Acta Mater., 2018, 160: 158 doi: 10.1016/j.actamat.2018.08.053
[48]	Song H Q, Tian F Y, Hu Q M, et al. Local lattice distortion in high-entropy alloys [J]. Phys. Rev. Mater., 2017, 1(2): 023404
[49]	Fang S S, Xiao X S, Xia L, et al. Relationship between the widths of supercooled liquid regions and bond parameters of Mg-based bulk metallic glasses [J]. J. Non-Cryst. Solids, 2003, 321(1-2): 120 doi: 10.1016/S0022-3093(03)00155-8
[50]	Chen R R, Qin G, Zheng H T, et al. Composition design of high entropy alloys using the valence electron concentration to balance strength and ductility [J]. Acta Mater., 2018, 144: 129 doi: 10.1016/j.actamat.2017.10.058
[51]	Moruzzi V L, Janak J F, Schwarz K. Calculated thermal properties of metals [J]. Phys. Rev., 1988, 37B(2) : 790
[52]	Javdan M, Gheisari K, Reihanian M. (FeCoNi)₇₅Cu_25- _x Si _x high entropy alloys prepared by mechanical alloying and spark plasma sintering: microstructure, deformation behavior and dynamic recrystallization kinetics [J]. Mater. Charact., 2024, 211: 113861 doi: 10.1016/j.matchar.2024.113861
[53]	Li X Q, Schönecker S, Li W, et al. Tensile and shear loading of four fcc high-entropy alloys: a first-principles study [J]. Phys. Rev., 2018, 97B(9) : 094102
[54]	Kang H Y, Yang X H, Sun X Y, et al. Microstructure and properties of CuCrNi _x TiZr high entropy alloys: experiments and first principles calculations [J]. J. Alloy. Compd., 2025, 1010: 177873 doi: 10.1016/j.jallcom.2024.177873
[55]	Shi W H, Chen L, Liang L Q, et al. First-principles calculation of phase stability and elastic properties of Cr _x MoNbTiV refractory high-entropy alloys [J]. AIP Adv., 2023, 13(9): 095222
[56]	Darvishi K R, Wang L. Elastic energy of multi-component solid solutions and strain origins of phase stability in high-entropy alloys [J]. Scripta Mater., 2022, 206: 114226 doi: 10.1016/j.scriptamat.2021.114226
[57]	Chen R, Weng L J, Zhang C B, et al. The influence of site preference on the elastic properties of FCC_CoCrFeNi multi-principal element alloy [J]. J. Alloy. Compd., 2023, 965: 171426 doi: 10.1016/j.jallcom.2023.171426
[58]	Wen J D, Xiao X X, Wang X, et al. First-principles calculation of mechanical properties of Ir-Rh alloy [J]. Precious Met., 2023, 44: 1
	文嘉栋, 肖祥兴, 王献等. Ir-Rh合金力学性能的第一性原理计算 [J]. 贵金属, 2023, 44: 1
[59]	Zhang H, Li X G, Guo G Q, et al. First-principle calculation on mechanical properties of FeAl _x NiCrMn high-entropy alloys [J]. Spec. Cast. Nonferrous Alloy., 2020, 40: 1172
	张辉, 李兴国, 郭古青等. FeAl _x NiCrMn系高熵合金力学性能的第一性原理计算 [J]. 特种铸造及有色合金, 2020, 40: 1172
[60]	Xiao H, Liu Y, Wang K, et al. Effects of Mn content on mechanical properties of FeCoCrNiMn _x (0 ≤ x ≤ 0.3) high-entropy alloys: a first-principles study [J]. Acta Metall. Sin. (Engl. Lett.) 2021, 34(4): 455
[61]	Stavroulakis P, Freeman C L, Patel D, et al. Successful prediction of the elastic properties of multiphase high entropy alloys in the AlTiVCr-Si system through a novel computational approach [J]. Materialia, 2022, 21: 101365 doi: 10.1016/j.mtla.2022.101365
[62]	Anderson O L. A simplified method for calculating the debye temperature from elastic constants [J]. J. Phys. Chem. Solids, 1963, 24(7): 909 doi: 10.1016/0022-3697(63)90067-2
[63]	Chang C, Zhang H, Lai Y, et al. First principles calculation of structural stability and mechanical properties of FeAlNiCrMn high entropy alloy [J]. Mater. Rep., 2022, 36: 62
	常超, 张辉, 来媛等. FeAlNiCrMn高熵合金结构稳定性和力学性能的第一性原理计算 [J]. 材料导报, 2022, 36: 62
[64]	Gao Y, Mao P L, Liu Z, et al. First-principles calculation of electronic structure and mechanical properties of binary phases in Mg-Zn-Y-La alloy [J]. Rare Met. Mater. Eng., 2019, 48(5): 1454
	高岩, 毛萍莉, 刘正等. Mg-Zn-Y-La合金中二元相的电子结构和力学性质的第一性原理计算 [J]. 稀有金属材料与工程, 2019, 48(5): 1454
[65]	Tian Y J, Xu B, Zhao Z S. Microscopic theory of hardness and design of novel superhard crystals [J]. Int. J. Refract. Met. Hard Mater., 2012, 33: 93 doi: 10.1016/j.ijrmhm.2012.02.021
[66]	Ranganathan S I, Murshed M R, Costa L. Heterogeneous anisotro-py index and scaling in two-phase random polycrystals [J]. Acta Mech., 2018, 229(6): 2631 doi: 10.1007/s00707-018-2114-6
[67]	Liao M Q, Liu Y, Cui P C, et al. Modeling of alloying effect on elastic properties in BCC Nb-Ti-V-Zr solid solution: from unary to quaternary [J]. Comput. Mater. Sci., 2020, 172: 109289 doi: 10.1016/j.commatsci.2019.109289
[68]	Song Q G, Qin G S, Yang B B, et al. Impurity concentration effects on the structures, ductile and electronic properties of Zr-doped gamma-TiAl alloys [J]. Acta Phys. Sin., 2016, 65: 046102
	宋庆功, 秦国顺, 杨宝宝等. 杂质浓度对Zr替位掺杂γ-TiAl合金的结构延性和电子性质的影响 [J]. 物理学报, 2016, 65: 046102
[69]	Wu Y N, Zhang Y, Li Z, et al. Prediction of NbTaTiZr-based high-entropy alloys with high strength or ductility: first-principles calculations [J]. J. Mater. Res. Technol., 2024, 30: 8854 doi: 10.1016/j.jmrt.2024.05.253
[70]	Hu Y L, Bai L H, Tong Y G, et al. First-principle calculation investigation of NbMoTaW based refractory high entropy alloys [J]. J. Alloy. Compd., 2020, 827: 153963 doi: 10.1016/j.jallcom.2020.153963
[71]	Tracy C L, Park S, Rittman D R, et al. High pressure synthesis of a hexagonal close-packed phase of the high-entropy alloy CrMnFeCoNi [J]. Nat. Commun., 2017, 8(1): 15634 doi: 10.1038/ncomms15634

[1]	HU Ming, WANG Qirui, QIU Jianke, LEI Xiaofei, ZHANG Jinhu, DONG Limin, YANG Rui. Effect of Drawing Reduction on Strength-ductility of Ultra-high Strength Ti-alloy Bar[J]. 材料研究学报, 2026, 40(8): 561-571.
[2]	YANG Lei, SHANG Xuewen, TIAN Xiaosheng, GAO Huiying, XU Lei. Variation of Microstructure and Mechanical Property of Powder Metallurgy Hot Isostatic Pressed TC11 Alloy After Thermal Exposure for 400 h[J]. 材料研究学报, 2026, 40(8): 572-582.
[3]	CHEN Yao, CHEN Zhiyong, BAI Chunguang. Microstructure, Texture, and Mechanical Properties of Ti₂AlNb Alloy Sheet[J]. 材料研究学报, 2026, 40(8): 583-594.
[4]	SONG Xiaotong, CHEN Sixu, QIU Jianke, HU Ming, ZHANG Mingjie, ZAN Xiaodong, LEI Jiafeng. Effect of Thermomechanical Processing on Fracture Toughness of Ti55531 Alloy Bar for Fasteners[J]. 材料研究学报, 2026, 40(8): 595-604.
[5]	ZHANG Mingyuan, WEN Ming, LI Sixie, ZHANG Bin, ZHANG Guangping. Effect of Processing Parameters on Magnetron Sputtering Preparation of High-quality Ni5Pt Films for Schottky Diodes[J]. 材料研究学报, 2026, 40(8): 613-623.
[6]	XIE Zhenjun, ZHU Yankun, ZHAO Zhenkai, LU Yandi, ZHOU Xianghai, CAO Ming, ZHANG Peng, ZHANG Zhefeng. Mechanism of Fatigue Crack Initiation Induced by Complex Inclusions in Bainite-Martensite Dual-phase Steel[J]. 材料研究学报, 2026, 40(7): 519-527.
[7]	WANG Na, LAN Zhonghua, QU Jinmeng, LIU Yanyun, LI Wanxi, LIU Huichao, FENG Liping. Flash Synthesis of Cellulose-derived Porous Carbon for Electrochemical Energy Storage[J]. 材料研究学报, 2026, 40(7): 535-542.
[8]	ZHOU Minghan, CHEN Shuanglong, WANG Qiushi, WANG Xuejiao, LIU Cailong. Fabrication and Temperature Sensing Performance of Ho³⁺/Yb³⁺ Co-doped α-Si₃N₄ Branched Nanowires[J]. 材料研究学报, 2026, 40(7): 543-552.
[9]	WANG Yuqing, WANG Jinhe, LI Kexin, FU Huameng, ZHANG Haifeng. Microstructure and Mechanical Properties for Composites of W/TiZrVAl High-entropy Alloy Sintered by Hot Isostatic Pressing[J]. 材料研究学报, 2026, 40(7): 553-560.
[10]	ZHENG Qinyuan, ZHENG Chengwu, LU Yi, ZHU Hailong, LIU Peng, LUAN Yikun, LI Dianzhong. Effect of Softening Annealing on Recrystallization and Austenite Transformation of a Cold-rolled Medium-Mn Steel[J]. 材料研究学报, 2026, 40(6): 401-413.
[11]	GAO Chong, XIONG Lixi, CHEN Zihao, LIANG Zhizhi, MA Heng, HE Kang, HE Jinshan, PANG Jianchao, ZHANG Zhefeng. Optimization of Fracture Toughness of Welded Joints of Q500 Steel Plates by Intercritical Annealing[J]. 材料研究学报, 2026, 40(6): 414-424.
[12]	XU Lei, LI Ruochen, TIAN Xiaosheng, LU Zhengguan. Influence of Defects in ЭП741 Alloy Powder on Mechanical Properties of Alloys Prepared by Hot Isostatic Pressing Process[J]. 材料研究学报, 2026, 40(6): 425-436.
[13]	DENG Zhiwen, JIA Chunni, LIU Tengyuan, LU Yi, ZHENG Chengwu, WANG Pei, LI Dianzhong. Crystal Plasticity Calculations on Influence of Mn-content on Transformation Induced Plasticity Effect for Medium-Mn Steels[J]. 材料研究学报, 2026, 40(6): 437-449.
[14]	JIANG Xingguo, SHEN Wenzhuo, YANG Tao, ZHANG Jiali, ZHONG Min, CAO He, GUO Shouwu. Enhancing Effect and Mechanism of Reduced Graphene Oxide on the Corrosion Resistance of Copper-based Composites[J]. 材料研究学报, 2026, 40(6): 450-456.
[15]	YANG Ruitao, LIANG Bin, PANG Shengyang, HU Chenglong, ZHANG Wei, FAN Junling, TANG Sufang. Wetting Behavior of Molten Cu-Si Alloy on Synthesized BN Powder of Varying Crystallinities[J]. 材料研究学报, 2026, 40(6): 457-464.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed