Strengthening mechanism and wear behavior of AlCrFeNiNb<sub><i>x</i></sub> high-entropy alloys from the perspective of phase modulation

HUANG Panyi; LIU Zhicheng; ZHOU Yongqiang; PENG Wenyi; QU Yuhai; ZHANG Aisheng; DENG Xiaohua; ZHANG Longhe; ZHOU Shiyi; ZHOU Jie

doi:10.7498/aps.74.20250978

Abstract
AlCoCrFeNi high-entropy alloys have consistently attracted attention due to their outstanding strength-to-ductility ratio. However, the substantial content of expensive cobalt in these alloys has somewhat limited their engineering applications. Consequently, there is an urgent need to design and develop high-performance, low-cost cobalt-free high-entropy alloys. AlCrFeNi alloys exhibit microstructures and properties similar to AlCoCrFeNi alloys. Simultaneously, the absence of Co significantly reduces costs and markedly improves casting performance. These alloys represent a potential structural material for harsh environments, demonstrating promising engineering applications. In order to explore the phase modulation mechanism of Nb element on AlCrFeNi alloy, this study combines experiments with first principles calculations to systematically investigate the effects of Nb on the microstructure, mechanical properties and wear resistance of AlCrFeNi alloy. The research results show that the AlCrFeNiNb_0.4 high-entropy alloy has the best mechanical properties and wear resistance.The doping of Nb changes the wear mechanism of the AlCrFeNi alloy and improves the wear resistance of the alloy. This is attributed to the phase modulation effect of Nb on AlCrFeNi alloy. On the one hand, it induces the precipitation of Laves phase, which has high hardness, and on the other hand, it solidly dissolves in the BCC and B2 phases of the alloy, significantly improving the mechanical properties of the two phases. In addition, Nb doping refines the microstructure of the AlCrFeNi alloy, which leads to an increase in the phase interface density, thus enhancing the hardness, yield strength and wear resistance of the alloy. First principles calculations show that the Nb atoms change the electronic structures of the BCC and B2 phases in the AlCrFeNi alloy, thereby enhancing the stability of the two phases and confirming the solid solution strengthening effect of Nb on the two phases. The Nb atoms form strong antibonds with most of the atoms in the two phases, which further explains the nature of the generation of a large number of Laves phases in the microstructure of the alloy after Nb doping.

Keywords:
AlCrFeNiNb_x high-entropy alloys /

first principles /

mechanical properties /

wear behavior
FullText HTML

Cited By

图 1 晶体模型与等效位点　(a) Al₂Cr₈Fe₈Ni₂; (b) Al₂Cr₇Fe8 Ni₂Nb; (c) Al₈Cr₂Fe₂Ni₈;(d) Al₈Cr₂FeNi₈Nb

Figure 1. Crystal models and equivalents for points: (a) Al₂Cr₈Fe₈Ni₂; (b) Al₂Cr₇Fe₈Ni₂Nb; (c) Al₈Cr₂Fe₂Ni₈; (d) Al₈Cr₂FeNi₈Nb.

DownLoad: Full-Size Img PowerPoint

图 2 AlCrFeNiNb_x高熵合金磨损性能测试　(a) 摩擦系数; (b) 磨损率

Figure 2. Wear performance test of AlCrFeNiNb_x HEAs: (a) Friction coefficient; (b) wear rate.

DownLoad: Full-Size Img PowerPoint

图 3 AlCrFeNiNb_x磨损SEM及EDS图　(a) x = 0; (b) x = 0.1; (c) x = 0.2; (d) x = 0.3; (e) x = 0.4

Figure 3. SEM and EDS plots of AlCrFeNiNb_x HEA wear: (a) x = 0; (b) x = 0.1; (c) x = 0.2; (d) x = 0.3; (e) x = 0.4.

DownLoad: Full-Size Img PowerPoint

图 4 AlCrFeNiNb_x高熵合金的XRD图谱　(a) 10°—90°; (b) 44°—45°

Figure 4. XRD patterns of AlCrFeNiNb_x HEAs: (a) 10°–90°; (b) 44°–45°

DownLoad: Full-Size Img PowerPoint

图 5 AlCrFeNiNb_x高熵合金微观组织BSE图及EDS图　(a) x = 0; (b) x = 0.1; (c) x = 0.2; (d) x = 0.3; (e) x = 0.4.

Figure 5. BSEM and EDS plots of microstructure of AlCrFeNiNb_x HEAs: (a) x = 0; (b) x = 0.1; (c) x = 0.2; (d) x = 0.3; (e) x = 0.4

DownLoad: Full-Size Img PowerPoint

图 6 AlCrFeNiNb_x高熵合金的(a)显微维氏硬度与(b)室温压缩曲线

Figure 6. (a) Microhardness and (b) room temperature compression curves of AlCrFeNiNb_x HEAs.

DownLoad: Full-Size Img PowerPoint

图 7 掺杂前后BCC相与B2相的(a)载荷-位移曲线和(b)纳米硬度以及弹性模量

Figure 7. (a) Load-displacement curves and (b) nanohardness and Young's modulus of BCC phase and B2 phase before and after doping.

DownLoad: Full-Size Img PowerPoint

图 8 体系态密度图　(a) Al₂Cr₈Fe₈Ni₂; (b) Al₂Cr₇Fe₈Ni₂Nb; (c) Al₈Cr₂Fe₂Ni₈; (d) Al₈Cr₂FeNi₈Nb

Figure 8. Density of state of systems: (a) Al₂Cr₈Fe₈Ni₂; (b) Al₂Cr₇Fe₈Ni₂Nb; (c) Al₈Cr₂Fe₂Ni₈; (d) Al₈Cr₂FeNi₈Nb.

DownLoad: Full-Size Img PowerPoint

图 9 体系差分电荷密度图　(a) Al₂Cr₈Fe₈Ni₂; (b) Al₂Cr₇Fe₈Ni₂Nb; (c) Al₈Cr₂Fe₂Ni₈; (d) Al₈Cr₂FeNi₈Nb

Figure 9. Electron density difference of systems: (a) Al₂Cr₈Fe₈Ni₂; (b) Al₂Cr₇Fe₈Ni₂Nb; (c) Al₈Cr₂Fe₂Ni₈; (d) Al₈Cr₂FeNi₈Nb.

DownLoad: Full-Size Img PowerPoint

表 1 各相成分值

Table 1. Component values at each phase.

Alloys	Phases	Al/%	Cr/%	Fe/%	Ni/%	Nb/%
Nb0	BCC	10.41	44.02	37.57	7.99	0
Nb0	B2	37.96	9.03	13.15	39.86	0
Nb0.1	BCC	10.77	46.23	35.73	6.70	0.57
	B2	32.70	13.13	16.97	35.86	1.34
	Laves	9.33	22.83	31.60	10.86	25.37
Nb0.2	BCC	9.13	46.35	36.03	6.23	2.26
	B2	32.27	13.85	16.60	35.92	1.36
	Laves	10.41	23.43	29.39	11.05	25.72
Nb0.3	BCC	10.30	42.97	36.25	7.04	3.45
	B2	37.34	10.14	13.26	37.81	1.45
	Laves	10.73	23.36	29.40	10.84	25.67
Nb0.4	BCC	10.79	39.49	35.14	7.36	7.23
	B2	34.32	12.44	15.00	36.80	1.47
	Laves	11.45	23.53	27.58	11.20	26.24

DownLoad: CSV

表 2 体系的总能量、缺陷形成能、形成热与结合能

Table 2. Total energy, defect formation energy, heat of formation and binding energy of the systems.

System	Site	E_f	H	E	E_total
Al₂Cr₈Fe₈Ni₂	—	—	–0.11667	–3.62827	–29079.07198
AlCr₈Fe₈Ni₂Nb	Al site	1.17184	–0.05808	–3.84808	–30623.59838
Al₂Cr₇Fe₈Ni₂Nb	Cr site	–0.00317	–0.11683	–3.90007	–28335.21599
Al₂Cr₈Fe₇Ni₂Nb	Fe site	1.10657	–0.06134	–3.85692	–29872.04588
Al₂Cr₈Fe₈NiNb	Ni site	0.76522	–0.07841	–3.92992	–29358.95247
Al₈Cr₂Fe₂Ni₈	—	—	–0.34288	–3.47834	–18426.86037
Al₇Cr₂Fe₂Ni₈Nb	Al site	0.51441	–0.31716	–3.73102	–19972.04421
Al₈CrFe₂Ni₈Nb	Cr site	–0.67442	–0.37660	–3.78370	–17683.67563
Al₈Cr₂FeNi₈Nb	Fe site	–1.45347	–0.41555	–3.83498	–19222.39432
Al₈Cr₂Fe₂Ni₇Nb	Ni site	–1.26742	–0.40625	–3.88161	–18708.77351

DownLoad: CSV

表 3 Nb掺杂前后BCC相键的布居数

Table 3. Bond populations in the BCC phase before and after Nb doping.

System	Bond	Population	Length
Al₂Cr₈Fe₈Ni₂	Ni—Ni	0.01	3.54777
	Fe—Ni	0.11	3.24825
	Fe—Fe	0.07	3.34922
	Cr—Ni	–0.03	3.48801
	Cr—Fe	–0.05	3.15932
	Cr—Cr	–0.37	3.28039
	Al—Ni	0.11	3.42543
	Al—Fe	0.11	3.20017
	Al—Cr	0.08	3.05610
	Al—Al	0.00	4.80639
Al₂Cr₇Fe₈Ni₂Nb	Ni—Ni	–0.02	3.73872
	Fe—Ni	0.10	3.32775
	Fe—Fe	0.07	3.34938
	Cr—Ni	–0.09	3.65638
	Cr—Fe	–0.05	3.13931
	Cr—Cr	–0.39	3.12486
	Al—Ni	0.13	3.40228
	Al—Fe	0.11	3.23175
	Al—Cr	0.10	2.99913
	Al—Al	0.00	4.85985
	Ni—Nb	0.57	2.58120
	Fe—Nb	–0.03	3.32742
	Cr—Nb	–0.31	3.75318
	Al—Nb	–0.14	3.66437

DownLoad: CSV

表 4 Nb掺杂前后B2相键的布居数

Table 4. Bond populations in the BCC phase before and after Nb doping.

System	Bond	Population	Length
Al₈Cr₂Fe₂Ni₈	Al—Al	0.01	3.20558
	Al—Cr	–0.44	3.07520
	Al—Fe	0.24	2.47738
	Al—Ni	0.27	2.70429
	Cr—Fe	–1.00	2.44941
	Cr—Ni	–0.40	2.50288
	Fe—Ni	–0.15	3.07799
	Ni—Ni	–0.20	3.21284
Al₈Cr₂FeNi₈Nb	Al—Al	–0.02	3.23276
	Al—Cr	–0.26	3.24161
	Al—Fe	0.21	2.84415
	Al—Nb	0.00	2.65091
	Al—Ni	0.24	2.87858
	Cr—Fe	–0.73	2.46354
	Cr—Nb	–2.36	2.45989
	Cr—Ni	–0.19	2.74444
	Fe—Ni	–0.14	3.22725
	Ni—Nb	–0.33	3.26054

DownLoad: CSV

表 5 各体系的弹性刚度常数

Table 5. Elastic stiffness constants of systems.

	Al₂Cr₈Fe₈Ni₂	Al₂Cr₇Fe₈Ni₂Nb	Al₈Cr₂Fe₂Ni₈	Al₈Cr₂FeNi₈Nb
C₁₁	128.29975	736.29805	270.3648	127.11465
C₂₂	177.42665	215.33585	691.93215	203.93235
C₃₃	267.0162	–375.11635	250.2832	1766.9252
C₁₂	178.20038	343.45855	93.53145	74.19628
C₂₃	160.14022	–33.38788	81.9077	256.06083
C₁₃	177.82828	304.61232	97.42585	345.99403
C₄₄	–92.7819	167.42425	31.8253	59.76855
C₅₅	–22.91365	–568.51245	53.94125	71.5073
C₆₆	81.31915	333.01795	64.64615	31.13195

DownLoad: CSV

表 6 各体系的弹性柔顺常数

Table 6. Elastic flexibility constants of systems.

	Al₂Cr₈Fe₈Ni₂	Al₂Cr₇Fe₈Ni₂Nb	Al₈Cr₂Fe₂Ni₈	Al₈Cr₂FeNi₈Nb
S₁₁	–0.0156972	0.0004691	0.00475	0.0242321
S₂₂	0.0010798	0.0025236	0.0015446	0.0065644
S₃₃	0.005798	0.0088133	0.0054491	0.0021923
S₁₂	0.0131561	0.0029681	–0.0004152	–0.0019679
S₂₃	–0.0082161	–0.0063358	–0.0003173	–0.0007382
S₁₃	0.0026282	–0.0003899	–0.002034	–0.0055097
S₄₄	0.0106177	–0.0063815	0.0665176	0.0392295
S₅₅	0.0225751	0.006832	0.0391124	0.0261333
S₆₆	0.0115169	–0.0040258	0.0181006	0.038512

DownLoad: CSV

表 7 各体系的弹性常数

Table 7. Elastic constants of systems.

Systems	B/GPa	G/GPa	E/GPa	H_V/GPa
Al₂Cr₈Fe₈Ni₂	168.320	107.811	266.529	15.356
Al₂Cr₇Fe₈Ni₂Nb	216.860	137.470	340.468	17.906
Al₈Cr₂Fe₂Ni₈	178.191	63.838	171.084	5.431
Al₈Cr₂FeNi₈Nb	221.891	79.373	212.751	6.325

DownLoad: CSV

map

[1]	Yeh J W, Chen S K, Lin S J, Gan J Y, Chin T S, Shun T T, Chang S Y 2004 Adv. Eng. Mater. 6 299 Google Scholar
[2]	Braeckman B R, Boydens F, Hidalgo H, Dutheil P, Jullien M, Thomann A L, Depla D 2015 Thin Solid Films 580 71 Google Scholar
[3]	Tsai M H, Yeh J W 2014 Mater. Res. Lett. 2 107 Google Scholar
[4]	Tsai K Y, Tsai M H, Ye J W 2013 Acta Mater. 61 4887 Google Scholar
[5]	Dong Y, Lu Y P, Kong J R, Zhang J J, Li T J 2013 J. Alloys Compd. 573 96 Google Scholar
[6]	Ding Q Q, Zhang Y, Chen X, Fu X Q, Chen D K, Chen S J, Gu L, Wei F, Bei H B, Gao Y F, Wen M R, Li J X, Zhang Z, Zhu T, Ritchie R O, Yu Q 2019 Nature 574 223 Google Scholar
[7]	Yang Y F, Hu F, Xia T, Li R H, Bai J Y, Zhu J Q, Zhang G F 2024 J. Alloys Compd. 986 177691
[8]	Hua Z L, Guo L, Zhang Y, Dai Y L, Zhang D C, Mei F S, Lin J G 2025 Intermetallics 180 108711 Google Scholar
[9]	Tian T, Zhang X L, Xue Y Z, Huang H B, Jiang Q Q, Tang J G 2024 Mol. Catal. 569 114571
[10]	Liu J H, Li Z H, Lin D Y, Tang Z X, Song X G, He P, Zhang S Y, Bian H, Fu W, Song Y 2024 J. Mater. Sci. Technol. 189 211 Google Scholar
[11]	Sonar T, Ivanov M, Trofimov E, Tingaev A, Suleymanova I 2024 Mater. Sci. Energy Technol. 7 35
[12]	Zhao Q, Ren Z X, Zhao P W, Yoshida K 2025 Phys. Lett. B 860 139196 Google Scholar
[13]	Gutierrez R E, Matanovic I, Polak M P, Morgan D, Schamiloglu E 2025 J. Electron Spectrosc. Relat. Phenom. 278 147512 Google Scholar
[14]	Doan D Q, Fang T H, Chen T H 2021 Sci. Rep. 11 13680 Google Scholar
[15]	Zhang Y, Zuo T T, Tang Z, Gao M C, Dahmen K A, Liaw P K, Lu Z P 2014 Prog. Mater. Sci. 61 1 Google Scholar
[16]	Jiang Z F, Chen W P, Xia Z B, Xiong W, Fu Z Q 2019 Intermetallics 108 45 Google Scholar
[17]	Zhang J J, Yang J J, Liu T G, Tian D H, Liu H C, Yang G C, Lu Y H, Shoji T 2024 J. Mater. Res. Technol. 33 6688 Google Scholar
[18]	Ma Q, Zhao W, Li X, Gao W F, Zhang H, Ma X, Lv Y X, Xiao G C 2024 Mater. Charact. 215 114146 Google Scholar
[19]	Wang Z W, Li Y C, Dong H, Wang Y 2025 Tribol. Int. 202 110379 Google Scholar
[20]	Munitz A, Salhov S, Guttmann G, Derimow N, Nahmany M 2019 Mater. Sci. Eng. A 742 1 Google Scholar
[21]	Segall M D, Lindan P J, Probert M A, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys. Condens. Matter 14 2717 Google Scholar
[22]	Wu T, Yang C, Yu L T, Zheng X F, Zhang L F, Jiang Y T, Xue X P, Lu Y H, Luan B L 2024 Appl. Surf. Sci. 677 161032 Google Scholar
[23]	Li Z, Gain A K, Cui Y L, Zhang L C 2025 Wear 570 205934 Google Scholar
[24]	Xie Y J, Jiang W Y, Xu K G, Wen X, Huang B S 2025 Mater. Today Commun. 43 111662 Google Scholar
[25]	Kang H Y, Yang X H, Sun X Y, Wang C Y, Xiao P 2025 J. Alloys Compd. 1010 177873 Google Scholar
[26]	Liu S, Zhan Y Z, Wu J Y, Chen X X, Ye H M 2016 Comput. Mater. Sci. 117 1 Google Scholar
[27]	Chen X Q, Niu H Y, Li D Z, Li Y Y 2011 Intermetallics 19 1275 Google Scholar
[28]	Sun L, Huang Y D, Zhao K F, Chen Z M, Shang X T, Xu W, Zhai W Y, Han P Y, Jia J, Peng J H 2025 Comput. Condens. Matter 43 e01027 Google Scholar
[29]	Pugh S F 1954 Philos. Mag. 45 823 Google Scholar
[30]	Hu W C, Liu Y, Li D J, Li K, Jin H L, Xu Y X, Zeng X Q 2014 Philos. Mag. 94 3945 Google Scholar

[1]	WU Hao, WANG Xu, WANG Jianyuan, ZHAI Wei, WEI Bingbo. Three-dimensional ultrasounds modulated solidification microstructure and mechanical property of (FeCoNiCrMn)₉₂Mo₈ high-entropy alloy. Acta Physica Sinica, doi: 10.7498/aps.74.20250657
[2]	BO Le, GAO Xiaoyu, NING Zhiliang, WANG Li, SUN Jianfei, ZHANG Zhenjiang, HUANG Yongjiang. Optimizing microstructure and mechanical properties of CoCrFeNi high-entropy alloy microfibers by electric current treatment. Acta Physica Sinica, doi: 10.7498/aps.74.20250518
[3]	HUA Sunmingqiang, KONG Detong, HU Xiao, SHE Xu, WANG Xiao, WANG Yuan. First-principles study of stabilities, electronic structures, and mechanical properties of M(Mn, Ti, Mo)-doped α-Fe. Acta Physica Sinica, doi: 10.7498/aps.74.20251044
[4]	Hu Ting-He, Li Zhi-Hao, Zhang Qian-Fan. First principles and molecular dynamics simulations of effect of dopants on properties of high strength steel for hydrogen storage vessels. Acta Physica Sinica, doi: 10.7498/aps.73.20231735
[5]	Chen Jing-Jing, Qiu Xiao-Lin, Li Ke, Zhou Dan, Yuan Jun-Jun. Mechanical performance analysis of nanocrystalline CoNiCrFeMn high entropy alloy: atomic simulation method. Acta Physica Sinica, doi: 10.7498/aps.71.20220733
[6]	Deng Shi-Jie, Zhao Yu-Hong, Hou Hua, Wen Zhi-Qin, Han Pei-De. Structural, mechanical and thermodynamic properties of Ti2AlX (X= C, N) at high pressure. Acta Physica Sinica, doi: 10.7498/aps.66.146101
[7]	Li Ming-Lin, Wan Ya-Ling, Hu Jian-Yue, Wang Wei-Dong. Molecular dynamics simulation of effects of temperature and chirality on the mechanical properties of single-layer molybdenum disulfide. Acta Physica Sinica, doi: 10.7498/aps.65.176201
[8]	Fan Tao, Zeng Qing-Feng, Yu Shu-Yin. Novel compounds in the hafnium nitride system: first principle study of their crystal structures and mechanical properties. Acta Physica Sinica, doi: 10.7498/aps.65.118102
[9]	Pan Xin-Dong, Wei Yan, Cai Hong-Zhong, Qi Xiao-Hong, Zheng Xu, Hu Chang-Yi, Zhang Xu-Xiang. Effect of Rh content on the mechanical properties of Ir-Rh alloy based on the first principle. Acta Physica Sinica, doi: 10.7498/aps.65.156201
[10]	Wang Hai-Yan, Hu Qian-Ku, Yang Wen-Peng, Li Xu-Sheng. Influence of metal element doping on the mechanical properties of TiAl alloy. Acta Physica Sinica, doi: 10.7498/aps.65.077101
[11]	Ma Bing-Yang, Zhang An-Ming, Shang Hai-Long, Sun Shi-Yang, Li Ge-Yang. Amorphizing and mechanical properties of co-sputtered Al-Zr alloy films. Acta Physica Sinica, doi: 10.7498/aps.63.136801
[12]	Ru Qiang, Li Yan-Ling, Hu She-Jun, Peng Wei, Zhang Zhi-Wen. The investigation of lithium insertion mechanism for Sn3InSb4 alloy based on first-principle calculation. Acta Physica Sinica, doi: 10.7498/aps.61.038210
[13]	Li Ai-Hong, Mu Yan-Qing, Yang Wei-Ming, Hou Hua, Han Pei-De, Zhang Su-Ying, Huang Zhi-Wei, Zhao Yu-Hong. First principles study on substitution behavior and alloying effects of Nb in Ni3Al. Acta Physica Sinica, doi: 10.7498/aps.60.047103
[14]	Hou Qing-Yu, Zao Chun-Wang, Li Ji-Jun, Wang Gang. Frist principles study of effect of high Al doping concentrationof p-type ZnO on electric conductivity performance. Acta Physica Sinica, doi: 10.7498/aps.60.047104
[15]	Hou Qing-Yu, Zhao Chun-Wang, Jin Yong-Jun, Guan Yu-Qin, Lin Lin, Li Ji-Jun. Effects of the concentration of Ga high doping on electric conductivity and red shift of ZnO from frist-principles. Acta Physica Sinica, doi: 10.7498/aps.59.4156
[16]	Hou Qing-Yu, Zhao Chun-Wang, Jin Yong-Jun. First-principles study on the effects of the concentration of Al-2N high codoping on the electric conducting performance of ZnO. Acta Physica Sinica, doi: 10.7498/aps.58.7136
[17]	Yu Wei-Yang, Tang Bi-Yu, Peng Li-Ming, Ding Wen-Jiang. Electronic structure and mechanical properties of α-Mg3Sb2. Acta Physica Sinica, doi: 10.7498/aps.58.216
[18]	Zhai Qiu-Ya, Yang Yang, Xu Jin-Feng, Guo Xue-Feng. Electrical resistivity and mechanical properties of rapidly solidified Cu-Sn hypoperitectic alloys. Acta Physica Sinica, doi: 10.7498/aps.56.6118
[19]	Li Teng, Li Wei, Pan Wei, Li Xiu-Mei. Effect of microstructure on the mechanical properties of Fe45—50 Cr30—35Co20—25Mo0—4Zr0—2 alloy. Acta Physica Sinica, doi: 10.7498/aps.54.4395
[20]	Zheng Li-Jing, Li Shu-Suo, Li Huan-Xi, Chen Chang-Qi, Han Ya-Fang, Dong Bao-Zhong. Small angle x-ray scattering study on microstructure and mechanical property evo lutions of equal-channel angular pressed 7050 Al alloy. Acta Physica Sinica, doi: 10.7498/aps.54.1665

Metrics

Abstract views: 300
PDF Downloads: 3
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Strengthening mechanism and wear behavior of AlCrFeNiNb_x high-entropy alloys from the perspective of phase modulation

Abstract

FullText HTML

Cited By

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Strengthening mechanism and wear behavior of AlCrFeNiNbx high-entropy alloys from the perspective of phase modulation

Abstract

FullText HTML

Cited By

Metrics

Publishing process

Authors

Referees

About Journal

About

Strengthening mechanism and wear behavior of AlCrFeNiNb_x high-entropy alloys from the perspective of phase modulation