Experimental and numerical studies on the sluggish diffusion in face centered cubic Co-Cr-Cu-Fe-Ni high-entropy alloys

doi:10.1016/j.jmst.2018.02.003

Abstract

Abstract:

On purpose of studying the sluggish diffusion of high-entropy alloys, three different face centered cubic Co-Cr-Cu-Fe-Ni high-entropy alloys were prepared, and assembled into three groups of sandwich-type diffusion multiple annealed at 1273, 1323, and 1373 K respectively. By means of the electron probe microanalyzer technique and recently developed numerical inverse method, the composition-dependent interdiffusivities at different temperatures were effectively evaluated by minimizing the residual between the model-predicted compositions/interdiffusion fluxes and the respectively experimental ones. After that, the tracer diffusivities were predicted based on the assessed mobility parameters and thermodynamic descriptions with the simplified ideal solution model. The comprehensive comparison between the interdiffusivities/tracer diffusivities in the Co-Cr-Cu-Fe-Ni high-entropy alloys and those in sub-binary, ternary, quaternary and other quinary alloys indicates that the sluggish diffusion exists in interdiffusion instead of tracer diffusion for the present Co-Cr-Cu-Fe-Ni high-entropy alloys.

Key words: High-entropy alloys, Co-Cr-Cu-Fe-Ni, Sluggish diffusion, Numerical inverse method, Diffusion multiple

Rui Wang, Weimin Chen, Jing Zhong, Lijun Zhang. Experimental and numerical studies on the sluggish diffusion in face centered cubic Co-Cr-Cu-Fe-Ni high-entropy alloys[J]. J. Mater. Sci. Technol., 2018, 34(10): 1791-1798.

Figures/Tables 10

Table 1 Summary of literature reports on diffusion in different HEAs.

Phase	System	Method^a	Type of Diffusivity	Code^b	Refs.
fcc	CoCrFeMnNi	QBDC & S-F	Tracer diffusivity	√	[7]
	CoCrFeNi	TMM	Interdiffusivity	√	[8]
	CoCrFeMnNi	Semi-empirical rules & Re-analyses of Ref. [7]	Tracer diffusivity	√	[9]
	AlCoCrFeNi	DMA & LM	Tracer diffusivity	√	[10]
	CoCrFeMnNi	DMA, LM & Re-analyses of Ref. [7]		√
	CoCrFeNi & CoCrFeMnNi	Radiotracer technique & Gaussian solution	Tracer diffusivity	×	[11]
	CoCrFeMnNi	DM & NIM	Interdiffusivity	√	[12]
			Tracer diffusivity	×
	CoCrFeMnNi	CALPHAD assessment	Tracer diffusivity	×	[13]
	CoCrCuFeNi	DM & NIM	Interdiffusivity	√	This work
			Tracer diffusivity	×

Table 2 Nominal and actual compositions of the presently prepared alloys.

Alloy	Nominal compositions (in at.%)	Actual compositions (in at.%)
1^#	Co_22.5Cr_22.5Cu_5.5Fe_22.5Ni_27.0	Co_22.5Cr_22.8Cu_5.4Fe_22.7Ni_26.6
2^#	Co_25.0Cr_25.0Fe_25.0Ni_25.0	Co_24.9Cr_25.3Fe_25.2Ni_24.6
3^#	Co_26.4Cr₂₂Cu_3.2Fe₂₂Ni_26.4	Co_26.4Cr_22.3Cu_3.0Fe_22.4Ni_25.9

Fig 1. XRD patterns of the alloys Co22.5Cr22.8Cu5.3Fe22.7Ni26.6 (1#), Co24.9Cr25.3Fe25.2Ni24.6 (2#), and Co26.4Cr22.3Cu3.0Fe22.4Ni25.9(3#).

Fig. 2. SEM micrographs of the alloys Co22.5Cr22.8Cu5.3Fe22.7Ni26.6 (1#), Co24.9Cr25.3Fe25.2Ni24.6 (2#), and Co26.4Cr22.3Cu3.0Fe22.4Ni25.9 (3#) homogenized at 1373 K for 168 h.

Fig. 3. Schematic diagram for the prepared sandwich-type diffusion multiples.

Fig. 4. Comparisons of the model-predicted concentration/interdiffusion profiles with the corresponding experimental data (symbols), and the evaluated diagonal interdiffusivities along the diffusion paths of the diffusion multiples annealed at 1273 K for 72 h.

Fig. 5. Comparisons of the model-predicted concentration/interdiffusion profiles with the corresponding experimental data (symbols), and the evaluated diagonal interdiffusivities along the diffusion paths of the diffusion multiples annealed at 1323 K for 72 h.

Fig. 6. Comparisons of the model-predicted concentration/interdiffusion profiles with the corresponding experimental data (symbols), and the evaluated diagonal interdiffusivities along the diffusion paths of the diffusion multiples annealed at 1373 K for 72 h.

Fig. 7. Comparisons of diagonal interdiffusivities determined in the present work with the reported experimental diffusion data at 1273 K, 1323 K or 1373 K in various subsystems of fcc CoCrCuFeNi system with Ni as the solvent: Co40Ni60 [40], Co4.9Ni95.1 [41], Cr5.1Ni94.9 [41], Fe40Ni60 [40], Co6Cu17Ni77 [27], Cr4Cu8Ni88 [30], Cu6Fe53Ni41 [26], Co25Cr25Fe25Ni25 [8], Co23.95Cr23.3Fe23Mn6.66Ni23.09 [12].

Fig. 8. Comparisons of Arrhenius plots of the tracer diffusivities determined in the present work with the reported temperature-dependent data on diffusion in various fcc systems: pure Co [42], pure Cu [43], pure Fe [44], pure Ni [45], Co in Ni [46], Cr in Ni [47], Fe in Ni [48], Cu60.97Ni29.49Zn9.54 [43], Fe-15Cr-20Ni [49], Co25Cr25Fe25Ni25 [11], Co20Cr20Fe20Mn20Ni20 [11], Co22.22Cr22.22Fe22.22Mn11.12Ni22.22 [10], Al20Co20Cr20Fe20Ni20 [10], Co23.95Cr23.3Fe23Mn6.66Ni23.09 [12].

References

[1]	J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang,Adv. Eng. Mater. 6(2004) 299-303.
[2]	Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Prog.Mater. Sci. 61(2014) 1-93.
[3]	L. Jiang, Y. Lu, W. Wu, Z. Cao, T. Li, J. Mater. Sci. Technol. 32(2016) 245-250.
[4]	Y. Yu, J. Wang, J. Li, J. Yang, H. Kou, W. Liu, J. Mater. Sci. Technol. 32(2016)470-476.
[5]	H. Jiang, L. Jiang, D. Qiao, Y. Lu, T. Wang, Z. Cao, T. Li, J. Mater. Sci. Technol. 33(2017) 712-717.
[6]	L. Jiang, H. Jiang, Y. Lu, T. Wang, Z. Cao, T. Li, J. Mater. Sci. Technol. 31(2015)397-402.
[7]	K.Y. Tsai, M.H. Tsai, J.W. Yeh, Acta Mater. 61(2013) 4887-4897.
[8]	K. Kulkarni, G.P.S. Chauhan, AIP Adv. 5(2015) 097162.
[9]	D.L. Beke, G. Erdélyi, Mater. Lett. 164(2016) 111-113.
[10]	J. D?abrowa, W. Kucza, G. Cie′slak, T. Kulik, M. Danielewski, J.W. Yeh, J. AlloysCompd. 674(2016) 455-462.
[11]	M. Vaidya, S. Trubel, B.S. Murty, G. Wilde, S.V. Divinski, J. Alloys Compd. 688(2016) 994-1001.
[12]	W. Chen, L. Zhang, J. Phase Equilib. Diffus. 38(2017) 457-465.
[13]	C. Zhang, F. Zhang, K. Jin, H. Bei, S. Chen, W. Cao, J. Zhu, D. Lv, J. Phase Equilib. Diffus. 38(2017) 434-444.
[14]	W. Chen, L. Zhang, Y. Du, C. Tang, B. Huang, Scr. Mater. 90(2014) 53-56.
[15]	W. Chen, J. Zhong, L. Zhang, MRS Commun. 6(2016) 295-300.
[16]	J. Zhong, W. Chen, L. Zhang, Calphad 60 (2018) 177-190.
[17]	W. Chen, Q. Li, L. Zhang, Materials 10 (2017) 961.
[18]	J. Chen, L. Zhang, J. Zhong, W. Chen, Y. Du, J. Alloys Compd. 688(2016)320-328.
[19]	S. Wen, Y. Tang, J. Zhong, L. Zhang, Y. Du, F. Zheng, J. Mater. Res. 32(2017)2188-2201.
[20]	H. Xu, W. Chen, L. Zhang, Y. Du, C. Tang, J. Alloys Compd. 644(2015) 687-693.
[21]	Y. Liu, W. Chen, J. Zhong, M. Chen, L. Zhang, Metall. Mater. Eng. 23(2017)191-206.
[22]	S. Deng, W. Chen, J. Zhong, L. Zhang, Y. Du, L. Chen, Calphad 56 (2017)230-240.
[23]	J.R. Manning, Acta Metall. 15(1967) 817-826.
[24]	W. Chen, L. Zhang, Y. Du, B. Huang, Philos. Mag. 94(2014) 1552-1577.
[25]	M.A. Dayananda, Metall. Trans. A 14 (1983) 1851-1858.
[26]	Y. Liu, L. Zhang, Y. Du, G. Sheng, J. Wang, D. Liang, Calphad 35 (2011)376-383.
[27]	J. Chen, Y. Liu, F. Lei, G. Sheng, Z. Kang, Calphad 47 (2014) 123-128.
[28]	J. Chen, Y. Liu, F. Lei, G. Sheng, Z. Kang, Calphad 48 (2015) 145-150.
[29]	J. Chen, Y. Liu, G. Sheng, F. Lei, Z. Kang, J. Alloys Compd. 621(2015)428-433.
[30]	G. Xu, Y. Liu, F. Lei, G. Sheng, Z. Kang, J. Alloys Compd. 649(2015) 307-312.
[31]	G. Ghosh, Acta Mater. 48(2000) 3719-3738.
[32]	J. Wang, H.S. Liu, L.B. Liu, Z.P. Jin, Calphad 32 (2008) 94-100.
[33]	C.E. Campbell, W.J. Boettinger, U.R. Kattner, Acta Mater. 50(2002) 775-792.
[34]	W. Zhang, D. Liu, L. Zhang, Y. Du, B. Huang, Calphad 45 (2014) 118-126.
[35]	Y. Liu, D. Liang, Y. Du, L. Zhang, D. Yu, Calphad 33 (2009) 695-703.
[36]	Y.W. Cui, M. Jiang, I. Ohnuma, K. Oikawa, R. Kainuma, K. Ishida, J. PhaseEquilib. Diffus. 29(2008) 2-10.
[37]	B. J?nsson, Scand. J. Metall. 24(1994) 201-208.
[38]	J.S. Kirkaldy, D.J. Young, The Institute of MetalsLondon, 1987.
[39]	B. J?nsson, J. Scand. Metall. 24(1995) 21-27.
[40]	T. Ustad, H. S?rum, Phys. Status Solidi A 20 (1973) 285-294.
[41]	S.B. Jung, T. Yamane, Y. Minamino, K. Hirao, H. Araki, S. Saji, J. Mater. Sci. Lett.11(1992) 1333-1337.
[42]	W. Bussmann, C. Herzig, W. Rempp, K. Maier, H. Mehrer, Phys. Status Solidi A56 (1979) 87-97.
[43]	K.J. Anusavice, R.T. Dehoff, Metall. Trans. 3(1972) 1279-1298.
[44]	I.G. Ivantsov, A.M. Blinkin, Fiz Metals Metall. 22(1966) 876-883.
[45]	H. Bakker, Phys. Status Solidi 28 (1968) 569-576.
[46]	K.I. Hirano, R.P. Agarwala, B.L. Averbach, M. Cohen, J. Appl. Phys. 33(1962)3049-3054.
[47]	J. R?uˇziˇcková, B. Million, Mater. Sci. Eng. 50(1981) 59-64.
[48]	C.F. Heuer, Materials Science and Engineering, University of Missouri-Rolla,1969.
[49]	S.J. Rothman, L.J. Nowicki, G.E. Murch, J. Phys. F: Metal Phys. 10(1980)383-398.