Anomalous crystal structure of γ″ phase in the Mg-RE-Zn(Ag) series alloys: Causality clarified by ab initio study

doi:10.1016/j.jmst.2019.05.065

Abstract

Abstract:

The crystal structure of the single-unit-cell thickness γ″ phase, as a key strengthening phase in Mg-RE-Zn (Ag) series alloys, has been extensively studied, and several structural models have been proposed in the past two decades. However, these reported models, and even the lattice constants at the same proposed structure, are scattered severely, which has led to considerable confusion and not available for further mechanical property simulation and prediction of Mg alloys containing this phase. In this study, by using first-principles calculations, the crystal structure of γ” phase is clarified, resolving the discrepancies among different experiments, and its intrinsic mechanical properties have also been studied for the first time. It is verified that the γ″ phase contains quasi-five atomic layers, instead of the previously reported tri-layer, and surprisingly, its crystal structure has many variants, which would change with the alloy composition. Besides, with the help of the simulated selected area electron diffraction (SAED) patterns, it is found that the atoms in the central layer remain partially ordered distribution, and this ordered extent primarily depends on the atomic ratio of RE: Zn(Ag) and the solute content in an alloy. That is, the ordered extent increases with decreasing the atomic ratio of RE:Zn(Ag) and/or increasing solute content of alloy, and vice versa. Ag and Zn dissolved in the γ″ phase would produce almost opposed mechanical anisotropy for the γ″ phase under the identical crystal structure, and the addition of Ag shows more efficient on increasing the shear modulus of γ″ phase.

Key words: First-principles, γ″ phase, Mg-RE-based series alloys, Crystal structure, Mechanical-properties

Junyuan Bai, Xueyong Pang, Xiangying Meng, Hongbo Xie, Hucheng Pan, Yuping Ren, Min Jiang, Gaowu Qin. Anomalous crystal structure of γ″ phase in the Mg-RE-Zn(Ag) series alloys: Causality clarified by ab initio study[J]. J. Mater. Sci. Technol., 2020, 36: 167-175.

Figures/Tables 12

Table 1 Summary of crystal structure of the γ″ phase reported in literatures.

Alloys	Refs	Alloy Composition (at.%)	Gd:Zn atomic ratio in alloys	Structural information
Mg-Gd-Zn	[17]	Mg-2Gd-1Zn	2:1	Ordered G.P zone, a = 5.56 Å, c = 5.21 Å, (0001)_α plate
	[6]	Mg-1Gd-0.4Zn-0.2 Zr	2.5:1	γ″ (Mg₇₀Gd₁₅Zn₁₅*) ordered hcp,P$\bar{6}$2m, a = 5.60 Å, c = 4.44 Å
	[24]	Mg-2.5Gd-1Zn	2.5:1	γ″ phase, a = 4.44 Å, c≈ 4.0 Å
	[25]	Mg-1.2Gd-1.8Zn	2:3	γ″ (Mg₇₀Gd₁₅Zn₁₅*), a = 5.56 Å, c≈ 3.90 Å
Mg-Gd-Ag	[18]	Mg-2.4Gd-0.4Ag-0.1 Zr	6:1	γ″ (Mg₄Gd₂Zn₃), a = 5.48 Å, c = 4.17 Å, (0001)_α plate
Mg-Y-Zn-Ag	[19]	Mg-1.76Y-0.48Ag-0.4Zn-0.17Zr	3.67:1	γ″ (Mg₄Y₂Ag₃), P6/mmm, a = 5.56 Å, c = 4.24 Å, (0001)_α plate
Mg-Nd-Zn	[14,61]	Mg-1Nd-1Zn	1:1	γ″ (Mg₅(Nd,Zn)) hcp,P$\bar{6}$2m, a = 5.50 Å, c = 5.20 Å, (0001)_α plate
Mg-Nd-Zn	[13]	Mg-0.6Nd-0.4La-0.3Zn	2:1	γ″ ((Mg_0.8Zn_0.2)₅Nd) hcp,P$\bar{6}$2m
Mg-Sm-Zn	[20]	Mg-1.74Sm-1Zn-Zr	1.74:1	γ″ ordered hexagonal G.P zones, a = 5.56 Å, c = 4.14 Å, (0001)_α plate

Fig. 1. The proposed sandwiched model of γ″ phase. (a) Projection of γ″ sandwiched model along the [10 $\bar{1}$ 0] γ″ direction, the left panel shows a unit cell structure and the right panel shows its 3 × 3 supercell. And the yellow, gray and dark blue balls represent the RE, Mg and Zn (Ag) atoms, respectively; (b) Schematic illustration of 3 × 3 supercell (stoichiometry: Mg5RE), where Arabic numerals represent the varied substitutional Mg atomic sites; (c) Schematic diagram of the calculated mechanical parameters for γ″ phase, the upper figure exhibits the (0001) basal plane and (2 $\bar{11}$0), (01 $\bar{1}$0) two prismatic planes, and the lower figure shows the angle (θ degrees) of the normal N to the plane (xyz) with respect to the [0001] direction.

Table 2 The α-Mg atomic layers test for the γ″ phase in Mg-Gd-Zn alloy and other optimized results of Mg-RE-Zn(Ag) alloys by the five-layer structural model.

layers	a (Å)	c (Å)	Alloys		a (Å)	c (Å)
3	5.53	3.50	Mg-Gd-Ag	Exp [18]	5.48	4.17
5	5.55	3.48	Mg-Gd-Ag	Calc*	5.65	3.51
7	5.53	3.52	Mg-Y-Zn-Ag	Exp [19]	5.56	4.24
9	5.56	3.43		Calc*(Mg-Y-Ag)	5.64	3.51
11	5.55	3.48		Calc*(Mg-Y-Zn)	5.54	3.45
13	5.55	3.44	Mg-Nd-Zn	Exp [14]	5.50	5.20
15	5.54	3.45	Mg-Nd-Zn	Calc*	5.58	3.60
17	5.53	3.46	Mg-Sm-Zn	Exp [20]	5.56	4.14
+U	5.53	3.49	Mg-Sm-Zn	Calc*	5.57	3.50

Fig. 2. Schematic illustration of the relaxed sandwiched model. The figure successively shows the projection of sandwiched model along the [1000 ] γ″, [11 $\bar{2}$0] γ″ and [$\bar{1}$100] γ″ directions, respectively.

Fig. 3. Formation energy of the γ″ phase in the Mg-RE-Zn(Ag) alloys. (a-f) Formation energy of the γ″ phase in the Mg-RE-Zn(Ag) alloys is plotted as a function of RE and Mg sites substituted by Zn (Ag) atoms.

Fig. 4. Diagram of the collected lowest formation energy at each substitutional fraction in Fig. 3.

Fig. 5. (a, b) The variation of c value for the γ″ phase in the Mg-Gd-Zn(Ag) alloys, and the insets represent the projection of the central layer along the [0001]γ″ direction; (c, d) Schematic illustration of the atomic arrangement of the central layer dependence on the RE:Zn (Ag) atomic ratio in alloys.

Fig. 6. Simulated SAED patterns along the [0001]α, [1$\bar{1}$00]α and [11$\bar{2}$0]α directions, respectively. (a-c) Simulated SAED patterns along the three directions above; (d-f) Simulated SAED patterns of the relaxed structural model proposed by Gu et al. [25]; (g-f) Simulated SAED patterns of structure A (Fig. 5(a)). The color of spots represents the intensity of diffraction, e.g., the red spots and dark blue spots correspond to the strongest and weakest diffraction intensity, respectively.

Fig. 7. (a) The atomic resolution HAADF-STEM image of γ″ phase in the Mg-2.4Gd-0.4Ag-0.1 Zr alloy along the [0001]γ″ direction reported by Zhang et al. [18]; (b) Schematic diagram of calibrated Gd (yellow spheres) and Ag (blue spheres) in the central layer. Region I, II and III belong to the same type structure, and except these three regions, the other Mg and Ag atoms remain partially ordered distribution.

Table 3 Mechanical parameters of all the proposed sandwiched models (GPa).

Alloy	Bulk	C11 (GPa)	C12 (GPa)	C13 (GPa)	C44 (GPa)	C33 (GPa)	B (GPa)	G (GPa)	E (GPa)	v	A
Pure Mg	Exp [42]	59.3	25.7	21.4	16.4	61.5	35.25	17.3	44.6	0.289	0.98
Pure Mg	Calc	58	26	21	17	57	34	17	43.7	0.289	1.06
Mg-Gd-Zn	A	75.6	21.6	15.3	23.6	89	38.3	27	65.8	0.21	0.87
	B	75.8	22.5	16	23.4	89	39	27	65.4	0.22	0.88
	C	76.3	22.6	17	23.5	89	39.4	26.8	65.5	0.22	0.87
	D	75.6	23	17.4	22	89	39.5	25.8	63.7	0.23	0.84
Mg-Gd-Ag	A₁	83.4	18.2	18	32	79.4	39	32	75.7	0.18	0.98
	B₁	83.3	18.6	20	32	76	40	31.6	75	0.19	0.99
	C₁	85.4	19.2	18.6	29.7	82.8	40.7	31.6	75.3	0.19	0.90

Table 4 Calculated elastic constants, Young’s modulus and shear modulus of γ″ phase (GPa).

Alloy	Single	C11	C12	C13	C44	C33	E(01$\bar{1}$0)	E(0001)	G(01$\bar{1}$0)	G(0001)
Mg-Gd-Zn	A	115	16	9.1	39	175.7	112.3	175.4	43.7	39.2
	B	116	17.8	10.3	38.6	174	112.3	172.4	43.2	38.6
	C	117.8	18	12.1	39	174	114.9	172.4	43.8	39.0
	D	115	18.8	12.8	33	174	111.1	172.4	39.2	33.1
Mg-Gd-Ag	A₁	142	10.2	13.9	77	133	140.8	129.9	71.4	76.9
	B₁	146	10.8	18.5	77	120	142.8	114.9	71.9	76.9
	C₁	154.7	11.8	15.3	66.2	147.2	151.5	144.9	68.7	66.2

Fig. 8. (a, b) Angular variation of E and G values of the γ″ phase in the Mg-Gd-Zn alloy; (c, d) Angular variation of E and G values of the γ″ phase in the Mg-Gd-Ag alloy; (e, f) Comparison of the E and G values between the structure A and structure A1.

References

[1]	T.M. Pollock, Science 328 (80) (2010) 986-987.
[2]	J.F. Nie, Physical Metallurgy of Light Alloys, fifth edn, Elsevier, 2014.
[3]	X.J. Wang, D.K. Xu, R.Z. Wu, X.B. Chen, Q.M. Peng, L. Jin, Y.C. Xin, Z.Q. Zhang, Y. Liu, X.H. Chen, G. Chen, K.K. Deng, H.Y. Wang, J. Mater. Sci. Technol. 34 (2018) 245-247.
[4]	H. Xie, H. Pan, Y. Ren, S. Sun, L. Wang, H. Zhao, B. Liu, S. Li, G. Qin, J. Phys. Chem. Lett. 9 (2018) 4373-4378.
[5]	H. Xie, H. Pan, Y. Ren, L. Wang, Y. He, X. Qi, G. Qin, Phys. Rev. Lett. 120 (2018) 85701.
[6]	J.F. Nie, K. Oh-ishi, X. Gao, K. Hono, Acta Mater. 56 (2008) 6061-6076.
[7]	J.F. Nie, X. Gao, S.M. Zhu, Scr. Mater. 53 (2005) 1049-1053.
[8]	X. Gao, J.F. Nie, Scr. Mater. 58 (2008) 619-622.
[9]	T. Honma, T. Ohkubo, S. Kamado, K. Hono, Acta Mater. 55 (2007) 4137-4150.
[10]	K. Yamada, H. Hoshikawa, S. Maki, T. Ozaki, Y. Kuroki, S. Kamado, Y. Kojima, Scr. Mater. 61 (2009) 636-639.
[11]	Y.M. Zhu, A.J. Morton, J.F. Nie, Scr. Mater. 58 (2008) 525-528.
[12]	Q. Wang, J. Chen, Z. Zhao, S. He, Mater. Sci. Eng. A 528 (2010) 323-328.
[13]	D. Choudhuri, S.G. Srinivasan, M.A. Gibson, Y. Zheng, D.L. Jaeger, H.L. Fraser, R. Banerjee, Nat. Commun. 8 (2017) 1-9.
[14]	D.H. Ping, K. Hono, J.F. Nie, Scr. Mater. 48 (2003) 1017-1022.
[15]	A.R. Natarajan, E.L.S. Solomon, B. Puchala, E.A. Marquis, A. Van Der Ven, Acta Mater. 108 (2016) 367-379.
[16]	H. Xie, H. Pan, Y. Ren, S. Sun, L. Wang, Y. He, G. Qin, J. Alloys. Compd. 738 (2018) 32-36.
[17]	M. Nishijima, K. Hiraga, M. Yamasaki, Y. Kawamura, Mater. Trans. 49 (2007) 227-229.
[18]	Y. Zhang, Y. Zhu, W. Rong, Y. Wu, L. Peng, J.F. Nie, N. Birbilis, Metall. Mater.Trans. A Phys.Metall. Mater. Sci. 49 (2018) 673-694.
[19]	Y.M. Zhu, K. Oh-ishi, N.C. Wilson, K. Hono, A.J. Morton, J.F. Nie, Metall. Mater. Trans. A 47 (2016) 927-940.
[20]	X. Xia, A.A. Luo, D.S. Stone, J. Alloys. Compd. 649 (2015) 649-655.
[21]	X. Gao, S.M. Zhu, B.C. Muddle, J.F. Nie, Scr. Mater. 53 (2005) 1321-1326.
[22]	J.C. Oh, T. Ohkubo, T. Mukai, K. Hono, Scr. Mater. 53 (2005) 675-679.
[23]	K. Oh-ishi, R. Watanabe, C.L. Mendis, K. Hono, Mater. Sci. Eng. A 526 (2009) 177-184.
[24]	Z. Li, J. Zheng, B. Chen, Mater. Charact. 120 (2016) 345-348.
[25]	X.F. Gu, T. Furuhara, T. Kiguchi, T.J. Konno, L. Chen, P. Yang, Scr. Mater. 146 (2018) 64-67.
[26]	Y. Zhang, T. Alam, B. Gwalani, W. Rong, R. Banerjee, L.M. Peng, J.F. Nie, N. Birbilis, Philos. Mag. Lett. 96 (2016) 212-219.
[27]	G. Kresse, J. Furthmüller, Phys. Rev. B - Condens.Matter Mater. Phys. 54 (1996) 11169-11186.
[28]	J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865-3868.
[29]	P.E. Blöchl, Phys. Rev. B 50 (1994) 17953-17979.
[30]	D. Joubert, Phys. Rev. B - Condens.Matter Mater. Phys. 59 (1999) 1758-1775.
[31]	J. Feng, B. Xiao, C.L. Wan, Z.X. Qu, Z.C. Huang, J.C. Chen, R. Zhou, W. Pan, Acta Mater. 59 (2011) 1742-1760.
[32]	J.F. Nie, N.C. Wilson, Y.M. Zhu, Z. Xu, Acta Mater. 106 (2016) 260-271.
[33]	A. Issa, J.E. Saal, C. Wolverton, Acta Mater. 83 (2015) 75-83.
[34]	L. Huber, I. Elfimov, J. Rottler, M. Militzer, Phys. Rev. B-Condens.Matter Mater. Phys. 85 (2012) 1-7.
[35]	M.C. Gao, A.D. Rollett, M. Widom, Phys. Rev. B 75 (2007).
[36]	D. Liu, X. Dai, X. Wen, G. Qin, X. Meng, Comput. Mater. Sci. 106 (2015) 180-187.
[37]	S. Shang, Y. Wang, Z.K. Liu, Appl. Phys. Lett. 90 (2007) 3-6.
[38]	J. Pokluda, M. Černý, M. Šob, Y. Umeno, Prog. Mater. Sci. 73 (2015) 127-158.
[39]	S. Boucetta, G. Uğur, J. Magnes. Alloy. 4 (2016) 123-127.
[40]	R. Hill, Proc. Phys. Soc. London Sect. A 65 (1952) 349-355.
[41]	Y. Liu, H. Ren, W.C. Hu, D.J. Li, X.Q. Zeng, K.G. Wang, J. Lu, J. Mater. Sci. Technol. 32 (2016) 1222-1231.
[42]	D. Tromans, Ijrras 6 (2011) 462-483.
[43]	H. Xie, H. Pan, Y. Ren, S. Sun, L. Wang, H. Zhao, B. Liu, X. Qi, G. Qin, Cryst. Growth Des. 18 (2018) 5866-5873.
[44]	J.F. Nie, IOP Conf. Ser. Mater. Sci. Eng. 219 (2017) 0-8.
[45]	F. Cao, J. Zheng, Y. Jiang, B. Chen, Y. Wang, T. Hu, Acta Mater. 164 (2019) 207-219.
[46]	T. Saito, F.J.H. Ehlers, W. Lefebvre, D. Hernandez-Maldonado, R. Bjørge, C.D. Marioara, S.J. Andersen, R. Holmestad, Acta Mater. 78 (2014) 245-253.
[47]	P. Donnadieu, Y. Shao, F. De Geuser, G.A. Botton, S. Lazar, M. Cheynet, M. De Boissieu, A. Deschamps, Acta Mater. 59 (2011) 462-472.
[48]	X.F. Gu, T. Furuhara, L. Chen, P. Yang, Scr. Mater. 150 (2018) 45-49.
[49]	Y. Guo, Y. Li, B. Liu, W. Liu, X. Liang, Q. Gu, Q. Li, J. Alloys. Compd. 750 (2018) 117-123.
[50]	K. Saito, M. Nishijima, K. Hiraga, Mater. Trans. 51 (2010) 1712-1714.
[51]	K. Saito, A. Yasuhara, K. Hiraga, J. Alloys. Compd. 509 (2011) 2031-2038.
[52]	Y.M. Zhu, A.J. Morton, J.F. Nie, Acta Mater. 58 (2010) 2936-2947.
[53]	Y.M. Zhu, M. Weyland, A.J. Morton, K. Oh-ishi, K. Hono, J.F. Nie, Scr. Mater. 60 (2009) 980-983.
[54]	Y.J. Wu, X.Q. Zeng, D.L. Lin, L.M. Peng, W.J. Ding, J. Alloys. Compd. 477 (2009) 193-197.
[55]	M. Yamasaki, M. Sasaki, M. Nishijima, K. Hiraga, Y. Kawamura, Acta Mater. 55 (2007) 6798-6805.
[56]	D. Egusa, E. Abe, Acta Mater. 60 (2012) 166-178.
[57]	P. Ravindran, L. Fast, P.A. Korzhavyi, B. Johansson, J. Wills, O. Eriksson, J. Appl. Phys. 84 (1998) 4891.
[58]	J.F. Nie, Metall. Mater. Trans. A 43 (2012) 3891-3939.
[59]	F. Pan, M. Yang, X. Chen, J. Mater. Sci. Technol. 32 (2016) 1211-1221.
[60]	M. Wang, B.B. He, M.X. Huang, J. Mater. Sci. Technol. 35 (2019) 394-395.
[61]	R. Wilson, C.J. Bettles, B.C. Muddle, J.F. Nie, Mater. Sci.Forum 419-422 (2003) 267-272.