Basal-plane stacking-fault energies of Mg alloys: A first-principles study of metallic alloying effects

doi:10.1016/j.jmst.2018.02.009

Abstract

Abstract:

Generalized stacking-fault energies (GSFEs) of basal-plane stacking faults I₁ and I₂ in Mg alloys have been studied based on first-principles calculations, where 43 alloying elements were considered. It is found that the most contributing features of alloying elements to GSFEs are bulk modulus, equilibrium volume, binding energy, atomic radius and ionization energy. Both bulk modulus and ionization energy exhibit positive relationships with GSFEs, and the others show opposite relationships. Multiple regressions have been performed to offer a quantitative prediction for basal-plane GSFEs in Mg-X systems. GSFEs, alloying effects of elements and the prediction model established within this work may provide guidelines for new Mg alloys design with better ductility.

Key words: First-principles calculations, Magnesium alloys, Stacking-fault energy, Alloying effect

Qing Dong, Zhe Luo, Hong Zhu, Leyun Wang, Tao Ying, Zhaohui Jin, Dejiang Li, Wenjiang Ding, Xiaoqin Zeng. Basal-plane stacking-fault energies of Mg alloys: A first-principles study of metallic alloying effects[J]. J. Mater. Sci. Technol., 2018, 34(10): 1773-1780.

Figures/Tables 10

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Alloying element	Ef	Eb	γI1	γus1	γI2	γus2	R[17]	Ei1[17]	Ei2[17]	Nve	Vhcp[18]	κhcp[18]
Alloying element	(eV)	(eV)	(mJ/m2)	(mJ/m2)	(mJ/m2)	(mJ/m2)	(pm)	(mJ/mol)	(mJ/mol)	Nve	(?3/atom)	(GPa)
Mg	0.00	0.00	16.1	86.9	37.6	89.6	160	738	1451	2	22.89	35.7
Li	-0.20	-0.26	18.1	95.6	47.6	97.5	152	520	7298	1	20.33	13.5
Be	1.24	-0.90	25.8	80.7	45.4	85.4	111	899	1757	2	7.92	121.1
Na	0.32	0.79	16.8	79.3	38.3	80.4	186	496	4562	1	37.18	7.6
Al	0.02	-1.93	13.1	86.0	21.3	86.3	143	578	1817	3	16.75	70.8
K	1.58	2.27	10.7	22.9	6.9	28.1	179	419	3051	1	74.02	3.5
Ca	0.10	-0.25	17.0	58.3	28.7	61.6	195	590	1145	2	41.93	17.7
Sc	-0.18	-2.96	17.0	91.7	34.6	94.5	210	631	1235	3	24.47	54.9
Ti	0.68	-3.21	2.3	108.7	22.4	106.9	147	658	1310	4	17.29	112.8
V	1.05	-3.11	18.0	117.2	50.2	120.5	134	650	1414	5	13.84	173.2
Cr	1.11	-5.42	19.7	115.6	48.4	118.8	128	653	1592	6	11.94	233.5
Mn	0.84	-1.61	12.1	110.2	37.5	111.5	127	717	1509	7	10.75	279.7
Fe	1.17	-2.46	-1.3	68.6	27.0	101.9	126	759	1561	8	10.18	288.3
Co	0.83	-2.98	23.4	113.8	63.5	119.0	125	758	1646	9	10.85	212.5
Ni	0.36	-3.41	24.7	100.4	63.2	106.8	124	737	1753	10	10.95	193.8
Cu	0.56	-1.75	21.1	86.6	50.5	90.9	128	745	1958	1	12.04	136.1
Zn	-0.07	0.38	17.6	79.5	32.7	82.1	134	906	1733	2	15.40	51.8
Ga	-0.20	-1.45	9.5	79.8	22.4	79.0	135	579	1979	3	19.18	45.9
Sr	0.72	0.66	16.7	32.9	15.6	30.1	215	549	1064	2	54.72	11.4
Y	-0.13	-2.75	15.6	69.9	26.4	74.7	180	616	1181	3	32.67	40.8
Zr	0.16	-4.73	-0.4	94.8	17.5	92.2	160	660	1267	4	23.44	95.3
Nb	0.86	-4.57	-6.0	113.0	19.9	110.5	146	664	1382	5	18.90	162.8
Mo	1.34	-3.37	4.8	132.0	42.7	132.9	139	685	1558	6	16.29	233.8
Tc	0.93	-4.57	16.9	145.3	63.0	147.9	136	702	1472	7	14.63	296.1
Ru	0.12	-6.19	22.7	147.4	72.6	151.3	134	711	1617	8	13.88	309.4
Rh	-0.90	-5.40	24.7	130.3	70.9	136.1	134	720	1744	9	14.26	251.1
Pd	-1.34	-3.50	23.1	111.9	64.0	120.0	137	805	1875	10	15.60	163.6
Ag	-0.43	-1.36	17.8	93.9	48.6	97.1	144	731	2073	1	18.01	91.1
Cd	-0.31	0.50	14.0	109.9	32.5	83.9	149	868	1631	2	23.00	35.8
In	-0.15	-1.11	7.4	75.0	16.9	74.8	167	558	1821	3	27.80	34.4
Sn	-0.51	-2.11	4.0	71.8	11.9	71.9	151	709	1412	4	27.79	47.6
La	0.28	-1.60	15.9	30.2	2.5	39.4	183	538	1067	3	37.26	26.1
Sm	-0.01	-2.93	16.1	62.2	18.9	61.5	180	543	1086	8	33.91	35.7
Hf	0.50	-4.43	0.0	98.1	16.0	96.0	159	680	1440	4	22.41	109.1
Ta	1.38	-5.41	-8.2	116.3	14.3	112.0	146	761		5	18.77	188.0
W	2.04	-4.72	1.4	136.5	36.5	136.8	139	770		6	16.62	274.3
Re	1.65	-4.63	15.5	154.9	57.9	156.7	137	760		7	14.99	366.8
Ir	-0.70	-6.71	26.9	134.4	71.4	141.2	136	880	880	9	14.68	339.0
Pt	-1.71	-5.62	24.6	103.6	65.8	110.6	139	870	1791	10	15.94	235.2
Au	-1.21	-2.64	17.5	84.6	46.0	89.6	144	890	1980	1	18.22	135.0
Hg	-0.55	0.82	9.6	73.2	23.7	76.6	151	1007	1810	2	30.75	9.5
Tl	0.05	-0.57	2.7	68.7	14.8	67.7	170	589	1971	3	31.25	27.2
Pb	-0.08	-1.61	1.8	67.5	11.6	67.0	175	716	1450	4	31.81	40.2
Bi	-0.34	-1.35	-4.3	53.7	-2.6	57.0	155	703	1610	5	31.73	52.0

Alloying element	Ef	Eb	γI1	γus1	γI2	γus2	R[17]	Ei1[17]	Ei2[17]	Nve	Vhcp[18]	κhcp[18]
Alloying element	(eV)	(eV)	(mJ/m2)	(mJ/m2)	(mJ/m2)	(mJ/m2)	(pm)	(mJ/mol)	(mJ/mol)	Nve	(?3/atom)	(GPa)
Mg	0.00	0.00	16.1	86.9	37.6	89.6	160	738	1451	2	22.89	35.7
Li	-0.20	-0.26	18.1	95.6	47.6	97.5	152	520	7298	1	20.33	13.5
Be	1.24	-0.90	25.8	80.7	45.4	85.4	111	899	1757	2	7.92	121.1
Na	0.32	0.79	16.8	79.3	38.3	80.4	186	496	4562	1	37.18	7.6
Al	0.02	-1.93	13.1	86.0	21.3	86.3	143	578	1817	3	16.75	70.8
K	1.58	2.27	10.7	22.9	6.9	28.1	179	419	3051	1	74.02	3.5
Ca	0.10	-0.25	17.0	58.3	28.7	61.6	195	590	1145	2	41.93	17.7
Sc	-0.18	-2.96	17.0	91.7	34.6	94.5	210	631	1235	3	24.47	54.9
Ti	0.68	-3.21	2.3	108.7	22.4	106.9	147	658	1310	4	17.29	112.8
V	1.05	-3.11	18.0	117.2	50.2	120.5	134	650	1414	5	13.84	173.2
Cr	1.11	-5.42	19.7	115.6	48.4	118.8	128	653	1592	6	11.94	233.5
Mn	0.84	-1.61	12.1	110.2	37.5	111.5	127	717	1509	7	10.75	279.7
Fe	1.17	-2.46	-1.3	68.6	27.0	101.9	126	759	1561	8	10.18	288.3
Co	0.83	-2.98	23.4	113.8	63.5	119.0	125	758	1646	9	10.85	212.5
Ni	0.36	-3.41	24.7	100.4	63.2	106.8	124	737	1753	10	10.95	193.8
Cu	0.56	-1.75	21.1	86.6	50.5	90.9	128	745	1958	1	12.04	136.1
Zn	-0.07	0.38	17.6	79.5	32.7	82.1	134	906	1733	2	15.40	51.8
Ga	-0.20	-1.45	9.5	79.8	22.4	79.0	135	579	1979	3	19.18	45.9
Sr	0.72	0.66	16.7	32.9	15.6	30.1	215	549	1064	2	54.72	11.4
Y	-0.13	-2.75	15.6	69.9	26.4	74.7	180	616	1181	3	32.67	40.8
Zr	0.16	-4.73	-0.4	94.8	17.5	92.2	160	660	1267	4	23.44	95.3
Nb	0.86	-4.57	-6.0	113.0	19.9	110.5	146	664	1382	5	18.90	162.8
Mo	1.34	-3.37	4.8	132.0	42.7	132.9	139	685	1558	6	16.29	233.8
Tc	0.93	-4.57	16.9	145.3	63.0	147.9	136	702	1472	7	14.63	296.1
Ru	0.12	-6.19	22.7	147.4	72.6	151.3	134	711	1617	8	13.88	309.4
Rh	-0.90	-5.40	24.7	130.3	70.9	136.1	134	720	1744	9	14.26	251.1
Pd	-1.34	-3.50	23.1	111.9	64.0	120.0	137	805	1875	10	15.60	163.6
Ag	-0.43	-1.36	17.8	93.9	48.6	97.1	144	731	2073	1	18.01	91.1
Cd	-0.31	0.50	14.0	109.9	32.5	83.9	149	868	1631	2	23.00	35.8
In	-0.15	-1.11	7.4	75.0	16.9	74.8	167	558	1821	3	27.80	34.4
Sn	-0.51	-2.11	4.0	71.8	11.9	71.9	151	709	1412	4	27.79	47.6
La	0.28	-1.60	15.9	30.2	2.5	39.4	183	538	1067	3	37.26	26.1
Sm	-0.01	-2.93	16.1	62.2	18.9	61.5	180	543	1086	8	33.91	35.7
Hf	0.50	-4.43	0.0	98.1	16.0	96.0	159	680	1440	4	22.41	109.1
Ta	1.38	-5.41	-8.2	116.3	14.3	112.0	146	761		5	18.77	188.0
W	2.04	-4.72	1.4	136.5	36.5	136.8	139	770		6	16.62	274.3
Re	1.65	-4.63	15.5	154.9	57.9	156.7	137	760		7	14.99	366.8
Ir	-0.70	-6.71	26.9	134.4	71.4	141.2	136	880	880	9	14.68	339.0
Pt	-1.71	-5.62	24.6	103.6	65.8	110.6	139	870	1791	10	15.94	235.2
Au	-1.21	-2.64	17.5	84.6	46.0	89.6	144	890	1980	1	18.22	135.0
Hg	-0.55	0.82	9.6	73.2	23.7	76.6	151	1007	1810	2	30.75	9.5
Tl	0.05	-0.57	2.7	68.7	14.8	67.7	170	589	1971	3	31.25	27.2
Pb	-0.08	-1.61	1.8	67.5	11.6	67.0	175	716	1450	4	31.81	40.2
Bi	-0.34	-1.35	-4.3	53.7	-2.6	57.0	155	703	1610	5	31.73	52.0

	data source	γI1(γI1')	γus1	γI2	γus2
Mg	This work	16.1	86.9	37.6	89.6
	Previous DFT work	18 [7]; 18 [19]; 17.1 [20]; 20 ± 1 [5]; 16 [21]; 17.98 [22]; 17.8 [23]	90 [7]; 86.2 [20]	33 [7]; 36 [19]; 36 [24]; 33.8 [20]; 30 [25]; 35 [26]; 30 [21]; 33.84 [22]; 38.3 [23]	92 [7]; 92[24] 87.6 [20]; 84.8 [25]; 86 [26]

	data source	γI1(γI1')	γus1	γI2	γus2
Mg	This work	16.1	86.9	37.6	89.6
	Previous DFT work	18 [7]; 18 [19]; 17.1 [20]; 20 ± 1 [5]; 16 [21]; 17.98 [22]; 17.8 [23]	90 [7]; 86.2 [20]	33 [7]; 36 [19]; 36 [24]; 33.8 [20]; 30 [25]; 35 [26]; 30 [21]; 33.84 [22]; 38.3 [23]	92 [7]; 92[24] 87.6 [20]; 84.8 [25]; 86 [26]

	γus2	κ_hcp	V_hcp	E_b	R	Ei1	E_f
γus2	1	0.87	-0.77	-0.76	-0.65	0.41	0.16
κ_hcp	0.87	1	-0.65	-0.77	-0.65	0.39	0.28
V_hcp	-0.77	-0.65	1	0.58	0.80	-0.57	0.01
E_b	-0.76	-0.77	0.58	1	0.40	-0.24	-0.03
R	-0.65	-0.65	0.80	0.40	1	-0.58	-0.12
Ei1	0.41	0.39	-0.57	-0.24	-0.58	1	-0.24
E_f	0.16	0.28	0.01	-0.03	-0.12	-0.24	1