Prediction on Phase Stabilities of the Zr-H System from the First-Principles

doi:10.1007/s40195-020-01113-0

Abstract

Abstract:

Basic fundamentals governing the hydrogenation of Zr and its alloys have both theoretical and practical importance. In this work, first-principles calculations have been performed to evaluate the relative stabilities of various possible phases in ZrH_x (x=1-2) under different temperatures and pressures. It was predicted that fct-γ and ε phases with various different H-atom configurations can be energetically favorable for ZrH_x (x=1, 1.25 and 1.5), while ZrH_1.75 and ZrH₂ prefer fct-ε phase only. Fcc-δ phase is less favored in energy at any H concentrations, but can be mechanically stable in some cases. The thermodynamically stable and metastable phase stability diagrams were then constructed for a wide temperature and H concentration range, to predict the environment-dependent formation of ZrH_x during hydrogenation.

Key words: Zr-H, Hydrogenation, Hydride, Phase stability, First-principles

Miao Chen, Wu Qin, Yixuan Hu, Yiren Wang, Yong Jiang, Xiaosong Zhou, Shuming Peng, Yibei Fu. Prediction on Phase Stabilities of the Zr-H System from the First-Principles[J]. Acta Metallurgica Sinica (English Letters), 2021, 34(4): 514-522.

Figures/Tables 6

References 50

[1]	P.W. Bickel, T.G. Berlincourt, Phys. Rev. B 2 4807 (1970)
[2]	K.B. Colas, A.T. Motta, J.D. Almer, M.R. Daymond, M. Kerr, A.D. Banchik, P. Vizcaino, J.R. Santisteban, Acta Mater. 58 6575 (2010) DOI URL PMID
[3]	Singh, P. Kuppusami, R. Thirumurugesan, R. Ramaseshan, M. Kamruddin, S. Dash, V. Ganesan, E. Mohandas, Appl. Surf. Sci. 257 9909 (2011)
[4]	H.O. Pierson, ed. 4 - carbides of group IV: Titanium, zirconium, and hafnium carbides. in Handbook of Refractory Carbides and Nitrides ( William Andrew Publishing, Westwood, NJ, 1996), pp. 55-80
[5]	G.J. Cheng, G. Huang, M. Chen, X.S. Zhou, J.H. Liu, S.M. Peng, W. Ding, H.F. Wang, L.Q. Shi, J. Nucl. Mater. 499 490 (2018)
[6]	C.E. Ells, J. Nucl. Mater. 28 129 (1968)
[7]	M.P. Cassidy, C.M. Wayman, Metall. Trans. A 11 57 (1980)
[8]	R.C. Bowman, B.D. Craft, J. Phys. C: Solid State Phys. 17 L477 (1984) DOI URL
[9]	R.C. Bowman, E.L. Venturini, B.D. Craft, A. Attalla, D.B. Sullenger, Phys. Rev. B 27 1474 (1983)
[10]	K. Niedźwiedź, B. Nowak, O.J. Żogał, J. Alloys Compd. 194 47 (1993)
[11]	R.C. Bowman Jr., B.D. Craft, J.S. Cantrell, E.L. Venturini, Phys. Rev. B 31 5604 (1985)
[12]	Żogal, A.H. Vuorimäki, E.E. Ylinen, K. Niedźwiedź, Z. Phys. B: Condens. Matter 96 293 (1995)
[13]	E. Zuzek, J.P. Abriata, A. San-Martin, F.D. Manchester, Bull. Alloy Phase Diagr 11 385 (1990) DOI URL
[14]	Aladjem , Solid State Phenom. 49-50 281 (1996)
[15]	J.S. Cantrell, R.C. Bowman Jr., D.B. Sullenger, J. Phys. Chem. 88 918 (1984)
[16]	J.H. Weaver, D.J. Peterman, D.T. Peterson, A. Franciosi, Phys. Rev. B 23 1692 (1981)
[17]	B.W. Veal, D.J. Lam, D.G. Westlake, Phys. Rev. B 19 2856 (1979)
[18]	K.G. Barraclough, C.J. Beevers, J. Nucl. Mater. 34 125 (1970)
[19]	D.O. Northwood, U. Kosasih, Int. Mater. Rev. 28 92 (1983)
[20]	A.M. Solodinin, E.B. Boyko, R.A. Andriyevskiy, Izv. Akad. Nauk SSSR, Met. 1, 198 (1978) in Russian; TR: Russ. Metall. 1, 178(1978)
[21]	B. Siegel, G.G. Libowitz, Metal Hydrides, Chap. 12, 545(1968)
[22]	S. Mishra, K.S. Sivaramakrihnan, M.K. Asundi, J. Nucl. Mater. 45 235 (1972)
[23]	K.G. Barraclough, C.J. Beevers, J. Less Common Met. 5 177 (1974)
[24]	R.W. Cahn, Adv. Mater. 3 628 (1991)
[25]	F. Ducastelle, R. Caudron, P. Costa, J. Phys. 31, 57 (1970)
[26]	M. Gupta, J.P. Burger, Phys. Rev. B 24 7099 (1981)
[27]	A.C. Switendick, J. Less Common Met. 101 191 (1984) DOI URL
[28]	D.A. Papaconstantopoulos, A.C. Switendick, J. Less Common Met. 103 317 (1984)
[29]	G.J. Ackland, Phys. Rev. Lett. 80 2233 (1998)
[30]	M. Gupta, Phys. Rev. Lett. 81 3300 (1998) URL PMID
[31]	M. Gupta, Phys. Rev. B 25 1027 (1982)
[32]	R. Quijano, R. de Coss, D.J. Singh, Phys. Rev. B 80 184103 (2009)
[33]	F. Wang, H.R. Gong, Int. J. Hydrog. Energy 37 9688 (2012)
[34]	C. Domain, R. Besson, A. Legris, Acta Mater. 50 3513 (2002)
[35]	H.L. Yakel, Acta Crystall. 11 46 (1958) DOI URL
[36]	W. Wolf, P. Herzig, J. Phys.: Condens. Matter 12 4535 (2000)
[37]	J. Furthmuller, J. Hafner, G. Kresse, Phys. Rev. B 50 15606 (1994)
[38]	W. Dong, G. Kresse, J. Furthmuller, J. Hafner, Phys. Rev. B 54 2157 (1996)
[39]	G. Kresse, D. Joubert, Phys. Rev. B 59 1758 (1999)
[40]	J. Leese, A.E. Lord, J. Appl. Phys. 39 3986 (1968)
[41]	R. Khodabakhsh, D.K. Ross, J. Phys. F: Met. Phys. 12 15 (1982)
[42]	G.C. Weatherly, Acta Metall. 29 501 (1981)
[43]	J.S. Cantrell, R.C.J. Bowman, D.B. Sullenger, Chem. Inform. 15 918 (1984)
[44]	R. Quijano, R. Decoss, D.J. Singh, Phys. Rev. B 80 2665 (2009)
[45]	P. Zhang, B.T. Wang, C.H. He, P. Zhang, Comput. Mater. Sci. 50 3297 (2011)
[46]	J. F. Nye, Oxford University Press(1958)
[47]	F. Mouhat, F.X. Coudert, Phys. Rev. B 90 224104 (2014)
[48]	P.J. Dobson, Phys. Bull. 36 506 (1985)
[49]	Y. Jiang, J.B. Adams, M. van Schilfgaarde, J. Chem. Phys. 123 64701 (2005) DOI URL PMID
[50]	F.D. Rossini, JANAF thermochemical tables: Stull, D. R. and Prophet, M. U.S. Government Printing Office: Washington. Second edition, 1971. J. Chem. Thermodyn. 4, 509(1972)

Hydride composition	H atom configuration	ΔE^f (eV/avg atom)	a (Å)	b (Å)	c (Å)	c/a	Predicted phase
ZrH	adeh	- 0.417	4.589	4.589	5.026	1.095	γ
	cdef	- 0.416	4.588	4.588	5.025	1.097	γ
	aefh	- 0.377	4.874	4.467	4.879	1.001	-
	cdfh	- 0.376	4.880	4.880	4.463	0.915	ε
	abfg	- 0.373	4.627	4.801	4.805	1.039	-
	defg	- 0.373	4.820	4.820	4.594	0.953	ε
	efgh	- 0.337	4.616	4.616	4.999	1.083	γ
	cdgh	- 0.337	5.000	4.582	4.648	0.930	-
	bceh	- 0.335	5.176	5.176	3.921	0.758	ε
	abce	- 0.323	5.039	5.039	4.162	0.826	ε
	Expt. [14]	-	4.60	4.60	4.97	1.080	γ
	Expt. [42]	-	4.596	4.596	4.969	1.081	γ
	GGA. [33]	-	4.61	4.61	5.04	1.093	γ
	GGA. [34]	-	4.58	4.58	5.04	1.100	γ
ZrH_1.25	bcdfg	- 0.452	4.624	4.624	5.036	1.089	γ
	bdefg	- 0.451	4.635	4.635	5.014	1.082	γ
	defgh	- 0.420	4.699	4.699	4.919	1.047	γ
	bdefh	- 0.420	4.644	4.913	4.760	1.025	-
	adefg	- 0.413	4.739	4.739	4.861	1.026	γ
	GGA [33]	-	4.79	4.79	5.20	1.086	γ
ZrH_1.5	acdefh	- 0.494	5.024	5.024	4.290	0.854	ε
	abcdef	- 0.487	4.778	4.806	4.786	1.002	-
	bcdfgh	- 0.486	4.778	4.778	4.815	1.008	γ
	abcefh	- 0.483	4.893	4.667	4.815	0.984	-
	bcefgh	- 0.483	4.744	4.744	4.888	1.030	γ
	Expt. [9]	-	4.65	4.65	4.96	1.067	γ
	GGA [33]	-	4.62	4.62	4.83	1.046	γ
	GGA [33]	-	5.03	5.03	4.28	0.851	ε
	GGA [34]	-	4.61	4.61	5.14	1.115	γ
ZrH_1.75	abcdefg	- 0.525	4.936	4.936	4.545	0.921	ε
	Expt. [43]	-	4.91	4.91	4.52	0.921	ε
	GGA [33]	-	4.97	4.97	4.47	0.899	ε
ZrH₂	abcdefgh	- 0.556	5.006	5.006	4.439	0.887	ε
	Expt. [43]	-	4.980	4.980	4.430	0.890	ε
	Expt. [11]	-	4.983	4.983	4.449	0.893	ε
	GGA [29]	-	5.000	5.000	4.450	0.890	ε
	GGA [44]	-	5.020	5.020	4.430	0.882	ε

Hydride composition	H atom configuration	ΔE^f (eV/avg atom)	a (Å)	b (Å)	c (Å)	c/a	Predicted phase
ZrH	adeh	- 0.417	4.589	4.589	5.026	1.095	γ
	cdef	- 0.416	4.588	4.588	5.025	1.097	γ
	aefh	- 0.377	4.874	4.467	4.879	1.001	-
	cdfh	- 0.376	4.880	4.880	4.463	0.915	ε
	abfg	- 0.373	4.627	4.801	4.805	1.039	-
	defg	- 0.373	4.820	4.820	4.594	0.953	ε
	efgh	- 0.337	4.616	4.616	4.999	1.083	γ
	cdgh	- 0.337	5.000	4.582	4.648	0.930	-
	bceh	- 0.335	5.176	5.176	3.921	0.758	ε
	abce	- 0.323	5.039	5.039	4.162	0.826	ε
	Expt. [14]	-	4.60	4.60	4.97	1.080	γ
	Expt. [42]	-	4.596	4.596	4.969	1.081	γ
	GGA. [33]	-	4.61	4.61	5.04	1.093	γ
	GGA. [34]	-	4.58	4.58	5.04	1.100	γ
ZrH_1.25	bcdfg	- 0.452	4.624	4.624	5.036	1.089	γ
	bdefg	- 0.451	4.635	4.635	5.014	1.082	γ
	defgh	- 0.420	4.699	4.699	4.919	1.047	γ
	bdefh	- 0.420	4.644	4.913	4.760	1.025	-
	adefg	- 0.413	4.739	4.739	4.861	1.026	γ
	GGA [33]	-	4.79	4.79	5.20	1.086	γ
ZrH_1.5	acdefh	- 0.494	5.024	5.024	4.290	0.854	ε
	abcdef	- 0.487	4.778	4.806	4.786	1.002	-
	bcdfgh	- 0.486	4.778	4.778	4.815	1.008	γ
	abcefh	- 0.483	4.893	4.667	4.815	0.984	-
	bcefgh	- 0.483	4.744	4.744	4.888	1.030	γ
	Expt. [9]	-	4.65	4.65	4.96	1.067	γ
	GGA [33]	-	4.62	4.62	4.83	1.046	γ
	GGA [33]	-	5.03	5.03	4.28	0.851	ε
	GGA [34]	-	4.61	4.61	5.14	1.115	γ
ZrH_1.75	abcdefg	- 0.525	4.936	4.936	4.545	0.921	ε
	Expt. [43]	-	4.91	4.91	4.52	0.921	ε
	GGA [33]	-	4.97	4.97	4.47	0.899	ε
ZrH₂	abcdefgh	- 0.556	5.006	5.006	4.439	0.887	ε
	Expt. [43]	-	4.980	4.980	4.430	0.890	ε
	Expt. [11]	-	4.983	4.983	4.449	0.893	ε
	GGA [29]	-	5.000	5.000	4.450	0.890	ε
	GGA [44]	-	5.020	5.020	4.430	0.882	ε

Hydride composition	H-atom configuration	Phase	C_ij (GPa)
Hydride composition	H-atom configuration	Phase	C₁₁	C₁₂	C₄₄	C₁₃	C₃₃	C₆₆
ZrH	adeh (γ)	γ	117.81	120.22	45.58	95.14	176.23	55.04
		ε	132.41	107.72	63.82	115.24	83.15	35.24
		δ	113.73	109.53	54.80
	cdef (γ)	γ	118.06	95.87	45.75	120.66	118.06	55.23
	cdef (γ)	δ	113.71	113.51	54.85
	cdfh (ε)	ε	143.94	105.30	69.91	106.16	106.16	55.25
	cdfh (ε)	δ	114.60	106.37	57.07
	bceh (ε)	ε	184.29	100.00	63.07	96.37	103.40	29.92
		γ	99.72	120.35	67.51	111.83	144.27	81.64
		δ	113.32	116.19	78.56
	defg (ε)	ε	136.62	101.07	70.05	109.56	109.60	55.07
	defg (ε)	δ	122.45	103.79	67.52
ZrH_1.25	bcdfg (γ)	γ	116.90	122.68	55.74	109.89	165.97	55.74
		ε	133.03	109.88	62.76	120.12	100.20	48.20
		δ	114.48	114.96	52.93
	bdefg (γ)	γ^*	166.52	108.89	53.70	108.89	117.05	55.65
	bdefg (γ)	δ	127.48	117.88	57.92
	defgh (γ)	γ	130.32	117.98	76.22	104.60	104.60	80.56
		ε*	164.63	100.89	78.98	111.51	92.69	46.78
		δ	133.07	102.82	79.07
	adefg (γ)	γ	119.01	120.80	66.64	114.86	136.41	73.00
		ε^*	156.77	106.17	71.30	116.95	92.20	92.20
		δ	124.55	117.07	69.20
ZrH_1.5	acdefh (ε)	ε	162.59	131.70	55.47	104.24	114.96	38.66
		γ	112.32	132.00	40.43	114.36	166.18	52.07
		δ	106.80	130.43	34.99
	bcefgh (γ)	γ	127.01	123.83	58.42	118.89	154.73	60.66
	bcefgh (γ)	δ	119.11	117.76	55.98
	bcdfgh (γ)	γ	137.47	117.48	68.44	116.23	152.49	72.71
	bcdfgh (γ)	δ	117.57	121.60	55.76
ZrH_1.75	abcdefg (ε)	ε	149.50	128.09	46.20	125.02	125.02	40.05
		γ	125.13	132.54	45.09	125.49	154.20	47.48
		δ	122.95	131.63	32.70
ZrH₂	abcdefgh (ε)	ε	163.88	146.06	34.85	112.60	142.05	52.41
		γ	132.00	141.73	36.92	119.00	185.79	34.97
		δ	113.85	141.78	12.85
	GGA [45] (ε)	ε	165.6	140.9	30.5	106.8	145.5	60.6
		γ	125.7	145.5	30.9	115.0	190.6	42.0
		δ	82.6	159.7	- 19.5

Hydride composition	H-atom configuration	Phase	C_ij (GPa)
Hydride composition	H-atom configuration	Phase	C₁₁	C₁₂	C₄₄	C₁₃	C₃₃	C₆₆
ZrH	adeh (γ)	γ	117.81	120.22	45.58	95.14	176.23	55.04
		ε	132.41	107.72	63.82	115.24	83.15	35.24
		δ	113.73	109.53	54.80
	cdef (γ)	γ	118.06	95.87	45.75	120.66	118.06	55.23
	cdef (γ)	δ	113.71	113.51	54.85
	cdfh (ε)	ε	143.94	105.30	69.91	106.16	106.16	55.25
	cdfh (ε)	δ	114.60	106.37	57.07
	bceh (ε)	ε	184.29	100.00	63.07	96.37	103.40	29.92
		γ	99.72	120.35	67.51	111.83	144.27	81.64
		δ	113.32	116.19	78.56
	defg (ε)	ε	136.62	101.07	70.05	109.56	109.60	55.07
	defg (ε)	δ	122.45	103.79	67.52
ZrH_1.25	bcdfg (γ)	γ	116.90	122.68	55.74	109.89	165.97	55.74
		ε	133.03	109.88	62.76	120.12	100.20	48.20
		δ	114.48	114.96	52.93
	bdefg (γ)	γ^*	166.52	108.89	53.70	108.89	117.05	55.65
	bdefg (γ)	δ	127.48	117.88	57.92
	defgh (γ)	γ	130.32	117.98	76.22	104.60	104.60	80.56
		ε*	164.63	100.89	78.98	111.51	92.69	46.78
		δ	133.07	102.82	79.07
	adefg (γ)	γ	119.01	120.80	66.64	114.86	136.41	73.00
		ε^*	156.77	106.17	71.30	116.95	92.20	92.20
		δ	124.55	117.07	69.20
ZrH_1.5	acdefh (ε)	ε	162.59	131.70	55.47	104.24	114.96	38.66
		γ	112.32	132.00	40.43	114.36	166.18	52.07
		δ	106.80	130.43	34.99
	bcefgh (γ)	γ	127.01	123.83	58.42	118.89	154.73	60.66
	bcefgh (γ)	δ	119.11	117.76	55.98
	bcdfgh (γ)	γ	137.47	117.48	68.44	116.23	152.49	72.71
	bcdfgh (γ)	δ	117.57	121.60	55.76
ZrH_1.75	abcdefg (ε)	ε	149.50	128.09	46.20	125.02	125.02	40.05
		γ	125.13	132.54	45.09	125.49	154.20	47.48
		δ	122.95	131.63	32.70
ZrH₂	abcdefgh (ε)	ε	163.88	146.06	34.85	112.60	142.05	52.41
		γ	132.00	141.73	36.92	119.00	185.79	34.97
		δ	113.85	141.78	12.85
	GGA [45] (ε)	ε	165.6	140.9	30.5	106.8	145.5	60.6
		γ	125.7	145.5	30.9	115.0	190.6	42.0
		δ	82.6	159.7	- 19.5