Investigation of interaction between α-Fe metal and H atom by ab-initio method

Ying-Jin Cheng; Chao-Fei Yang; Gang Xue; Tao Wang; Lei Zhang; Mei-E Li

doi:10.7498/aps.69.20191775

Journals >Acta Physica Sinica >Volume 69 >Issue 5 >Page 053101-1 > Article

Acta Physica Sinica
Vol. 69, Issue 5, 053101-1 (2020)

Investigation of interaction between α-Fe metal and H atom by ab-initio method

Ying-Jin Cheng^1、*, Chao-Fei Yang¹, Gang Xue¹, Tao Wang¹, Lei Zhang², and Mei-E Li²

Author Affiliations

¹Luoyang Ship Material Research Institute, Luoyang 471023, China

²State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China

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DOI: 10.7498/aps.69.20191775 Cite this Article

Ying-Jin Cheng, Chao-Fei Yang, Gang Xue, Tao Wang, Lei Zhang, Mei-E Li. Investigation of interaction between α-Fe metal and H atom by ab-initio method [J]. Acta Physica Sinica, 2020, 69(5): 053101-1 Copy Citation Text

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Fig. 1. Crystalline structure of α-Fe+H: (a) T-site; (b) O-site.

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Partial electronic density of state of α-Fe+H (T-site): (a) Free H atom and interstitial H atom; (b) Fe atom in perfect α-Fe crystal and the nearest neighbour of interstitial H atom; (c) H atom in tetrahedral interstice; (d) the nearest neighbour Fe atom of interstitial H atom.

Fig. 2. Partial electronic density of state of α-Fe+H (T-site): (a) Free H atom and interstitial H atom; (b) Fe atom in perfect α-Fe crystal and the nearest neighbour of interstitial H atom; (c) H atom in tetrahedral interstice; (d) the nearest neighbour Fe atom of interstitial H atom.

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Fig. 3. Electron density difference of α-Fe+H(T-site).

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Fig. 4. Crystalline structure of α-Fe+(nH-Vac): (a) α-Fe+Vac; (b)α-Fe+(3H-Vac); (c) α-Fe+(4H-Vac); (d) α-Fe+(5H-Vac); (e) α-Fe+(1H-Vac); (f) α-Fe+(2H-Vac); (g) α-Fe+(6H-Vac).

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Fig. 5. Isoelectronic density surface and electron density difference of α-Fe+(nH-Vac): (a) Electron density difference of α-Fe+Vac in surface (100); (b) electron density difference of α-Fe+Vac in surface (110); (c) isoelectric density surface of α-Fe+Vac; (d) electron density difference of α-Fe+(2H-Vac) in surface (010); (e) isoelectric density surface of α-Fe+(2H-Vac).

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Fig. 6. Crystalline structure of α-Fe+Vac+H(T-site).

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Fig. 7. Formation energy of defects at 0 K for different H chemical potentials.

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Fig. 8. Equilibrium concentration of defects for different temperature and H chemical potentials: (a) Equilibrium concentration of vacancies; (b) equilibrium concentration of H occupying in vacancies; (c) equilibrium concentration of H occupying in interstitial positions.

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Fig. 9. Equilibrium total concentration of H of α-Fe containing vacancies.

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Fig. 10. Schematic diagram of Devnathan-Stachurski double electrolytic cell.

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晶体类型	a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	V/Å	空间群
α-Fe+H(T-site)	5.6843	5.6612	5.6804	89.999	89.999	90.000	5.6843	115(P-4m2)
α-Fe+H(O-site)	5.8019	5.6112	5.6112	90.000	90.000	90.000	5.8019	123(P4/mmm)

Table 1. [in Chinese]

晶体类型	${E_{{\rm{crystal}}}}$/eV	${E_{{\rm{ZP}}}}$/eV	${E_{{\rm{bind}}}}$/eV	$E_{{\rm{form}}}$/eV	$\Delta H_{{ {\rm{sol} } } }^{\rm{H} }$/eV
α-Fe+H(T-site)	–13861.050	0.246	5.182	0.390	0.390
α-Fe	–13845.344	—	5.530	—

Table 2. [in Chinese]

晶体类型	原子	轨道电荷占据数			总布居	净布居
晶体类型	原子	s	p	d	总布居	净布居
α-Fe-H(T-site)	H	1.34	0	0	1.34	–0.34
	Fe2, Fe4	0.62	0.66	6.65	7.93	0.07
	Fe3, Fe11	0.62	0.67	6.65	7.94	0.06
	Fe12, Fe10	0.65	0.72	6.62	7.99	0.01
	Fe1, Fe9, Fe13, Fe14, Fe16	0.65	0.72	6.62	7.99	0.01
	Fe8, Fe6	0.65	0.74	6.61	8.01	–0.01
α-Fe	Fe	0.68	0.70	6.62	8.00	0
自由态	H	1.00	0	0	1.00	0

Table 3. [in Chinese]

晶体类型	原子对	距离/Å	键布居
α-Fe-H (T-site)	Fe2-H	1.6494	0.16
	Fe3-H	1.6507	0.16
	Fe2-Fe3	2.5558	–0.09
	Fe2-Fe4	2.7286	–0.14
	Fe8-Fe11	2.4783	0.17
	Fe3-Fe12	2.4471	0.18
	Fe8-Fe16	2.8401	0.05
	Fe7-Fe8	2.4601	0.15
α-Fe-H (O-site)	Fe2-Fe4	2.6287	–0.28
α-Fe	Fe-Fe	2.4400	0.14
α-Fe	Fe-Fe	2.8174	0.06

Table 4. [in Chinese]

晶体类型	a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	V/Å	空间群
α-Fe+Vac	5.6033	5.6033	5.6033	90.000	90.000	90.000	175.923	221 ${\rm{(}}Pm\overline {{\rm{3}}m} )$
α-Fe+(Vac-1H)	5.6321	5.6103	5.6103	90.000	90.001	89.999	177.270	99 ${\rm{(}}P{\rm{4}}MM)$
α-Fe+(Vac-2H)	5.6285	5.6285	5.6484	90.000	90.000	90.000	178.940	123(P4/MMM)
α-Fe+(Vac-3H)	5.6297	5.6598	5.6853	90.004	90.011	90.002	181.154	25(PMM2)
α-Fe+(Vac-4H)	5.6727	5.6943	5.6723	89.966	90.540	89.973	183.221	38(AMM2)
α-Fe+(Vac-5H)	5.6905	5.7086	5.7093	90.000	90.004	90.002	185.467	99 ${\rm{(}}P{\rm{4}}MM)$
α-Fe+(Vac-6H)	5.7407	5.7270	5.7208	89.433	89.691	89.692	188.064	5(C2)

Table 5.

Lattice parameters and crystalline structure of α-Fe+(nH-Vac).

α-Fe+(nH-Vac)的晶格常数和晶体结构

晶体类型	${E_{{\rm{crystal}}}}$/eV	${E_{{\rm{ZP}}}}$/eV	${E_{{\rm{bind}}}}$/eV	$E_{{\rm{form}}}$/eV	$\Delta H_{_{ {\rm{sol} } } }^{\rm{H} }$/eV
α–Fe+Vac	–12977.593	—	5.369	2.416	—
α–Fe+(Vac-1H)	–12993.933	0.141	5.055	1.928	–0.347
α–Fe+(Vac-2H)	–13010.262	0.295	4.777	1.450	–0.324
α–Fe+(Vac-3H)	–13026.330	0.478	4.513	1.234	–0.034
α–Fe+(Vac-4H)	–13042.359	0.670	4.275	1.056	0.014
α–Fe+(Vac-5H)	–13058.299	0.889	4.055	0.968	0.131
α–Fe+(Vac-6H)	–13073.995	1.149	3.842	1.123	0.438

Table 6.

Binding energy, formation energy, and heat of solution of α-Fe+(nH-Vac).

α-Fe+(nH-Vac)的结合能、形成能和溶解热

晶体类型	$E_{{\rm{trap}}}^{\rm{H}}$/eV
晶体类型	不考虑 ${E_{{\rm{ZP}}}}$	考虑 ${E_{{\rm{ZP}}}}$
α-Fe+(Vac-1H)	0.633	0.778
α-Fe+(Vac-2H)	0.623	0.627
α-Fe+(Vac-3H)	0.361	0.211
α-Fe+(Vac-4H)	0.322	–0.011
α-Fe+(Vac-5H)	0.227	–0.297
α-Fe+(Vac-6H)	–0.028	–0.772

Table 7.

Hydrogen trapping energy of α-Fe+(nH-Vac)

α-Fe+(nH-Vac)对H原子的陷阱能

晶体类型	原子	轨道电荷占据数			总布居	净布居
晶体类型	原子	s	p	d	总布居	净布居
α-Fe+Vac	Fe7, Fe11, Fe13	0.74	0.72	6.68	8.13	–0.13
	Fe3, Fe5, Fe9	0.68	0.73	6.63	8.04	–0.04
	其余Fe原子	0.66	0.67	6.60	7.93	0.07
α-Fe+(Vac-2H)	Fe13	0.71	0.71	6.73	8.15	–0.15
	Fe9	0.66	0.70	6.62	7.98	0.02
	Fe11	0.71	0.71	6.65	8.07	–0.07
α-Fe+Vac—α-Fe+(Vac-6H)	H1	1.20—1.22	0	0	1.20—1.22	–0.20— –0.22
自由态	H	1.00	0	0	1.00	0

Table 8.

Atomic orbital population of α-Fe+(nH-Vac).

α-Fe+(nH-Vac)晶体原子轨道布居

晶体类型	${E_{{\rm{crystal}}}}$/eV	${E_{{\rm{ZP}}}}$/eV	${E_{{\rm{bind}}}}$/eV	$E_{{\rm{form}}}$/eV	$\Delta H_{{ {\rm{sol} } } }^{\rm{H} }$/eV
α–Fe+Vac+H(T-site)	–12993.354 — –12993.353	0.248—0.250	5.012	2.755—2.756	0.339—0.340

Table 9.

Binding energy, formation energy, and heat of solution of α-Fe+Vac+H(T-site).

α-Fe+Vac+H(T-site)的结合能、形成能和溶解热

温度/K	μ_H/eV	c^H/%
温度/K	μ_H/eV	计算值	实验值
298.15	–0.239	2.08 × 10^–2	4.41 × 10^–22.88 × 10^–2, 其中晶格溶H占总扩散H含量的43%^[2]

Table 10.

Calculated and test value of equilibrium concentration of H atom.

H平衡溶解度计算值和实验值

Ying-Jin Cheng, Chao-Fei Yang, Gang Xue, Tao Wang, Lei Zhang, Mei-E Li. Investigation of interaction between α-Fe metal and H atom by ab-initio method [J]. Acta Physica Sinica, 2020, 69(5): 053101-1

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