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Dissolving, trapping and detrapping mechanisms of hydrogen in bcc and fcc transition metals
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Figures

Image of FIG. 1.

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FIG. 1.

The three positions of H in bcc transition metals. The blue spheres show the positions of the bcc lattice sites, and grey spheres are the positions of H at TIS (a), OIS (b) and NOS (c). The cube at the body center in (c) expresses a vacancy.

Image of FIG. 2.

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FIG. 2.

The energies landscape of H located at TIS, OIS and NOS in bcc metals, and H located at TIS, OIS and NOS (or NTS) in fcc metals. ZPE corrections are considered here, and the dotted line segment indicates the energy difference of H at most stable interstitial site and the most stable site in a vacancy in all the twelve metals. The down-arrow suggests that H is more energetically favorable to stay in vacancy.

Image of FIG. 3.

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FIG. 3.

The energy differences of H at OIS with TIS and TIS with NOS in bcc metals, OIS with TIS, OIS with Vac in fcc metals (Vac represents NOS for Ni, Pd, Cu and Ag, while NTS for Pt and Au). The results with and without ZPE corrections are compared. The up-arrow indicates the energy is increased by ZPE, while down-arrow expresses the energy is decreased by ZPE.

Image of FIG. 4.

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FIG. 4.

The four positions for H in fcc transition metals. The blue spheres show the positions of the fcc lattice sites, and grey spheres are the positions of H at TIS (a), OIS (b), NOS (c) and NTS in vacancy (d). The cube expresses the monovacancy in (c) and (d).

Image of FIG. 5.

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FIG. 5.

The expansion ratio η of the primitive cell containing a Vac-H n complex as a function of n in six bcc metals (a), and six fcc metals (b). The zero point indicates that the primitive cell experiences no expansion or attraction. The cubes at the center of the bcc and fcc structures express Vac-H n complexes in (a) and (b).

Image of FIG. 6.

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FIG. 6.

The formation energy (E f (V + H n )), chemical energy (E c (V + H n )) and distortion energy (E d (V + H n )) of Vac-H n complex as a function of n in all the six bcc metals considered. Cubic function fittings are performed for the formation energy of Vac-H n complex in Cr, Mo and W, and linear function fittings are performed for the formation energy of Vac-H n complex in V, Nb and Ta.

Image of FIG. 7.

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FIG. 7.

Two sorts of atomic configurations for H atoms trapped one by one in a single vacancy in fcc metals considered. The configuration of H atoms at all six NOS for Ni, Pd, Cu and Ag (a), and the configuration of H atoms at all eight NTS for Pt and Au (b). The cube expresses a monovacancy in both (a) and (b).

Image of FIG. 8.

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FIG. 8.

The formation energy (E f (V + H n )), chemical energy (E c (V + H n )) and distortion energy (E d (V + H n )) of Vac-H n complex as a function of n in all the six fcc metals considered. Linear function fittings are performed for the formation energy of Vac-H n complex in all the six fcc metals.

Image of FIG. 9.

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FIG. 9.

The detrapping temperatures of H in Vac-H n complex in all the bcc metals as well as Ni, Pd, Cu, and Ag as a function of the number of H atom n at a heating rate of 10 K/min. The lines indicate room temperature (RT).

Image of FIG. 10.

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FIG. 10.

The detrapping temperatures of H in Vac-H n complex in W as a function of the number of H atom n. The heating rates of 1 K/min, 5 K/min, 40 K/min, 320 K/min, 450 K/min and 600 K/min are considered to examine the influence of heating rate on the detrapping temperature of H located in a vacancy. The lines indicate room temperature.

Tables

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Table I.

Lattice constant a 0 (Å), bulk modulus B 0 (Mbar), and vacancy formation energy E Vac (eV) of the metals obtained in the present work together with the results of other calculations and experiments.

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Table II.

Trapping energies (eV) of H atoms introduced one by one in a single vacancy in all the bcc transition metals with and without ZPE corrections. ZPE corrections do not change the maximum number of H atoms accommodated in a vacancy in these metals.

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Table III.

Trapping energies (in eV) of H atoms introduced one by one to a single vacancy in all the fcc transition metals with and without considering ZPE corrections. One can see that ZPE corrections do not change the maximum number of H atoms accommodated in a vacancy in these metals.

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Table IV.

The lowest-energy barriers E d of H diffusion from one TIS to the nearest TIS in bcc metals V, Nb, Ta, Cr, Mo and W, as well as from OIS to the nearest TIS in fcc metals Ni, Pd, Cu and Ag. The rigid lattice approximation is used to calculate the diffusion barriers of H in bcc metals. The normal modes of H at ground state (TIS in V, Nb, Ta, Cr, Mo and W, OIS Ni, Pd, Cu and Ag) ν, saddle point ν* are presented. The imaginary frequency on the saddle point ν corresponds to vibration in the direction of the reaction coordinate. The values of Δ ZPE are also presented.

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/content/aip/journal/adva/3/1/10.1063/1.4789547
2013-01-18
2014-04-23

Abstract

First-principles calculations are performed to investigate the dissolving, trapping and detrapping of H in six bcc (V, Nb, Ta, Cr, Mo, W) and six fcc (Ni, Pd, Pt, Cu, Ag, Au) metals. We find that the zero-point vibrations do not change the site-preference order of H at interstitial sites in these metals except Pt. One vacancy could trap a maximum of 4 H atoms in Au and Pt, 6 H atoms in V, Nb, Ta, Cr, Ni, Pd, Cu and Ag, and 12 H atoms in Mo and W. The zero-point vibrations never change the maximum number of H atoms trapped in a single vacancy in these metals. By calculating the formation energy of vacancy-H (Vac-H n ) complex, the superabundant vacancy in V, Nb, Ta, Pd and Ni is demonstrated to be much more easily formed than in the other metals, which has been found in many metals including Pd, Ni and Nb experimentally. Besides, we find that it is most energetically favorable to form Vac-H1 complex in Pt, Cu, Ag and Au, Vac-H4 in Cr, Mo and W, and Vac-H6 in V, Nb, Ta, Pd and Ni. At last, we examine the detrapping behaviors of H atoms in a single vacancy and find that with the heating rate of 10 K/min a vacancy could accommodate 4, 5 and 6 H atoms in Cr, Mo and W at room temperature, respectively. The detrapping temperatures of all H atoms in a single vacancy in V, Nb, Ta, Ni, Pd, Cu and Ag are below room temperature.

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Scitation: Dissolving, trapping and detrapping mechanisms of hydrogen in bcc and fcc transition metals
http://aip.metastore.ingenta.com/content/aip/journal/adva/3/1/10.1063/1.4789547
10.1063/1.4789547
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