- Email: [email protected]
The influence of stacking faults on hydrogen storage in TiCx
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 9 2 6 2 e9 2 6 6
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
The influence of stacking faults on hydrogen storage in TiCx Haimin Ding*, Xiaoliang Fan, Kaiyu Chu, Biqiang Du, Jinfeng Wang School of Energy Power and Mechanical Engineering, North China Electric Power University, Baoding 071003, PR China
article info
abstract
Article history:
The hydrogen storage ability of TiCx with stacking faults (SFs) is studied in this work. It is
Received 9 February 2014
found that the absorption of hydrogen atoms is possible in both TiCx with and without SFs.
Received in revised form
And, besides the carbon vacancy sites, the hydrogen atoms can also occupy the tetrahedral
1 April 2014
sites in the SFs layers. More importantly, it is confirmed that the diffusion of hydrogen in
Accepted 3 April 2014
TiCx with SFs is much easier than that in TiCx without SFs, especially the diffusion around
Available online 27 April 2014
the SFs layers. The energy barrier for diffusion of the hydrogen atom in the SFs layers and diffusion from the SF layer to the next layer is only 0.099 eV and 0.185 eV, respectively.
Keywords:
Therefore, bringing in the SFs in TiCx with ordered carbon vacancies will be an effective
Density functional theory (DFT)
method to solve the diffusion problem during the processes of hydrogen storage.
Diffusion
Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Fault
Introduction Hydrogen is considered to be an ideal energy carrier for both mobile and stationary applications [1]. For the time being, hydrogen storage is one of the key challenges in developing hydrogen economy, therefore, hydrogen storage materials have been widely studied. It has been reported that many materials can be used for storage of hydrogen, such as light metals [2e5], carbon materials [6e9], and transition metals [10e13]. Among transition metals, Ti is well known for absorbing large quantities of hydrogen, which leads to the formation of titanium dihydride, TiH2 [14,15]. However, the embrittlement of hydride limits its widely application. In recent years, it has been found that, the carbide of Ti, TiC, can also absorb hydrogen when it contains carbon vacancies and the capacity of more than 2.9 wt.% can be obtained [16,17]. Furthermore, its
absorption and desorption process is more stable than Ti due to the similar crystal structure between the reactant TiCx and the product TiCxHy. However, according to our previous theoretical study by first-principles calculations [18] and experimental results reported in Nguyen et al’s work [19], it has been found that the diffusion of hydrogen atoms in TiCx is difficult and, even in TiCx with ordered carbon vacancies, its diffusion coefficient is still much lower than that of other materials candidates for hydrogen storage, which makes the diffusion be the limiting step of hydrogen storage in TiCx. Therefore, taking effective methods to improve the diffusion processes of hydrogen in TiC crystal will be essential for the application of TiCx in hydrogen storage field. As mentioned above, the existence of carbon vacancies is key for hydrogen storage in TiCx. In our recent works, it has been found that the carbon vacancies can also induce the formation of stack faults (SFs) in TiCx [20]. It is known that the stacking fault energy (SFE) is generally high in TiCx [21], but
* Corresponding author. Tel.: þ86 312 7525041; fax: þ86 312 7525045. E-mail addresses: [email protected], [email protected] (H. Ding). http://dx.doi.org/10.1016/j.ijhydene.2014.04.038 0360-3199/Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 9 2 6 2 e9 2 6 6
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the SFE can be reduced with increasing the content of the carbon vacancies. When the content of carbon vacancies is high and the carbon vacancies are ordered, the formation of SFs in TiCx will even be thermally favorable. What is more important is that, when SFs are formed in TiCx, carbon vacancies prefer to combine with SFs and the diffusion barrier energy of carbon vacancies in SFs layers will be seriously decreased from 2.21 eV in TiCx without SFs to about 0.03 eV [20]. Considering that the diffusion of hydrogen is commonly easier than that of the carbon vacancies, it is thought that the diffusion of hydrogen atoms in TiCx with SFs may also become much easier. And if it is confirmed, the diffusion problem of hydrogen in TiCx can be solved by bringing in SFs. Therefore, in this work, first-principles calculations have been performed to study the hydrogen storage of TiCx with SFs and the diffusions of hydrogen atoms in and around SFs layer are specially analyzed.
Method of calculations The calculations are based on the density-functional theory and performed with CASTEP. It has been reported that the calculation of interaction between hydrogen and vacancy is sensitive to the choice of the approximation for the exchange and correlation functionals [22]. Although the generalized gradient approximation (GGA) is commonly considered to be better than local density approximation (LDA) in studying of many aspects, such as the bulk properties of materials [23], it has been found that the calculation results of LDA are in better agreement with experimental data in studying of the vacancy-hydrogen interaction in solids [22]. Therefore, The LDA was utilized for structure optimization and energy calculation in this work. The TiC (111) plane with a slab of 8.5-layers and 20 A of vacuum region in the z-direction was used. It is known that the (111) plane is polar and can therefore be either Ti- or Cterminated. But, according to the previous work [24], Cterminated (111) surface is not stable, so Ti-terminated (111) is only considered. The configurations of TiC(111) with ideal sequence and with a SF are shown in Fig. 1(a) and (b), respectively. The plane-wave cut off energy of 350 eV was employed, which assured a tolerances of energy and displacement A, respecconvergence of 5.0 106 eV/atom and 5.0 104 tively. The grids of K-points are sampled by 9 5 1. In addition, the diffusion of hydrogen atoms in TiCx was studied by the linear synchronous transit (LST) optimization method. The feasibility of hydrogen storage in TiCx and its relationship with carbon vacancies has been confirmed by previous works as mentioned above [16e19]. Therefore, in this work, we mainly study the hydrogen storage properties in TiCx with SFs and compare with that in TiCx without SFs. The formation energy of hydrogen storage is firstly calculated by the Equation (1): H
Ef ¼
E 2 EnH tot Etot n 2 n
(1)
where n is the number of hydrogen atoms, EnH tot is the total energy of the system with n hydrogen atoms, Etot is the total
Fig. 1 e Configurations used in this study. The blue and red balls represent Ti and C, respectively. (a) the ideal sequence; (b) the stacking sequence. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
energy of TiCx without hydrogen atoms, and EH2 is the total energy of the hydrogen molecule [25].
Results and discussions As mentioned above, the SFs can only be formed in TiCx with amount of carbon vacancies, especially in TiCx with ordered carbon vacancies, in which some {111} carbon planes will be empty. As reported by Bursik et al. and Barsoum et al. that, in TiCx with x ¼ 0.67, one third of {111}
Fig. 2 e The positions of carbon vacancies and hydrogen atom in TiCx (a, b) the positions of carbon vacancies in TiCx with and without SFs; (c, d) the possible sites for multiple hydrogen occupancy in TiCx with and without SFs.
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carbon planes is empty and the two other thirds are fully occupied, while in TiCx with x ¼ 0.5, {111} carbon planes will be alternately full and empty [26,27]. In addition, carbon vacancies also prefer to combine with SFs as reported in our previous work [20]. Therefore, during calculation the absorption of hydrogen in TiCx with SFs, the configuration with ordered carbon vacancies locating in the SF layer is used, as shown in Fig. 2(a) in which two carbon vacancies are resided in position 1 and 2. And the configuration of TiCx without SFs but with ordered carbon vacancies is used as comparison, as shown in Fig. 2(b). The formation energies of a single hydrogen atom residing in one carbon vacancy site and two hydrogen atoms locating in two carbon vacancy sites whose configurations are designated as 1H-v and 2H-v are firstly calculated by Equation (1) and the results are shown in Table 1. It can be seen that the formation energy of a single hydrogen atom absorbed in the carbon vacancy site in TiCx with SFs is about 1.08 eV/atom which is a little smaller than that in TiCx without SFs. When all the carbon vacancies are occupied by the hydrogen atoms, the formation energies are 1.13 eV/atom in TiCx with SFs and 1.19 eV/atom in that without SFs. Those results indicate that the absorbing of hydrogen atoms is possible in both TiCx with and without SFs. The hydrogen atoms locating in the carbon vacancies (the octahedral sites) are only considered in the above calculations, and this is reasonable when the concentration of hydrogen is low. However, when concentration of the absorbed hydrogen atoms is high, hydrogen can also occupy the tetrahedral sites. Therefore, in the following, the absorption of hydrogen atoms on both octahedral and tetrahedral sites is studied. The positions of them are shown in Fig. 2(c) and (d) and the configurations are designated as 4H-v-t. It can be seen that the formation energies is 0.85 eV/atom in TiCx with SFs and 0.79 eV/atom in that without SFs. This confirms that the multiple hydrogen occupancy of the carbon vacancy in the SF layer of TiCx is also possible. The above results further confirm that, no matter with or without SFs, the absorption of hydrogen in TiCx with carbon vacancies is thermally favorable. In the following sections, the diffusion of the absorbed hydrogen atoms will be mainly examined by the linear synchronous transit (LST) optimization method. In the LST optimization, a series of single point energy calculations are performed on a set of linearly interpolated structures between an initial and final state. The maximum energy structure along this path provides a first estimate of the transition state structure. Then, an energy minimization in directions conjugate to the reaction pathway is performed [28]. This yields a structure closer to the true transition state which can be used to determine the energy barrier of the diffusion process.
Two diffusion paths have been considered in the calculations. The first one is the diffusion of the hydrogen atom in the same layer, as Path I and III shows in Fig. 3(a) and (b). The second one is migrating the hydrogen atom from a neighboring layer to the next, as Path II and IV shows in Fig. 3. The calculated results are shown in Fig. 4. As Fig. 4(a) and (b) shows, in TiCx without SFs, the energy barrier for diffusion of the hydrogen atom in the same layer which contains ordered carbon vacancies (Path I in Fig. 3(a)) is 0.497 eV, while it is 0.891 eV if the hydrogen atom is migrated from a neighboring layer to the next (Path II in Fig. 3(a)). This further confirms that the diffusion of hydrogen atoms in TiCx with ideal sequence is difficult and the results are in good agreement with Nguyen et al’s work [19]. When TiC contains a SF and the hydrogen atoms are absorbed and diffused in the SF layer which also contains ordered carbon vacancies. It is interesting to notice that the energy barrier for diffusion of hydrogen from one vacancy site to another (Path III in Fig. 3(b)) is 0.039 eV as shown in Fig. 4(c). The negative value indicates that this diffusion process contains an intermediate state. Therefore, the actual diffusion processes for Path III should be two steps. The first one is diffusion from one vacancy site to the intermediate state and then to another vacancy site. The calculated diffusion energy profile for this process is shown in Fig. 4(d). It can be seen that the energy barrier for diffusion of hydrogen from one vacancy site to the intermediate state is 0.088 eV, while it is 0.099 eV for that from the intermediate state to another vacancy site. Both of them are much smaller than that in TiCx without SFs as shown in Fig. 4(a).
Table 1 e Formation energies of absorbing hydrogen atoms in different positions (eV/atom). Configurations
1H-v
2H-v
4H-v-t
In TiCx with SFs In TiCx without SFs
1.08 1.13
1.13 1.19
0.85 0.79
Fig. 3 e The diffusion paths of the hydrogen atom (a) diffusion paths in TiCx without SFs; (b) diffusion paths in TiCx with a SF.
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Fig. 4 e The calculated diffusion energy profile (a, b) diffusion energy profile for Path I and II; (c) diffusion energy profile for Path III; (d) diffusion energy profile for Path III with two steps; (e) diffusion energy profile for Path IV.
For the diffusion from the neighboring layer to the SF layer (Path IV in Fig. 3(b)), the energy barrier is 0.185 eV as shown in Fig. 4(e) and it is still much smaller than that shown in Fig. 4(b). All the results demonstrate that diffusion of hydrogen atoms in TiCx with SFs is easier, especially in the SF layers. Considering the existence of the carbon vacancies in TiC, especially ordered carbon vacancies, is the necessary condition for both hydrogen storage [16e19] and formation of SFs, while the carbon vacancies prefer to segregate around SFs [20] and diffusion of hydrogen atoms in and around SF layers are also much easier as this work shows, bringing in the SFs in TiCx with ordered carbon vacancies will be an effective
method to simultaneously solve both the hydrogen storage and diffusion problem.
Conclusion In summary, the hydrogen storage ability of TiCx with SFs is studied in this work. It is found that the absorption of hydrogen atoms is possible in both TiCx with and without SFs. And, besides the carbon vacancy sites, the hydrogen atoms can also occupy the tetrahedral sites in the SFs layers. More importantly, it is confirmed that the diffusion of hydrogen in
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TiCx with SFs is much easier than that in TiCx without SFs, especially the diffusion around the SFs layers. The energy barrier for diffusion of the hydrogen atom in the SFs layers and diffusion from the SF layer to the next layer is only 0.099 eV and 0.185 eV, respectively. Therefore, bringing in the SFs in TiCx with ordered carbon vacancies will be an effective method to solve the diffusion problem during the processes of hydrogen storage.
Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 51301068), the Natural Science Foundation of Hebei Province (No. E2014502003) and the Fundamental Research Funds for the Central Universities (No. 2014MS116 and 2014ZD37).
references
[1] Sakintuna B, Lamari-Darkrim F, Hirscher M. Metal hydride materials for solid hydrogen storage:a review. Int J Hydrogen Energy 2007;32:1121e40. [2] Zhu M, Wang H, Ouyang LZ, Zeng MQ. Composite structure and hydrogen storage properties in Mg-based alloys. Int J Hydrogen Energy 2006;31:251e7. [3] Bouaricha S, Dodelet JP, Guay D, Huot J, Boily S, Schulz R. Hydriding behavior of MgeAl and leached MgeAl compounds prepared by high energy ball-milling. J Alloys Compd 2000;297:282e93. [4] Moroz S, Tan XF, Pierce J, Greaves M, Duguid A, Dumur K, et al. Systems based on hypo-eutectic MgeMg2Ni alloys for medium to large scale hydrogen storage and delivery. J Alloys Compd 2013;580:S329e32. [5] Jain A, Miyaoka H, Ichikawa T, Kojima Y. Correlation between electrochemical behavior and hydrogen storage properties of LieSn system. J Alloys Compd 2013;580:S211e5. [6] Darkrim FL, Malbrunot P, Tartaglia GP. Review of hydrogen storage by adsorption in carbon nanotubes. Int J Hydrogen Energy 2002;27:193e202. [7] Cabria I, Lo´pez MJ, Alonso JA. Simulation of the hydrogen storage in nanoporous carbons with different pore shapes. Int J Hydrogen Energy 2011;36:10748e59. [8] Hirscher M, Becher M. Hydrogen storage in carbon nanotubes. J Nanosci Nanotech 2003;3(1e2):3e17. [9] Silambarasan D, Surya VJ, Vasu V, Iyakutti K. Investigation of single-walled carbon nanotubes titanium metal composite as a possible hydrogen storage medium. Int J Hydrogen Energy 2013;38:14654e60. [10] Takasaki A, Furuya Y, Ojima K, Taneda Y. Hydrogen evolution from cathodically charged Ti3Al-based titanium aluminium alloy. J Alloys Compd 1995;224:269e73.
[11] Schlapbach L, Zu¨ttel A. Hydrogen-storage materials for mobile applications. Nature 2001;414:353e8. [12] Anik M, Baksan B, Orbay TO, Ku¨c¸u¨kdeveci N, Aybar AB, ¨ zden RC, et al. Hydrogen storage characteristics of Ti2Ni O alloy synthesized by the electro-deoxidation technique. Intermetallics 2014;46:51e5. [13] Pickering L, Li J, Reed D, Bevan AI, Book D. TieVeMn based metal hydrides for hydrogen storage. J Alloys Compd 2013;580:S233e7. [14] Trefilov VI, Timofeeva II, Klochkov LI, Morozov IA, Morozova RA. Effects of temperature change and hydrogen content on titanium hydride crystal lattice volume. Int J Hydrogen Energy 1996;21:1101e3. [15] Shao H, Felderhoff M, Schuth F. Hydrogen storage properties of nanostructured MgH2/TiH2 composite prepared by ball milling under high hydrogen pressure. Int J Hydrogen Energy 2011;36:10828e33. [16] Gringoz A, Glandut N, Valette S. Electrochemical hydrogen storage in TiC0.6, not in TiC0.9. Electrochem Commun 2009;11:2044e7. [17] Nozaki T, Homma H, Hatano Y. Pressure-composition isotherms of TiC1xeH system at elevated temperatures. Mater Trans 2011;52:526e30. [18] Ding HM, Fan XL, Li CY, Liu XF, Jiang D, Wang CY. Firstprinciples study of hydrogen storage in non-stoichiometric TiCx. J Alloys Compd 2013;551:67e71. [19] Nguyen J, Glandut N, Jaoul C, Lefort P. Electrochemical hydrogen insertion in substoichiometric titanium carbide TiC0.6:influence of carbon vacancy ordering. Langmuir 2013;29:12036e42. [20] Ding HM, Fan XL, Chu KY, Zhang XC, Liu XF. The influence of carbon vacancies on the stacking fault energy of TiC. J Eur Ceram Soc 2014;34:1893e7. [21] Chien FR, Nutt SR, Cummings D. Defect structures in single crystal TiC. Phil Mag A 1993;68:325e48. [22] Vekilova OY, Bazhanov DI, Simak SI, Abrikosov IA. Firstprinciples study of vacancy-hydrogen interaction in Pd. Phys Rev B 2009;80:024101. [23] Arya A, Carter EA. Structure, bonding, and adhesion at the TiC(100)/Fe(110) interface from first principles. J Chem Phys 2003;118:8982e96. [24] Johansson LI. Electronic and structural properties of transition metal carbide and nitride surfaces. Surf Sci Rep 1995;21:177e250. [25] Chris G, Walle VD, Neugebauer J. First-principles surface phase diagram for hydrogen on GaN surfaces. Phys Rev Lett 2002;88:066103. [26] Bursik J, Weatherly GC. Ordering of substoichiometric d-TiCx phase in TieVeC alloys. Phys Stat Sol A 1999;174:327e35. [27] Barsoum MW. The Mnþ1AXn phases: a new class of solids; thermodynamically stable nanolaminates. Prog Solid State Chem 2000;28:201e81. [28] Govind N, Petersen M, Fitzgerald G, King-Smith D, Andzelm J. A generalized synchronous transit method for transition state location. Comput Mater Sci 2003;28:250e8.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
The influence of stacking faults on hydrogen storage in TiCx Haimin Ding*, Xiaoliang Fan, Kaiyu Chu, Biqiang Du, Jinfeng Wang School of Energy Power and Mechanical Engineering, North China Electric Power University, Baoding 071003, PR China
article info
abstract
Article history:
The hydrogen storage ability of TiCx with stacking faults (SFs) is studied in this work. It is
Received 9 February 2014
found that the absorption of hydrogen atoms is possible in both TiCx with and without SFs.
Received in revised form
And, besides the carbon vacancy sites, the hydrogen atoms can also occupy the tetrahedral
1 April 2014
sites in the SFs layers. More importantly, it is confirmed that the diffusion of hydrogen in
Accepted 3 April 2014
TiCx with SFs is much easier than that in TiCx without SFs, especially the diffusion around
Available online 27 April 2014
the SFs layers. The energy barrier for diffusion of the hydrogen atom in the SFs layers and diffusion from the SF layer to the next layer is only 0.099 eV and 0.185 eV, respectively.
Keywords:
Therefore, bringing in the SFs in TiCx with ordered carbon vacancies will be an effective
Density functional theory (DFT)
method to solve the diffusion problem during the processes of hydrogen storage.
Diffusion
Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Fault
Introduction Hydrogen is considered to be an ideal energy carrier for both mobile and stationary applications [1]. For the time being, hydrogen storage is one of the key challenges in developing hydrogen economy, therefore, hydrogen storage materials have been widely studied. It has been reported that many materials can be used for storage of hydrogen, such as light metals [2e5], carbon materials [6e9], and transition metals [10e13]. Among transition metals, Ti is well known for absorbing large quantities of hydrogen, which leads to the formation of titanium dihydride, TiH2 [14,15]. However, the embrittlement of hydride limits its widely application. In recent years, it has been found that, the carbide of Ti, TiC, can also absorb hydrogen when it contains carbon vacancies and the capacity of more than 2.9 wt.% can be obtained [16,17]. Furthermore, its
absorption and desorption process is more stable than Ti due to the similar crystal structure between the reactant TiCx and the product TiCxHy. However, according to our previous theoretical study by first-principles calculations [18] and experimental results reported in Nguyen et al’s work [19], it has been found that the diffusion of hydrogen atoms in TiCx is difficult and, even in TiCx with ordered carbon vacancies, its diffusion coefficient is still much lower than that of other materials candidates for hydrogen storage, which makes the diffusion be the limiting step of hydrogen storage in TiCx. Therefore, taking effective methods to improve the diffusion processes of hydrogen in TiC crystal will be essential for the application of TiCx in hydrogen storage field. As mentioned above, the existence of carbon vacancies is key for hydrogen storage in TiCx. In our recent works, it has been found that the carbon vacancies can also induce the formation of stack faults (SFs) in TiCx [20]. It is known that the stacking fault energy (SFE) is generally high in TiCx [21], but
* Corresponding author. Tel.: þ86 312 7525041; fax: þ86 312 7525045. E-mail addresses: [email protected], [email protected] (H. Ding). http://dx.doi.org/10.1016/j.ijhydene.2014.04.038 0360-3199/Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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the SFE can be reduced with increasing the content of the carbon vacancies. When the content of carbon vacancies is high and the carbon vacancies are ordered, the formation of SFs in TiCx will even be thermally favorable. What is more important is that, when SFs are formed in TiCx, carbon vacancies prefer to combine with SFs and the diffusion barrier energy of carbon vacancies in SFs layers will be seriously decreased from 2.21 eV in TiCx without SFs to about 0.03 eV [20]. Considering that the diffusion of hydrogen is commonly easier than that of the carbon vacancies, it is thought that the diffusion of hydrogen atoms in TiCx with SFs may also become much easier. And if it is confirmed, the diffusion problem of hydrogen in TiCx can be solved by bringing in SFs. Therefore, in this work, first-principles calculations have been performed to study the hydrogen storage of TiCx with SFs and the diffusions of hydrogen atoms in and around SFs layer are specially analyzed.
Method of calculations The calculations are based on the density-functional theory and performed with CASTEP. It has been reported that the calculation of interaction between hydrogen and vacancy is sensitive to the choice of the approximation for the exchange and correlation functionals [22]. Although the generalized gradient approximation (GGA) is commonly considered to be better than local density approximation (LDA) in studying of many aspects, such as the bulk properties of materials [23], it has been found that the calculation results of LDA are in better agreement with experimental data in studying of the vacancy-hydrogen interaction in solids [22]. Therefore, The LDA was utilized for structure optimization and energy calculation in this work. The TiC (111) plane with a slab of 8.5-layers and 20 A of vacuum region in the z-direction was used. It is known that the (111) plane is polar and can therefore be either Ti- or Cterminated. But, according to the previous work [24], Cterminated (111) surface is not stable, so Ti-terminated (111) is only considered. The configurations of TiC(111) with ideal sequence and with a SF are shown in Fig. 1(a) and (b), respectively. The plane-wave cut off energy of 350 eV was employed, which assured a tolerances of energy and displacement A, respecconvergence of 5.0 106 eV/atom and 5.0 104 tively. The grids of K-points are sampled by 9 5 1. In addition, the diffusion of hydrogen atoms in TiCx was studied by the linear synchronous transit (LST) optimization method. The feasibility of hydrogen storage in TiCx and its relationship with carbon vacancies has been confirmed by previous works as mentioned above [16e19]. Therefore, in this work, we mainly study the hydrogen storage properties in TiCx with SFs and compare with that in TiCx without SFs. The formation energy of hydrogen storage is firstly calculated by the Equation (1): H
Ef ¼
E 2 EnH tot Etot n 2 n
(1)
where n is the number of hydrogen atoms, EnH tot is the total energy of the system with n hydrogen atoms, Etot is the total
Fig. 1 e Configurations used in this study. The blue and red balls represent Ti and C, respectively. (a) the ideal sequence; (b) the stacking sequence. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
energy of TiCx without hydrogen atoms, and EH2 is the total energy of the hydrogen molecule [25].
Results and discussions As mentioned above, the SFs can only be formed in TiCx with amount of carbon vacancies, especially in TiCx with ordered carbon vacancies, in which some {111} carbon planes will be empty. As reported by Bursik et al. and Barsoum et al. that, in TiCx with x ¼ 0.67, one third of {111}
Fig. 2 e The positions of carbon vacancies and hydrogen atom in TiCx (a, b) the positions of carbon vacancies in TiCx with and without SFs; (c, d) the possible sites for multiple hydrogen occupancy in TiCx with and without SFs.
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carbon planes is empty and the two other thirds are fully occupied, while in TiCx with x ¼ 0.5, {111} carbon planes will be alternately full and empty [26,27]. In addition, carbon vacancies also prefer to combine with SFs as reported in our previous work [20]. Therefore, during calculation the absorption of hydrogen in TiCx with SFs, the configuration with ordered carbon vacancies locating in the SF layer is used, as shown in Fig. 2(a) in which two carbon vacancies are resided in position 1 and 2. And the configuration of TiCx without SFs but with ordered carbon vacancies is used as comparison, as shown in Fig. 2(b). The formation energies of a single hydrogen atom residing in one carbon vacancy site and two hydrogen atoms locating in two carbon vacancy sites whose configurations are designated as 1H-v and 2H-v are firstly calculated by Equation (1) and the results are shown in Table 1. It can be seen that the formation energy of a single hydrogen atom absorbed in the carbon vacancy site in TiCx with SFs is about 1.08 eV/atom which is a little smaller than that in TiCx without SFs. When all the carbon vacancies are occupied by the hydrogen atoms, the formation energies are 1.13 eV/atom in TiCx with SFs and 1.19 eV/atom in that without SFs. Those results indicate that the absorbing of hydrogen atoms is possible in both TiCx with and without SFs. The hydrogen atoms locating in the carbon vacancies (the octahedral sites) are only considered in the above calculations, and this is reasonable when the concentration of hydrogen is low. However, when concentration of the absorbed hydrogen atoms is high, hydrogen can also occupy the tetrahedral sites. Therefore, in the following, the absorption of hydrogen atoms on both octahedral and tetrahedral sites is studied. The positions of them are shown in Fig. 2(c) and (d) and the configurations are designated as 4H-v-t. It can be seen that the formation energies is 0.85 eV/atom in TiCx with SFs and 0.79 eV/atom in that without SFs. This confirms that the multiple hydrogen occupancy of the carbon vacancy in the SF layer of TiCx is also possible. The above results further confirm that, no matter with or without SFs, the absorption of hydrogen in TiCx with carbon vacancies is thermally favorable. In the following sections, the diffusion of the absorbed hydrogen atoms will be mainly examined by the linear synchronous transit (LST) optimization method. In the LST optimization, a series of single point energy calculations are performed on a set of linearly interpolated structures between an initial and final state. The maximum energy structure along this path provides a first estimate of the transition state structure. Then, an energy minimization in directions conjugate to the reaction pathway is performed [28]. This yields a structure closer to the true transition state which can be used to determine the energy barrier of the diffusion process.
Two diffusion paths have been considered in the calculations. The first one is the diffusion of the hydrogen atom in the same layer, as Path I and III shows in Fig. 3(a) and (b). The second one is migrating the hydrogen atom from a neighboring layer to the next, as Path II and IV shows in Fig. 3. The calculated results are shown in Fig. 4. As Fig. 4(a) and (b) shows, in TiCx without SFs, the energy barrier for diffusion of the hydrogen atom in the same layer which contains ordered carbon vacancies (Path I in Fig. 3(a)) is 0.497 eV, while it is 0.891 eV if the hydrogen atom is migrated from a neighboring layer to the next (Path II in Fig. 3(a)). This further confirms that the diffusion of hydrogen atoms in TiCx with ideal sequence is difficult and the results are in good agreement with Nguyen et al’s work [19]. When TiC contains a SF and the hydrogen atoms are absorbed and diffused in the SF layer which also contains ordered carbon vacancies. It is interesting to notice that the energy barrier for diffusion of hydrogen from one vacancy site to another (Path III in Fig. 3(b)) is 0.039 eV as shown in Fig. 4(c). The negative value indicates that this diffusion process contains an intermediate state. Therefore, the actual diffusion processes for Path III should be two steps. The first one is diffusion from one vacancy site to the intermediate state and then to another vacancy site. The calculated diffusion energy profile for this process is shown in Fig. 4(d). It can be seen that the energy barrier for diffusion of hydrogen from one vacancy site to the intermediate state is 0.088 eV, while it is 0.099 eV for that from the intermediate state to another vacancy site. Both of them are much smaller than that in TiCx without SFs as shown in Fig. 4(a).
Table 1 e Formation energies of absorbing hydrogen atoms in different positions (eV/atom). Configurations
1H-v
2H-v
4H-v-t
In TiCx with SFs In TiCx without SFs
1.08 1.13
1.13 1.19
0.85 0.79
Fig. 3 e The diffusion paths of the hydrogen atom (a) diffusion paths in TiCx without SFs; (b) diffusion paths in TiCx with a SF.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 9 2 6 2 e9 2 6 6
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Fig. 4 e The calculated diffusion energy profile (a, b) diffusion energy profile for Path I and II; (c) diffusion energy profile for Path III; (d) diffusion energy profile for Path III with two steps; (e) diffusion energy profile for Path IV.
For the diffusion from the neighboring layer to the SF layer (Path IV in Fig. 3(b)), the energy barrier is 0.185 eV as shown in Fig. 4(e) and it is still much smaller than that shown in Fig. 4(b). All the results demonstrate that diffusion of hydrogen atoms in TiCx with SFs is easier, especially in the SF layers. Considering the existence of the carbon vacancies in TiC, especially ordered carbon vacancies, is the necessary condition for both hydrogen storage [16e19] and formation of SFs, while the carbon vacancies prefer to segregate around SFs [20] and diffusion of hydrogen atoms in and around SF layers are also much easier as this work shows, bringing in the SFs in TiCx with ordered carbon vacancies will be an effective
method to simultaneously solve both the hydrogen storage and diffusion problem.
Conclusion In summary, the hydrogen storage ability of TiCx with SFs is studied in this work. It is found that the absorption of hydrogen atoms is possible in both TiCx with and without SFs. And, besides the carbon vacancy sites, the hydrogen atoms can also occupy the tetrahedral sites in the SFs layers. More importantly, it is confirmed that the diffusion of hydrogen in
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 9 2 6 2 e9 2 6 6
TiCx with SFs is much easier than that in TiCx without SFs, especially the diffusion around the SFs layers. The energy barrier for diffusion of the hydrogen atom in the SFs layers and diffusion from the SF layer to the next layer is only 0.099 eV and 0.185 eV, respectively. Therefore, bringing in the SFs in TiCx with ordered carbon vacancies will be an effective method to solve the diffusion problem during the processes of hydrogen storage.
Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 51301068), the Natural Science Foundation of Hebei Province (No. E2014502003) and the Fundamental Research Funds for the Central Universities (No. 2014MS116 and 2014ZD37).
references
[1] Sakintuna B, Lamari-Darkrim F, Hirscher M. Metal hydride materials for solid hydrogen storage:a review. Int J Hydrogen Energy 2007;32:1121e40. [2] Zhu M, Wang H, Ouyang LZ, Zeng MQ. Composite structure and hydrogen storage properties in Mg-based alloys. Int J Hydrogen Energy 2006;31:251e7. [3] Bouaricha S, Dodelet JP, Guay D, Huot J, Boily S, Schulz R. Hydriding behavior of MgeAl and leached MgeAl compounds prepared by high energy ball-milling. J Alloys Compd 2000;297:282e93. [4] Moroz S, Tan XF, Pierce J, Greaves M, Duguid A, Dumur K, et al. Systems based on hypo-eutectic MgeMg2Ni alloys for medium to large scale hydrogen storage and delivery. J Alloys Compd 2013;580:S329e32. [5] Jain A, Miyaoka H, Ichikawa T, Kojima Y. Correlation between electrochemical behavior and hydrogen storage properties of LieSn system. J Alloys Compd 2013;580:S211e5. [6] Darkrim FL, Malbrunot P, Tartaglia GP. Review of hydrogen storage by adsorption in carbon nanotubes. Int J Hydrogen Energy 2002;27:193e202. [7] Cabria I, Lo´pez MJ, Alonso JA. Simulation of the hydrogen storage in nanoporous carbons with different pore shapes. Int J Hydrogen Energy 2011;36:10748e59. [8] Hirscher M, Becher M. Hydrogen storage in carbon nanotubes. J Nanosci Nanotech 2003;3(1e2):3e17. [9] Silambarasan D, Surya VJ, Vasu V, Iyakutti K. Investigation of single-walled carbon nanotubes titanium metal composite as a possible hydrogen storage medium. Int J Hydrogen Energy 2013;38:14654e60. [10] Takasaki A, Furuya Y, Ojima K, Taneda Y. Hydrogen evolution from cathodically charged Ti3Al-based titanium aluminium alloy. J Alloys Compd 1995;224:269e73.
[11] Schlapbach L, Zu¨ttel A. Hydrogen-storage materials for mobile applications. Nature 2001;414:353e8. [12] Anik M, Baksan B, Orbay TO, Ku¨c¸u¨kdeveci N, Aybar AB, ¨ zden RC, et al. Hydrogen storage characteristics of Ti2Ni O alloy synthesized by the electro-deoxidation technique. Intermetallics 2014;46:51e5. [13] Pickering L, Li J, Reed D, Bevan AI, Book D. TieVeMn based metal hydrides for hydrogen storage. J Alloys Compd 2013;580:S233e7. [14] Trefilov VI, Timofeeva II, Klochkov LI, Morozov IA, Morozova RA. Effects of temperature change and hydrogen content on titanium hydride crystal lattice volume. Int J Hydrogen Energy 1996;21:1101e3. [15] Shao H, Felderhoff M, Schuth F. Hydrogen storage properties of nanostructured MgH2/TiH2 composite prepared by ball milling under high hydrogen pressure. Int J Hydrogen Energy 2011;36:10828e33. [16] Gringoz A, Glandut N, Valette S. Electrochemical hydrogen storage in TiC0.6, not in TiC0.9. Electrochem Commun 2009;11:2044e7. [17] Nozaki T, Homma H, Hatano Y. Pressure-composition isotherms of TiC1xeH system at elevated temperatures. Mater Trans 2011;52:526e30. [18] Ding HM, Fan XL, Li CY, Liu XF, Jiang D, Wang CY. Firstprinciples study of hydrogen storage in non-stoichiometric TiCx. J Alloys Compd 2013;551:67e71. [19] Nguyen J, Glandut N, Jaoul C, Lefort P. Electrochemical hydrogen insertion in substoichiometric titanium carbide TiC0.6:influence of carbon vacancy ordering. Langmuir 2013;29:12036e42. [20] Ding HM, Fan XL, Chu KY, Zhang XC, Liu XF. The influence of carbon vacancies on the stacking fault energy of TiC. J Eur Ceram Soc 2014;34:1893e7. [21] Chien FR, Nutt SR, Cummings D. Defect structures in single crystal TiC. Phil Mag A 1993;68:325e48. [22] Vekilova OY, Bazhanov DI, Simak SI, Abrikosov IA. Firstprinciples study of vacancy-hydrogen interaction in Pd. Phys Rev B 2009;80:024101. [23] Arya A, Carter EA. Structure, bonding, and adhesion at the TiC(100)/Fe(110) interface from first principles. J Chem Phys 2003;118:8982e96. [24] Johansson LI. Electronic and structural properties of transition metal carbide and nitride surfaces. Surf Sci Rep 1995;21:177e250. [25] Chris G, Walle VD, Neugebauer J. First-principles surface phase diagram for hydrogen on GaN surfaces. Phys Rev Lett 2002;88:066103. [26] Bursik J, Weatherly GC. Ordering of substoichiometric d-TiCx phase in TieVeC alloys. Phys Stat Sol A 1999;174:327e35. [27] Barsoum MW. The Mnþ1AXn phases: a new class of solids; thermodynamically stable nanolaminates. Prog Solid State Chem 2000;28:201e81. [28] Govind N, Petersen M, Fitzgerald G, King-Smith D, Andzelm J. A generalized synchronous transit method for transition state location. Comput Mater Sci 2003;28:250e8.