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Ab initio study on destabilizing mechanism of magnesium hydride by Ti and Fe co-doping
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 4 4 ( 2 0 1 9 ) 8 2 5 2 e8 2 6 0
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Ab initio study on destabilizing mechanism of magnesium hydride by Ti and Fe co-doping Kwang-Jin Um a, Ju-Hyok Wi b,*, Song-Il Hong b, Nam-Hyok Kim c, Su-Il Ri b a
Department of Solid Material, University of Science, Unjong District, Pyongyang, DPR Korea Department of Computational Material, Institute of Physics, Unjong District, Pyongyang, DPR Korea c Department of Theory Physics, Kim Il Song University, Daesong District, Pyongyang, DPR Korea b
article info
abstract
Article history:
A first-principle calculation based on density functional theory (DFT) was performed to
Received 27 September 2018
study the destabilizing mechanism of Ti and Fe co-doped MgH2. The calculated heats of
Received in revised form
formation show that Ti and Fe co-doped MgH2 system is thermo-dynamically favorable for
28 December 2018
practical hydrogen storage. The doping of Fe combined with Ti into the MgH2 rutile type
Accepted 22 January 2019
structure is more energetically favorable relative to Fe single-doping into the same struc-
Available online 8 March 2019
ture. We calculated the electronic structure, bond lengths and Bader atomic charges of the co-doped system and compared with those of the pure MgH2. Based on phonon calculation,
Keywords:
we also estimated the thermo-dynamical properties such as entropy and specific heat
Hydrogen storage
capacity as well as lattice vibrations. The obtained results indicate that Ti and Fe co-doping
Metal hydride
is an effective method in order to destabilize magnesium hydride.
Ab initio calculation
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Heat of formation Thermo-dynamics
Introduction The growing demands for energy and the serious environmental pollution by the traditional fossil fuels including coal, oil and natural gas, have facilitated the research to find new and pollution-free energy resources. One of the clean energy carriers alternatively to the fossil fuels, hydrogen has be attracted by many researchers last decades [1e3]. The using hydrogen as a fuel could provide a high energetic efficiency and zero emission of CO2 including other polluting species, especially if hydrogen is used through fuel cells [1,4]. However, the development of hydrogen power system faces the obstacles concerning its storage. In fact, hydrogen
storage system has to have a high volumetric, gravimetric density and fast ad/desorption rate at relatively low temperatures, and a high recycling stability. Hydrogen storage through metal hydrides is one of the most promising methods due to its high hydrogen storage density [5e8]. Metal hydrides, especially magnesium hydride, MgH2 is one of the potential candidates among on board hydrogen storage systems for automotive applications due to its high hydrogen storage capacity (~7.6 wt%), good reversibility and low cost [9]. Unfortunately, MgH2 has a slow ad/desorbing kinetics and a high dissociation temperature, usually above 300 C under 1 bar hydrogen pressure. Such behavior is attributed to the fact that magnesium hydride has a high thermo-dynamic stability and very low hydrogen diffusion coefficient.
* Corresponding author. E-mail address: [email protected] (J.-H. Wi). https://doi.org/10.1016/j.ijhydene.2019.01.192 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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In order to improve the hydrogen storage properties of MgH2, many efforts have been devoted, including confining Mg/MgH2 into porous structure [10,11], refining particles into nanoscale [12,13], adding active catalysts [14e17], and alloying with other elements [18,19]. The MgH2 composites prepared by ball milling with adding a small amounts of nanostructured transition metals showed much better hydrogen desorption properties than the ball-milled pure MgH2 itself [20,21]. In addition, doping effects of various alloying elements including Al, Ti, Fe, Ni, Cu, and Nb were tested theoretically to improve the thermo-dynamic properties of MgH2 [22]. The obtained results demonstrated that 3d transition metals doping destabilize magnesium hydrides thermo-dynamically through reducing of heats of formation. On the other hand, the MgH2/TiH2 mixture prepared by a high-energy, high-pressure milling technique decompose into metallic Mg and TiH2, releasing a large amounts of hydrogen (5.91 wt%) at 126 Ce313 C. This hydrogen desorption temperature is much lower than that of asreceived pure MgH2 [23]. Many experimental studies confirmed that magnesium hydride was destabilized thermo-dynamically by additives such as 3d transition metals or their hydrides. The theoretical results suggested also that the ab/desorbing kinetics of MgH2 could be improved by the solution of Ti [24]. Recently, Mg hydride prepared with an additive nano-SiO2 by high energy ball milling was studied in term of the desorption temperature [25], and they also reported the experimental results on the hydrogen ab/desorption property of MgH2 used nano-silicon carbide and nickel as catalysts [26]. Mg and Fe are immiscible, but intermetallic hydride Mg2FeH6 can be formed in the presence of hydrogen [27]. Mg2FeH6 has attracted considerable attention as it has a high volumetric and gravimetric hydrogen capacity up to 150 kg/m3 and 5.47 wt%, respectively. In addition, the component Fe is the cheapest material among all metals. However, the heat of formation of Mg2FeH6 (98 kJ/mol H2 [28]) is higher than that of MgH2 (74.0 kJ/mol [29]) and its desorption temperature is above 320 C [30]. Experimental results support the theoretical predictions that the thermo-dynamics and kinetics of MgH2 could be improved efficiently by more than one additive, and the phenomenon is called synergistic effect [31e35]. A computational study of the magnesium hydrides showed that the co-doping with Al and Y could effectively decrease the bond strength between Mg and H, because the conduction band moves below the Fermi level and the dopants are hybridized with Mg strongly [36]. It was observed that nanostructured composite MgH2eTiCr1.2Fe0.6 prepared by high-energy mechanical alloying had the dehydrogenation temperature of 262 C with a hydrogen release of 5.5 wt% [37]. Another co-doping system used in the first principle study is a ternary intermetallic hydride (Mg, Fe, Ni)H2 system [35]. In the system, it was concluded that Mg12Ni2Fe4H36 was more favorable in dehydrogenation than pure Mg18H36 by comparing calculated enthalpies of formation. It was reported that the adsorption enhancement of MgeFeeTi thin films is due to improved kinetics rather than any altered thermodynamics and FeTi solid solution may act as an effective pathway for hydrogen diffusion [38]. To the best our
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knowledge, there is still a lack of systematic study of the structural, electronic and thermo-dynamic properties of Ti and Fe co-doped MgH2 system. In this paper, we have studied MgH2 system with co-doped Ti and Fe by a first-principles calculation. Bond strengths of Mg-H and the thermo-dynamic properties of Mg12Ti2Fe4H36 have been investigated through Bader charge analysis and phonon calculation. In section Method of calculation the computational method is briefly presented, followed by the results and discussion. Finally, there is a conclusion in section Conclusions.
Method of calculation Self-consistent calculations were carried out using the standard plane-wave PW scf code of the QUANTUM-ESPRESSO package within the density functional theory (DFT) [39]. The generalized gradient approximation (GGA) of the PerdewWang 91(PW91) [40] was adopted for the exchangecorrelation energy functional and a plane wave basis set with kinetic energy cutoff of 40Ry was used. The Gaussian smearing method was used to describe partial occupancies of each wave function, with smearing value of 0.01eV. Before the electronic structures were calculated, geometric relaxations were performed in order to optimize the structures. In the relaxations both lattice parameters and all atomic coordinates were varied. In the present study, the Brillouin zone was sampled with a 3 3 7 Monkhorst-Pack k-point mesh for geometry optimization and a 5 5 9 Monkhorst-Pack k-point mesh for electronic structures to save the accuracy of total energies depending on k-mesh size and the computing time. The total energy convergence for the self-consistent calculation was set to 105 Ry, and all structures were fully optimized using the BFGS (BroydeneFletchereGoldfarbeShanno) method [41] until Hellman-Feynman forces were less than 4 104Ry/bohr. These criterions guarantee the chemical accuracy of calculated results. We have also calculated the density of states (DOS and PDOS) of pure MgH2 and Ti and Fe co-doped MgH2 to estimate the bonding properties between metal atoms and hydrogen atoms. In addition to DOS and PDOS calculations, Bader atomic charges were also calculated, which evaluates the ionicity of atoms in supercells. Bader atomic charge is a charge which is contained in regions called atomic basins surrounded by the zero-flux surfaces of the electronic density gradient vector field Vr. Additionally, phonon calculation was calculated in order to investigate the influence of lattice vibrations on stability and thermo-dynamic properties at finite temperatures. The used program package PHON [42] to evaluate the vibration energy contribution to thermo-dynamic properties within the QHA (quasi harmonic approximation) is based on the small displacement method. The cell parameters, atomic positions and the forces obtained from QUANTUM ESPRESSO were used as input data of PHON to generate the force constants, the dynamical matrix and the phonon frequencies. The phonon DOS was also calculated with a 24 24 12 k-point mesh to compute thermo-dynamic properties at temperatures between 300 K and 600 K.
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Results and discussion
Table 1 e The initial internal coordinates of MgH2 3 £ 3 £ 1 supercell model used in calculations.
Geometric optimizations
Atom
The MgH2 has three types of structure (a, b, g), depending on temperature and pressure, while it crystallizes in tetragonal symmetry (P42/mnm, group No. 136), so called rutile type structure in the ambient temperature and pressure. In its unit cell, two Mg atoms occupy Wyckoff position 2a (0, 0, 0) and four H atoms occupy 4f (0.303, 0.303, 0) [43] and experimentally measured lattice parameters are a ¼ 4.501 Å and c ¼ 3.010 Å [44]. In this study, we employed the 3 3 1 supercell (Mg18H36) with 3 times size of the unit cell along only the a and the b axes in order to research co-doped Mg12Ti2Fe4H36 system (Fig. 1). The initial non-equivalent Wyckoff positions of Mg and H atoms are tabulated in Table 1. It was found both experimentally and theoretically that beyond 20 at. % Ti content, the rutile structure characteristic of pure MgH2 is no longer stable, and the hydride transforms into a fluorite-type structure, similar to that of the transition metal dihydride [45]. Therefore we discussed the case which two Ti atoms were substituted in wyckoff 2a of rutile type Mg18H36 supercell and wyckoff 4f for four Fe atoms in order to save it's hydrogen capacity. Before total energy calculations, we performed the structural relaxations, followed by electronic calculations for Mg18H36 and co-doped Mg12Ti2Fe4H36 system. Table 2 shows the values of geometric parameters of both systems after the relaxations, except z ¼ 0 coordinates. To examine the accuracy of our calculation for the doped system, we have also studied the well-known Mg2FeH6 hydride. The structural geometry of Mg2FeH6 is analogous to that of cubic K2PtCl6 (fluorite-type) structure (Fm3m, group No. 225) [46] Mg2FeH6 has an experimental measured lattice constant a ¼ 6.443 Å and contains 36 atoms per unit cell, and Mg and Fe atoms occupy fixed Wyckoff positions 8c (1/4, 1/4, 1/4) and 4a (0, 0, 0), respectively. However, H atoms have variable Wyckoff positions 24e (x, 0, 0) [47]. The lattice constant of the relaxed structure is a ¼ 6.408 Å, which is close to experimental data [46].
Heats of formation and electronic structures The heat of formation is the most important thermo-dynamic quantity of hydrides and dehydrogenation temperature
Wyckoff positions
x
y
z
2a 4g 8i 4f 4f 4f 4f 8i 8i 8i
0 2/3 1/3 1/3 0.1016 0.4350 0.2317 0.1016 0.1016 0.4350
0 1/3 0 1/3 0.1016 0.4350 0.2317 0.4350 0.7683 0.7683
0 0 0 0 0 0 0 0 0 0
Mg1 Mg2 Mg3 Mg4 H1 H2 H3 H4 H5 H6
Table 2 e Relaxed structures of the considered supercells: Lattice parameters and Wyckoff positions of Mg1-Mg4, H1-H6. Cell parameters
Mg18H36
Mg12Ti2Fe4H36
a (nm) c (nm) V0 (nm3)
1.3566 0.3013 0.5545
1.2723 0.2899 0.4693
Wyckoff positions
x
y
x
y
Mg1 Mg2 Mg3 Mg4 H1 H2 H3 H4 H5 H6
0.0000 0.6667 0.3333 0.3333 0.1015 0.4348 0.2319 0.1015 0.1015 0.4348
0.0000 0.3333 0.0000 0.3333 0.1015 0.4348 0.2319 0.4348 0.7681 0.7681
0.0000 0.6540 0.3233 0.3220 0.1049 0.4331 0.2079 0.1094 0.1039 0.4330
0.0000 0.3460 0.0179 0.3220 0.1049 0.4331 0.2079 0.4425 0.7627 0.7432
depends mainly on the heat of formation. The heat of formation DH of hydrides can be defined as the difference between sum of total energies of products and that of reactants. DH ¼ Etot(products)-Etot(reactants)
(1)
Reactions related to the formation of the hydrides Mg18H36 and Mg12Ti2Fe4H36 are as follows: 18Mg þ 18H2/Mg18H36
(2)
Fig. 1 e Top (a) and side (b) views of MgH2 3 £ 3 £ 1 supercell model. Mg1, Mg2, Mg3 and Mg4 denote four non-equivalent positions for Mg, respectively.
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12Mgþ2Tiþ4Fe þ 18H2/Mg12Ti2Fe4H36
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(3)
We calculated the heats of formation of the hydrides based on these reactions using the following equations: DH(Mg18H36) ¼ Etot(Mg18H36)18Etot(Mg)18Etot(H2)
(4)
DH(Mg12Ti2Fe4H36) ¼ Etot(Mg12Ti2Fe4H36)12Etot(Mg)2Etot(Ti) (5) 4Etot(Fe)18Etot (H2) The total energies per atom of Mg, Ti and Fe were calculated using the lattice parameters given in Kittel. C (2005) [48] and are equal to 79.3133, 116.7335 and 253.5457Ry, respectively. The Etot (H2) was calculated by using a cubic unit cell of 10 10 10 Å. The calculated HH bond length, 0.752 Å and the total energy of H2 molecule, 2.3367Ry are in good agreement with other computational data [49]. The calculated total energies and heats of formation of the considered hydrides are listed in Table 3. Our result is close to the experimental value 74.0 kJ/mol H2 for MgH2 [29]. As seen Table 3, the heat of formation of Mg12Ti2Fe4H36 is much small in absolute magnitude than that of Mg18H36. and this fact indicates that Mg12Ti2Fe4H36 is thermo-dynamically more favorable for practical hydrogen ad/desorption than Mg18H36. Furthermore it demonstrates that the co-doping by Ti and Fe plays a crucial role in decreasing the stability of magnesium hydride, leading to the improvement of hydrogen storage characteristics. The relative stability of the doped system relative to the pure MgH2 can be evaluated by the difference between the heat of formation of the doped hydride and that of the pure one. From energy point of view, the smaller relative stability corresponds to the more favorable doping. Ab initio calculated relative stabilities of the single-doped rutile type systems with Ti and Fe were 22.91 kJ/mol H2 and 33.34 kJ/mol H2, respectively [22]. This indicates that the Fe substitution in MgH2 rutile type structure is more difficult than that of Ti in the same structure. Ab initio calculated our relative stability of the co-doped system is 26.43 kJ/mol H2. Hence, the doping of Fe combined with Ti into the MgH2 rutile type structure is more energetically favorable than the single-doping of Fe into the same structure. Therefore we suggest that Mg12Ti2Fe4H36 system may be possible practically through first Ti substitution and sequent Fe substitution. In order to understand the destabilizing mechanism of magnesium hydride, the electronic structure of co-doped system was also calculated as well as one of Mg18H36 system. Density of states (DOS) of pure system are presented in Fig. 2. The top panel is the total DOS and the next panels show the partial density of electronic states of Mg and H, respectively. In according to Fig. 2, Mg18H36 is an insulator with the
Table 3 e The total energy and heat of formation of MgH2 and Mg12Ti2Fe4H36. Hydride Mg18H36 Mg12Ti2Fe4H36
Total energy (Ry)
Heat of formation (kJ/mol H2)
1470.5712 2241.9787
63.58 37.15
Fig. 2 e Total and partial electronic densities of states of MgH2.
energy band gap of 3.74eV between the valence band (VB) and conduction band (CB). The VB is mainly dominated by the contribution from H s orbital and the CB mainly originates from Mg s and Mg p orbitals, which means a strong ionic bonding formation due to the charge transfer from Mg to H. Additionally, Mg s and Mg p orbital hybridizing with H s orbital in the valence band can also be seen, which contributes to somewhat covalent bonding interactions between Mg and H. Thus, the bonding characteristic in Mg18H36 is a mixture of ionic and covalent bonding. The relatively large band gap of Mg18H36 leads to a poor MgeH dissociation. In order to recovery the metallic property of Mg in dehydrogenation process, it is necessary that electrons should be transferred from H to Mg. Consequently the pure magnesium hydride has to receive much energy in order to release hydrogen due to the large energy band gap. That is why pure magnesium hydride is thermo-dynamically stable and its decomposition temperature is significantly high. The total and partial DOSs of the Mg12Ti2Fe4H36 system are shown in Fig. 3. The total DOS and partial DOSs of metallic atoms (Ti, Fe, Mg3 and Mg4) are plotted in the left-hand side and the partial DOSs of H atoms (H1eH6) in the right-hand side. The total DOS curve shows the band gap of 0eV, indicating clearly metallic characteristics. In the system, electrons transferring from H to Mg can be take placed easily, thus the bond between metallic and H atom can be also broke easily. It is interesting to note that the VB near the Fermi level is mainly attributed to Fe d and the CB near the Fermi level is mainly dominated by the contribution from Ti d. Furthermore we can see that the band gap disappear by both the contributions of Fe d and Ti d, so Ti and Fe co-doped magnesium hydride transforms into the conductor. Thermal conductivity of hydrides is very important in the sense that dehydrogenation process involves heating. We expect that the thermal conductivity of MgH2 would be improved by insulator-metal transition via Ti
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Fig. 3 e Total and partial electronic densities of states of Mg12Ti2Fe4H36.
and Fe co-doping. The distributions of PDOS peaks of Ti and Fe d orbitals are mainly concentrated in the energy region from 6.1 to 2.5eV and overlap well with Mg p and H s orbitals. The orbital hybridizing of Mg and H in co-doped system is weak than in pure system, resulting in weakening MgeH bond strength. The highest DOS peaks of H1, H2, H3 and H6 are located in the energy range from 4.9 to 3.5eV and H4 and H5 range from 3 to 2.7eV. Hence, Ti and Fe d orbitals are mainly hybridized with H1, H2, H3, and H6 s orbitals, and H4 and H5 s orbitals are mainly hybridized with Mg p orbitals. The PDOSs of H and Mg atoms in the VB of Fig. 3 are smaller than those in Fig. 2, indicating weaker bonding interaction between Mg and H. The weak bonding interaction between Mg and H in the co-doped system is the reason that the co-doping with Ti and Fe has a positive influence on the thermodynamical improvement.
Bond lengths and bader charge analysis Bonding lengths is a useful item to evaluate bonding strength straightforwardly by comparing them. Table 4 lists the bond
lengths between metal atoms in Mg18H36 and Mg12Ti2Fe4H36 supercell. In Table 4, the bond lengths are 4.522 Å for Mg1eMg3 bond and 3.535 Å for other bonds with an average of 3.655 Å, which is in good agreement with other theoretical results [36,44]. In co-doped system, all of the bond lengths between metal atoms are shorter than those of the pure system, ranging from 3.122 Å to 4.123 Å with an average of 3.446 Å. The TieFe bond length of 3.129 Å is short by about 11% in comparison with that of Mg1eMg2, which implies the strong bond strength and alloying trend. The bond lengths of TieMg3 and TieMg4 were shorter than corresponding bond lengths in pure system by 9 and 0.5%, respectively, while the bond lengths were reduced by 12% for FeeMg3 and 5% for FeeMg4, respectively compared pure system. For the co-doped system, the distance between Mg3 and Mg4 was also decreased by about 3%. Consequently it can be inferred that decreasing of these bond lengths imply the enhancements of bond strengths between metallic atoms and furthermore the bond strengths between H and metallic atoms would be weakened. The bond lengths between H and metallic atoms are presented in Table 5. H atoms form octahedrons around metal
between metallic elements in the MgH2 and Mg12Ti2Fe4H36. Table 4 e Calculated the bond distance (A) MgH2
Mg1-Mg2 3.535
Mg1-Mg3 4.522
Mg1-Mg4 3.535
Mg2-Mg3 3.535
Mg2-Mg4 3.535
Mg3-Mg4 3.535
Mg12Ti2Fe4H36
Ti-Fe 3.129
Ti-Mg3 4.123
Ti-Mg4 3.518
Fe-Mg3 3.122
Fe-Mg4 3.354
Mg3-Mg4 3.428
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between H and metallic atoms in Mg18H36 and Mg12Ti2Fe4H36. Table 5 e Calculated the bond lengths (A) MgH2
Mg12 Ti2 Fe4 H36
bonding
distance
bonding
distance
bonding
distance
bonding
distance
Mg1-H1 Mg1-H2
1.948 1.958
Mg2-H1 Mg2-H3 Mg2-H6
1.958 1.958 1.947
Mg3-H4 (1) Mg3-H4 (2) Mg3-H5 Mg3-H6
1.948 1.958 1.947 1.958
Mg4-H2 Mg4-H3 Mg4-H5
1.947 1.958 1.958
bonding
distance
bonding
distance
bonding
distance
bonding
distance
Ti-H1 Ti-H2
1.889 1.884
Fe-H1 Fe-H3 Fe-H6
1.698 1.744 1.587
Mg3-H4 (1) Mg3-H4 (2) Mg3-H5 Mg3-H6
1.913 1.938 1.900 1.879
Mg4-H2 Mg4-H3 Mg4-H5
2.000 2.054 1.887
Fig. 4 e The octahedrons of H atoms around metallic atom.
atoms: H1, H2 around Mg1, H1, H3, H4 around Mg2, H4, H5, H6 around Mg3 and H2, H3, H5 around Mg4, as shown in Fig. 4. Calculated results show that the bond lengths range from 1.947 Å to 1.958 Å for Mg18H36 and from 1.587 Å to 2.054 Å for Mg12Ti2Fe4H36. Bond lengths between Fe and H atoms were decreased by more than 10% in co-doped system compared with pure system, while TieH and Mg3eH were decreased by 1e4%. Nevertheless overall bond lengths have decreasing tendency by co-doping, such behavior was reversed for Mg4eH2 and Mg4eH3: bond lengths were increased significantly. In spite of the reduced supercell volume as co-doped, the bond lengths of MgeH do not decreased substantially and partially increased largely. Largely increased bond lengths might contribute to the weakening bond strength and further to the reducing hydrogen desorption temperature. In order to study the bonding features between metallic and H atoms in more detail, we performed Bader charge analysis
for the considered systems based on Bader's theory of atoms in molecules. It is addressed that Bader excess charge (BEC) is a crucial quantity in Bader charge analysis, which is defined as difference between the charge contained in a Bader atom and its atomic charge. It is possible to estimate the ionic degree of bonds approximately to some extents through comparing BEC. Table 6 lists BECs for pure and co-doped systems. The more positive BEC, the more cationic is the atom and the less negative BEC, the less anionic is the atom. In according to Table 6, BECs of Mg and H atoms reveal that the bonds between Mg and H are all strongly ionic for the pure system. As Ti and Fe are doped, BECs of H atoms except for H4 and H5 are reduced substantially in absolute magnitude and BECs of Mg atoms are increased slightly than those of pure system. Mg atoms have much bigger BECs than dopants Ti and Fe, especially þ0.475 for Fe. Furthermore, less negative BECs of H1, H2, H3 and H6 atoms imply that the ionicity of Ti-H and Fe-H bonds are weakened, thus ion bond strengths are also weakened. The reason for less negative BECs of H atoms is attributed to less positive BECs of Ti and Fe compared with Mg, while small BECs of Ti and Fe compared with Mg are correlated to their electronegativity. As compared with pure MgH2, not only the positive BECs of Mg3 and Mg4 but also the negative BECs of H4 and H5 are increased slightly, which reveals a little enhancement of ion bond strengths of Mg3-H4, Mg3-H5 and Mg4-H5.
Thermo-dynamical properties and lattice vibrations We determined thermo-dynamical properties (entropy and specific heat capacity at constant temperatures) from the phonon calculation of MgH2 and Mg12Ti2Fe4H36, and Table 7 show them with experimental data [50]. In phonon calculation, the forces on the atoms were evaluated for the 3 3 1 MgH2 supercell as they were displaced from their equilibrium positions. For the sake of convenience, the unit of entropy and specific heat capacity was set with 1 eV K1 per supercell, containing 54 atoms. At all temperatures the predicted
Table 6 e Bader charges of component elements for Mg18H36 and Mg12Ti2Fe4H36. Mg18H36
Mg12 Ti2Fe4 H36
Atom
Mg1
Mg2
Mg3
Mg4
H1
BEC
þ1.629
Atom
Ti
BEC
þ1.487
H2
H3
H4
H5
H6
þ1.628
þ1.629
þ1.629
Fe
Mg3
Mg4
0.821
0.815
0.808
0.820
0.815
0.809
H1
H2
H3
H4
H5
H6
þ0.475
þ1.645
þ1.646
0.437
0.659
0.492
0.815
0.821
0.648
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Table 7 e Entropy and specific heat capacity at constant temperatures calculated at different temperatures, compared with experimental data [46]. Temperature (K)
MgH2 3
S (10
300 400 500 600
eV K
1
per supercell)
Mg12Ti2Fe4H36 3
Cp(10
1
eV K
per supercell)
Present Work
Ref. [46]
Present Work
Ref. [46]
6.062 8.265 10.302 12.167
5.840 7.954 9.884 11.663
6.665 8.318 9.583 10.512
6.622 8.074 9.241 10.295
3
S (10 eV K1 per supercell)
Cp(103 eV K1 per supercell)
6.001 8.004 9.840 11.525
6.127 7.487 8.620 9.515
entropies and heat capacities of MgH2 show smaller deviations than 4% from the corresponding references values. Hence we suggest that our phonon calculations describe the vibrational properties of MgH2 within a degree of high accuracy. On the other hand, the thermo-dynamical values of the co-doped system are smaller than the corresponding ones of the pure magnesium hydride but the differences of them are not so much within a few percent. We show Figs. 5 and 6 for the total and partial phonon DOS of MgH2. and Mg12Ti2Fe4H36, respectively. We found that there are no negative phonon frequencies in the case of pure MgH2, as shown in Fig. 5. And the high frequency modes (above 300 cm1) are dominated by H atoms, and the low frequency modes (below 300 cm1) are dominated by Mg atoms, because the Mg atom is much heavier than H atom. Due to the mostly ionic interaction between H and Mg atoms in MgH2, there is hardly coupling between the vibrations of two atoms in Fig. 5 b and c. However, Fig. 6 is shown some negative phonon frequencies (negative frequencies are representative of imaginary
frequencies), and the negative frequency modes are dominated by Ti atoms in Fig. 6 b, which indicates that Mg12Ti2Fe4H36 is dynamically unstable. Although it is so, we can see the important properties of co-doped magnesium hydride with Ti and Fe. In Fig. 5 c, H atom phonon DOS is below about 1470 cm1 with some small zero-phonon gaps, but in Fig. 6 c, below about 1950 cm1 with comparatively wide zero-phonon gaps. Therefore, we know that the phonon frequency modes of H atoms are shifted to higher frequency region. It is also shown that in the case co-doped unlike pure MgH2, phonon DOSs of individual H atoms are localized remarkably, especially for H1, H2 and H3. This indicates that the presence of the co-doped atoms have a large influence on lattice vibrations of H atoms. Consequently we found that as Ti and Fe are co-doped, entropy and specific heat capacity change only a little, but the variation of lattice vibrations is considerably great from the study of thermo-dynamical and lattice vibration properties for Mg18H36 and Mg12Ti2Fe4H36 based on phonon calculation.
Fig. 5 e The calculated (a) total phonon DOS, (b) Mg atom phonon DOS and (c) H atom phonon DOS of MgH2.
Fig. 6 e The calculated (a) total phonon DOS, (b) Metal atom phonon DOS and (c) H atom phonon DOS of Mg12Ti2Fe4H36.
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Conclusions [10]
Ti and Fe co-doping effects on the destabilizing of MgH2 were studied by the first principles calculations based on DFT. The heats of formation of Mg18H36 and Mg12Ti2Fe4H36 determined by calculation of total energy show that magnesium hydride is thermo-dynamically destabilized by Ti and Fe co-doping. We compared our relative stability of the Ti and Fe co-doped system with the one of the Ti/Fe single-doped system referred in reference [22], which indicate that the doping of Fe combined with Ti into the MgH2 rutile type structure is more energetically favorable relative to Fe single-doping into the same structure. The electronic structures show that as Ti and Fe co-doped, energy band gap disappear due to the contribution of Fe in VB and Ti in CB. Also the hybridizing between Mg and H atoms is weakened compared to pure system. Bader charge analysis shows that the ionicity of H atoms is reduced due to the low iconicity of Ti and Fe compared with Mg. Therefore it may be concluded that dopants Ti and Fe codoping will be an effective method in order to destabilize the magnesium hydride. Deep understanding of the effect of codoping of Ti and Fe on (de-)hydrogenation of MgH2 requires a further investigation of (de-)hydrogenation kinetics, which is beyond the scope of the present investigation. As Ti and Fe are co-doped, entropy and specific heat capacity change only a little, and the phonon frequency modes of H atoms are shifted to higher frequency region and are localized remarkably. Our study might be useful to investigate the effects of co-doped atoms for the improvement in the hydrogenationdehydrogenation properties of MgH2, even if the present codoped system is dynamically unstable from the phonon calculation results.
references
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Ab initio study on destabilizing mechanism of magnesium hydride by Ti and Fe co-doping Kwang-Jin Um a, Ju-Hyok Wi b,*, Song-Il Hong b, Nam-Hyok Kim c, Su-Il Ri b a
Department of Solid Material, University of Science, Unjong District, Pyongyang, DPR Korea Department of Computational Material, Institute of Physics, Unjong District, Pyongyang, DPR Korea c Department of Theory Physics, Kim Il Song University, Daesong District, Pyongyang, DPR Korea b
article info
abstract
Article history:
A first-principle calculation based on density functional theory (DFT) was performed to
Received 27 September 2018
study the destabilizing mechanism of Ti and Fe co-doped MgH2. The calculated heats of
Received in revised form
formation show that Ti and Fe co-doped MgH2 system is thermo-dynamically favorable for
28 December 2018
practical hydrogen storage. The doping of Fe combined with Ti into the MgH2 rutile type
Accepted 22 January 2019
structure is more energetically favorable relative to Fe single-doping into the same struc-
Available online 8 March 2019
ture. We calculated the electronic structure, bond lengths and Bader atomic charges of the co-doped system and compared with those of the pure MgH2. Based on phonon calculation,
Keywords:
we also estimated the thermo-dynamical properties such as entropy and specific heat
Hydrogen storage
capacity as well as lattice vibrations. The obtained results indicate that Ti and Fe co-doping
Metal hydride
is an effective method in order to destabilize magnesium hydride.
Ab initio calculation
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Heat of formation Thermo-dynamics
Introduction The growing demands for energy and the serious environmental pollution by the traditional fossil fuels including coal, oil and natural gas, have facilitated the research to find new and pollution-free energy resources. One of the clean energy carriers alternatively to the fossil fuels, hydrogen has be attracted by many researchers last decades [1e3]. The using hydrogen as a fuel could provide a high energetic efficiency and zero emission of CO2 including other polluting species, especially if hydrogen is used through fuel cells [1,4]. However, the development of hydrogen power system faces the obstacles concerning its storage. In fact, hydrogen
storage system has to have a high volumetric, gravimetric density and fast ad/desorption rate at relatively low temperatures, and a high recycling stability. Hydrogen storage through metal hydrides is one of the most promising methods due to its high hydrogen storage density [5e8]. Metal hydrides, especially magnesium hydride, MgH2 is one of the potential candidates among on board hydrogen storage systems for automotive applications due to its high hydrogen storage capacity (~7.6 wt%), good reversibility and low cost [9]. Unfortunately, MgH2 has a slow ad/desorbing kinetics and a high dissociation temperature, usually above 300 C under 1 bar hydrogen pressure. Such behavior is attributed to the fact that magnesium hydride has a high thermo-dynamic stability and very low hydrogen diffusion coefficient.
* Corresponding author. E-mail address: [email protected] (J.-H. Wi). https://doi.org/10.1016/j.ijhydene.2019.01.192 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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In order to improve the hydrogen storage properties of MgH2, many efforts have been devoted, including confining Mg/MgH2 into porous structure [10,11], refining particles into nanoscale [12,13], adding active catalysts [14e17], and alloying with other elements [18,19]. The MgH2 composites prepared by ball milling with adding a small amounts of nanostructured transition metals showed much better hydrogen desorption properties than the ball-milled pure MgH2 itself [20,21]. In addition, doping effects of various alloying elements including Al, Ti, Fe, Ni, Cu, and Nb were tested theoretically to improve the thermo-dynamic properties of MgH2 [22]. The obtained results demonstrated that 3d transition metals doping destabilize magnesium hydrides thermo-dynamically through reducing of heats of formation. On the other hand, the MgH2/TiH2 mixture prepared by a high-energy, high-pressure milling technique decompose into metallic Mg and TiH2, releasing a large amounts of hydrogen (5.91 wt%) at 126 Ce313 C. This hydrogen desorption temperature is much lower than that of asreceived pure MgH2 [23]. Many experimental studies confirmed that magnesium hydride was destabilized thermo-dynamically by additives such as 3d transition metals or their hydrides. The theoretical results suggested also that the ab/desorbing kinetics of MgH2 could be improved by the solution of Ti [24]. Recently, Mg hydride prepared with an additive nano-SiO2 by high energy ball milling was studied in term of the desorption temperature [25], and they also reported the experimental results on the hydrogen ab/desorption property of MgH2 used nano-silicon carbide and nickel as catalysts [26]. Mg and Fe are immiscible, but intermetallic hydride Mg2FeH6 can be formed in the presence of hydrogen [27]. Mg2FeH6 has attracted considerable attention as it has a high volumetric and gravimetric hydrogen capacity up to 150 kg/m3 and 5.47 wt%, respectively. In addition, the component Fe is the cheapest material among all metals. However, the heat of formation of Mg2FeH6 (98 kJ/mol H2 [28]) is higher than that of MgH2 (74.0 kJ/mol [29]) and its desorption temperature is above 320 C [30]. Experimental results support the theoretical predictions that the thermo-dynamics and kinetics of MgH2 could be improved efficiently by more than one additive, and the phenomenon is called synergistic effect [31e35]. A computational study of the magnesium hydrides showed that the co-doping with Al and Y could effectively decrease the bond strength between Mg and H, because the conduction band moves below the Fermi level and the dopants are hybridized with Mg strongly [36]. It was observed that nanostructured composite MgH2eTiCr1.2Fe0.6 prepared by high-energy mechanical alloying had the dehydrogenation temperature of 262 C with a hydrogen release of 5.5 wt% [37]. Another co-doping system used in the first principle study is a ternary intermetallic hydride (Mg, Fe, Ni)H2 system [35]. In the system, it was concluded that Mg12Ni2Fe4H36 was more favorable in dehydrogenation than pure Mg18H36 by comparing calculated enthalpies of formation. It was reported that the adsorption enhancement of MgeFeeTi thin films is due to improved kinetics rather than any altered thermodynamics and FeTi solid solution may act as an effective pathway for hydrogen diffusion [38]. To the best our
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knowledge, there is still a lack of systematic study of the structural, electronic and thermo-dynamic properties of Ti and Fe co-doped MgH2 system. In this paper, we have studied MgH2 system with co-doped Ti and Fe by a first-principles calculation. Bond strengths of Mg-H and the thermo-dynamic properties of Mg12Ti2Fe4H36 have been investigated through Bader charge analysis and phonon calculation. In section Method of calculation the computational method is briefly presented, followed by the results and discussion. Finally, there is a conclusion in section Conclusions.
Method of calculation Self-consistent calculations were carried out using the standard plane-wave PW scf code of the QUANTUM-ESPRESSO package within the density functional theory (DFT) [39]. The generalized gradient approximation (GGA) of the PerdewWang 91(PW91) [40] was adopted for the exchangecorrelation energy functional and a plane wave basis set with kinetic energy cutoff of 40Ry was used. The Gaussian smearing method was used to describe partial occupancies of each wave function, with smearing value of 0.01eV. Before the electronic structures were calculated, geometric relaxations were performed in order to optimize the structures. In the relaxations both lattice parameters and all atomic coordinates were varied. In the present study, the Brillouin zone was sampled with a 3 3 7 Monkhorst-Pack k-point mesh for geometry optimization and a 5 5 9 Monkhorst-Pack k-point mesh for electronic structures to save the accuracy of total energies depending on k-mesh size and the computing time. The total energy convergence for the self-consistent calculation was set to 105 Ry, and all structures were fully optimized using the BFGS (BroydeneFletchereGoldfarbeShanno) method [41] until Hellman-Feynman forces were less than 4 104Ry/bohr. These criterions guarantee the chemical accuracy of calculated results. We have also calculated the density of states (DOS and PDOS) of pure MgH2 and Ti and Fe co-doped MgH2 to estimate the bonding properties between metal atoms and hydrogen atoms. In addition to DOS and PDOS calculations, Bader atomic charges were also calculated, which evaluates the ionicity of atoms in supercells. Bader atomic charge is a charge which is contained in regions called atomic basins surrounded by the zero-flux surfaces of the electronic density gradient vector field Vr. Additionally, phonon calculation was calculated in order to investigate the influence of lattice vibrations on stability and thermo-dynamic properties at finite temperatures. The used program package PHON [42] to evaluate the vibration energy contribution to thermo-dynamic properties within the QHA (quasi harmonic approximation) is based on the small displacement method. The cell parameters, atomic positions and the forces obtained from QUANTUM ESPRESSO were used as input data of PHON to generate the force constants, the dynamical matrix and the phonon frequencies. The phonon DOS was also calculated with a 24 24 12 k-point mesh to compute thermo-dynamic properties at temperatures between 300 K and 600 K.
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Results and discussion
Table 1 e The initial internal coordinates of MgH2 3 £ 3 £ 1 supercell model used in calculations.
Geometric optimizations
Atom
The MgH2 has three types of structure (a, b, g), depending on temperature and pressure, while it crystallizes in tetragonal symmetry (P42/mnm, group No. 136), so called rutile type structure in the ambient temperature and pressure. In its unit cell, two Mg atoms occupy Wyckoff position 2a (0, 0, 0) and four H atoms occupy 4f (0.303, 0.303, 0) [43] and experimentally measured lattice parameters are a ¼ 4.501 Å and c ¼ 3.010 Å [44]. In this study, we employed the 3 3 1 supercell (Mg18H36) with 3 times size of the unit cell along only the a and the b axes in order to research co-doped Mg12Ti2Fe4H36 system (Fig. 1). The initial non-equivalent Wyckoff positions of Mg and H atoms are tabulated in Table 1. It was found both experimentally and theoretically that beyond 20 at. % Ti content, the rutile structure characteristic of pure MgH2 is no longer stable, and the hydride transforms into a fluorite-type structure, similar to that of the transition metal dihydride [45]. Therefore we discussed the case which two Ti atoms were substituted in wyckoff 2a of rutile type Mg18H36 supercell and wyckoff 4f for four Fe atoms in order to save it's hydrogen capacity. Before total energy calculations, we performed the structural relaxations, followed by electronic calculations for Mg18H36 and co-doped Mg12Ti2Fe4H36 system. Table 2 shows the values of geometric parameters of both systems after the relaxations, except z ¼ 0 coordinates. To examine the accuracy of our calculation for the doped system, we have also studied the well-known Mg2FeH6 hydride. The structural geometry of Mg2FeH6 is analogous to that of cubic K2PtCl6 (fluorite-type) structure (Fm3m, group No. 225) [46] Mg2FeH6 has an experimental measured lattice constant a ¼ 6.443 Å and contains 36 atoms per unit cell, and Mg and Fe atoms occupy fixed Wyckoff positions 8c (1/4, 1/4, 1/4) and 4a (0, 0, 0), respectively. However, H atoms have variable Wyckoff positions 24e (x, 0, 0) [47]. The lattice constant of the relaxed structure is a ¼ 6.408 Å, which is close to experimental data [46].
Heats of formation and electronic structures The heat of formation is the most important thermo-dynamic quantity of hydrides and dehydrogenation temperature
Wyckoff positions
x
y
z
2a 4g 8i 4f 4f 4f 4f 8i 8i 8i
0 2/3 1/3 1/3 0.1016 0.4350 0.2317 0.1016 0.1016 0.4350
0 1/3 0 1/3 0.1016 0.4350 0.2317 0.4350 0.7683 0.7683
0 0 0 0 0 0 0 0 0 0
Mg1 Mg2 Mg3 Mg4 H1 H2 H3 H4 H5 H6
Table 2 e Relaxed structures of the considered supercells: Lattice parameters and Wyckoff positions of Mg1-Mg4, H1-H6. Cell parameters
Mg18H36
Mg12Ti2Fe4H36
a (nm) c (nm) V0 (nm3)
1.3566 0.3013 0.5545
1.2723 0.2899 0.4693
Wyckoff positions
x
y
x
y
Mg1 Mg2 Mg3 Mg4 H1 H2 H3 H4 H5 H6
0.0000 0.6667 0.3333 0.3333 0.1015 0.4348 0.2319 0.1015 0.1015 0.4348
0.0000 0.3333 0.0000 0.3333 0.1015 0.4348 0.2319 0.4348 0.7681 0.7681
0.0000 0.6540 0.3233 0.3220 0.1049 0.4331 0.2079 0.1094 0.1039 0.4330
0.0000 0.3460 0.0179 0.3220 0.1049 0.4331 0.2079 0.4425 0.7627 0.7432
depends mainly on the heat of formation. The heat of formation DH of hydrides can be defined as the difference between sum of total energies of products and that of reactants. DH ¼ Etot(products)-Etot(reactants)
(1)
Reactions related to the formation of the hydrides Mg18H36 and Mg12Ti2Fe4H36 are as follows: 18Mg þ 18H2/Mg18H36
(2)
Fig. 1 e Top (a) and side (b) views of MgH2 3 £ 3 £ 1 supercell model. Mg1, Mg2, Mg3 and Mg4 denote four non-equivalent positions for Mg, respectively.
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12Mgþ2Tiþ4Fe þ 18H2/Mg12Ti2Fe4H36
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(3)
We calculated the heats of formation of the hydrides based on these reactions using the following equations: DH(Mg18H36) ¼ Etot(Mg18H36)18Etot(Mg)18Etot(H2)
(4)
DH(Mg12Ti2Fe4H36) ¼ Etot(Mg12Ti2Fe4H36)12Etot(Mg)2Etot(Ti) (5) 4Etot(Fe)18Etot (H2) The total energies per atom of Mg, Ti and Fe were calculated using the lattice parameters given in Kittel. C (2005) [48] and are equal to 79.3133, 116.7335 and 253.5457Ry, respectively. The Etot (H2) was calculated by using a cubic unit cell of 10 10 10 Å. The calculated HH bond length, 0.752 Å and the total energy of H2 molecule, 2.3367Ry are in good agreement with other computational data [49]. The calculated total energies and heats of formation of the considered hydrides are listed in Table 3. Our result is close to the experimental value 74.0 kJ/mol H2 for MgH2 [29]. As seen Table 3, the heat of formation of Mg12Ti2Fe4H36 is much small in absolute magnitude than that of Mg18H36. and this fact indicates that Mg12Ti2Fe4H36 is thermo-dynamically more favorable for practical hydrogen ad/desorption than Mg18H36. Furthermore it demonstrates that the co-doping by Ti and Fe plays a crucial role in decreasing the stability of magnesium hydride, leading to the improvement of hydrogen storage characteristics. The relative stability of the doped system relative to the pure MgH2 can be evaluated by the difference between the heat of formation of the doped hydride and that of the pure one. From energy point of view, the smaller relative stability corresponds to the more favorable doping. Ab initio calculated relative stabilities of the single-doped rutile type systems with Ti and Fe were 22.91 kJ/mol H2 and 33.34 kJ/mol H2, respectively [22]. This indicates that the Fe substitution in MgH2 rutile type structure is more difficult than that of Ti in the same structure. Ab initio calculated our relative stability of the co-doped system is 26.43 kJ/mol H2. Hence, the doping of Fe combined with Ti into the MgH2 rutile type structure is more energetically favorable than the single-doping of Fe into the same structure. Therefore we suggest that Mg12Ti2Fe4H36 system may be possible practically through first Ti substitution and sequent Fe substitution. In order to understand the destabilizing mechanism of magnesium hydride, the electronic structure of co-doped system was also calculated as well as one of Mg18H36 system. Density of states (DOS) of pure system are presented in Fig. 2. The top panel is the total DOS and the next panels show the partial density of electronic states of Mg and H, respectively. In according to Fig. 2, Mg18H36 is an insulator with the
Table 3 e The total energy and heat of formation of MgH2 and Mg12Ti2Fe4H36. Hydride Mg18H36 Mg12Ti2Fe4H36
Total energy (Ry)
Heat of formation (kJ/mol H2)
1470.5712 2241.9787
63.58 37.15
Fig. 2 e Total and partial electronic densities of states of MgH2.
energy band gap of 3.74eV between the valence band (VB) and conduction band (CB). The VB is mainly dominated by the contribution from H s orbital and the CB mainly originates from Mg s and Mg p orbitals, which means a strong ionic bonding formation due to the charge transfer from Mg to H. Additionally, Mg s and Mg p orbital hybridizing with H s orbital in the valence band can also be seen, which contributes to somewhat covalent bonding interactions between Mg and H. Thus, the bonding characteristic in Mg18H36 is a mixture of ionic and covalent bonding. The relatively large band gap of Mg18H36 leads to a poor MgeH dissociation. In order to recovery the metallic property of Mg in dehydrogenation process, it is necessary that electrons should be transferred from H to Mg. Consequently the pure magnesium hydride has to receive much energy in order to release hydrogen due to the large energy band gap. That is why pure magnesium hydride is thermo-dynamically stable and its decomposition temperature is significantly high. The total and partial DOSs of the Mg12Ti2Fe4H36 system are shown in Fig. 3. The total DOS and partial DOSs of metallic atoms (Ti, Fe, Mg3 and Mg4) are plotted in the left-hand side and the partial DOSs of H atoms (H1eH6) in the right-hand side. The total DOS curve shows the band gap of 0eV, indicating clearly metallic characteristics. In the system, electrons transferring from H to Mg can be take placed easily, thus the bond between metallic and H atom can be also broke easily. It is interesting to note that the VB near the Fermi level is mainly attributed to Fe d and the CB near the Fermi level is mainly dominated by the contribution from Ti d. Furthermore we can see that the band gap disappear by both the contributions of Fe d and Ti d, so Ti and Fe co-doped magnesium hydride transforms into the conductor. Thermal conductivity of hydrides is very important in the sense that dehydrogenation process involves heating. We expect that the thermal conductivity of MgH2 would be improved by insulator-metal transition via Ti
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Fig. 3 e Total and partial electronic densities of states of Mg12Ti2Fe4H36.
and Fe co-doping. The distributions of PDOS peaks of Ti and Fe d orbitals are mainly concentrated in the energy region from 6.1 to 2.5eV and overlap well with Mg p and H s orbitals. The orbital hybridizing of Mg and H in co-doped system is weak than in pure system, resulting in weakening MgeH bond strength. The highest DOS peaks of H1, H2, H3 and H6 are located in the energy range from 4.9 to 3.5eV and H4 and H5 range from 3 to 2.7eV. Hence, Ti and Fe d orbitals are mainly hybridized with H1, H2, H3, and H6 s orbitals, and H4 and H5 s orbitals are mainly hybridized with Mg p orbitals. The PDOSs of H and Mg atoms in the VB of Fig. 3 are smaller than those in Fig. 2, indicating weaker bonding interaction between Mg and H. The weak bonding interaction between Mg and H in the co-doped system is the reason that the co-doping with Ti and Fe has a positive influence on the thermodynamical improvement.
Bond lengths and bader charge analysis Bonding lengths is a useful item to evaluate bonding strength straightforwardly by comparing them. Table 4 lists the bond
lengths between metal atoms in Mg18H36 and Mg12Ti2Fe4H36 supercell. In Table 4, the bond lengths are 4.522 Å for Mg1eMg3 bond and 3.535 Å for other bonds with an average of 3.655 Å, which is in good agreement with other theoretical results [36,44]. In co-doped system, all of the bond lengths between metal atoms are shorter than those of the pure system, ranging from 3.122 Å to 4.123 Å with an average of 3.446 Å. The TieFe bond length of 3.129 Å is short by about 11% in comparison with that of Mg1eMg2, which implies the strong bond strength and alloying trend. The bond lengths of TieMg3 and TieMg4 were shorter than corresponding bond lengths in pure system by 9 and 0.5%, respectively, while the bond lengths were reduced by 12% for FeeMg3 and 5% for FeeMg4, respectively compared pure system. For the co-doped system, the distance between Mg3 and Mg4 was also decreased by about 3%. Consequently it can be inferred that decreasing of these bond lengths imply the enhancements of bond strengths between metallic atoms and furthermore the bond strengths between H and metallic atoms would be weakened. The bond lengths between H and metallic atoms are presented in Table 5. H atoms form octahedrons around metal
between metallic elements in the MgH2 and Mg12Ti2Fe4H36. Table 4 e Calculated the bond distance (A) MgH2
Mg1-Mg2 3.535
Mg1-Mg3 4.522
Mg1-Mg4 3.535
Mg2-Mg3 3.535
Mg2-Mg4 3.535
Mg3-Mg4 3.535
Mg12Ti2Fe4H36
Ti-Fe 3.129
Ti-Mg3 4.123
Ti-Mg4 3.518
Fe-Mg3 3.122
Fe-Mg4 3.354
Mg3-Mg4 3.428
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between H and metallic atoms in Mg18H36 and Mg12Ti2Fe4H36. Table 5 e Calculated the bond lengths (A) MgH2
Mg12 Ti2 Fe4 H36
bonding
distance
bonding
distance
bonding
distance
bonding
distance
Mg1-H1 Mg1-H2
1.948 1.958
Mg2-H1 Mg2-H3 Mg2-H6
1.958 1.958 1.947
Mg3-H4 (1) Mg3-H4 (2) Mg3-H5 Mg3-H6
1.948 1.958 1.947 1.958
Mg4-H2 Mg4-H3 Mg4-H5
1.947 1.958 1.958
bonding
distance
bonding
distance
bonding
distance
bonding
distance
Ti-H1 Ti-H2
1.889 1.884
Fe-H1 Fe-H3 Fe-H6
1.698 1.744 1.587
Mg3-H4 (1) Mg3-H4 (2) Mg3-H5 Mg3-H6
1.913 1.938 1.900 1.879
Mg4-H2 Mg4-H3 Mg4-H5
2.000 2.054 1.887
Fig. 4 e The octahedrons of H atoms around metallic atom.
atoms: H1, H2 around Mg1, H1, H3, H4 around Mg2, H4, H5, H6 around Mg3 and H2, H3, H5 around Mg4, as shown in Fig. 4. Calculated results show that the bond lengths range from 1.947 Å to 1.958 Å for Mg18H36 and from 1.587 Å to 2.054 Å for Mg12Ti2Fe4H36. Bond lengths between Fe and H atoms were decreased by more than 10% in co-doped system compared with pure system, while TieH and Mg3eH were decreased by 1e4%. Nevertheless overall bond lengths have decreasing tendency by co-doping, such behavior was reversed for Mg4eH2 and Mg4eH3: bond lengths were increased significantly. In spite of the reduced supercell volume as co-doped, the bond lengths of MgeH do not decreased substantially and partially increased largely. Largely increased bond lengths might contribute to the weakening bond strength and further to the reducing hydrogen desorption temperature. In order to study the bonding features between metallic and H atoms in more detail, we performed Bader charge analysis
for the considered systems based on Bader's theory of atoms in molecules. It is addressed that Bader excess charge (BEC) is a crucial quantity in Bader charge analysis, which is defined as difference between the charge contained in a Bader atom and its atomic charge. It is possible to estimate the ionic degree of bonds approximately to some extents through comparing BEC. Table 6 lists BECs for pure and co-doped systems. The more positive BEC, the more cationic is the atom and the less negative BEC, the less anionic is the atom. In according to Table 6, BECs of Mg and H atoms reveal that the bonds between Mg and H are all strongly ionic for the pure system. As Ti and Fe are doped, BECs of H atoms except for H4 and H5 are reduced substantially in absolute magnitude and BECs of Mg atoms are increased slightly than those of pure system. Mg atoms have much bigger BECs than dopants Ti and Fe, especially þ0.475 for Fe. Furthermore, less negative BECs of H1, H2, H3 and H6 atoms imply that the ionicity of Ti-H and Fe-H bonds are weakened, thus ion bond strengths are also weakened. The reason for less negative BECs of H atoms is attributed to less positive BECs of Ti and Fe compared with Mg, while small BECs of Ti and Fe compared with Mg are correlated to their electronegativity. As compared with pure MgH2, not only the positive BECs of Mg3 and Mg4 but also the negative BECs of H4 and H5 are increased slightly, which reveals a little enhancement of ion bond strengths of Mg3-H4, Mg3-H5 and Mg4-H5.
Thermo-dynamical properties and lattice vibrations We determined thermo-dynamical properties (entropy and specific heat capacity at constant temperatures) from the phonon calculation of MgH2 and Mg12Ti2Fe4H36, and Table 7 show them with experimental data [50]. In phonon calculation, the forces on the atoms were evaluated for the 3 3 1 MgH2 supercell as they were displaced from their equilibrium positions. For the sake of convenience, the unit of entropy and specific heat capacity was set with 1 eV K1 per supercell, containing 54 atoms. At all temperatures the predicted
Table 6 e Bader charges of component elements for Mg18H36 and Mg12Ti2Fe4H36. Mg18H36
Mg12 Ti2Fe4 H36
Atom
Mg1
Mg2
Mg3
Mg4
H1
BEC
þ1.629
Atom
Ti
BEC
þ1.487
H2
H3
H4
H5
H6
þ1.628
þ1.629
þ1.629
Fe
Mg3
Mg4
0.821
0.815
0.808
0.820
0.815
0.809
H1
H2
H3
H4
H5
H6
þ0.475
þ1.645
þ1.646
0.437
0.659
0.492
0.815
0.821
0.648
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Table 7 e Entropy and specific heat capacity at constant temperatures calculated at different temperatures, compared with experimental data [46]. Temperature (K)
MgH2 3
S (10
300 400 500 600
eV K
1
per supercell)
Mg12Ti2Fe4H36 3
Cp(10
1
eV K
per supercell)
Present Work
Ref. [46]
Present Work
Ref. [46]
6.062 8.265 10.302 12.167
5.840 7.954 9.884 11.663
6.665 8.318 9.583 10.512
6.622 8.074 9.241 10.295
3
S (10 eV K1 per supercell)
Cp(103 eV K1 per supercell)
6.001 8.004 9.840 11.525
6.127 7.487 8.620 9.515
entropies and heat capacities of MgH2 show smaller deviations than 4% from the corresponding references values. Hence we suggest that our phonon calculations describe the vibrational properties of MgH2 within a degree of high accuracy. On the other hand, the thermo-dynamical values of the co-doped system are smaller than the corresponding ones of the pure magnesium hydride but the differences of them are not so much within a few percent. We show Figs. 5 and 6 for the total and partial phonon DOS of MgH2. and Mg12Ti2Fe4H36, respectively. We found that there are no negative phonon frequencies in the case of pure MgH2, as shown in Fig. 5. And the high frequency modes (above 300 cm1) are dominated by H atoms, and the low frequency modes (below 300 cm1) are dominated by Mg atoms, because the Mg atom is much heavier than H atom. Due to the mostly ionic interaction between H and Mg atoms in MgH2, there is hardly coupling between the vibrations of two atoms in Fig. 5 b and c. However, Fig. 6 is shown some negative phonon frequencies (negative frequencies are representative of imaginary
frequencies), and the negative frequency modes are dominated by Ti atoms in Fig. 6 b, which indicates that Mg12Ti2Fe4H36 is dynamically unstable. Although it is so, we can see the important properties of co-doped magnesium hydride with Ti and Fe. In Fig. 5 c, H atom phonon DOS is below about 1470 cm1 with some small zero-phonon gaps, but in Fig. 6 c, below about 1950 cm1 with comparatively wide zero-phonon gaps. Therefore, we know that the phonon frequency modes of H atoms are shifted to higher frequency region. It is also shown that in the case co-doped unlike pure MgH2, phonon DOSs of individual H atoms are localized remarkably, especially for H1, H2 and H3. This indicates that the presence of the co-doped atoms have a large influence on lattice vibrations of H atoms. Consequently we found that as Ti and Fe are co-doped, entropy and specific heat capacity change only a little, but the variation of lattice vibrations is considerably great from the study of thermo-dynamical and lattice vibration properties for Mg18H36 and Mg12Ti2Fe4H36 based on phonon calculation.
Fig. 5 e The calculated (a) total phonon DOS, (b) Mg atom phonon DOS and (c) H atom phonon DOS of MgH2.
Fig. 6 e The calculated (a) total phonon DOS, (b) Metal atom phonon DOS and (c) H atom phonon DOS of Mg12Ti2Fe4H36.
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 4 4 ( 2 0 1 9 ) 8 2 5 2 e8 2 6 0
Conclusions [10]
Ti and Fe co-doping effects on the destabilizing of MgH2 were studied by the first principles calculations based on DFT. The heats of formation of Mg18H36 and Mg12Ti2Fe4H36 determined by calculation of total energy show that magnesium hydride is thermo-dynamically destabilized by Ti and Fe co-doping. We compared our relative stability of the Ti and Fe co-doped system with the one of the Ti/Fe single-doped system referred in reference [22], which indicate that the doping of Fe combined with Ti into the MgH2 rutile type structure is more energetically favorable relative to Fe single-doping into the same structure. The electronic structures show that as Ti and Fe co-doped, energy band gap disappear due to the contribution of Fe in VB and Ti in CB. Also the hybridizing between Mg and H atoms is weakened compared to pure system. Bader charge analysis shows that the ionicity of H atoms is reduced due to the low iconicity of Ti and Fe compared with Mg. Therefore it may be concluded that dopants Ti and Fe codoping will be an effective method in order to destabilize the magnesium hydride. Deep understanding of the effect of codoping of Ti and Fe on (de-)hydrogenation of MgH2 requires a further investigation of (de-)hydrogenation kinetics, which is beyond the scope of the present investigation. As Ti and Fe are co-doped, entropy and specific heat capacity change only a little, and the phonon frequency modes of H atoms are shifted to higher frequency region and are localized remarkably. Our study might be useful to investigate the effects of co-doped atoms for the improvement in the hydrogenationdehydrogenation properties of MgH2, even if the present codoped system is dynamically unstable from the phonon calculation results.
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