Geometric, Electronic, and Magnetic Properties of MgH2: Influence of

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Geometrical, Electronic and Magnetic Properties of MgH: Influence of Charged Defects 2

Francisco Gaztañaga, Carla Romina Luna, Mario Sandoval, Carlos Eugenio Macchi, and Paula V. Jasen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06827 • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 23, 2016

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The Journal of Physical Chemistry

Geometrical, Electronic and Magnetic Properties of MgH2: Influence of Charged Defects F. Gaztañagaa, Carla R. Lunaa,b, M. Sandoval a,b, C. Macchic, P. Jasen*a,b

a

Departamento de Física, Universidad Nacional del Sur, Av. Alem 1253, B8000CPB, Bahía

Blanca, Argentina. b

Instituto de Física del Sur (IFISUR, UNS−CONICET), Av. Alem 1253, B8000CPB, Bahía

Blanca, Argentina. c

Instituto de Física de Materiales Tandil and CIFICEN (UNCPBA-CONICET-CICPBA),

Pinto 399, B7000GHG Tandil, Argentina

* Corresponding author: E-mail: [email protected] . Phone: +54 291 4595101, ext 2843.

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Abstract A study on the effect of the presence of charged vacancy on the electronic and magnetic properties of perfect magnesium hydride is presented. To this aim spin polarized ab-initio calculations for the MgH2 structure containing a H vacancy or a Mg vacancy or a H-Mg divacancy were used. For each case three possible charge states (q = +1, 0 and −1) were taken into account. The calculated parameters were the vacancy formation energy, band gap, magnetic moment, Fermi level position with respect to the top of the valence band and the bottom of the conduction band and density of states curves. From the calculations, it was found that positive and negative charged H vacancies and the negative charged divacancy are the most probable formed defects. Besides the presence of a negative or neutral H vacancy produces to an important reduction of the band gap, which should improve the semiconductor behavior of the material. Furthermore the charged H vacancies provoke an important local rearrangement in the structure of the hydride. On the other hand, the positive charged Mg vacancy induces the highest magnetic moment.


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1. Introduction It is well known that the use of fossil fuels, due to CO2 emissions, leads to global environmental problems and produces economical impact. These issues motivate the use of alternative energies being friendly with the environment. Last years, hydrogen vector has be seen as an excellent alternative energy source for the new economy. However, there are many technologic issues to be solved related to hydrogen storage. The scientific community has studied several solid state materials trying to find a solution for this problem.1 In particular; magnesium hydride (MgH2) is considered a promising candidate as material for hydrogen storage due to its low cost, availability and non-toxicity among others. However, the MgH2 activation energy for hydrogen kinetic desorption is relatively high.2 One alternative for this inconvenient is the addition of transition metals (TM) or defects like vacancies.3-9 Native point defects can be electrically charged and affect numerous properties such as structure, thermal diffusion rates, trapping and recombination rates for electrons and holes and luminescence quenching rates.10 The thermodynamic of charged defects has been discussed in numerous journal articles and books.11-14 On the other hand, in the literature have been reported several studies about the microscopic mechanisms operating in the hydrogenation and de-hydrogenation process in magnesium hydride which are related to the formation and diffusivity of vacancies in bulk MgH2.15-17 For example, Hao et al. used Density Functional Theory (DFT) calculation to study the influence of charged defects on the diffusion of H in MgH2 and NaMgH3.17 These authors found that the physically relevant defects are charged and that H diffusion is dominated by the mobility of negatively charged H interstitials. To elucidate the thermodynamics of H vacancies in MgH2 Grau-Crespo et al. used ab initio calculations and a formulation based on statistical mechanics.

18

They found that at temperatures and 3

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hydrogen partial pressures of practical interest, MgH2 is capable to accommodate only a very small concentrations of hydrogen vacancies, mainly isolated vacancies instead vacancy clusters. This behavior differs to that expected from a simple energetic analysis. For the best of our knowledge, there is not available quantitative information through spin polarized ab-initio calculation regarding the influence of charged vacancies on the chemical and physical properties in magnesium hydride. Under this scenario, the motivation of the present work is to study the geometrical, electronic and magnetic properties of perfect MgH2 and this hydride containing defects in different charge state. Specifically, under the frame of the DFT we made spin polarized ab-initio calculations for the MgH2 structure containing a H vacancy ( VH ), or a Mg vacancy ( VMg ) or a di-vacancy H-Mg ( VH −Mg ); for each case three possible charge states (q = +1, 0 and −1) were taken into account. In all systems, the following parameters were calculated: vacancy formation energy, band gap, magnetic moment, Fermi level position with respect to the top of the valence band and the bottom of the conduction band and density of states (DOS) curves. The present work is organized as follow. In Section 2 Computational methods are described. In Section 3 we report and discuss the obtained results and, in section 4 we give the conclusions of the present work. 2. Computational methods Calculations have been performed within the frame of spin polarized DFT as implemented in the Vienna Ab-initio Simulation Package (VASP) code.19-21 The projector augmented wave (PAW) pseudopotential was used to account the electron-ion core interaction, using the PW91 functional as the generalized gradient approximation (GGA) for the exchange-correlation term.22


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The MgH2 can crystallize in rutile structure (P42/mnm, group No. 136). To model this structure a supercell with 72 atoms (24 Mg and 48 H atoms) was used (see Figure 1-a). The calculated lattice parameters were a= 4.501 Å, c/a = 0.669 and x = 0.305Å. These values are in good agreement with those experimentally and theoretically obtained.15,23 Vacancies were simulated by removing individual atoms from the supercell (see Figure 1b). For the ionic relaxation calculations, the Brillouin zone was sampled using a 4 × 4 × 4 Monkhorst−Pack k-points mesh.24 The supercell was fully relaxed without constraints using the conjugate gradient algorithm. The convergence criteria was set to be 10−4 eV/Å on each atom and the calculation was considered to converge when the difference in the total energy of the supercell between consecutive steps did not exceed 10−4 eV. Finally, to compute formation energies, magnetic moment, density of states and positron lifetime a 15x15x15 k-points grid was employed. In the calculation, for the plane-wave basis set a cut-off of 650 eV was used. The methodology on the formation calculations energy of charged defect is is still an open issue.5,15,17,25-26 Under this scenario, in the present work the formalism proposed by Van de Walle et al.14-15,26 was used. In such way, the formation energy Eform of a type X vacancy in the charge state q is

Eform (Xq) = Etot(Xq) - Etot(bulk) + ∑ ni (µi + Eref,i ) + q (EF + EV +∆V)

(1)

where Etot(Xq) is the total energy of defective supercell and Etot(bulk) corresponds to the total energy of the same without defects (i.e., perfect supercell) and ni is the number of removed atoms of specie i with chemical potential µi. In particular, for H and Mg species 5 ACS Paragon Plus Environment


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their chemical potentials are referenced to the energy per atom of H2 molecule and bulk Mg respectively i.e. Eref,H = 1/2 Etot (H2) and Eref,Mg = Etot(Mg). Furthermore the chemical potentials are restricted to the boundaries given by the stability of the hydride µMg+2µH = ∆Hf (MgH2), with µMg ≤ 0 and µH ≤ 0. Where ∆Hf (MgH2) is the formation enthalpy of bulk MgH2. Particularly H-poor conditions are the most relevant for H desorption, in which case µMg = 0 and µH = 1/2 ∆Hf (MgH2). Finally, EF is the Fermi level, referenced to the valenceband maximum (EV) of the host material and ∆V is a correction factor to EV for the shift in the electrostatic potential respect to that perfect MgH2 due to the introduction of charged defects.15,17,26-27

Figure 1. Crystal structure of perfect MgH2 (a) and local structure around were the defects be generate (b).


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3. Results and discussion Table 1 summarized the calculated parameters for perfect MgH2 and for the structure including vacancy like-defects. In the case of the hydride without vacancies the computed band gap (Eg) is 3.79 eV. This value is in good agreement with other theoretical reported values in the literature.

28-29

obtained (5.6 ± 0.1 eV

30

However, the Eg value is smaller than those experimentally

). As reported for several semiconductors and insulators, this

discrepancy can be attributed to that the Kohn–Sham formalism implemented in DFT resulting in underestimation of band gaps values.31 The presence of vacancies produces a band gap reduction respect to the bulk. This change is more significant for VH0 and VH− , with a reduction of 65.4 % and 68.8% respectively. These types of defects are responsible for the apparition of occupied and unoccupied states within the band gap zone (see discussion below). For the other vacancy types the Eg decrease between a 6% and 10% approximately. As can be seen in Table 1 in all cases, except for VH− , the Fermi level is located near to the top of the valence band (VB). Indicating that the MgH2 containing native charged vacancies behaves as a p-semiconductor. This is in good agreement with the reported by Karazhanov and co-workers .32 Summarizing, it could be conclude that vacancies are the most likely physical cause for the band gap reduction. In addition, vacancies in MgH2 would mainly affect the electronic structure near the Fermi level or create a defect level in the band gap.33



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Table 1. For perfect and defective MgH2 band gap (Eg), percentage change of Eg respect to perfect MgH2 (%), magnetic moment (µ), Fermi level location with respect to the valence and conduction bands (∆VB and ∆CB) and vacancy formation energy (Eform) calculated in the intrinsic Fermi level (2.6 eV). The defects are identified by VXq where q and X correspond to charge state and atomic species removed respectively. Eg (eV)

%

µ (µB)

∆VB (eV)

∆CB (eV)

Eform (eV)

Bulk

3.79

-

0.00

0.93

2.86

-

VH0

1.31

65.4

0.15

0.39

0.92

1.23

VH−

1.18

68.8

0.00

0.60

0.58

0.77

VH+

3.41

10.0

0.00

0.90

2.51

0.66

0 VMg

3.51

7.3

0.30

-0.19

3.71

6.54

− VMg

3.56

6.1

0.00

-0.02

3.57

2.48

+ VMg

3.42

9.7

0.74

-0.32

3.74

10.57

VH0−Mg

3.57

5.8

0.01

0.03

3.54

4.13

VH−−Mg

3.43

9.4

0.00

0.91

2.52

0.13

VH+−Mg

3.50

7.6

0.49

-0.15

3.65

8.26

System

The formation energy calculations are performed from DFT formalism where GGA is considered. In the cited literature, several authors support the applicability of this method for defect systems due to fairly accurate total energies in large systems, of around 100 atoms, when two corrections are considered: Band-edge corrections due to the approximate DFT functional and Corrections due to the supercell approximation.34-35 The calculated formation energies as a function of the Fermi level (EF) in the band gap zone are shown in Figure 2. The lower limit EF = 0 corresponds to the top of the valence band (VB) while the 8 ACS Paragon Plus Environment

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upper limit is associated with the bottom of the conduction band (CB). Under H-poor conditions the results indicate that the defects with the highest probability to be formed are V H+ , VH− and VH−−Mg , therefore their concentration could be higher than other defects. In the case of VH0 the Eform is 1.23 eV (see Table 1 and Figure 2); several authors reported a similar value.13-14,24 Without other defects or impurities, the charge neutrality would pin the EF at 2.66 eV in which V H+ and VH− have the same Eform = 0.72 eV. Similar EF and Eform values were reported by Wang et al.27 Several authors reported a value of around 1.1 eV.15,17,27 Such difference could be attributed to the H chemical potential used for Eform calculation. For example using in our calculation µH = -0.33 eV (taken from Park et al.15) we obtained V H+ and VH− formation energies of 0.99 eV; this value is in good agreement with those reported by Hao et al. and Park et al.5,15 Moreover, as can by deduced from Figure 2, independently of the charge state, the incorporation of an H vacancy as a first neighbor to a Mg one significantly reduces the Eform. According to Yang et al. the formation energies and electron occupation in the conduction band can be treated assuming that there exist a singly charged acceptor with a formation energy of Eform = EF.

25

While the hole occupation in the valence band can be

treated as a singly ionized donor with a formation energy of Eform = Eg - EF. It must be considered that for each type of occupation, there is a transition energy level in the VB or CB respectively. In Figure 2, these formation energies are presented with dotted lines. It can be seen that the straight line Eform = EF is located above the intersection point between the lines corresponding to the VH+ and VH− formation energies as function of EF. As a result, beyond the intersection point more VH− is formed than VH+ due to lower formation energy of



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VH− for higher Fermi energies as a consequence the Fermi level will be pulled back. In the intersection point, both vacancies have the same formation energy (0.72 eV), and then the

VH− formation will be accompanied by the formation of VH+ in an almost equal number. In other words, most acceptors will be compensated by donors or vice versa and therefore the formation of charge-compensated defects will spontaneously occur. Under this condition the charged defect compensation behavior is self-regulated.25

Figure 2. Defect formation energies (Eform) as a function of Fermi energy (EF) for MgH2 containing native defects, each one in their different charge state. The dotted lines indicate Eform = EF and Eform = Eg- EF.

DOS analysis shown a strong hybridization of Mg and H states in the VB and CB for total DOS (TDOS) of perfect MgH2 (see Figure 3). This fact supports the idea of a strong 10 ACS Paragon Plus Environment

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covalence bond between Mg and H atoms. The spin up and spin down contribution are symmetric which is in agreement with a zero magnetic moment for the perfect hydride (see Table 1).

Figure 3. DOS curves for perfect MgH2. Total (a), PDOS for Mg atom (b) and PDOS for H atom (c).

Figure 4 shows the DOS curves for the hydride with an H vacancy with different charge state. When the negative H vacancy ( VH− ) is generated the TDOS shows an occupied spin up and spin down state localized in the band gap, which is responsible for their reduction. The Fermi level is pushed up to higher energies, transforming this hydride in a n-type semiconductor (see Figure 4-a). Figure 4-b and -c, shows that the major contributions to the trap state come from Mg1, which is a near neighbor to the vacancy site (see Figure 1-b). In the case of neutral H vacancy ( VH0 ) the most notorious change is that the state localized in the band gap is occupied for spin up contribution and unoccupied for spin down contributions (see Figures 4 -d, -e and -f). This behavior around the Fermi level is responsible for the appearing of a small magnetic moment (0.15 µB in Table 1). These results are in good agreement with that reported by Grau-Crespo and colleagues.18 For the positive H vacancy ( VH+ ) the TDOS curves is similar to that in the perfect MgH2, the only 11 ACS Paragon Plus Environment


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change is a peak at 2.5 eV for both spin up and spin down contributions for the Mg atom PDOS (see Figures 4-g and -h, respectively). The PDOS for H atom is almost unaffected (see Figure 4-i). Also, the spin up and spin down contribution are symmetric which result in a zero magnetic moment for this system (see also Table 1).

Figure 4. DOS curves for MgH2 with a H vacancy. Total (a), PDOS for Mg atom (b) and PDOS for H atom (c) in the case of VH− . Total (d), PDOS for Mg atom (e) and PDOS for H atom (f) in the case of VH0 . Total (g), PDOS for Mg atom (h) and PDOS for H atom (i) in the case of VH+ . The atoms for PDOS are displayed in figure 1(b)).

The DOS curves for MgH2 with a Mg vacancy are shown in Figure 5. It can be seen that the curves are shifted to higher energies, being responsible that the Fermi level cross the VB. In all cases the main contribution at the Fermi level comes from H atom nearest neighbors to the vacancy site (see Figures 5-b to -i). This behavior is reasonable considering that the Mg 12 ACS Paragon Plus Environment

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− is surrounded by six H atoms (see Figure 1-b). For VMg the spin up and spin down 0 + contributions are symmetric while for VMg and VMg are asymmetric. The shift between spin

contributions is only visible in the VB (see Figure 5-d to i). The most important induced + magnetic moment is detected in the case of VMg (see Figure 5-g) with a value of 0.74 µB.

Figure 5. DOS curves for MgH2 with a Mg vacancy. Total (a), PDOS for Mg atom (b) and − PDOS for H atom (c) in the case of VMg . Total (d), PDOS for Mg atom (e) and PDOS for H 0 . Total (g), PDOS for Mg atom (h) and PDOS for H atom (i) in atom (f) in the case of VMg + the case of VMg . The atoms for PDOS are displayed in figure 1(b).

Finally, Figure 6 shown the DOS curves for a di-vacancy formed by the removal of an H and an Mg atom with different charge state. It can be seen in Figure 6-a that the TDOS 13 ACS Paragon Plus Environment


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corresponding to the case of VH−−Mg is similar to that obtained for the perfect hydride. In the cases of VH0−Mg and VH+−Mg the DOS curves are pushed up to higher energies (see Figures 6-d to -i)). The PDOS shown that the major contribution around the Fermi level is from H atoms (see Figure 6-c, -e and -i). Particularly, the DOS curves for the VH0−Mg shows a little different between spin up and spin down contributions resulting in a very small induced magnetic moment (0.01 µB, see Table 1). In the case of VH+−Mg the DOS curves are asymmetric, with an appreciable induced magnetic moment (0.49 µB).

Figure 6. DOS curves for MgH2 with a di-vacancy. Total (a), PDOS for Mg atom (b) and PDOS for H atom (c) in the case of VH−−Mg . Total (d), PDOS for Mg atom (e) and PDOS for H atom (f) in the case of VH0−Mg . Total (g), PDOS for Mg atom (h) and PDOS for H atom (i) in the case of VH+−Mg . The atoms for PDOS are displayed in figure 1(b).


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Summarizing, the introduction of native vacancy defects affect the hydride electronic behavior mainly around the Fermi level. Being the VB the most affected in all cases. In + some cases the introduction of defects induced a magnetic moment, being VMg the most

important. For neutral and negative charged H vacancies a trap state appears in the band gap, generating an important reduction in it.

Figure 7: Topological location of the magnetic moments in the crystal structure for: VH0 0 + (a), VMg (b), VMg (c), and VH+−Mg (d). The removed atom or atoms are indicated by white

dotted spheres. The topological distribution of magnetic moments is shown on figure 7. We can see that the magnetic moments are concentrate in the atoms closest to the defects site in the case of VH0 , 0 + and VMg (see Figure 7-a to c). For the system with a VH+−Mg the magnetic moment is VMg

mainly located in the H atoms first neighbors to the Mg vacancy (see Figure 7-d). Figure 8 show the local structural changes induced by vacancy incorporation in MgH2. In the case of VH− the Mg atoms first neighbors are relaxed toward the vacancy site, from 1.854 Å to 1.809 Å and 1.938 Å to 1.649 Å (see Figure 1-b and Figure 8-a). This effect can be attributed to the Coulomb interaction between Mg atoms and the VH− . On the other hand, 15 ACS Paragon Plus Environment


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the presence of a VH0 practically does not change the Mg atomic positions with respect to the perfect hydride (Figure 8-b). Finally, if a positive charge state is considered for VH the Mg atoms first neighbor to the vacancy move away. The nearest Mg atom move about 0.304 Å and the others two Mg 0.266 Å (Figure 8-c). Wang et al. reported a similar result.27 Regarding the incorporation of Mg isolated vacancy, the first neighbors are six H atoms. The presence of VMg shows an opposite behavior in the structural relaxation compared with that observed for a VH (see Figure 8-d to -f). This fact could be attributed to the ionic character of MgH2. When the VMg is considered with a negative charge state, four H atoms move away 0.164 Å and the others two remain practically in their initial positions (see Figure 8-d). For the neutral state of VMg , only four H atoms change their positions shifting away approximately 0.103 Å from the vacancy site (see Figure 8-e). In addition, for positive charge state of VMg the H atoms are slightly relaxed inward, around 0.04 Å (see Figure 8-f). Finally when VH −Mg is considered, for all charge states studied, the Mg atoms neighbors to VH site move away around of 0.203 Å. Moreover the H atoms, nearby to VMg , are relaxed away but this shift depend on the charge state of VH −Mg . This behavior is similar to isolated VMg and it can be seen in Figure 8-g to -i.


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− 0 Figure 8: Local structure around defect site for VH− (a), VH0 (b), VH+ (c), VMg (d), VMg (e), + (f), VH−−Mg (g), VH0−Mg (h) and VH+−Mg (i). VMg

Mg

H

VH

VMg.



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4. Conclusions In the present work, the geometrical, electronic and magnetic properties of perfect MgH2 and this hydride containing defects in different charge state using spin polarized DFT calculations were studied. From the obtained results it can be concluded that: • The formation energy results indicated that H defects are found to be prone in charged states, while for Mg vacancies the lowest energy formation corresponds to the negative charged state. In the case of charged divacancies, the effect of complexing a Mg vacancy with an H one results in a decrease of the energy formation values. • The major structural local rearrangements are produced for charged defects. In particular the case of the charged H vacancy presents the most important changes. • The DOS curves it can bee concluded that the introduction of native defects affects the electronic behavior mainly around the Fermi level. In the case of negative charged and neutral H vacancies, trap states appear around the EF producing an important reduction in the band gap. Also the curves shown that only few cases have spin-polarized states. • In only few cases spin-polarized states were observed. Among them, the positive charged Mg vacancy has the major induced magnetic moment value. Summarizing, it is important to remark that our results indicate that the positive and negative charged H vacancies and the negative charged divacancy are the most probable formed defects. Then, the energy stabilization could improve the hydrogen storage capability of the magnesium hydride. The introduction of negative and neutral H vacancy


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produces an important reduction of the band gap, which should improve the semiconductor behavior of the material.

Acknowledgement We acknowledge for funding Agencia Nacional de Promoción Científica y Tecnológica (Argentina) (PICT 2014-1351), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET - Argentina) (PIP #114-201101-00151 and PIP 2014-2016. Res. N° 5013/14. Código: 11220130100436CO), Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CIC-BA), SEGECyT (UNS) and SECAT (UNCPBA). CRL, PJ and CM are members of CONICET and MS acknowledge a fellowship from CONICET.



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