- Email: [email protected]
Structural phase transitions in MgH2 under high pressure
Solid State Communications 148 (2008) 403–405
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Structural phase transitions in MgH2 under high pressure Shouxin Cui a,∗ , Wenxia Feng a , Haiquan Hu a , Zhenbao Feng a , Yuanxu Wang b a
School of Physics Science and Information Technology, Liaocheng University, Liaocheng 252059, PR China
b
Institute of Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng 475004, PR China
article
info
Article history: Received 29 June 2008 Received in revised form 6 September 2008 Accepted 12 September 2008 by J.R. Chelikowsky Available online 23 September 2008
a b s t r a c t Understanding of the structural stability and bonding nature of MgH2 is considered as essential for improving its hydrogen storage properties. Here, we present the sequence of phase transformation and bonding nature by first-principles calculation. The calculations indicate that there exist a phase sequence of α → γ → β → , δ -MgH2 phase is not stable under high pressure. All phases of MgH2 have a strong ionic character with the analysis of the charge-density distribution and density of states. Making its ionic bonding weaker is considered to improve the dehydrogenation performance of MgH2 . © 2008 Elsevier Ltd. All rights reserved.
PACS: 61.50.Ks 71.15.Mb 71.20.-b Keywords: A. Insulator D. Phase transition E. Ab initio
Exploring a safe, cost-effective, and fully hydrogenation reversible hydrogen storage material with a higher gravimetric hydrogen density in excess of of 6.5 wt% is one of the targets for developing next-generation energy storage systems [1,2]. Magnesium is an attractive material for hydrogen-storage applications because of its light weight, low manufacture cost, and high hydrogen-storage capacity (7.66 wt%). However, its slow hydriding/dehydriding kinetics and high dissociation temperature (nearly 573K) limit its practical applications [3]. In order to improve the hydrogenstorage properties of MgH2 alloys, understanding of its structural stability and bonding nature under extreme conditions is considered essential. α -MgH2 crystallizes in the rutile-type structure(P42 /mnm) at ambient conditions [4,5]. At high temperatures and pressures, α MgH2 transform into the orthorhombic γ -MgH2 (α -PbO2 type). Recently, to probe the structural sequence of MgH2 at high pressures, Bortz et al. confirmed the crystal structure of γ -MgH2 from the x-ray and neutron power diffraction data collected at 2 GPa, but they didn’t give the transition pressure [6]. Vajeeston et al. have investigated pressure-induced structural transitions in MgH2 [7,8] using the first-principles pseudopotential method and predicted that the transition from α -MgH2 to γ -MgH2
∗
Corresponding author. Tel.: +86 635 8231218; fax: +86 635 8238055. E-mail address: [email protected] (S. Cui).
0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.09.033
occurred at 0.39 GPa. However, Moriwaki et al. reported the transition pressure of 9 GPa [9] from x-ray diffraction (XRD) measurements at room temperature. Owing to the difficulties in determining accurately the hydrogen positions in a metal matrix by XRD measurements, several critical issues for the phase transition sequence of MgH2 under compression are still under debate in experiments. Under further compression, several other ¯ Pbc21 , Pbca, Pnnm, high-pressure phases (with space group Pa3, ¯ et al.) were proposed in theory [8,9], and the ab initio Fm3m pseudopotential calculations established the sequence of the phase transition is α → γ → β(Pa3¯ ) → δ(Pbc21 ) → (Pnma) [7,8]. Recently, a metastable phase of MgH2 (I41 /amd, group 141), which meets all the mechanical stability criteria for a tetragonal crystal, has been suggested through full-potential linearized augmented plane-wave (FP-LAPW) calculations [10]. Very recently, a new pressure-induced transition from the α MgH2 phase to an orthorhombic CaCl2 (Pnnm) phase is predicted by ab initio phonon calculations [11]. Accordingly, much more careful experimental and theoretical efforts are needed to further understand the high pressure behaviors of MgH2 . The calculations presented in this study were performed within the density functional theory, using the plane-wave pseudopotential method [12]. We used the generalized gradient approximation for the exchange-correlation functional [13]. The norm-conserving pseudopotentials were employed to model the ion-electron interactions [14]. The energy cutoff of the plane-wave
404
S. Cui et al. / Solid State Communications 148 (2008) 403–405
Table 1 Calculated structural parameters for α -MgH2 at ambient pressure, compared with experimental and previously theoretical values
Present work Theorya Theoryb Exp.c Exp.d
a (Å)
c (Å)
u
4.514 4.485 4.499 4.515 4.501
2.992 2.999 3.00 3.019 3.010
0.3039 0.304 0.305 0.304 0.304
Internal parameter u is the fractional coordinates of H atoms. a Reference [7]. b Reference [11]. c Reference [9]. d Reference [6].
Fig. 1. Calculated enthalpy differences of all these actual and possible structures of MgH2 with respect to α -MgH2 as a function of pressure. Fig. 3. The electronic total and partial density of states for α -MgH2 and γ -MgH2 .
Fig. 2. Pressure–volume relation of MgH2 solid in the most stable structural phases.
basis was chosen as 600 eV. The Brillouin zone was sampled by Monkhorst-Pack k points grids. The chosen plane-wave cutoff and the number of k points were carefully checked to ensure the total energy converged to better than 1 meV/atom. The tolerance in the self-consistent field (SCF) calculation is less than 10−8 eV/atom. For a given external hydrostatic pressure, both the parameters of the unit cell and the internal coordinates of the atoms are fully relaxed until forces had converged to less than 0.01 eV/Å and all the stress components are less than 0.02 GPa. The calculated structural parameters for α -MgH2 , together with experimental [9,6] and previous theoretical [7,11] data are listed in Table 1. It is clear that our calculated results are in excellent agreement with experiments and previous calculations. To investigate the pressure-induced structural transition, we have
carried out calculations for several possible types of structural phases [7]. The computed relative enthalpy with respect to α MgH2 versus pressure relation for all the actual and possible structural phases are shown in Fig. 1. The calculated transition pressure for the α → γ transformation is 1.2 GPa (Fig. 1). Because of the these two structures taking nearly the same structural arrangements, the relative enthalpy for them are nearly the same at the equilibrium pressure, which may be the reason why these two structures in experiments coexisted in a certain pressure range [8,9]. The subsequent phase transformations from γ - to β -MgH2 and β - to -MgH2 (AlAu2 -type structure also called cotunnite-type) occur at 9.7 GPa and 17.1 GPa, respectively, and the reported δ -MgH2 , I41 /amd and CaCl2 phases are not stable under high pressure. From Fig. 1, we can see that the β -MgH2 and δ -MgH2 separated by a small enthalpy barrier of about 1 meV, which suggests that the relative stability of these two phases are very easily affected by external factors (for example temperature and pressure). While recent powder XRD experiments reported the structural sequence was α → γ → δ → [9]. Our computed phase sequence is not consistent with the experimental observation [9,8] and previous theoretical calculations [7]. These discrepancies might be attributed to the neglect of zero-point fluctuations (T = 0 K) in the theoretical calculations and high pressure diffraction experiments were performed at room temperature on a sample with likely defects and impurities. The calculated P–V relation of MgH2 solid is shown in Fig. 2. It can be seen that there is small collapse in the volume (about 1.75%) accompanying the α → γ transition. The equilibrium volume for β -MgH2 is found to be 4.9% smaller than that of γ -MgH2 , and 5.8% volume reduction for β → phase transition. The electronic total and partial density of states (DOS) for α and γ phase are shown in Fig. 3. The calculated energy gap is 3.60 eV
S. Cui et al. / Solid State Communications 148 (2008) 403–405
405
The volume reductions accompanying the phase transition are obtained. The δ , CaCl2 type structures are not stable phases. α MgH2 turns out to be an insulator, which is consistent with experimental observation, and the theoretical calculations show that the high-pressure phases also exhibit insulating behavior. The DOS and valence charge density contour reveal that all phases of MgH2 have a strong ionic character. We consider that its ionic bonding must be made weaker to improve the dehydrogenation performance of MgH2 . Acknowledgments This work was financially supported by Science Foundation for Youth of Liaocheng University (No. X071046). Special thanks should go to the Natural Science Foundation of Shandong Province of China (No. Y2006A02) and the National Natural Science Foundation of China (Grant No. 60571062). Fig. 4. Valence charge density plots for α -MgH2 in the (001) plane.
and 3.81 eV for α - and γ -MgH2 , respectively. The width of valence band (VB) is 7.41 eV and 7.84 eV for α and γ phase, respectively. The increased width of VB is attributed to the reduction in the distance of Mg-H bond under high pressure. According to Fig. 3, the entire whole of VB for these two phases is dominated mainly by H s state which implies that the Mg valence electrons transfer to the H sites under high pressure. The DOS (Fig. 3) show that there exist strong ionic interaction between Mg and H. Fig. 4 shows the charge density contour in the (001) plane for α -MgH2 . Charge density maps serve as a complementary tool for achieving a proper understanding of the electronic structure of the system being studied. In the figure, we see that the valence electrons of Mg mostly transfer to the H sites, thus showing that there is strong ionic bonding between Mg and H atoms. For other various MgH2 polymorphs, there are nearly in the same bonding situation. To conclude, theoretical calculations predict that α -MgH2 transforms into the γ , β , and phases under high pressure, and the transition pressure is 1.2 GPa, 9.7 GPa and 17.1 GPa, respectively.
References [1] L. Schlapbach, A. Züttel, Nature 414 (2001) 353. [2] Hydrogen Storage Challenges, Fuel Cells and Infrastructure Technologies Program-Hydrogen Storage, Energy Efficiency and Renewable Energy, US Department of Energy. http://www.eere.energy.gov/hydrogenandfuelcells/ storage/storage_challenges.html. [3] F.E. Pinkerton, B.G. Wicke, Ind. Phys. 10 (2004) 20. [4] J.P. Bastide, B. Bonnetot, J.M. Letoffe, P. Claudy, Mater. Res. Bull. 15 (1980) 1215. [5] W.H. Zachariasen, C.E. Holley Jr., J.F. Stamper Jr., Acta Crystallogr. A 16 (1963) 352. [6] M. Bortz, B. Bertheville, G. Böttger, K. Yvon, J. Alloys Compd. 287 (1999) L4. [7] P. Vajeeston, P. Ravindran, A. Kjekshus, H. Fjellvåg, Phys. Rev. Lett. 89 (2002) 175506. [8] P. Vajeeston, P. Ravindran, B.C. Hauback, H. Fjellvåg, A. Kjekshus, S. Furuseth, M. Hanfland, Phys. Rev. B 73 (2006) 224102. [9] T. Moriwaki, Y. Akahama, H. Kawamura, J. Phys. Soc. Japan 75 (2006) 074603. [10] Y. Song, Z.X. Guo, Appl. Phys. Lett. 89 (2006) 111911. [11] L.J. Zhang, Y.C. Wang, T. Cui, Y. Li, Y.W. Li, Z. He, Y.M. Ma, G.T. Zou, Phys. Rev. B 75 (2007) 144109. [12] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Modern Phys. 64 (1992) 1045. [13] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [14] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Structural phase transitions in MgH2 under high pressure Shouxin Cui a,∗ , Wenxia Feng a , Haiquan Hu a , Zhenbao Feng a , Yuanxu Wang b a
School of Physics Science and Information Technology, Liaocheng University, Liaocheng 252059, PR China
b
Institute of Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng 475004, PR China
article
info
Article history: Received 29 June 2008 Received in revised form 6 September 2008 Accepted 12 September 2008 by J.R. Chelikowsky Available online 23 September 2008
a b s t r a c t Understanding of the structural stability and bonding nature of MgH2 is considered as essential for improving its hydrogen storage properties. Here, we present the sequence of phase transformation and bonding nature by first-principles calculation. The calculations indicate that there exist a phase sequence of α → γ → β → , δ -MgH2 phase is not stable under high pressure. All phases of MgH2 have a strong ionic character with the analysis of the charge-density distribution and density of states. Making its ionic bonding weaker is considered to improve the dehydrogenation performance of MgH2 . © 2008 Elsevier Ltd. All rights reserved.
PACS: 61.50.Ks 71.15.Mb 71.20.-b Keywords: A. Insulator D. Phase transition E. Ab initio
Exploring a safe, cost-effective, and fully hydrogenation reversible hydrogen storage material with a higher gravimetric hydrogen density in excess of of 6.5 wt% is one of the targets for developing next-generation energy storage systems [1,2]. Magnesium is an attractive material for hydrogen-storage applications because of its light weight, low manufacture cost, and high hydrogen-storage capacity (7.66 wt%). However, its slow hydriding/dehydriding kinetics and high dissociation temperature (nearly 573K) limit its practical applications [3]. In order to improve the hydrogenstorage properties of MgH2 alloys, understanding of its structural stability and bonding nature under extreme conditions is considered essential. α -MgH2 crystallizes in the rutile-type structure(P42 /mnm) at ambient conditions [4,5]. At high temperatures and pressures, α MgH2 transform into the orthorhombic γ -MgH2 (α -PbO2 type). Recently, to probe the structural sequence of MgH2 at high pressures, Bortz et al. confirmed the crystal structure of γ -MgH2 from the x-ray and neutron power diffraction data collected at 2 GPa, but they didn’t give the transition pressure [6]. Vajeeston et al. have investigated pressure-induced structural transitions in MgH2 [7,8] using the first-principles pseudopotential method and predicted that the transition from α -MgH2 to γ -MgH2
∗
Corresponding author. Tel.: +86 635 8231218; fax: +86 635 8238055. E-mail address: [email protected] (S. Cui).
0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.09.033
occurred at 0.39 GPa. However, Moriwaki et al. reported the transition pressure of 9 GPa [9] from x-ray diffraction (XRD) measurements at room temperature. Owing to the difficulties in determining accurately the hydrogen positions in a metal matrix by XRD measurements, several critical issues for the phase transition sequence of MgH2 under compression are still under debate in experiments. Under further compression, several other ¯ Pbc21 , Pbca, Pnnm, high-pressure phases (with space group Pa3, ¯ et al.) were proposed in theory [8,9], and the ab initio Fm3m pseudopotential calculations established the sequence of the phase transition is α → γ → β(Pa3¯ ) → δ(Pbc21 ) → (Pnma) [7,8]. Recently, a metastable phase of MgH2 (I41 /amd, group 141), which meets all the mechanical stability criteria for a tetragonal crystal, has been suggested through full-potential linearized augmented plane-wave (FP-LAPW) calculations [10]. Very recently, a new pressure-induced transition from the α MgH2 phase to an orthorhombic CaCl2 (Pnnm) phase is predicted by ab initio phonon calculations [11]. Accordingly, much more careful experimental and theoretical efforts are needed to further understand the high pressure behaviors of MgH2 . The calculations presented in this study were performed within the density functional theory, using the plane-wave pseudopotential method [12]. We used the generalized gradient approximation for the exchange-correlation functional [13]. The norm-conserving pseudopotentials were employed to model the ion-electron interactions [14]. The energy cutoff of the plane-wave
404
S. Cui et al. / Solid State Communications 148 (2008) 403–405
Table 1 Calculated structural parameters for α -MgH2 at ambient pressure, compared with experimental and previously theoretical values
Present work Theorya Theoryb Exp.c Exp.d
a (Å)
c (Å)
u
4.514 4.485 4.499 4.515 4.501
2.992 2.999 3.00 3.019 3.010
0.3039 0.304 0.305 0.304 0.304
Internal parameter u is the fractional coordinates of H atoms. a Reference [7]. b Reference [11]. c Reference [9]. d Reference [6].
Fig. 1. Calculated enthalpy differences of all these actual and possible structures of MgH2 with respect to α -MgH2 as a function of pressure. Fig. 3. The electronic total and partial density of states for α -MgH2 and γ -MgH2 .
Fig. 2. Pressure–volume relation of MgH2 solid in the most stable structural phases.
basis was chosen as 600 eV. The Brillouin zone was sampled by Monkhorst-Pack k points grids. The chosen plane-wave cutoff and the number of k points were carefully checked to ensure the total energy converged to better than 1 meV/atom. The tolerance in the self-consistent field (SCF) calculation is less than 10−8 eV/atom. For a given external hydrostatic pressure, both the parameters of the unit cell and the internal coordinates of the atoms are fully relaxed until forces had converged to less than 0.01 eV/Å and all the stress components are less than 0.02 GPa. The calculated structural parameters for α -MgH2 , together with experimental [9,6] and previous theoretical [7,11] data are listed in Table 1. It is clear that our calculated results are in excellent agreement with experiments and previous calculations. To investigate the pressure-induced structural transition, we have
carried out calculations for several possible types of structural phases [7]. The computed relative enthalpy with respect to α MgH2 versus pressure relation for all the actual and possible structural phases are shown in Fig. 1. The calculated transition pressure for the α → γ transformation is 1.2 GPa (Fig. 1). Because of the these two structures taking nearly the same structural arrangements, the relative enthalpy for them are nearly the same at the equilibrium pressure, which may be the reason why these two structures in experiments coexisted in a certain pressure range [8,9]. The subsequent phase transformations from γ - to β -MgH2 and β - to -MgH2 (AlAu2 -type structure also called cotunnite-type) occur at 9.7 GPa and 17.1 GPa, respectively, and the reported δ -MgH2 , I41 /amd and CaCl2 phases are not stable under high pressure. From Fig. 1, we can see that the β -MgH2 and δ -MgH2 separated by a small enthalpy barrier of about 1 meV, which suggests that the relative stability of these two phases are very easily affected by external factors (for example temperature and pressure). While recent powder XRD experiments reported the structural sequence was α → γ → δ → [9]. Our computed phase sequence is not consistent with the experimental observation [9,8] and previous theoretical calculations [7]. These discrepancies might be attributed to the neglect of zero-point fluctuations (T = 0 K) in the theoretical calculations and high pressure diffraction experiments were performed at room temperature on a sample with likely defects and impurities. The calculated P–V relation of MgH2 solid is shown in Fig. 2. It can be seen that there is small collapse in the volume (about 1.75%) accompanying the α → γ transition. The equilibrium volume for β -MgH2 is found to be 4.9% smaller than that of γ -MgH2 , and 5.8% volume reduction for β → phase transition. The electronic total and partial density of states (DOS) for α and γ phase are shown in Fig. 3. The calculated energy gap is 3.60 eV
S. Cui et al. / Solid State Communications 148 (2008) 403–405
405
The volume reductions accompanying the phase transition are obtained. The δ , CaCl2 type structures are not stable phases. α MgH2 turns out to be an insulator, which is consistent with experimental observation, and the theoretical calculations show that the high-pressure phases also exhibit insulating behavior. The DOS and valence charge density contour reveal that all phases of MgH2 have a strong ionic character. We consider that its ionic bonding must be made weaker to improve the dehydrogenation performance of MgH2 . Acknowledgments This work was financially supported by Science Foundation for Youth of Liaocheng University (No. X071046). Special thanks should go to the Natural Science Foundation of Shandong Province of China (No. Y2006A02) and the National Natural Science Foundation of China (Grant No. 60571062). Fig. 4. Valence charge density plots for α -MgH2 in the (001) plane.
and 3.81 eV for α - and γ -MgH2 , respectively. The width of valence band (VB) is 7.41 eV and 7.84 eV for α and γ phase, respectively. The increased width of VB is attributed to the reduction in the distance of Mg-H bond under high pressure. According to Fig. 3, the entire whole of VB for these two phases is dominated mainly by H s state which implies that the Mg valence electrons transfer to the H sites under high pressure. The DOS (Fig. 3) show that there exist strong ionic interaction between Mg and H. Fig. 4 shows the charge density contour in the (001) plane for α -MgH2 . Charge density maps serve as a complementary tool for achieving a proper understanding of the electronic structure of the system being studied. In the figure, we see that the valence electrons of Mg mostly transfer to the H sites, thus showing that there is strong ionic bonding between Mg and H atoms. For other various MgH2 polymorphs, there are nearly in the same bonding situation. To conclude, theoretical calculations predict that α -MgH2 transforms into the γ , β , and phases under high pressure, and the transition pressure is 1.2 GPa, 9.7 GPa and 17.1 GPa, respectively.
References [1] L. Schlapbach, A. Züttel, Nature 414 (2001) 353. [2] Hydrogen Storage Challenges, Fuel Cells and Infrastructure Technologies Program-Hydrogen Storage, Energy Efficiency and Renewable Energy, US Department of Energy. http://www.eere.energy.gov/hydrogenandfuelcells/ storage/storage_challenges.html. [3] F.E. Pinkerton, B.G. Wicke, Ind. Phys. 10 (2004) 20. [4] J.P. Bastide, B. Bonnetot, J.M. Letoffe, P. Claudy, Mater. Res. Bull. 15 (1980) 1215. [5] W.H. Zachariasen, C.E. Holley Jr., J.F. Stamper Jr., Acta Crystallogr. A 16 (1963) 352. [6] M. Bortz, B. Bertheville, G. Böttger, K. Yvon, J. Alloys Compd. 287 (1999) L4. [7] P. Vajeeston, P. Ravindran, A. Kjekshus, H. Fjellvåg, Phys. Rev. Lett. 89 (2002) 175506. [8] P. Vajeeston, P. Ravindran, B.C. Hauback, H. Fjellvåg, A. Kjekshus, S. Furuseth, M. Hanfland, Phys. Rev. B 73 (2006) 224102. [9] T. Moriwaki, Y. Akahama, H. Kawamura, J. Phys. Soc. Japan 75 (2006) 074603. [10] Y. Song, Z.X. Guo, Appl. Phys. Lett. 89 (2006) 111911. [11] L.J. Zhang, Y.C. Wang, T. Cui, Y. Li, Y.W. Li, Z. He, Y.M. Ma, G.T. Zou, Phys. Rev. B 75 (2007) 144109. [12] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Modern Phys. 64 (1992) 1045. [13] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [14] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993.