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Structure and electronic properties of BaH2 at high pressure
Solid State Communications 149 (2009) 1944–1946
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Structure and electronic properties of BaH2 at high pressure John S. Tse a,∗ , Zhe Song a , Yansun Yao a , Jesse S. Smith b , Serge Desgreniers b , Dennis D. Klug c a
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E2
b
Laboratorie de physique des solides denses, Department of Physics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
c
Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6
article
info
Article history: Received 27 April 2009 Received in revised form 9 July 2009 Accepted 25 July 2009 by S. Das Sarma Available online 30 July 2009 PACS: 61.10.-I 61.50.Ah 63.20.Kr 74.25.K
abstract The structure of BaH2 at high pressure up to 58 GPa has been investigated with synchrotron powder xray diffraction. A structural phase transition from the low pressure Ni2 In structure to a simple hexagonal structure, which started at 40 GPa and was completed at approximately 45 GPa, was confirmed. A loss of Raman signal in this pressure range suggests that an insulator to metal transition has occurred. This observation is corroborated with first-principles calculations. The investigation of the electron–phonon coupling shows that the metallic phase is a very weak superconductor with an estimated superconducting critical temperature Tc in the range of mK. © 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Superconductors C. x-ray scattering D. Electron–phonon interaction E. High pressure
1. Introduction Simple hydrides are suggested to exhibit superconducting behavior under pressure by recent extensive theoretical and experimental investigations [1]. So far, these studies have been focused mainly on group III and IV hydrides. An optimistic prediction of the superconducting critical temperature (Tc ), in excess of 200 K [2], was first made for silane, although more refined calculations showed that the Tc [3,4] is somewhat lower. Experimentally, silane was indeed found to metallize at around 50 GPa [5] and becomes a superconductor with a maximum Tc of 17 K at 120 GPa [6]. In contrast, aluminum hydride [7] was found to be metallic at 100 GPa, but not superconducting. Alkaline earth metal hydrides form another class of possible superconductors. It has been shown that CaH2 [8], SrH2 [9], and BaH2 [10,11] transform to a hexagonal Ni2 In (P63 /mmc) close-packed structure under pressure. In the Ni2 In structure, alkaline earth metal hydrides are found to be stable over a large pressure range, except for BaH2 , which transformed into a simple hexagonal (SH) structure at 50 GPa. The structural transition in BaH2 is accompanied by a 15%
∗
Corresponding author. Tel.: +1 306 966 610; fax: +1 306 966 6400. E-mail address: [email protected] (J.S. Tse).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.07.044
volume reduction, indicating substantial changes in the bonding. A theoretical calculation of the electronic properties of BaF2 [12] in the Ni2 In phase suggested that it is metallic. In comparison, BaH2 in the Ni2 In structure is not metallic, however, it is not unreasonable to speculate that higher pressure SH polymorph of BaH2 may be metallic. Anticipating that very low frequency vibrations due to the Ba atoms, that may enhance electron–phonon coupling (EPC) [13] and the high frequency H vibrations [1] in favour of a large Debye temperature, the metallic phase may be a superconductor as well. In a previous study [10], the Ni2 In → SH transition in BaH2 is clearly identified, but the property of the SH, in particular, whether it is a metal, has not been established. The objectives of this investigation are to characterize the electronic state of BaH2 in the high pressure SH structure and to explore the possibility of a superconducting state. For this purpose, the high pressure structure and properties of BaH2 are studied with synchrotron radiation powder x-ray diffraction, Raman spectroscopy measurements, and first-principles calculations. 2. Experimental and theoretical details Barium hydride powder (99.5% metals analysis, Strem Chemicals) was loaded into gasketed diamond anvil cells (DAC) under an inert gas (argon) atmosphere. No pressure-transmitting
J.S. Tse et al. / Solid State Communications 149 (2009) 1944–1946
medium was used since BaH2 is extremely sensitive to moisture and readily hydrolyzes with common pressure-transmitting media, such as methanol/ethanol or silicone oil. Pressure measurements were obtained with the ruby luminescence technique, using a calibration appropriate for non-hydrostatic pressure conditions [14]. Angle-dispersive powder x-ray diffraction measurements were performed at the Hard X-ray MicroAnalysis (HXMA) beamline at the Canadian Light Source [15] with X-ray wavelength of 0.56356(3) Å [16]. X-ray diffraction images recorded using a mar345 detector were processed and integrated with FIT2D [17], and pattern indexing was carried out using XRDA [18] to obtain the lattice parameters. Raman spectroscopy measurements were performed using the 488 nm line of an Ar+ laser. Spectra in the 60–1350 cm−1 range were collected in the near-backscattering geometry using a Jobin–Yvon S3000 triple-grating subtractive spectrograph equipped with a liquid nitrogen-cooled CCD detector. The spectral resolution was 4 cm−1 . Pseudopotential plane-wave density functional perturbation calculations were performed with the Quantum-ESPRESSO code [19]. Norm-conserving pseudopotentials using the Perdew–Burke– Ernzerhof exchange-correlation (PBE) [20] for H and Ba were used. The 5p electrons of Ba are treated as valence. The kinetic energy cutoff was 50 Ry. Variable cell structural optimizations were performed at selected pressures using Wentzcovitch’s symmetryconserving algorithm [21]. Monkhorst–Pack (MP) [22] meshes were used for Brillouin zone (BZ) integrations in the electronic calculations (k-mesh), phonon and EPC calculations (q-mesh). The electronic band structure and density of states (DOS) were computed with a 36 × 36 × 36 k-mesh. The linear response method was used to compute phonons on a 4 × 4 × 4 q-mesh with a 16 × 16 × 16 k-mesh for the first BZ integrations. EPC matrix elements were computed in the first BZ on a 4 × 4 × 4 q-mesh, using individual EPC matrices obtained with a 32 × 32 × 32 kmesh, using the perturbative linear response theory [19]. Convergence was confirmed by employing higher kinetic energy cutoffs and denser k-meshes and comparing those computed directly at selected phonon points. In the EPC calculations, convergence to the zero-width limit was achieved with a 32 × 32 × 32 k-mesh employing Gaussian function broadening with a half-width of 0.03 Ry.
1945
a
b
Fig. 1. (a) Powder diffraction patterns for BaH2 measured at 15.0 (Ni2 In, dotted line) and 56.9 (SH, solid line) GPa (λ = 0.56356 Å). (inset) A comparison of measured and calculated unit cell parameters for the Ni2 In and SH phase of BaH2 . Closed and open symbols indicate data taken on increasing and decreasing pressure, respectively. The high pressure SH structure has the P6/mmm space group, with Ba forming a hexagonal lattice, and H located at (1/3, 2/3, z ) and (2/3, 1/3, −z ) sites forming a two-dimensional honeycomb layer sandwiched between the Ba layers. (b) Raman spectra of BaH2 as a function of pressure.
3. Results and discussion Representative diffraction patterns measured at 15 and 57 GPa are shown in Fig. 1(a). BaH2 transformed from the cotunnite (Pnma) to Ni2 In (P63 /mmc) structure at 1.6 GPa. At 41 GPa, an abrupt change in the powder diffraction image was observed, indicating the onset of a structural transition. This change in the diffraction image was accompanied by a distinct change in sample appearance, as part of the sample became opaque. The corresponding pattern can be indexed with a SH cell, a = 3.2741(5) Å and c = 2.9518(4) Å at 41 GPa. This result is in general agreement with that of a previous study [10], however the onset of the transition at 41 GPa is approximately 10 GPa lower than that previously reported. The lower transition pressure in the present study can be explained by the absence of a pressure transmitting medium. The two phase transitions [10,11] have been previously reported and analyzed in detail and, therefore, will not be repeated here. A Raman spectrum obtained at the initial loading pressure of 1.5 GPa was consistent with that expected for the cotunnite structure [11]. As the pressure was increased above 1.6 GPa, the spectra exhibited only two Raman-active modes, consistent with that expected for the Ni2 In phase. Fig. 1(b) shows selected spectra taken on increasing pressure (note that above 30 GPa the highwavenumber mode is obscured by the intense Raman mode from the diamond anvil). As in the diffraction experiment, at 44 GPa a portion of the sample became opaque, and the low-wavenumber
mode could only be observed by exciting the transparent portion of the sample. Above 50 GPa the entire sample was opaque and the low-wavenumber mode was absent. The spectral features are suggestive of a metallic state. Spectra taken on decreasing pressure (not shown) demonstrated recovery of both the Ni2 In and cotunnite phases, indicating no decomposition had taken place. To confirm the metallic characteristic, theoretical band structure calculations were performed. The calculated lattice parameters for the Ni2 In and SH structures of BaH2 are compared with experiment in the inset of Fig. 1(a). In the Ni2 In phase, the calculations significantly underestimate the size of the c-axis, while the agreement with the a-axis is excellent. This is not a deficiency of the theoretical method. The anomalously low compressibility in the c-axis is attributed to the lack of hydrostaticity, resulting from the absence of a pressure transmitting medium and/or preferred orientation of the sample. A similar discrepancy between the theoretically predicted and measured c-axis lattice constant was found in the Ni2 In phases of BaF2 and SrH2 [23,24]. In the case of BaF2 , a detailed investigation found that this discrepancy disappeared when a quasi-hydrostatic pressure transmission medium was employed [23]. Furthermore, the agreement between calculated and observed [23] lattice parameters is excellent for the SH phase. The calculated electronic band structure and DOS of BaH2 in the SH structure at 50 GPa is shown in Fig. 2(a). The lack of an energy gap indicates that SH BaH2 is metallic. It was suggested
1946
J.S. Tse et al. / Solid State Communications 149 (2009) 1944–1946
a
780 K, the predicted Tc with nominal Coulomb pseudopotential parameters (µ∗ ) [30] of 0.1 and 0.12 are 4 and 0.2 mK, respectively. In passing, it may be significant to point out that, as in this case, the Eliashberg spectral functions for conventional superconductors, such as Al and Pb [31], are often similar to the corresponding VDOS. In contrast, recent calculations on group IV hydrides [3,4,28] show that their VDOS are very different from the spectral functions. This may indicate the EPC in the latter systems is localized in a few vibrational modes that may be a signature of the high Tc . 4. Summary In summary, the change in the electronic properties in the BaH2 Ni2 In → SH phase transition is characterized. Raman measurements and first-principles calculations confirm that SH BaH2 is metallic. The possibility of superconductivity in the SH phase has been investigated with the study of the electron phonon coupling mechanism. It is shown that BaH2 is a weak superconductor with a Tc in the order of mK at 60 GPa. The very low critical temperature may pose an experimental challenge to confirming the theoretical prediction.
b
References Fig. 2. (a) Calculated electronic band structure of SH BaH2 , DOS, and projected DOS on the Ba atom of SH and Ni2 In BaH2 at 50 GPa. (b) Phonon band structure, Eliashberg spectral function (α 2 F (ω)) and vibrational density of states (VDOS) for SH BaH2 at 50 GPa.
that the Ni2 In → SH phase transition is driven by the Ba s → d rehybridization [10]. Inspection of the projected density of states (PDOS) for SH and Ni2 In BaH2 structures calculated at 50 GPa, as depicted in Fig. 2(a), shows the Ba d electron density in the conduction band of insulating Ni2 In is already quite significant. Not surprisingly, the closing of the bandgap in the SH structure led to a very high Ba d electron DOS at the Fermi level. This observation confirms a substantial mixing of the Ba s and d orbitals accompanying the Ni2 In → SH transition. Two electronic bands cross the Fermi surface, but the band dispersions are rather weak, in particular, along the Γ → A → L direction. There is also a relatively flat conduction band in the M → K direction near the Fermi level. The simultaneous occurrence of dispersive and flat bands has been suggested as being a favorable for potential superconductivity [25]. Moreover, the light H atoms are expected to increase the Debye temperature. In addition, it was shown previously that low frequency Ba vibrations may help to enhance electron–phonon interactions [26]. To investigate this possibility, the phonon band structure, EPC parameter (λ), and the Eliashberg spectral function (α 2 F (ω)) [27] were calculated with density functional perturbation theory at 60 GPa. The phonon band structure and spectral function are shown in Fig. 2(b). As expected, both spectra clearly separated into two regions with the low frequency modes below 275 cm−1 dominated by Ba motions and the high frequency band from 1000– 1300 cm−1 being predominantly H vibrations. The EPC is given by the inverse first moment of the spectral function (λ =
R∞
α 2 F (ω)
2 0 dω). Although the Ba atoms contribute significantly ω to the low frequency modes, the integrated EPC in the low frequency region is very small. The overall EPC for SH BaH2 at 60 GPa is only 0.22, which is much lower than the predicted values for group IV hydrides, SiH4 [3,4], GeH4 [28], and SnH4 [13]. The superconducting critical temperature, Tc can be estimated from the Allan–Dynes modification h i [29] of the McMillan equation Tc =
ωlog 1.2
1.04(1+λ)
exp − λ−µ∗ (1+0.62λ)
. At 60 GPa and using a hωlog i of
[1] N.W. Ashcroft, Phys. Rev. Lett. 92 (2004) 187002. [2] J. Feng, W. Grochala, T. Jaron, R. Hoffman, A. Bergara, N.W. Ashcroft, Phys. Rev. Lett. 96 (2006) 017006. [3] Y. Yao, J.S. Tse, Y. Ma, K. Tanaka, Europhys. Lett. 78 (2007) 37003. [4] X.-J. Chen, J.-L. Wang, V. Struzhkin, H.-K. Mao, R.J. Hemley, H.-Q. Lin, Phys. Rev. Lett. 101 (2008) 077002. [5] X. Chen, V. Struzhkin, Y. Song, A. Goncharov, M. Ahart, Z. Liu, H. Mao, R. Hemley, Proc. Natl. Acad. Sci. 105 (2008) 20. [6] M.I. Eremets, I.A. Trojan, S.A. Medvedev, J.S. Tse, Y. Yao, Science 319 (2008) 1506. [7] I. Goncharenko, M.I. Eremets, M. Hanfland, J.S. Tse, M. Amboage, Y. Yao, I.A. Trojan, Phys. Rev. Lett. 100 (2008) 045504. [8] J.S. Tse, D.D. Klug, S. Desgreniers, J.S. Smith, R. Flacau, Z. Liu, J. Hu, N. Chen, D.T. Jiang, Phys. Rev. B 75 (2007) 134108. [9] K. Kinoshita, M. Nishimura, Y. Akahama, H. Kawamura, Proc. 20th AIRAPT T10P048. [10] K. Kinoshita, M. Nishimura, Y. Akahama, H. Kawamura, Solid State Commun. 141 (2007) 69. [11] J.S. Smith, S. Desgreniers, J.S. Tse, D.D. Klug, J. Appl. Phys. 102 (2007) 043520. [12] V. Kanchana, G. Vaitheeswaran, M. Rajagopalan, J. Alloys Compounds 359 (2003) 66. [13] J.S. Tse, Y. Yao, K. Tanaka, Phys. Rev. Lett. 98 (2007) 117004. [14] H.K. Mao, P.M. Bell, J.W. Shaner, D.J. Steinberg, J. Appl. Phys. 49 (1978) 3276. [15] D.T. Jiang, N. Chen, L. Zhang, K. Malgorzata, G. Wright, R. Igarashi, D. Beauregard, M. Kirkham, M. McKibben, CP882, X-ray Absorption Fine Structure—XAFS 3, in: B. Hedman and P. Pianetta, American Institute of Physics, 2007. [16] J.S. Smith, S. Desgreniers, J. Sync. Rad. 16 (2009) 83. [17] A.P. Hammersley, S.O. Svensson, M. Hanfland, A.N. Fitch, D. Häusermann, High Press. Res. 14 (1996) 235; S. Desgreniers, K. Lagarec, J. Appl. Crystallogr 27 (1994) 432. [18] S. Desgreniers, K. Lagarec, J. Appl. Crystallogr 27 (1994) 432; J. Appl. Crystallogr 31 (1998) 109. [19] S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Modern Phys. 73 (2001) 515; P. Giannozzi, et al., http://www.quantum-espresso.org. [20] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [21] R.M. Wentzcovitch, J.L. Martins, G.D. Price, Phys. Rev. Lett. 70 (1993) 3947. [22] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [23] J.S. Smith, S. Desgreniers, J.S. Tse, J. Sun, D.D. Klug, Y. Ohishi, Phys. Rev. B 79 (2009) 134104. [24] J.S. Smith, S. Desgreniers, D.D. Klug, J.S. Tse, Solid. State Commun. 179 (2009) 830. [25] A. Simon, Angew. Chem., Int. Ed. Engl. 36 (1997) 1788. [26] J.S. Tse, T. Iitaka, K. Parlinski, Europhys. Lett. 75 (2006) 153. [27] J.P. Carbotte, Rev. Modern Phys. 62 (1990) 1027. [28] G. Gao, A.R. Oganov, A. Bergara, M. Martinez-Canales, T. Cui, T. Iitaka, Y. Ma, G. Zou, Phys. Rev. Lett. 101 (2008) 107002. [29] P.B. Allen, D.C. Dynes, Phys. Rev. B 11 (1975) 1895. [30] P. Morel, P.W Anderson, Phys. Rev. 125 (1962) 1263. [31] S.Y. Savrasov, D.Y. Savrasov, Phys. Rev. B. 54 (1996) 16487.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Structure and electronic properties of BaH2 at high pressure John S. Tse a,∗ , Zhe Song a , Yansun Yao a , Jesse S. Smith b , Serge Desgreniers b , Dennis D. Klug c a
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E2
b
Laboratorie de physique des solides denses, Department of Physics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
c
Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6
article
info
Article history: Received 27 April 2009 Received in revised form 9 July 2009 Accepted 25 July 2009 by S. Das Sarma Available online 30 July 2009 PACS: 61.10.-I 61.50.Ah 63.20.Kr 74.25.K
abstract The structure of BaH2 at high pressure up to 58 GPa has been investigated with synchrotron powder xray diffraction. A structural phase transition from the low pressure Ni2 In structure to a simple hexagonal structure, which started at 40 GPa and was completed at approximately 45 GPa, was confirmed. A loss of Raman signal in this pressure range suggests that an insulator to metal transition has occurred. This observation is corroborated with first-principles calculations. The investigation of the electron–phonon coupling shows that the metallic phase is a very weak superconductor with an estimated superconducting critical temperature Tc in the range of mK. © 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Superconductors C. x-ray scattering D. Electron–phonon interaction E. High pressure
1. Introduction Simple hydrides are suggested to exhibit superconducting behavior under pressure by recent extensive theoretical and experimental investigations [1]. So far, these studies have been focused mainly on group III and IV hydrides. An optimistic prediction of the superconducting critical temperature (Tc ), in excess of 200 K [2], was first made for silane, although more refined calculations showed that the Tc [3,4] is somewhat lower. Experimentally, silane was indeed found to metallize at around 50 GPa [5] and becomes a superconductor with a maximum Tc of 17 K at 120 GPa [6]. In contrast, aluminum hydride [7] was found to be metallic at 100 GPa, but not superconducting. Alkaline earth metal hydrides form another class of possible superconductors. It has been shown that CaH2 [8], SrH2 [9], and BaH2 [10,11] transform to a hexagonal Ni2 In (P63 /mmc) close-packed structure under pressure. In the Ni2 In structure, alkaline earth metal hydrides are found to be stable over a large pressure range, except for BaH2 , which transformed into a simple hexagonal (SH) structure at 50 GPa. The structural transition in BaH2 is accompanied by a 15%
∗
Corresponding author. Tel.: +1 306 966 610; fax: +1 306 966 6400. E-mail address: [email protected] (J.S. Tse).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.07.044
volume reduction, indicating substantial changes in the bonding. A theoretical calculation of the electronic properties of BaF2 [12] in the Ni2 In phase suggested that it is metallic. In comparison, BaH2 in the Ni2 In structure is not metallic, however, it is not unreasonable to speculate that higher pressure SH polymorph of BaH2 may be metallic. Anticipating that very low frequency vibrations due to the Ba atoms, that may enhance electron–phonon coupling (EPC) [13] and the high frequency H vibrations [1] in favour of a large Debye temperature, the metallic phase may be a superconductor as well. In a previous study [10], the Ni2 In → SH transition in BaH2 is clearly identified, but the property of the SH, in particular, whether it is a metal, has not been established. The objectives of this investigation are to characterize the electronic state of BaH2 in the high pressure SH structure and to explore the possibility of a superconducting state. For this purpose, the high pressure structure and properties of BaH2 are studied with synchrotron radiation powder x-ray diffraction, Raman spectroscopy measurements, and first-principles calculations. 2. Experimental and theoretical details Barium hydride powder (99.5% metals analysis, Strem Chemicals) was loaded into gasketed diamond anvil cells (DAC) under an inert gas (argon) atmosphere. No pressure-transmitting
J.S. Tse et al. / Solid State Communications 149 (2009) 1944–1946
medium was used since BaH2 is extremely sensitive to moisture and readily hydrolyzes with common pressure-transmitting media, such as methanol/ethanol or silicone oil. Pressure measurements were obtained with the ruby luminescence technique, using a calibration appropriate for non-hydrostatic pressure conditions [14]. Angle-dispersive powder x-ray diffraction measurements were performed at the Hard X-ray MicroAnalysis (HXMA) beamline at the Canadian Light Source [15] with X-ray wavelength of 0.56356(3) Å [16]. X-ray diffraction images recorded using a mar345 detector were processed and integrated with FIT2D [17], and pattern indexing was carried out using XRDA [18] to obtain the lattice parameters. Raman spectroscopy measurements were performed using the 488 nm line of an Ar+ laser. Spectra in the 60–1350 cm−1 range were collected in the near-backscattering geometry using a Jobin–Yvon S3000 triple-grating subtractive spectrograph equipped with a liquid nitrogen-cooled CCD detector. The spectral resolution was 4 cm−1 . Pseudopotential plane-wave density functional perturbation calculations were performed with the Quantum-ESPRESSO code [19]. Norm-conserving pseudopotentials using the Perdew–Burke– Ernzerhof exchange-correlation (PBE) [20] for H and Ba were used. The 5p electrons of Ba are treated as valence. The kinetic energy cutoff was 50 Ry. Variable cell structural optimizations were performed at selected pressures using Wentzcovitch’s symmetryconserving algorithm [21]. Monkhorst–Pack (MP) [22] meshes were used for Brillouin zone (BZ) integrations in the electronic calculations (k-mesh), phonon and EPC calculations (q-mesh). The electronic band structure and density of states (DOS) were computed with a 36 × 36 × 36 k-mesh. The linear response method was used to compute phonons on a 4 × 4 × 4 q-mesh with a 16 × 16 × 16 k-mesh for the first BZ integrations. EPC matrix elements were computed in the first BZ on a 4 × 4 × 4 q-mesh, using individual EPC matrices obtained with a 32 × 32 × 32 kmesh, using the perturbative linear response theory [19]. Convergence was confirmed by employing higher kinetic energy cutoffs and denser k-meshes and comparing those computed directly at selected phonon points. In the EPC calculations, convergence to the zero-width limit was achieved with a 32 × 32 × 32 k-mesh employing Gaussian function broadening with a half-width of 0.03 Ry.
1945
a
b
Fig. 1. (a) Powder diffraction patterns for BaH2 measured at 15.0 (Ni2 In, dotted line) and 56.9 (SH, solid line) GPa (λ = 0.56356 Å). (inset) A comparison of measured and calculated unit cell parameters for the Ni2 In and SH phase of BaH2 . Closed and open symbols indicate data taken on increasing and decreasing pressure, respectively. The high pressure SH structure has the P6/mmm space group, with Ba forming a hexagonal lattice, and H located at (1/3, 2/3, z ) and (2/3, 1/3, −z ) sites forming a two-dimensional honeycomb layer sandwiched between the Ba layers. (b) Raman spectra of BaH2 as a function of pressure.
3. Results and discussion Representative diffraction patterns measured at 15 and 57 GPa are shown in Fig. 1(a). BaH2 transformed from the cotunnite (Pnma) to Ni2 In (P63 /mmc) structure at 1.6 GPa. At 41 GPa, an abrupt change in the powder diffraction image was observed, indicating the onset of a structural transition. This change in the diffraction image was accompanied by a distinct change in sample appearance, as part of the sample became opaque. The corresponding pattern can be indexed with a SH cell, a = 3.2741(5) Å and c = 2.9518(4) Å at 41 GPa. This result is in general agreement with that of a previous study [10], however the onset of the transition at 41 GPa is approximately 10 GPa lower than that previously reported. The lower transition pressure in the present study can be explained by the absence of a pressure transmitting medium. The two phase transitions [10,11] have been previously reported and analyzed in detail and, therefore, will not be repeated here. A Raman spectrum obtained at the initial loading pressure of 1.5 GPa was consistent with that expected for the cotunnite structure [11]. As the pressure was increased above 1.6 GPa, the spectra exhibited only two Raman-active modes, consistent with that expected for the Ni2 In phase. Fig. 1(b) shows selected spectra taken on increasing pressure (note that above 30 GPa the highwavenumber mode is obscured by the intense Raman mode from the diamond anvil). As in the diffraction experiment, at 44 GPa a portion of the sample became opaque, and the low-wavenumber
mode could only be observed by exciting the transparent portion of the sample. Above 50 GPa the entire sample was opaque and the low-wavenumber mode was absent. The spectral features are suggestive of a metallic state. Spectra taken on decreasing pressure (not shown) demonstrated recovery of both the Ni2 In and cotunnite phases, indicating no decomposition had taken place. To confirm the metallic characteristic, theoretical band structure calculations were performed. The calculated lattice parameters for the Ni2 In and SH structures of BaH2 are compared with experiment in the inset of Fig. 1(a). In the Ni2 In phase, the calculations significantly underestimate the size of the c-axis, while the agreement with the a-axis is excellent. This is not a deficiency of the theoretical method. The anomalously low compressibility in the c-axis is attributed to the lack of hydrostaticity, resulting from the absence of a pressure transmitting medium and/or preferred orientation of the sample. A similar discrepancy between the theoretically predicted and measured c-axis lattice constant was found in the Ni2 In phases of BaF2 and SrH2 [23,24]. In the case of BaF2 , a detailed investigation found that this discrepancy disappeared when a quasi-hydrostatic pressure transmission medium was employed [23]. Furthermore, the agreement between calculated and observed [23] lattice parameters is excellent for the SH phase. The calculated electronic band structure and DOS of BaH2 in the SH structure at 50 GPa is shown in Fig. 2(a). The lack of an energy gap indicates that SH BaH2 is metallic. It was suggested
1946
J.S. Tse et al. / Solid State Communications 149 (2009) 1944–1946
a
780 K, the predicted Tc with nominal Coulomb pseudopotential parameters (µ∗ ) [30] of 0.1 and 0.12 are 4 and 0.2 mK, respectively. In passing, it may be significant to point out that, as in this case, the Eliashberg spectral functions for conventional superconductors, such as Al and Pb [31], are often similar to the corresponding VDOS. In contrast, recent calculations on group IV hydrides [3,4,28] show that their VDOS are very different from the spectral functions. This may indicate the EPC in the latter systems is localized in a few vibrational modes that may be a signature of the high Tc . 4. Summary In summary, the change in the electronic properties in the BaH2 Ni2 In → SH phase transition is characterized. Raman measurements and first-principles calculations confirm that SH BaH2 is metallic. The possibility of superconductivity in the SH phase has been investigated with the study of the electron phonon coupling mechanism. It is shown that BaH2 is a weak superconductor with a Tc in the order of mK at 60 GPa. The very low critical temperature may pose an experimental challenge to confirming the theoretical prediction.
b
References Fig. 2. (a) Calculated electronic band structure of SH BaH2 , DOS, and projected DOS on the Ba atom of SH and Ni2 In BaH2 at 50 GPa. (b) Phonon band structure, Eliashberg spectral function (α 2 F (ω)) and vibrational density of states (VDOS) for SH BaH2 at 50 GPa.
that the Ni2 In → SH phase transition is driven by the Ba s → d rehybridization [10]. Inspection of the projected density of states (PDOS) for SH and Ni2 In BaH2 structures calculated at 50 GPa, as depicted in Fig. 2(a), shows the Ba d electron density in the conduction band of insulating Ni2 In is already quite significant. Not surprisingly, the closing of the bandgap in the SH structure led to a very high Ba d electron DOS at the Fermi level. This observation confirms a substantial mixing of the Ba s and d orbitals accompanying the Ni2 In → SH transition. Two electronic bands cross the Fermi surface, but the band dispersions are rather weak, in particular, along the Γ → A → L direction. There is also a relatively flat conduction band in the M → K direction near the Fermi level. The simultaneous occurrence of dispersive and flat bands has been suggested as being a favorable for potential superconductivity [25]. Moreover, the light H atoms are expected to increase the Debye temperature. In addition, it was shown previously that low frequency Ba vibrations may help to enhance electron–phonon interactions [26]. To investigate this possibility, the phonon band structure, EPC parameter (λ), and the Eliashberg spectral function (α 2 F (ω)) [27] were calculated with density functional perturbation theory at 60 GPa. The phonon band structure and spectral function are shown in Fig. 2(b). As expected, both spectra clearly separated into two regions with the low frequency modes below 275 cm−1 dominated by Ba motions and the high frequency band from 1000– 1300 cm−1 being predominantly H vibrations. The EPC is given by the inverse first moment of the spectral function (λ =
R∞
α 2 F (ω)
2 0 dω). Although the Ba atoms contribute significantly ω to the low frequency modes, the integrated EPC in the low frequency region is very small. The overall EPC for SH BaH2 at 60 GPa is only 0.22, which is much lower than the predicted values for group IV hydrides, SiH4 [3,4], GeH4 [28], and SnH4 [13]. The superconducting critical temperature, Tc can be estimated from the Allan–Dynes modification h i [29] of the McMillan equation Tc =
ωlog 1.2
1.04(1+λ)
exp − λ−µ∗ (1+0.62λ)
. At 60 GPa and using a hωlog i of
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