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Journal of Alloys and Compounds 330 ­ 332 ( 2002 ) 462 ­ 466

www.elsevier.com / locate / jallcom

L

Giant tunnelling effect of hydrogen and deuterium in a manganese
a, b a c b a V.E. Antonov *, B. Dorner , V.K. Fedotov , G. Grosse , A.S. Ivanov , A.I. Kolesnikov , V.V. Sikolenko d , F.E. Wagner c

d

Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia b Institute Laue-Langevin, B.P. 156, F-38042 Grenoble Cedex 9, France c ¨ ¨ Physik-Department E 15, Technische U niversitat Munchen, D-85747 Garching, Germany Frank laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow District, Russia

a

Abstract The crystal structure of a solid solution optical deuterium vibrations at 5 K was tunnelling origin of the strong peaks at 6.4 deuterium solutions in a-Mn, respectively. of 3.5 at.% deuterium in a-Mn was determined by neutron diffraction and the spectrum of studied by inelastic neutron scattering ( INS ). The results give conclusive evidence of the and 1.6 meV observed earlier at temperatures up to 100 K in the INS spectra of hydrogen and © 2002 Elsevier Science B.V. All rights reserved.

Keywords: Hydrogen / deuterium tunnelling; Neutron spectroscopy; Neutron diffraction

1. Introduction The solubility of hydrogen in a-Mn was recently found to reach a few atomic percent under high hydrogen pressures [1]. A neutron diffraction investigation showed that hydrogen forms an unusual sublattice in the aMnH 0.073 high-pressure phase and occupies the 12e type ° interstitial positions arranged in small dumb-bells 0.68 A long [2]. An inelastic neutron scattering ( INS ) study [2] of a-MnH 0.073 at 90 K revealed a high-energy band of optical hydrogen vibrations split into three peaks, in accordance with the low site symmetry of the hydrogen positions, and also a strong low-energy peak at 6.4 meV which was tentatively attributed to the splitting of the vibrational ground state of hydrogen due to tunnelling between the adjacent 12e sites. Hydrogen tunnelling in metals has been studied for many years already, but the tunnelling splitting of the hydrogen ground state never exceeded 0.2 meV; the integral intensity of the tunnelling peak was by orders of magnitude less than in a-MnH 0.073 and the effect was observed only at temperatures below 10 K [3]. Taking also into account that the observation of a quantum effect at temperatures as high as 90 K is a rare event, the nature of the giant tunnelling effect in a-MnH 0.073 deserved thorough justification.
* Corresponding author. E-mail address: antonov@issp.ac.ru ( V.E. Antonov).

Further results of INS studies nevertheless strongly corroborated the assumption of the tunnelling origin of the 6.4 meV peak in the spectrum of a-MnH 0.073 [4]. The results include the temperature and the neutron momentum-transfer dependences of the intensity of this peak and also the temperature dependence of the intensity of a similar peak at 1.6 meV in the INS spectrum of a-MnD 0.05 . The most stringent argument, however, was the very fact that the peak moves from 6.4 meV for hydrogen to 1.6 meV for deuterium, because this decrease in energy is too large to result from mechanisms other than tunnelling. Moreover, the positions of these H and D peaks agree with roughly estimated values, D H 55 meV and D D 51.5 meV, 0 0 for the splitting of the hydrogen and deuterium vibrational ground states due to tunnelling. These values follow from the relation:

D0 ¯ (1 / 2 )"v0 exp(2mv0 , 2 / " )
[5] if one substitutes the measured energy "v H 5 73 meV 0 ] H [2,4] and the energy "v D 5 "v 0 /OE2 ¯ 51 meV of H and D 0 ° local vibrations along the line 2, 5 0.68 A which connects the 12e sites in a dumb-bell. m is the mass of the H or D atom. This estimation, which is a key argument in favour of the tunnelling nature of the observed effects, was nevertheless based on the rather questionable assumptions that the crystal structure and the distance 2, between the adjacent 12e positions are the same for a-MnH 0.073 and a-MnD 0.05

0925-8388 / 02 / $ ­ see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01533-X


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and that the ratio of frequencies of the H and D optical vibrations is harmonic. In the present work, the crystal structure of a deuterium solid solution in a-Mn was determined by neutron diffraction and the spectrum of deuterium optical vibrations was studied by INS.

2. Sample preparation and experimental details A 6.5 g sample of a solid solution of deuterium in a-MnH was prepared from freshly powdered manganese metal of 99.99 wt.% purity and a grain size of 0.05 ­ 0.1 mm. To load the sample with deuterium, the powder was exposed to a deuterium pressure of 0.6 GPa at 3508C for 5 h with subsequent rapid cooling to room temperature. The method was the same as previously applied to load a-Mn with hydrogen [1], the only difference being that thermal decomposition of AlD 3 instead of AlH 3 was used to produce the high-pressure gaseous deuterium. Regretfully, the AlD 3 was contaminated with hydrogen. The synthesised sample therefore also contained hydrogen and, as the INS investigation showed ( Section 3.2 ), had an atomic ratio of H / D ¯ 0.08. The total content ( H 1 D )/Mn 5 0.0377( 2 ) of both hydrogen isotopes was determined by hot extraction into a calibrated volume at temperatures up to 5508C using a 25 mg portion of the sample. The composition of the sample was thus a-MnD 0.035 H 0.003 . The neutron diffraction spectrum of this sample was measured at room temperature with a high-resolution Fourier diffractometry system ( HRFD ) installed at the pulsed reactor IBR-2 of the JINR, Dubna. The data were analysed with a computer program [6] based on the Rietveld profile refinement technique. The INS spectrum of the a-MnD 0.035 H 0.003 sample and, for comparison, also of the 8 g powder a-MnH 0.073 sample from Refs. [2,4] were measured at 5 K with the neutron spectrometer IN1 BeF at the hot source of the high-flux reactor at the ILL, Grenoble. The scattering angle was fixed at 908 and a Cu( 220 ) monochromator was used to scan the energy of incoming neutrons. The final energy of neutrons that passed through the cold Be filter analyser and were recorded by the counters was assumed to be 3 meV. The energy resolution of the spectrometer was Dv /v ¯ 7%. A background spectrum from an empty aluminium sample holder was measured under the same conditions and then subtracted from the raw INS spectra of the samples.

profile analysis of the neutron diffraction patterns of aMnH 0.073 showed [2] that hydrogen randomly occupies interstitial positions 12e inside distorted octahedra of manganese atoms on 24g1 and 24g2 sites, as schematically shown by the right inset in Fig. 1. The 12e sites form dumb-bells positioned rather far apart, at the centres of the edges and faces of the unit cell of a-Mn with a 5 8.9403 ° A, see the left inset in Fig. 1. Because of the small distance ° of 2, 5 0.68 A between the 12e sites in a dumb-bell, these positions cannot be occupied by hydrogen at the same time due to the `blocking effect' [7] requiring that the distance between hydrogen atoms in a metal should not be less than ° 2 A. An occupancy of half of the 12e sites corresponds to an H / Mn atomic ratio of x 5 6/58 ¯ 0.103. In the MnH 0.073 sample hydrogen therefore filled about 70% of the accessible interstices. The structure parameters of a-Mn and a-MnH 0.073 studied by neutron diffraction in Ref. [2] with the HRFD diffractometer at 300 K are given in Table 1. In the present work, the parameters of a-MnH 0.073 , corrected for the lattice parameter, the type of the hydrogen isotope and its concentration, were used as starting parameters for the profile analysis of the neutron diffraction pattern of aMnD 0.035 H 0.003 shown in Fig. 2. The quality of the refinement is illustrated by the difference spectrum at the bottom of Fig. 2. The final refined values of the structure parameters of a-MnD 0.035 H 0.003 are given at the bottom of Table 1. In the course of refinement of the a-Mn, a-MnH 0.073 and a-MnD 0.035 H 0.003 structures, the site occupancies for Mn atoms were fixed to one, and the other structure parameters listed in Table 1 were subject to fitting. The

3. Results and discussion

3.1. Neutron diffraction
The cubic unit-cell of the a-Mn structure, space group ¯ I43 m, contains 58 atoms located on the four crystallographically inequivalent sites 2a, 8c, 24g1 , and 24g2 . A

Fig. 1. The a-MnH 0.073 solid solution. On the right: two adjacent positions 12e partly occupied by hydrogen (open circles 9 and 10 ) and their nearest environment of two tetrahedra formed by manganese atoms on positions 24g1 (shaded circles 1 ­ 4 ) and on positions 24g2 (solid circles 5 ­ 8 ); the Mn atoms 1 ­ 4, 5, and 6 form a distorted octahedron around the H atom on position 9. On the left: the arrangement of dumb-bells of 12e positions in the unit cell of a-Mn. Bottom: the INS spectrum measured at 23 K with the TFXA spectrometer at ISIS, UK [10].


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Table 1 Positional parameters (X, Y, Z ), thermal factors (B ) and site occupancies (v ) for a-Mn [2] and for the solid solutions a-MnH 0.073 [2] and a-MnD 0.035 H 0.003 ( present work) according to a Rietveld profile refinement of the neutron diffraction data collected at 300 K with the HRFD diffractometer at JINR, Dubna Phase a-Mn ° a 5 8.9138( 3 ) A R p / R e x 5 5.0 / 3.1 Atom Mn Mn Mn Mn Mn Mn Mn Mn H Mn Mn Mn Mn D Site 2a 8c 24g 24g 2a 8c 24g 24g 12e 2a 8c 24g 24g 12e X 0 0.315( 2 ) 0.354( 2 ) 0.090( 2 ) 0 0.319( 2 ) 0.355( 1 ) 0.091( 1 ) 0 0 0.318( 2 ) 0.356( 1 ) 0.090( 1 ) 0 Y 0 0.315( 2 ) 0.354( 2 ) 0.090( 2 ) 0 0.319( 2 ) 0.355( 1 ) 0.091( 1 ) 0 0 0.318( 2 ) 0.356( 1 ) 0.090( 1 ) 0 Z 0 0.315( 2 ) 0.033( 2 ) 0.280( 2 ) 0 0.319( 0.034( 0.281( 0.538( 0 0.318( 0.035( 0.281( 0.539( °2 B (A ) 0.72 0.45 0.48 0.44 0.74 0.45 0.61 0.45 1.57 0.5 0.3 0.36 0.36 1.2

v
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.34( 2 ) 1.00 1.00 1.00 1.00 0.18( 2 )

1 2

a-MnH 0.073( 1 ) ° a 5 8.9403( 3 ) A R p / R e x 5 5.2 / 4.0

1 2

2 1 1 2

) ) ) )

a-MnD 0.035 H 0.003 ° a 5 8.9279( 2 ) A R p / R e x 5 3.6 / 2.2

1 2

2 1 1 2

) ) ) )

R p and R

ex

¯ are the obtained and expected profile factors. Cubic structure, space group I43 m ( No. 217 ).

resulting site occupancy of the H atoms in a-MnH 0.073 and of the D atoms in a-MnD 0.035 H 0.003 corresponds to the ratios H / Mn 5 (12 / 58)v 5 0.070( 4 ) and D / Mn 5 0.037( 4 ), which agree with the compositions of the solutions. Within the experimental error the coordinates obtained for the Mn atoms in the unit cell of a-Mn do not change on hydrogen / deuterium uptake. The coordinates of the H and D atoms coincide within the experimental error and give 2,H 5 ° ° 0.68( 3 ) A and 2,D 5 0.70( 3 ) A. As seen from Fig. 3, the values of the lattice parameter of a-MnD 0.035 H 0.003 and a-MnH 0.073 form a single linear dependence if plotted as a function of the atomic ratio x 5 (H 1 D ) / Mn. This implies that the dissolution of H and D results in virtually the same lattice expansion of the a-Mn metal. The increase in the atomic volume, Va , of

°3 a-Mn corresponds to a value of Va / x 5 1.50( 3 ) A / H atom which lies near the lower limit of the interval 1.5 ­ 3 °3 A / H atom characteristic of hydrides of transition metals [8,9].

3.2. Inelastic neutron scattering
A representative INS spectrum of a-MnH 0.073 that was measured recently [10] with better resolution than in Ref. [2] is shown in Fig. 1. The strong peak attributed to hydrogen tunnelling is centred at 6.2 meV, three peaks of the fundamental optical H modes are observed at 74, 107

Fig. 2. The neutron powder diffraction pattern of a-MnD 0.035 H 0.003 measured at 300 K with the HRFD diffractometer at JINR, Dubna (dots), its profile fit calculated with the structure parameters listed in Table 1 (solid line) and the difference between the experimental and calculated spectra ( the curve at the bottom). For clarity, the smooth incoherent component is subtracted from the experimental spectrum.

Fig. 3. The lattice parameter of solid H and D solutions in a-Mn at 300 K as a function of the total content x 5 (H 1 D ) / Mn of both hydrogen isotopes, the data from Table 1. The solid line shows the linear fit ° a 5 ( 8.9139 1 0.363x) A.


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and 130 meV, and one peak of the second optical H band is seen at around 190 meV, all in reasonable agreement with the results in Ref. [2]. The peak at 74 meV presumably corresponds to a low-energy mode of H vibrations along the line connecting the sites in a dumb-bell because relative to this line the nearest-neighbour Mn atoms are most distant and positioned symmetrically (see the right inset in Fig. 1 ). The peaks at 107 and 130 meV can be assigned to vibrations perpendicular to this line. Fig. 4a shows the INS spectra of a-MnH 0.073 and a-MnD 0.035 H 0.003 in the range of optical vibrations measured in the present work at a temperature of 5 K. The peak positions in the spectrum of a-MnH 0.073 are virtually the same as in Fig. 1. Hydrogen and deuterium peaks in the spectrum of a-MnD 0.035 H 0.003 have comparable intensities due to the large incoherent neutron scattering crosssection of hydrogen. Under the assumption that the energy of similar optical ]] ] modes is by a factor of oem D / m H ¯OE2 lower for D atoms than for H atoms (a harmonic case) and that only excita-

tions from the lower ground state take place at a temperature as low as 5 K ( the upper ground state is nearly empty ), the INS spectrum of deuterium in aMnD 0.035 H 0.003 in the range of optical vibrations can be approximated by the spectrum of hydrogen in a-MnH 0.073 ] plotted as a function of "vD 5 D D /2 1 ( "vH 2 D H /2 )/OE2. 0 0 This modelled deuterium spectrum is plotted in Fig. 4b by the dashed line. Its comparison with the experimental spectra in Fig. 4a shows that the peak at about 107 meV in the spectrum of a-MnD 0.035 H 0.003 is due to neutron scattering on H atoms only. The difference between the spectra of a-MnD 0.035 H 0 .003 and a-MnH 0.073 normalised to the integral intensity of the 107 meV peak yields the `experimental' spectrum of deuterium in a-MnD 0.035 H 0.003 plotted in Fig. 4b by the solid line. The elimination of the H contribution in the difference spectrum is not perfect, however, because the peaks in the spectrum of a-MnH 0.073 are broader than those in the spectrum of a-MnD 0.035 H 0.003 . In particular, a small peak at 107 meV still remains in the difference spectrum and the deuterium peak at 73 meV is noticeably deformed. The difference spectrum is nevertheless very similar to the deuterium spectrum calculated in a harmonic approximation (dashed line in Fig. 4b) and the positions of the two peaks at 51 meV and 92 meV, which do not overlap with the hydrogen peaks in the spectrum of aMnD 0.035 H 0.003 , coincide with the calculated ones within the experimental error. The fundamental modes of hydrogen and deuterium vibrations in a-Mn thus demonstrate harmonic behaviour, and the value "v D 5 51 meV used in Ref. [4] to estimate 0 the energy of tunnelling splitting in a-MnD 0.05 was correct. The ratio of integral intensities of the 73 meV and the 51 meV peak in the INS spectra, respectively, of a-MnH 0.073 and a-MnD 0.035 H 0 .003 normalised to the intensity of the 107 meV peak gives an atomic ratio of H / D ¯ 0.08 for the deuterated sample. This is the isotopic composition of that sample referred to throughout the paper.

4. Conclusions The experiment shows that hydrogen and deuterium dissolved in a-Mn occupy interstitial positions of the same type 12e and with the same distance 2, between the adjacent positions. The energies "v H and "v D of the H 0 0 and D optical vibrations follow a harmonic ratio, ]] ] oem D / m H ¯OE2. These findings strongly corroborate the assumption of the tunnelling origin of the 6.4 meV and 1.6 meV peaks in the spectrum of a-MnH 0.073 and of aMnD 0.05 , respectively [4], because the difference between the energies of these peaks is too large to result from mechanisms other than tunnelling. In fact, the energy 6.4 meV of the H peak should almost not depend on the mass

Fig. 4. (a) The experimental INS spectra of a-MnD 0.035 H 0.003 (open circles) and a-MnH 0.073 (solid circles) measured at 5 K with the IN1 BeF spectrometer at ILL, Grenoble. ( b) The difference between the above spectra considered as the INS spectrum of a-MnD 0.035 (solid curve) and the INS spectrum of a-MnH 0.073 plotted as a function of "vD 5 D D /2 1 0 ] ( "vH 2 D H / 2 ) /OE2 to simulate the spectrum of a-MnD x in a harmonic 0 approximation (dashed line).


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V.E. Antonov et al. / Journal of Alloys and Compounds 330 ­ 332 ( 2002 ) 462 ­ 466 [2] V.K. Fedotov, V.E. Antonov, K. Cornell, G. Grosse, A.I. Kolesnikov, V.V. Sikolenko, V.V. Sumin, F.E. Wagner, H. Wipf, J. Phys.: Condens. Matter 10 ( 1998 ) 5255. [3] A. Magerl, A.J. Dianoux, H. Wipf, K. Neumaier, I.S. Anderson, Phys. Rev. Lett. 56 ( 1986 ) 159. [4] A.I. Kolesnikov, V.E. Antonov, S.M. Bennington, B. Dorner, V.K. Fedotov, G. Grosse, J.C. Li, S.F. Parker, F.E. Wagner, Physica B 263 ­ 264 ( 1999 ) 421. ´ [5] S.L. Drechsler, G.M. Vujicic, N.M. Plakida, J. Phys. F: Met. Phys. 14 ( 1984 ) L243. [6] V.B. Zlokazov, V.V. Chernyshev, J. Appl. Crystallogr. 25 ( 1992 ) 447. [7] V.A. Somenkov, V.P. Glazkov, Z. Phys. Chem. N.F. 117 ( 1979 ) 125. ¨ [8] H. Peisl, in: G. Alefeld, J. Volkl ( Eds.), Hydrogen in Metals I, Springer, Berlin, 1978, p. 53. [9] E.G. Ponyatovsky, V.E. Antonov, I.T. Belash, in: A.M. Prokhorov, A.S. Prokhorov ( Eds.), Problems in Solid-State Physics, Mir, Moscow, 1984, p. 109. [10] A.I. Kolesnikov, V.E. Antonov, V.K. Fedotov, A.J. Dianoux, B. Dorner, A. Hewat, A.S. Ivanov, G. Grosse, F.E. Wagner, in: H.G. Buttner, C. Vettier ( Eds.), Annual Report 99: Scientific Highlights, ILL, Grenoble, 2000, p. 66.

of the hydrogen isotope if the peak were due to crystal field or magnetic effects or due to `lattice' vibrations. The ] peak energy should only decrease to 6.4 /OE2 ¯ 4.5 meV when H is substituted for D if the peak were due to optical hydrogen vibrations. At the same time, the observed positions of the H and D peaks both agree with the energies D H ¯ 5 meV and D D ¯ 1.5 meV of the tunnelling 0 0 splitting of the hydrogen and deuterium vibrational ground states as roughly estimated using the experimental values of 2,, "v H and "v D [4]. 0 0

Acknowledgements This work was supported by grant No. 99-02-17299 from the Russian Foundation for Basic Research. One of the authors ( V.E.A.) thanks the Organising Committee of MH2000 for financial support to attend the Symposium.

References
[1] V.E. Antonov, T.E. Antonova, N.A. Chirin, E.G. Ponyatovsky, M. Baier, F.E. Wagner, Scripta Mater. 34 ( 1996 ) 1331.