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Neutron scattering investigation of the hydrogen dynamics in transition metals
ARTICLE IN PRESS
Physica B 350 (2004) e553–e555
Neutron scattering investigation of the hydrogen dynamics in transition metals I. Padureanua,*, D. Aranghela, R. Kahnb, A. Radulescua,c, V.V. Sumind a
‘Horia Hulubei’ National Institute for Physics and Nuclear Engineering, Bucharest, Romania b Laboratoire Leon Brillouin, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France c Institut fur 52425 Julich, Germany . Festkorperforschung, Forschungszentrum Julich, . . d Frank Laboratory of Neutron Physics, Joint Institute of Nuclear Research, 141980, Dubna, Russia
Abstract A study by inelastic neutron scattering of the hydrogen vibrations in titanium-based alloys containing vanadium and carbon is reported. The measurements performed at two temperatures 5 and 300 K are analyzed in terms of the phonon density of states, gð_oÞ: A good separation of the optic and acoustic spectrum is observed. In the range of very low temperatures such as 5 K a drastic decrease of the spectral intensity has to be noted. A clear feature in the energy loss interval is observed at _o=1.53 meV. This excitation could be assigned to a resonant vibration mode of the hydrogen in the host lattice. The intensity, both of the optic, acoustic and resonant modes as well as of the quasi-elastic scattering decrease in a proportional way with the hydrogen content in the studied samples. r 2004 Elsevier B.V. All rights reserved. Keywords: Inelastic neutron scattering; Hydrogen dynamics; Transition metals
The dynamics of the hydrogen in transition metals, local modes, hydrogen vibrations and hydrogen trapping, solubility limit of hydrogen in various alloys quantum diffusion of trapped— hydrogen interstitial as well as the role of tunnel splitting has received great attention within last two decades. At present these are the focus of an important number of experimental and theoretical investigations [1–5]. From the inelastic neutron scattering (INS) it was observed that as a result of interaction between the nitrogen and hydrogen atoms, the hydrogen local mode is splitting into *Corresponding author. France and Instituto Ciencia Materials de Aragon, CSIC, Zaragoza, Spain. Tel.: +4021-404-2300; fax: +4021-457-44-40. Email-address: padu@ifin.nipne.ro (I. Padureanu).
three peaks. The lattice dynamics calculation showed that such splits can be explained by N–H or H–H interactions that cause the deformations fields. From (INS), we are also expecting to get new information concerning the influence of guest at substitutional and interstitial sites or impurity atoms on the solubility limit and the interstitial sites of hydrogen in the titanium-based alloys. The mechanism that could explain the increase of the solubility limit is hydrogen trapping by the respective guest or impurity atoms. Another question is whether the type of interstitial site changes in the presence of additional guest or impurity atoms. Particularly in the case of simple trapping where the hydrogen is expected to occupy interstitial sites in the neighbourhood of the trapping atom, a change of the interstitial site
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.176
ARTICLE IN PRESS I. Padureanu et al. / Physica B 350 (2004) e553–e555
gð_oÞ can be derived from the double differential scattering cross-section measured into a solid angle bounded by the angles y1 and y2 with a uniform distribution of the angles between these limits Z y2 ds d2 s dy ¼ DF sin y dE y1 ;y2 dO dE y1 e2W Q4 Q4 E 2 e=k2 T 1gðeÞ: Q e e B 1
T = 300K Ti 0.8V0. 2 C 0.59 H 0.36
90 meV
81 meV
12
99 meV
Here Q1 and Q2 are the minimum and maximum values of the wave vectors transfer, 2W is the Debye-Waller factor, e ¼ _o is the energy transferred by the neutron during the scattering
10
44 meV
6
30 meV
8
14 meV
g(ε) [arb. units]
4
2
0 0
20
40
60
80
100
120
140
160
30 meV
4
87 meV
44 meV
T = 300K Ti0.8V0.2 C0.59 H0.18
74 meV
6
99 meV
ε [meV]
15 meV
may well take place. However, it was found that hydrogen in niobium still occupies tetrahedral interstitial sites in the presence of the guest and impurity atoms mentioned [4,5]. The present paper reports the preliminary results of an inelastic neutron scattering study in which the density of states of the hydrogen vibrations in titanium based alloys containing vanadium and carbon are derived. The changes in metal–metal interactions can be derived from the acoustic part of the INS spectrum. From the structure of the optic peak one can get information about H–H interactions, the finite life time of the excited states, lattice disorder, multi-phonon processes, etc. We also are looking for the possible existence of the resonant modes of the hydrogen bound to the lattice host atoms. The inelastic neutron scattering spectra were measured with the inelastic time of flight Spectrometer Mibemol installed at the Orphee reactor in LLB, CEA—Saclay. In this study we have used a cold neutrons beam ( corresponding to an with a wavelength l=5.2 A incident energy E0 =3.025 meV. The medium resolution of the spectrometer is De=e=3–5% for energy transfers between 1 and 70 meV and De=e=5–7% at higher energy transfers between 70 and 150 meV. The scattering spectra were taken over an angular range within of the interval 25.5 – 137 at two temperatures, 300 K and 5 K. Well known corrections for a time of flight technique have been applied to the experimental spectra. The dynamic quantity analysed in this paper is the generalised phonon frequency spectrum gð_oÞ: In the case of the incoherent scattering gð_oÞ can be obtained directly from the measured incoherent function Sinch ðQ; oÞ: The phonon spectrum could be also derived from lattice dynamical models but in many cases these are not reliable. Therefore, several authors tried to obtain gð_oÞ from the inelastic neutrons scattering based on the approach proposed in the paper [6]. In this paper the authors have dealt with the determination of the density of states (DOS) by means of the inelastic scattering of the neutrons. The theoretical approach relies on the one-phonon annihilation cross section of a polycrystalline material. For samples which scatter both coherent and incoherent the
g(ε) [arb. units]
e554
2
0 0
40
80
120
160
ε [meV]
Fig. 1. The phonon density of states for acoustic and optic vibrations.
ARTICLE IN PRESS I. Padureanu et al. / Physica B 350 (2004) e553–e555 T = 5K
0.4 0.3 0.2
p(ε) [arbitrary units]
process, kB is the Boltzman’s constant, T is the temperature of the sample, gðeÞ is the phonon density of states, Q ¼ K0 K; K0 and K are the wave vectors and E0 ; E the energies of the incident and scattered neutrons. In Fig. 1 is shown the phonon density of states obtained on the (FCC) samples Ti0.8V0.2C0.59H0.18 and Ti0.8V0.2C0.59H0.36 from the approach described above. The frequency spectrum in the energy loss range is shown in Fig. 2. This feature is also observed in the energy gain range but its intensity is lower. A theoretical attempt to describe the optical peak started from the Einstein model of the independent oscillators. It was concluded that the width of this peak is too large and reveals a fine structure, which can not be explained in terms of such model. Another attempt has been made with an improved lattice dynamical model proposed [7]. The theory proposed in [7] based on a central force potential can explain the splitting of the optical peak but not its large broadening observed in the experiment. The reason of this broadening could be the H–H interactions, the finite lifetime of the excited states and other multiple processes. Our observations show a weak dependence of the acoustic and optic features with the hydrogen concentration. An exception is the intensity of peaks, which depends proportionally of hydrogen amount. The origin of the observed peak at low temperature of 5 K could be assigned to the tunnelling or resonance effect. A first analysis by means of the two-site model commonly used to account for low-temperature anomalies in amorphous substances [8,9] led to the conclusion that a tunnelling effect has to be present at much lower energy transfer. The feature at energy transfer e=1.53 meV is about 4 times higher then the energy of tunnelling splitting. Therefore we concluded that the peak located at 1.53 meV in the loss energy range is a resonant mode. The detailed balance principle is respected. To bring more light on the origin of this feature
e555
Ti0.8V0.2C0.59 H0.18
0.1 0.0 -2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
-0.8
-0.6
-0.4
-0.2
0.4 0.3
Ti0.8V0.2C0.59H0.36
0.2 0.1 0.0 -2.0
-1.8
-1.6
-1.4
-1.2
-1.0
ε [meV]
Fig. 2. The low-frequency spectrum corresponding to the hydrogen resonant mode.
new investigations are planned for very small H concentration.
Acknowledgements I. Padureanu and D. Aranghel gratefully acknowledge support by Laboratoire Leon Brillouin, CEA Saclay and European Commission (HPRI-CT-1999-00032).
References [1] V.V. Sumin, Mater. Sci. Eng. A 230 (1997) 63. [2] A. Magerl, A.J. Dianoux, H. Wipf, K. Weumaier, I.S. Anderson, Phys. Rev. Lett. 56 (1986) 159. [3] H. Wipf, K. Neumaier, Phys. Rev. Lett. 52 (1984) 1308. [4] D. Richter, J.J. Rush, J.M. Rowe, Phys. Rev. B 27 (1983) 6227. [5] J.J. Rush, T.J. Udovic, N.F. Berk, D. Richter, A. Magerl, Europhys. Lett. 48 (1999) 187. [6] M.M. Bredov, Sov. Phys. Solid State 9 (1967) 1. [7] G.L. Slaggie, J. Phys. Chem. Solids 29 (1968) 923. [8] P.W. Anderson, B.I. Halperin, C.M. Varma, Philos. Mag. 25 (1972) 1. [9] W.A. Phillips, J. Low Temp. Phys. 7 (1972) 351.
Physica B 350 (2004) e553–e555
Neutron scattering investigation of the hydrogen dynamics in transition metals I. Padureanua,*, D. Aranghela, R. Kahnb, A. Radulescua,c, V.V. Sumind a
‘Horia Hulubei’ National Institute for Physics and Nuclear Engineering, Bucharest, Romania b Laboratoire Leon Brillouin, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France c Institut fur 52425 Julich, Germany . Festkorperforschung, Forschungszentrum Julich, . . d Frank Laboratory of Neutron Physics, Joint Institute of Nuclear Research, 141980, Dubna, Russia
Abstract A study by inelastic neutron scattering of the hydrogen vibrations in titanium-based alloys containing vanadium and carbon is reported. The measurements performed at two temperatures 5 and 300 K are analyzed in terms of the phonon density of states, gð_oÞ: A good separation of the optic and acoustic spectrum is observed. In the range of very low temperatures such as 5 K a drastic decrease of the spectral intensity has to be noted. A clear feature in the energy loss interval is observed at _o=1.53 meV. This excitation could be assigned to a resonant vibration mode of the hydrogen in the host lattice. The intensity, both of the optic, acoustic and resonant modes as well as of the quasi-elastic scattering decrease in a proportional way with the hydrogen content in the studied samples. r 2004 Elsevier B.V. All rights reserved. Keywords: Inelastic neutron scattering; Hydrogen dynamics; Transition metals
The dynamics of the hydrogen in transition metals, local modes, hydrogen vibrations and hydrogen trapping, solubility limit of hydrogen in various alloys quantum diffusion of trapped— hydrogen interstitial as well as the role of tunnel splitting has received great attention within last two decades. At present these are the focus of an important number of experimental and theoretical investigations [1–5]. From the inelastic neutron scattering (INS) it was observed that as a result of interaction between the nitrogen and hydrogen atoms, the hydrogen local mode is splitting into *Corresponding author. France and Instituto Ciencia Materials de Aragon, CSIC, Zaragoza, Spain. Tel.: +4021-404-2300; fax: +4021-457-44-40. Email-address: padu@ifin.nipne.ro (I. Padureanu).
three peaks. The lattice dynamics calculation showed that such splits can be explained by N–H or H–H interactions that cause the deformations fields. From (INS), we are also expecting to get new information concerning the influence of guest at substitutional and interstitial sites or impurity atoms on the solubility limit and the interstitial sites of hydrogen in the titanium-based alloys. The mechanism that could explain the increase of the solubility limit is hydrogen trapping by the respective guest or impurity atoms. Another question is whether the type of interstitial site changes in the presence of additional guest or impurity atoms. Particularly in the case of simple trapping where the hydrogen is expected to occupy interstitial sites in the neighbourhood of the trapping atom, a change of the interstitial site
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.176
ARTICLE IN PRESS I. Padureanu et al. / Physica B 350 (2004) e553–e555
gð_oÞ can be derived from the double differential scattering cross-section measured into a solid angle bounded by the angles y1 and y2 with a uniform distribution of the angles between these limits Z y2 ds d2 s dy ¼ DF sin y dE y1 ;y2 dO dE y1 e2W Q4 Q4 E 2 e=k2 T 1gðeÞ: Q e e B 1
T = 300K Ti 0.8V0. 2 C 0.59 H 0.36
90 meV
81 meV
12
99 meV
Here Q1 and Q2 are the minimum and maximum values of the wave vectors transfer, 2W is the Debye-Waller factor, e ¼ _o is the energy transferred by the neutron during the scattering
10
44 meV
6
30 meV
8
14 meV
g(ε) [arb. units]
4
2
0 0
20
40
60
80
100
120
140
160
30 meV
4
87 meV
44 meV
T = 300K Ti0.8V0.2 C0.59 H0.18
74 meV
6
99 meV
ε [meV]
15 meV
may well take place. However, it was found that hydrogen in niobium still occupies tetrahedral interstitial sites in the presence of the guest and impurity atoms mentioned [4,5]. The present paper reports the preliminary results of an inelastic neutron scattering study in which the density of states of the hydrogen vibrations in titanium based alloys containing vanadium and carbon are derived. The changes in metal–metal interactions can be derived from the acoustic part of the INS spectrum. From the structure of the optic peak one can get information about H–H interactions, the finite life time of the excited states, lattice disorder, multi-phonon processes, etc. We also are looking for the possible existence of the resonant modes of the hydrogen bound to the lattice host atoms. The inelastic neutron scattering spectra were measured with the inelastic time of flight Spectrometer Mibemol installed at the Orphee reactor in LLB, CEA—Saclay. In this study we have used a cold neutrons beam ( corresponding to an with a wavelength l=5.2 A incident energy E0 =3.025 meV. The medium resolution of the spectrometer is De=e=3–5% for energy transfers between 1 and 70 meV and De=e=5–7% at higher energy transfers between 70 and 150 meV. The scattering spectra were taken over an angular range within of the interval 25.5 – 137 at two temperatures, 300 K and 5 K. Well known corrections for a time of flight technique have been applied to the experimental spectra. The dynamic quantity analysed in this paper is the generalised phonon frequency spectrum gð_oÞ: In the case of the incoherent scattering gð_oÞ can be obtained directly from the measured incoherent function Sinch ðQ; oÞ: The phonon spectrum could be also derived from lattice dynamical models but in many cases these are not reliable. Therefore, several authors tried to obtain gð_oÞ from the inelastic neutrons scattering based on the approach proposed in the paper [6]. In this paper the authors have dealt with the determination of the density of states (DOS) by means of the inelastic scattering of the neutrons. The theoretical approach relies on the one-phonon annihilation cross section of a polycrystalline material. For samples which scatter both coherent and incoherent the
g(ε) [arb. units]
e554
2
0 0
40
80
120
160
ε [meV]
Fig. 1. The phonon density of states for acoustic and optic vibrations.
ARTICLE IN PRESS I. Padureanu et al. / Physica B 350 (2004) e553–e555 T = 5K
0.4 0.3 0.2
p(ε) [arbitrary units]
process, kB is the Boltzman’s constant, T is the temperature of the sample, gðeÞ is the phonon density of states, Q ¼ K0 K; K0 and K are the wave vectors and E0 ; E the energies of the incident and scattered neutrons. In Fig. 1 is shown the phonon density of states obtained on the (FCC) samples Ti0.8V0.2C0.59H0.18 and Ti0.8V0.2C0.59H0.36 from the approach described above. The frequency spectrum in the energy loss range is shown in Fig. 2. This feature is also observed in the energy gain range but its intensity is lower. A theoretical attempt to describe the optical peak started from the Einstein model of the independent oscillators. It was concluded that the width of this peak is too large and reveals a fine structure, which can not be explained in terms of such model. Another attempt has been made with an improved lattice dynamical model proposed [7]. The theory proposed in [7] based on a central force potential can explain the splitting of the optical peak but not its large broadening observed in the experiment. The reason of this broadening could be the H–H interactions, the finite lifetime of the excited states and other multiple processes. Our observations show a weak dependence of the acoustic and optic features with the hydrogen concentration. An exception is the intensity of peaks, which depends proportionally of hydrogen amount. The origin of the observed peak at low temperature of 5 K could be assigned to the tunnelling or resonance effect. A first analysis by means of the two-site model commonly used to account for low-temperature anomalies in amorphous substances [8,9] led to the conclusion that a tunnelling effect has to be present at much lower energy transfer. The feature at energy transfer e=1.53 meV is about 4 times higher then the energy of tunnelling splitting. Therefore we concluded that the peak located at 1.53 meV in the loss energy range is a resonant mode. The detailed balance principle is respected. To bring more light on the origin of this feature
e555
Ti0.8V0.2C0.59 H0.18
0.1 0.0 -2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
-0.8
-0.6
-0.4
-0.2
0.4 0.3
Ti0.8V0.2C0.59H0.36
0.2 0.1 0.0 -2.0
-1.8
-1.6
-1.4
-1.2
-1.0
ε [meV]
Fig. 2. The low-frequency spectrum corresponding to the hydrogen resonant mode.
new investigations are planned for very small H concentration.
Acknowledgements I. Padureanu and D. Aranghel gratefully acknowledge support by Laboratoire Leon Brillouin, CEA Saclay and European Commission (HPRI-CT-1999-00032).
References [1] V.V. Sumin, Mater. Sci. Eng. A 230 (1997) 63. [2] A. Magerl, A.J. Dianoux, H. Wipf, K. Weumaier, I.S. Anderson, Phys. Rev. Lett. 56 (1986) 159. [3] H. Wipf, K. Neumaier, Phys. Rev. Lett. 52 (1984) 1308. [4] D. Richter, J.J. Rush, J.M. Rowe, Phys. Rev. B 27 (1983) 6227. [5] J.J. Rush, T.J. Udovic, N.F. Berk, D. Richter, A. Magerl, Europhys. Lett. 48 (1999) 187. [6] M.M. Bredov, Sov. Phys. Solid State 9 (1967) 1. [7] G.L. Slaggie, J. Phys. Chem. Solids 29 (1968) 923. [8] P.W. Anderson, B.I. Halperin, C.M. Varma, Philos. Mag. 25 (1972) 1. [9] W.A. Phillips, J. Low Temp. Phys. 7 (1972) 351.