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Muon spin rotation in an NiTi metallic glass hydride
Journal of the Less-Common
770
Muon spin rotation in an Ni-Ti hydride R. L. Havill, J. M. Titman Department
of Physics,
Metals, 172-l 74 (1991) 770-775
metallic glass
and N. Cowlam
University of Sheffield, Shefield
S3 7RH (U.K.)
Abstract Measurements of the muon spin rotation in an Ni-Ti glassy metal-hydrogen system are reported. The muon depolarization rate is found to be due to the coupling of the muon spins and hydrogen nuclear moments. Motional narrowing occurs above about 150 K and takes place in two stages. It is suggested that the depolarization rate can best be described if it is assumed that the motion of the muon is faster than that of the hydrogen in the first stage of the narrowing. In the second stage the increase of temperature causes the hydrogen diffusion rate to overtake that of the muon and the fluctuation of the dipole fields at the muon is due principally to the motion of the hydrogens.
1. Introduction Muon spin rotation (PSR) experiments in metal-hydrogen systems are usually interpreted by supposing that the muons and the hydrogen occupy the same interstitial sites in the metal matrix [l-3]. Furthermore, in transition metal alloys in particular the dominant term in the muon depolarization rate arises from the interaction of the muon spin moment and the dipolar field of the nuclear spins of the hydrogen. Owing to the relatively small gyromagnetic ratios involved, the coupling to the metal nuclei is negligible in comparison. At large hydrogen concentrations the diffusive motion of the muons is thought to be constrained by the presence of the hydrogen so that motional narrowing of the depolarization occurs at temperatures consistent with the motion of the hydrogen atoms rather than the diffusion of the muons. The relation between this correlated motion and the depolarization rate is not well understood. It is generally found that the correlation decay rates of the dipole fields at the muon are much less than the hydrogen-hopping rates given by other types of experiment, e.g. nuclear magnetic resonance (NMR), even though similar activation energies are encountered [l-3]. The present paper reports measurements of the muon spin rotation in the N&T&, glassy metal-hydrogen system. The depolarization rate of the muons is shown to be largely dependent on the coupling between the muon and proton spins. Motional narrowing of the muon linewidth commences above 150 K at a relatively slow rate but this is enhanced considerably above 220 K. In general agreement with the remarks made above, the correlation
0022-5088/91/$3.50
0
Elsevier Sequoia/Printed
in The Netherlands
771
time calculated from the narrowed line above 220 K is about an order of magnitude greater than the interval between hops of the hydrogens as determined from the nuclear magnetic relaxation rate [4]. We will show that the correlation times are consistent with the notion that the hopping rate of the muons is less than that of the hydrogen above 220 K and greater below. Unlike previous interpretations we suggest that the motional narrowing takes place through the slow movement of the muons at the lower temperatures and this motion remains slow relative to the hydrogens at the higher temperatures. We offer an explanation of the long muon correlation time in terms of the motion of the hydrogens alone.
2. Experimental
details
The sample of Ni,,Ti,, was prepared by melting the constituent metals in an argon arc furnace and melt spinning to produce a metallic glass ribbon. Charging with hydrogen was accomplished by the electrolysis of dilute sulphuric acid with a platinum anode and the specimen as the cathode, achieving a hydrogen-to-metal ratio of 1.5. The pSR measurements were made on the pulsed muon spectrometer at the ISIS neutron spallation source of the Rutherford Appleton Laboratory. Sample temperatures were maintained in the range 20-340 K by a helium refrigerator and the depolarization measurements were carried out in tranverse geometry and a magnetic field of 22 mT. At sufficiently low temperatures the polarization decay can be expected to follow a gaussian time dependence G(t) = exp( ---a?‘) where 20’ is the frequency second moment of the static dipole coupling. At temperatures above about 250 K strong motional narrowing is observed to occur and a more appropriate shape is G(t) = exp( -i-t) where 2 = 2a2z and z is the correlation time of the fluctuating dipolar field at the muon. The initial data analysis was carried out by fitting these functions, together with the appropriate muon half-life, to the decay of the precession signal. The background signal including the very small contribution to the second moment from the metal spins was determined by measurements on a sample without hydrogen. The variation of o and i with temperature after correction for this background is shown in Fig. 1. 3. Discussion The second hydrogen nuclear
moment 20’ spins I is
for muons
embedded
in a rigid
lattice
of
100
200
300
Temperahue - K&#n
Fig. 1. Depolarization rate of the muon spin rotation in Ni,STi,,-H after correction for background signals. The figure shows the rate CJobtained by fitting gaussian decays to the data below 250 K. Lorentzian fits are shown above this temperature.
where yr and ym are the gyromagnetic ratios of the hydrogen and muon respectively [5]. The sum over the muon-hydrogen separation is not readily evaluated for a disordered material. According to Kai et al. [6j, the hydrogen separation is r = 2.56 A and, assuming a muon replaces a hydrogen, the observed value of the second moment is obtained if the sum is replaced by 9.4r -6. This compares quite well with the sum over a simple cubic lattice, which is 8.5re6 [5]. The hydrogens are thought to occupy distorted tetrahedral sites in the metal matrix so that the coordination of the near-neighbour hydrogens may be less than the six of the cubic lattice. Of course, a small reduction in r can reduce the numerical factor significantly and in the absence of more precise calculations we conclude that the depolarization rate is a consequence of the muon-hydrogen dipolar coupling. A similar calculation based on the data given in ref. 6 shows that the metal nuclei contribute about 0.2% of the second moment. It follows that the narrowing observed at higher temperatures is likely to be due to the motion of the muons or the hydrogens. Assuming that the muon-hydrogen dipole coupling can be represented by an exponentially decaying correlation function with characteristic time r [5], the depolarization function pertaining to the motionally narrowed case is G(t) =exp{
-!&s”r”[exp(G)-lifl)
Analysis of the data on the basis of this function gives the correlation times shown in Fig. 2, where it can be seen that it has an Arrhenius dependence on temperature above about 220 K. The solid line represents an activation energy of 0.22 eV and this value is comparable with the activation energy of 0.26 eV obtained for the hopping diffusion of the hydrogen from the dipolar
773
.
L-. 3-O
40
50
6.0
RedpocorTanpnM(1ooOm
Fig. 2. Correlation time 7 of the fluctuating dipole field at the muon. The solid line indicates an activation energy of 0.22 eV. The interval between hops of the hydrogens as derived for the NMR data of ref. 4 is shown by the dotted line.
relaxation of the NMR [4]. At lower temperatures the data fall below the solid line. Even though the experimental uncertainty in z is large here, this effect appears to be real since it arises from the observation that c is consistently lower between 150 and 200 K than the static value determined from the average of the data below 100 K. Similar observations of a slow reduction in the depolarization rate at the onset of the motional narrowing have been observed in both amorphous Cu-Ti [7] and Ni-Zr [3] metalhydrogen systems. The value of the second moment and the similarity of the activation energies indicate clearly that the motional narrowing is related to the hydrogen diffusion. An estimate of the interval between hops of the hydrogen atoms may be derived from the longitudinal nuclear magnetic relaxation rate, but the value obtained depends to some extent on the model used to analyse the data. The dotted line in Fig. 2 is calculated from the data in ref. 4 and gives the interval as a function of temperature under the assumption that the hopping rate is equal to the Larmor frequency at the minimum in the relaxation time. Measurements of the transverse rate down to 215 K confirm the general trend. For temperatures above 220 K the hopping rate is much less than the correlation time of the dipole fields at the muon. However, the extrapolation of this line indicates that cross-over occurs at lower temperatures and the relation between the magnitudes of these times is reversed. If this is so, then the narrowing of the depolarization at low temperatures would seem to be a consequence of the motion of the muon relative to an almost static array of hydrogens. The most puzzling feature of pSR in all metal-hydrogen systems, including the present experiment, is that the muon correlation times are much longer than the residence time of the hydrogens. A short review
774
of the earlier work is given in ref. 2. It has been pointed out [8] that the use of a simple exponential decay to describe the correlation of the dipole fields at the muon is in error if a distribution of jump rates exists, as, for example, in a disordered system. A detailed analysis should almost certainly include this possibility, but we suggest that it may be of secondary importance since the effect occurs in both crystalline and amorphous systems. The problem arises because it is generally supposed that the intrinsic hopping rate of the muons is greater than that of the hydrogens. Consequently, when most of the available sites are filled by hydrogen, the muons follow the hydrogen motion. Hence the correlation time of the muon may then be identified with its mean residence time, which in turn is the same as the residence time of the hydrogens. It is possible to give a different explanation in the present experiment if it is accepted that the muons have the lower intrinsic jump rate. The evidence for this is the observed cross-over in hydrogen and muon rates and the low activation energy at the onset of motional narrowing. Extrapolation of the low temperature hopping rate implies that the muons become the less rapidly moving particles above 220 K and that the high temperature motional narrowing is brought about by the motion of the hydrogens alone. In this case the muon spins are subject to weak interactions in which a hop of a neighbouring hydrogen atom only partially removes the time correlation in the dipolar fields, Our data indicate that the equivalent of about nine neighbours is required to destroy the correlation, in keeping with the requirement that the characteristic time is about an order of magnitude greater than the interval between hops. The origin of the low temperature motion is not clear since the muons may be blocked by the surrounding hydrogens. However, on account of its chemical affinity for titanium the hydrogen tends to favour those sites with a high proportion of titanium atoms and it may be that the muons can escape into the nickel-rich sites. Other evidence for the slow motion of muons in transition metal alloys can be found in the very limited extent of the observed narrowing in both crystalline and amorphous Cu,,Zr, when no hydrogen is present [9]. The results from pSR measurements in all the amorphous transition metal alloys mentioned above may be explained in this way, but we should be cautious in suggesting that our explanation is universal since there is evidence to show, e.g. in ZrV, [2], that in other metal&hydrogen systems the muons may have the more rapid motion.
References 1 M. R. Chowdhury, G. A. Styles, E. F. W. Seymour and G. H. Eaton, J. Phys.: Condens. Mutter, 1 (1989) 4659-4665. 2 R. Hempelmann, D. Richter, 0. Hartman, E. Karlsson and R. Wappling, J. Chem. Phys., 90 (1989) 1935-1949. 3 P. Boyer and A. Baudry, IOP Ann. Solid State Physics Conf., Nottingham, December 1988, IOP Publishing, Bristol, 1989, pp. 65-72.
775 4 5 6 7
M. A. Crouch, R. L. Havill and J. M. Titman, J. Phys. F: Met. Phys.. 16 (1986) 99-108. A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1970. K. Kai, S. Ikeda, T. Fukunaga, N. Watanabe and K. Suzuki, Physica B, 120 (1983) 342 346. S. W. Harris, 0. Hartmann, R. Hempelmann, A. J. Maeland, D. Richter, C. A. Scott, T. Sundquist, E. Wackelgard and R. Wappling, IOP Ann. Solid State Physics Conf.. Nottingham, December 1988, Short Meetings Series No 22, 73-06, IOP Publishing, Bristol, 1989. 8 A. M. Stoneham, IOP Ann. Solid State Physics Conf., Nottingham. December 198X. Short Meetings Series No 22, 45-53, IOP Publishing, Bristol, 1989. 9 S. G. Barsov Pt al., Hyperfine Interact., 31 (1986) 113.
770
Muon spin rotation in an Ni-Ti hydride R. L. Havill, J. M. Titman Department
of Physics,
Metals, 172-l 74 (1991) 770-775
metallic glass
and N. Cowlam
University of Sheffield, Shefield
S3 7RH (U.K.)
Abstract Measurements of the muon spin rotation in an Ni-Ti glassy metal-hydrogen system are reported. The muon depolarization rate is found to be due to the coupling of the muon spins and hydrogen nuclear moments. Motional narrowing occurs above about 150 K and takes place in two stages. It is suggested that the depolarization rate can best be described if it is assumed that the motion of the muon is faster than that of the hydrogen in the first stage of the narrowing. In the second stage the increase of temperature causes the hydrogen diffusion rate to overtake that of the muon and the fluctuation of the dipole fields at the muon is due principally to the motion of the hydrogens.
1. Introduction Muon spin rotation (PSR) experiments in metal-hydrogen systems are usually interpreted by supposing that the muons and the hydrogen occupy the same interstitial sites in the metal matrix [l-3]. Furthermore, in transition metal alloys in particular the dominant term in the muon depolarization rate arises from the interaction of the muon spin moment and the dipolar field of the nuclear spins of the hydrogen. Owing to the relatively small gyromagnetic ratios involved, the coupling to the metal nuclei is negligible in comparison. At large hydrogen concentrations the diffusive motion of the muons is thought to be constrained by the presence of the hydrogen so that motional narrowing of the depolarization occurs at temperatures consistent with the motion of the hydrogen atoms rather than the diffusion of the muons. The relation between this correlated motion and the depolarization rate is not well understood. It is generally found that the correlation decay rates of the dipole fields at the muon are much less than the hydrogen-hopping rates given by other types of experiment, e.g. nuclear magnetic resonance (NMR), even though similar activation energies are encountered [l-3]. The present paper reports measurements of the muon spin rotation in the N&T&, glassy metal-hydrogen system. The depolarization rate of the muons is shown to be largely dependent on the coupling between the muon and proton spins. Motional narrowing of the muon linewidth commences above 150 K at a relatively slow rate but this is enhanced considerably above 220 K. In general agreement with the remarks made above, the correlation
0022-5088/91/$3.50
0
Elsevier Sequoia/Printed
in The Netherlands
771
time calculated from the narrowed line above 220 K is about an order of magnitude greater than the interval between hops of the hydrogens as determined from the nuclear magnetic relaxation rate [4]. We will show that the correlation times are consistent with the notion that the hopping rate of the muons is less than that of the hydrogen above 220 K and greater below. Unlike previous interpretations we suggest that the motional narrowing takes place through the slow movement of the muons at the lower temperatures and this motion remains slow relative to the hydrogens at the higher temperatures. We offer an explanation of the long muon correlation time in terms of the motion of the hydrogens alone.
2. Experimental
details
The sample of Ni,,Ti,, was prepared by melting the constituent metals in an argon arc furnace and melt spinning to produce a metallic glass ribbon. Charging with hydrogen was accomplished by the electrolysis of dilute sulphuric acid with a platinum anode and the specimen as the cathode, achieving a hydrogen-to-metal ratio of 1.5. The pSR measurements were made on the pulsed muon spectrometer at the ISIS neutron spallation source of the Rutherford Appleton Laboratory. Sample temperatures were maintained in the range 20-340 K by a helium refrigerator and the depolarization measurements were carried out in tranverse geometry and a magnetic field of 22 mT. At sufficiently low temperatures the polarization decay can be expected to follow a gaussian time dependence G(t) = exp( ---a?‘) where 20’ is the frequency second moment of the static dipole coupling. At temperatures above about 250 K strong motional narrowing is observed to occur and a more appropriate shape is G(t) = exp( -i-t) where 2 = 2a2z and z is the correlation time of the fluctuating dipolar field at the muon. The initial data analysis was carried out by fitting these functions, together with the appropriate muon half-life, to the decay of the precession signal. The background signal including the very small contribution to the second moment from the metal spins was determined by measurements on a sample without hydrogen. The variation of o and i with temperature after correction for this background is shown in Fig. 1. 3. Discussion The second hydrogen nuclear
moment 20’ spins I is
for muons
embedded
in a rigid
lattice
of
100
200
300
Temperahue - K&#n
Fig. 1. Depolarization rate of the muon spin rotation in Ni,STi,,-H after correction for background signals. The figure shows the rate CJobtained by fitting gaussian decays to the data below 250 K. Lorentzian fits are shown above this temperature.
where yr and ym are the gyromagnetic ratios of the hydrogen and muon respectively [5]. The sum over the muon-hydrogen separation is not readily evaluated for a disordered material. According to Kai et al. [6j, the hydrogen separation is r = 2.56 A and, assuming a muon replaces a hydrogen, the observed value of the second moment is obtained if the sum is replaced by 9.4r -6. This compares quite well with the sum over a simple cubic lattice, which is 8.5re6 [5]. The hydrogens are thought to occupy distorted tetrahedral sites in the metal matrix so that the coordination of the near-neighbour hydrogens may be less than the six of the cubic lattice. Of course, a small reduction in r can reduce the numerical factor significantly and in the absence of more precise calculations we conclude that the depolarization rate is a consequence of the muon-hydrogen dipolar coupling. A similar calculation based on the data given in ref. 6 shows that the metal nuclei contribute about 0.2% of the second moment. It follows that the narrowing observed at higher temperatures is likely to be due to the motion of the muons or the hydrogens. Assuming that the muon-hydrogen dipole coupling can be represented by an exponentially decaying correlation function with characteristic time r [5], the depolarization function pertaining to the motionally narrowed case is G(t) =exp{
-!&s”r”[exp(G)-lifl)
Analysis of the data on the basis of this function gives the correlation times shown in Fig. 2, where it can be seen that it has an Arrhenius dependence on temperature above about 220 K. The solid line represents an activation energy of 0.22 eV and this value is comparable with the activation energy of 0.26 eV obtained for the hopping diffusion of the hydrogen from the dipolar
773
.
L-. 3-O
40
50
6.0
RedpocorTanpnM(1ooOm
Fig. 2. Correlation time 7 of the fluctuating dipole field at the muon. The solid line indicates an activation energy of 0.22 eV. The interval between hops of the hydrogens as derived for the NMR data of ref. 4 is shown by the dotted line.
relaxation of the NMR [4]. At lower temperatures the data fall below the solid line. Even though the experimental uncertainty in z is large here, this effect appears to be real since it arises from the observation that c is consistently lower between 150 and 200 K than the static value determined from the average of the data below 100 K. Similar observations of a slow reduction in the depolarization rate at the onset of the motional narrowing have been observed in both amorphous Cu-Ti [7] and Ni-Zr [3] metalhydrogen systems. The value of the second moment and the similarity of the activation energies indicate clearly that the motional narrowing is related to the hydrogen diffusion. An estimate of the interval between hops of the hydrogen atoms may be derived from the longitudinal nuclear magnetic relaxation rate, but the value obtained depends to some extent on the model used to analyse the data. The dotted line in Fig. 2 is calculated from the data in ref. 4 and gives the interval as a function of temperature under the assumption that the hopping rate is equal to the Larmor frequency at the minimum in the relaxation time. Measurements of the transverse rate down to 215 K confirm the general trend. For temperatures above 220 K the hopping rate is much less than the correlation time of the dipole fields at the muon. However, the extrapolation of this line indicates that cross-over occurs at lower temperatures and the relation between the magnitudes of these times is reversed. If this is so, then the narrowing of the depolarization at low temperatures would seem to be a consequence of the motion of the muon relative to an almost static array of hydrogens. The most puzzling feature of pSR in all metal-hydrogen systems, including the present experiment, is that the muon correlation times are much longer than the residence time of the hydrogens. A short review
774
of the earlier work is given in ref. 2. It has been pointed out [8] that the use of a simple exponential decay to describe the correlation of the dipole fields at the muon is in error if a distribution of jump rates exists, as, for example, in a disordered system. A detailed analysis should almost certainly include this possibility, but we suggest that it may be of secondary importance since the effect occurs in both crystalline and amorphous systems. The problem arises because it is generally supposed that the intrinsic hopping rate of the muons is greater than that of the hydrogens. Consequently, when most of the available sites are filled by hydrogen, the muons follow the hydrogen motion. Hence the correlation time of the muon may then be identified with its mean residence time, which in turn is the same as the residence time of the hydrogens. It is possible to give a different explanation in the present experiment if it is accepted that the muons have the lower intrinsic jump rate. The evidence for this is the observed cross-over in hydrogen and muon rates and the low activation energy at the onset of motional narrowing. Extrapolation of the low temperature hopping rate implies that the muons become the less rapidly moving particles above 220 K and that the high temperature motional narrowing is brought about by the motion of the hydrogens alone. In this case the muon spins are subject to weak interactions in which a hop of a neighbouring hydrogen atom only partially removes the time correlation in the dipolar fields, Our data indicate that the equivalent of about nine neighbours is required to destroy the correlation, in keeping with the requirement that the characteristic time is about an order of magnitude greater than the interval between hops. The origin of the low temperature motion is not clear since the muons may be blocked by the surrounding hydrogens. However, on account of its chemical affinity for titanium the hydrogen tends to favour those sites with a high proportion of titanium atoms and it may be that the muons can escape into the nickel-rich sites. Other evidence for the slow motion of muons in transition metal alloys can be found in the very limited extent of the observed narrowing in both crystalline and amorphous Cu,,Zr, when no hydrogen is present [9]. The results from pSR measurements in all the amorphous transition metal alloys mentioned above may be explained in this way, but we should be cautious in suggesting that our explanation is universal since there is evidence to show, e.g. in ZrV, [2], that in other metal&hydrogen systems the muons may have the more rapid motion.
References 1 M. R. Chowdhury, G. A. Styles, E. F. W. Seymour and G. H. Eaton, J. Phys.: Condens. Mutter, 1 (1989) 4659-4665. 2 R. Hempelmann, D. Richter, 0. Hartman, E. Karlsson and R. Wappling, J. Chem. Phys., 90 (1989) 1935-1949. 3 P. Boyer and A. Baudry, IOP Ann. Solid State Physics Conf., Nottingham, December 1988, IOP Publishing, Bristol, 1989, pp. 65-72.
775 4 5 6 7
M. A. Crouch, R. L. Havill and J. M. Titman, J. Phys. F: Met. Phys.. 16 (1986) 99-108. A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1970. K. Kai, S. Ikeda, T. Fukunaga, N. Watanabe and K. Suzuki, Physica B, 120 (1983) 342 346. S. W. Harris, 0. Hartmann, R. Hempelmann, A. J. Maeland, D. Richter, C. A. Scott, T. Sundquist, E. Wackelgard and R. Wappling, IOP Ann. Solid State Physics Conf.. Nottingham, December 1988, Short Meetings Series No 22, 73-06, IOP Publishing, Bristol, 1989. 8 A. M. Stoneham, IOP Ann. Solid State Physics Conf., Nottingham. December 198X. Short Meetings Series No 22, 45-53, IOP Publishing, Bristol, 1989. 9 S. G. Barsov Pt al., Hyperfine Interact., 31 (1986) 113.