Hydrogen Dynamics in Partially Quasicrystalline Zr69.5Cu12Ni11Al7.5

Article pubs.acs.org/JPCC

Hydrogen Dynamics in Partially Quasicrystalline Zr69.5Cu12Ni11Al7.5: A Fast Field-Cycling Relaxometric Study Anton Gradišek* and Tomaž Apih Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia ABSTRACT: We studied hydrogen dynamics in a partially quasicrystalline hydrogen storage alloy Zr69.5Cu12Ni11Al7.5 by a combination of fast fieldcycling nuclear magnetic relaxometry and diffusometry in static fringe field. We demonstrate that proton spin−lattice relaxation cannot be explained using a single activation energy for proton hopping between the interstitial sites. Instead, the behavior is better explained using a Gaussian distribution of activation energies, with the average value closely matching the one obtained in independent direct diffusion measurements. Knowing the diffusion constant and the correlation times for proton jumps, we estimate the average jump length.

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INTRODUCTION Zirconium- and titanium-based quasicrystals are known to exhibit good hydrogen absorption properties,1 both due to favorable hydrogen chemistry (low binding energy to hydrogen atoms) and to their structure with a high number of available interstitial sites. Typical building blocks of quasicrystals include Mackay icosahedral clusters with 20 tetrahedral interstitials inside its inner icosahedral shell and 60 tetrahedral and 20 octahedral interstitials between the inner and outer shell. Another example is the Bergman cluster with 20 tetrahedral interstitials within its inner shell and 120 interstitials between the inner and outer shell, but with no octahedral interstitial sites. In addition, quasicrystalline materials exhibit excellent mechanical properties2 (high strength, hardness, and elasticity). The reason lies in the absence of long-range order that hinders crack propagation, thus making these systems less prone to mechanical damage due to lattice expansion upon hydrogen absorption, in a process known as hydrogen embrittlement. In the past years, the most studied quasicrystalline systems for hydrogen storage have been Ti−Zr−Ni3−7 and Zr−Cu− Ni−Al.8−13 Nuclear magnetic resonance (NMR) is probably the most versatile method to study hydrogen dynamics in metal hydrides. Various NMR techniques include NMR spectra line shape analysis, spin−lattice relaxation, and diffusion measurements in magnetic field gradient. Hydrogen self-diffusion in simple-structure metals, such as PdHx, TiHx, or ZrCr2 hydride, is in the range D = 10−8−10−6 cm2/s at room temperature.14 In these cases, diffusion measurements are typically carried out by the means of pulsed field gradient technique (PFG) through the diffusion-induced spin echo attenuation. On the other hand, hydrogen diffusion in systems with complex or disordered structures, such as quasicrystals11,13 and metallic glasses,12,15 was found to be considerably smaller, in the 10−11−10−8 cm2/s range. In these systems, diffusion is too slow to be determined © 2015 American Chemical Society

by the PFG technique since proton magnetization mostly relaxes due to spin−spin relaxation (T2) processes before diffusion could significantly attenuate the spin echo. Instead, the static fringe field (SFF) technique with stimulated echo sequence was employed for the measurements, taking advantage of a large static magnetic field gradient in the fringe field of a superconducting magnet that can reach up to 80 T/ m.16 In this approach, the echo amplitude decays through a combination of diffusion and spin−lattice relaxation (T1), a process significantly longer than the spin−spin relaxation, thus enabling measurements of slower diffusion processes. In previous studies of partially quasicrystalline (icosahedral) alloy Zr69.5Cu12Ni11Al7.5,11,13 diffusion in a series of samples loaded with different hydrogen-to-metal H/M ratios was investigated in the temperature range between room temperature and 440 K. Diffusion was found to follow the classical thermally activated over-the-barrier hopping model, with D = D0 exp(−Ea/kBT), where D0 is a diffusion prefactor and Ea is the activation energy for proton jumps between the interstitial sites. Within the experimental precision, the Ea value was found to be 365 ± 15 meV, independent of the H/M ratio. The D0 value showed a decrease with an increasing H/M ratio, which was attributed to the creation of defects in the structure upon hydrogenation, thus reducing the number of interstitial sites available for diffusion.11 In this paper, we investigate whether hydrogen diffusion can indeed be explained with a single value of activation energy for proton jumps or if it is more appropriate to consider a distribution of energies instead (as previously attempted in metallic glasses,17,18 quasicrystalline Ti45Zr38Ni17,4,5 and even in Received: February 1, 2015 Revised: April 19, 2015 Published: April 22, 2015 10677

DOI: 10.1021/acs.jpcc.5b01047 J. Phys. Chem. C 2015, 119, 10677−10681

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The Journal of Physical Chemistry C a crystalline Laves phase19). The complex structure of the sample, with a manifold of different interstitial sites and consequently with a multitude of energy differences between these sites, indeed indicates that a distribution of activation energies seems a reasonable model and that the activation energy, obtained by the direct diffusion measurements, is only the average value. The question of a distribution of correlation times for hopping in a complex system also arose in the studies of deuterium dynamics in icosahedral and amorphous modifications of the Ti40Zr40Ni20 system,7 where it was addressed by using the empirical stretched exponential Kohlrausch−Williams−Watts function gω = exp{−(t/τc)α} for deuterium NMR spectra analysis. It should be stressed, however, that this approach is only empirical and does not provide more detailed insight into local distributions of activation energies or correlation times. In the present study, we look at proton spin−lattice relaxation by means of fast fieldcycling relaxometry (FFC). This technique enables us to measure spin−lattice relaxation over four decades of Larmor frequencies, corresponding to magnetic field strengths from 0.5 T to the Earth’s magnetic field. The method employs an electromagnet field with a rapid switching rate20 and is often used in studies of systems where dynamic processes take place on very different time scales, such as collective motions in liquid crystals.21,22 To best of our knowledge, this is the first time this method was applied to study a metal hydride system.

−1 −1 −1 T1−1 = T1d + T1e + T1p

(1)

At low temperatures, protons can be treated as static; therefore, the only contribution to relaxation comes from interactions with conducting electrons and paramagnetic impurities. The electron contribution can be described by the Korringa relation, T−1 1e = KT, where K is the Korringa constant and is proportional to the square of the electron state density at the Fermi level.23 The paramagnetic contribution is typically treated as temperature-independent and, if present, often completely masks the electron contribution at low temperatures.24 Since the value of (T1T) −1 is approximately constant at low temperatures for Zr69.5Cu12Ni11Al7.5,11 we can neglect the paramagnetic contribution and estimate the value of K to be 0.0045 K−1 s−1. Total proton relaxation is therefore the sum of dipolar and electron contributions. To treat the dipolar contribution, we use a simple, BPP-like model ⎛ ⎞ τc 4τc 1 ⎟ = A⎜ + 2 2 2 2 T1d 1 + 4ω τc ⎠ ⎝ 1 + ω τc

(2)

where A is the prefactor; ω = 2πν0 where ν0 is the Larmor frequency; and τc is the correlation time for proton jumps. Originally, this model was developed by Bloembergen, Purcell, and Pound (BPP), assuming an exponential correlation function for random dipolar field fluctuations.25 Later, this model was expanded to address relaxation due to specific processes, such as isotropic diffusion by Torrey. Torrey’s model26 differs from our BPP-like model by a factor of 2 in the second term, and the prefactor (for protons, spin 1/2) is (2π/ 5)(μ0/4π)2γ4Hℏ2(n/a30). Here, n is the spin density, and a0 is the closest interspin distance. Other, more detailed models have been proposed by Sholl27 and Wolf28 to address phenomena like random-walk diffusion and taking into account particular crystal structure. Since these models require a better knowledge of structural parameters (the distribution of distances in our system is not known in greater detail), we resort to the simplest form, eq 2, which should nevertheless adequately describe experimental results. For a pair of protons, a jump of either of the spins substantially disturbs the interaction; therefore, τc equals τd/2, where τd is the mean dwell time for the hydrogen in an interstitial site. The average time between proton jumps should then match the value of the correlation time of the fluctuations of the dipolar interaction. As proton jumps are thermally activated, the correlation time is likely to have the Arrhenius form

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EXPERIMENTAL SECTION The partially quasicrystalline Zr69.5Cu12Ni11Al7.5 sample was prepared by melt spinning technique, as described in ref 8, and electrolytically charged9 with hydrogen to the 0.65 H/M ratio. 1 H spin−lattice relaxation times were measured using a Stelar Spinmaster 2000 fast field-cycling relaxometer. Relaxation times were measured in the temperature range from 294 to 394 K at selected Larmor frequencies 0.5, 1, 2, 4, 8, and 18 MHz, the latter being the highest achievable frequency in our setup. As is often done in the NMR relaxometry community, we use proton NMR frequency units as a measure for the magnetic field; e.g., B = 18 MHz actually stands for 18 MHz × 2π/γH = 0.423 T, where γH is the proton gyromagnetic ratio. Two types of sequences were used in the FFC measurements.20 For 8 and 18 MHz measurements, the nonpolarized sequence (NP) was used, where the sample is kept to relax in zero field initially, and the magnetization build-up as a function of time in the chosen field (Brlx) is then measured. For lower frequencies, a prepolarized sequence (PP) was used. Here, the sample is first exposed to the polarizing field (in our case, Bpol = 18 MHz) for sufficiently long time for magnetization to reach its equilibrium value and then left to relax at a chosen lower field (also Brlx). In both cases, magnetization at a chosen time is measured at the detection frequency, Bdet = 9.25 MHz.

⎛ E ⎞ τc = τ0 exp⎜ a ⎟ ⎝ kBT ⎠

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(3)

where τ0 (also referred to as τ∞ in some sources since this is the value of τc when T → ∞) is a prefactor and Ea is the activation energy for proton jumps. Temperature dependence of T−1 1d with the above τc exhibits a maximum at ωτc ∼ 1, while far from the maximum (where ωτc ≫1 or ωτc ≪1) eq 2 can be simplified in the asymptotic forms

ANALYSIS AND DISCUSSION Proton spin−lattice relaxation in a metal hydride originates from fluctuations in interactions of proton spins with other protons or with their surroundings. The main contributions to −1 the total relaxation rate, T−1 1 , are T1d from proton dipole− −1 dipole interactions, T1e from hyperfine interactions with the −1 unpaired spins of conducting electrons, and T1p from interactions with paramagnetic impurities, if those are present. The total relaxation rate can be expressed as a sum of all contributions18

⎛ E ⎞ 1 = C exp⎜ ± a ⎟ T1d ⎝ kBT ⎠

(4)

where C ∼ 1/ω τ0 for ωτc ≫1 and C ∼ τ0 for ωτc ≪1. While measuring either of the two asymptotic regions is sufficient to 2

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DOI: 10.1021/acs.jpcc.5b01047 J. Phys. Chem. C 2015, 119, 10677−10681

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where T−1 1d is given by eqs 2 and 3. Several distributions were tested on the experimental data. Dashed lines in Figure 1 represent the fit with the lowest root-mean-square error (RMSE) for a single activation energy (Ea = 221 meV, τ0 = 2.13 × 10−11 s), and a discrepancy is clearly visible. A model, assuming two separated activation energies, turns out to be inaccurate as well. Better agreement with the model, in view of smaller RMSE, is obtained using a continuous distribution of activation energies. Considering a uniform (“box-like”) distribution of energies, with upper and lower boundaries being free model parameters, the best agreement with the experimental values is obtained for activation energies between 260 and 380 meV and τ0 = 10−12 s. However, the best agreement is obtained using a model with a Gaussian distribution of activation energies

determine the activation energy of the thermally activated process, analysis of the region around the relaxation rate maximum is required for a precise τc determination. When limited to a single value of magnetic field, detecting the maximum can sometimes be problematic since it may lay outside the temperature range, achievable with the experimental setup (or perhaps above the sample stability range). Measurements using FFC relaxometry are therefore advantageous since the relaxation maximum appears at lower temperatures and is more pronounced at lower magnetic fields, as opposed to higher fields. Temperature dependencies of spin−lattice relaxation rates, measured at selected Larmor frequencies, are shown in Figure 1. A maximum in relaxation is clearly visible for lower values of Brlx, indicating that the dipolar mechanism contributes to relaxation prominently in this temperature range.

ρ (E ) =

Each of the T−1 1 temperature dependencies at fixed frequency can be independently fitted with the above model, the fitted curve matching the experimental points reasonably well. However, the model parameters obtained for each data set (activation energy Ea and prefactor for the correlation time for proton jumps τ0) are significantly different. The values for activation energies are scattered between 200 and 250 meV and the values of τ0 between 10−12 and 10−10 s. This indicates that the BPP-like model with a single activation energy for proton jumps does not apply to our system, as the model parameters should be independent of the Larmor frequency. A proper model should be able to simultaneously reproduce all experimental points with a single set of parameters. A complex structure of the sample, containing several different interstitial sites (enabling various types of proton jumps), indicates that a better approach is to consider a distribution of activation energies for proton jumps, ρ(E), as opposed to a single one. Dipolar contribution to relaxation time can then be expressed as −1

∫0

∞

−1 T1d (E)ρ(E)dE

(6)

where the average activation energy Ea and the standard deviation of the distribution σ are used as free fitting parameters. Gaussian distributions of activation energies have been used for a similar analysis before.4,5,18,19 Fits with optimal parameters are shown as solid lines at Figure 1. The average activation energy Ea is 367 ± 30 meV with the standard deviation σ = 46 ± 5 meV, the prefactor for the correlation time τ0 = 2.34 ± 0.2 × 10−13 s, and A = 3.8 ± 0.1 × 109 s−2. In the fitting procedure, the values of Ea and τ0 are not completely independent in the minimization process; therefore, we give ranges of their values within which reasonably good fits could be obtained. The values are close to those obtained for quasicrystalline Ti45Zr38Ni17, where similar models produced σ ∼ 40−60 meV.4,5 The value of A can be roughly estimated using the Torrey model with a0 ≥ 2.1 Å (which is the closest distance in between protons in a metal hydride, limited by the repulsive electrostatic interaction, as calculated by Switendick29). The estimate matches the order of the magnitude of the value obtained by the fitting process; however, for a more detailed calculation, better knowledge of the system structure would be required. In our analysis, we assumed that the prefactor τ0 is constant, thus independent of temperature and without any site-related distribution. This assumption is a reasonable approximation as the main contribution to the temperature-dependent τc originates from the exponential factor exp(Ea/kBT). Given the distribution of the activation energies for proton jumps, it is informative to have a look at the distribution of the correlation times ρ(τc). Knowing the relation between the activation energy and the correlation time, it is straightforward to calculate the distribution dρ/dτc

Figure 1. Spin−lattice relaxation rates for partially quasicrystalline Zr69.5Cu12Ni11Al7.5 at chosen Larmor frequencies (Brlx). Solid lines represent a simultaneous fit, considering a Gaussian distribution of activation energies, as described in the text. Dashed lines represent the best simultaneous fit which considers a single activation energy for proton jumps.

̃ = T1d

⎛ (E − E )2 ⎞ 1 a ⎟ exp⎜ − σ 2π 2σ 2 ⎠ ⎝

dρ dρ dE × (τc) = dτc dE dτc ⎛ τc ⎜ kBT log τ − Ea 1 0 = exp⎜ − σ 2π 2σ 2 ⎜⎜ ⎝

(

2

⎞

) ⎟⎟ × k T B

⎟⎟ ⎠

τc

(7)

where ρ(E) is the assumed Gaussian distribution (eq 6) and dE/dτc is calculated from eq 3. The distribution of the correlation times at some chosen temperatures is shown in Figure 2. However, the existence of a distribution of activation

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DOI: 10.1021/acs.jpcc.5b01047 J. Phys. Chem. C 2015, 119, 10677−10681

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Figure 3. Spin−lattice relaxation rates as a function of Larmor frequency for partially quasicrystalline Zr69.5Cu12Ni11Al7.5 at two chosen temperatures. Solid lines represent a simulation with the parameters, obtained from temperature dependence measurements for a Gaussian distribution of activation energies. Figure 2. Distribution of correlation times at some chosen temperatures for partially quasicrystalline Zr69.5Cu12Ni11Al7.5. The distributions are calculated using eq 7 and assuming a Gaussian distribution of activation energies for proton jumps. The vertical dashed lines indicate the value of the correlation time at the average value of the activation energy, τc = τ0 exp(Ea/kBT). It is interesting to notice that this value does not correspond to the maximum of distribution of τcit corresponds to the center-of-mass of the distribution instead, as the values of τc span over several orders of magnitude.

two chosen temperatures, 403 and 373 K. At temperatures below 370 K, proton relaxation at low frequencies becomes faster, bringing T1 well below 1 ms and thus under the measuring limit of the setup. Using the parameters obtained form the temperature-dependence measurements, the field dependence of relaxation rate was simulated, shown as solid lines in Figure 3. The measurements are in a perfect agreement with the simulated values, bringing a further confirmation to the model used. The average value of Ea obtained from the field-cycling measurements is in a perfect agreement with the value, obtained in previous measurements of hydrogen diffusion in this sample in a SFF setup with the stimulated echo pulse sequence (Ea = 365 meV).11 The agreement between the values indicates that the hydrogen motion, related to the long-range diffusion process, is the main contributor to the spin−lattice relaxation in this temperature range. Knowing the proton diffusion constant and the correlation time for proton jumps, we can estimate the average jump length a using the following relation14,18

energies for proton jumps and therefore of a distribution of correlation times for these jumps does not change the overall interpretation of the diffusion constant, D, which reflects a long-range process that averages out distributions of individual parameters, at least on the time scales of diffusion measurements,11 which are several orders of magnitude longer than the average correlation time. At this point, it is interesting to analyze how a distribution of activation energies affects the magnetization relaxation or buildup curve we obtain when measuring a single T1 value (at a chosen temperature and Larmor frequency). At a first glance, one would expect that the magnetization recovery curve would consist of a sum of exponential curves or a stretch exponent function, exp(−t/T1)α, where α is a stretch exponent, as jumps take place between different sites and with different rates. However, the magnetization curves we measure behave perfectly monoexponentially. The reason behind this is the fact that each proton visits a great number of different interstitial sites within the duration of the experiment (T1 ≫ τc); therefore, the magnetization recovery we measure is the average of the whole proton ensemble. Differences from a single-jump-type behavior only become apparent during the analysis of a large number of temperature- and frequencydependent measurementsas demonstrated here for hydrogen in Zr69.5Cu12Ni11Al7.5. Additionally, significant discrepancies from a monoexponential magnetization decay curve can hint at localized dynamic processes, such as preferential hopping between a small number of closely separated sites. Fast field-cycling relaxometry allows another type of experiment, measuring the field dependence of T1 at a fixed temperature. Figure 3 shows the so-called dispersion profiles at

D=

fT a 2 6τc

(8)

where f T is the tracer correlation factor (0 < f T < 1) that addresses the geometrical correlation between the consecutive jumpsan atom that has just jumped has a larger probability of making a reverse jump than jumping to another site (as it may be occupied by another atom). For low concentrations, the value of f T approaches 1. Since D and τc both share Arrheniuslike temperature dependence with the same Ea, we get a temperature-independent value of a = (6Dτc)1/2 = (6D0τ0)1/2. Considering D0 = 1.2 ± 0.2 × 10−7 m2/s,11 we estimate a = 4.1 ± 0.5 Å. This is comparable to, though slightly larger than, the typical values found in the literature. Quasielastic neutron scattering (QNS) experiments in C15-type hydrides have shown that the average jump lengths are distinctly longer than the distances between the nearest-neighbor tetrahedral sites (a is between 2 and 3.6 Å).14 In ref 14, the usual approximation is a ∼ 3 Å. 10680

DOI: 10.1021/acs.jpcc.5b01047 J. Phys. Chem. C 2015, 119, 10677−10681

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The Journal of Physical Chemistry C

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(8) Köster, U.; Meinhardt, J.; Roos, S.; Liebertz, H. Formation of Quasicrystals in Bulk Glass Forming Zr-Cu-Ni-Al Alloys. Appl. Phys. Lett. 1996, 69, 179−181. (9) Zander, D.; Leptien, H.; Köster, U.; Eliaz, N.; Eliezer, D. Hydrogenation of Zr-Based Metallic Glasses and Quasicrystals. J. NonCryst. Solids 1999, 250−252, 893−897. (10) Wehner, B. I.; Meinhardt, J.; Köster, U.; Alves, H.; Eliaz, N.; Eliezer, D. Oxidation and Hydrogenation of Quasicrystals. Mater. Sci. Eng., A 1997, 226, 1008−1011. (11) Apih, T.; Khare, V.; Klanjšek, M.; Jeglič, P.; Dolinšek, J. Hydrogen Diffusion in Partially Quasicrystalline Zr69.5Cu12Ni11Al7.5. Phys. Rev. B 2003, 68, 212202 1−4. (12) Apih, T.; Bobnar, M.; Dolinšek, J.; Jastrow, L.; Zander, D.; Köster, U. Influence of the Hydrogen Content on Hydrogen Diffusion in the Zr69.5Cu12Ni11Al7.5 Metallic Glass. Solid State Commun. 2005, 134, 337−341. (13) Dolinšek, J.; Apih, T.; Klanjšek, M.; Kim, H. J.; Köster, U. Hydrogen Diffusion in Quasicrystalline and Amorphous Zr-Cu-Ni-Al. Catal. Today 2007, 120, 351−357. (14) Fukai, Y. The Metal-Hydrogen System, 2nd ed.; Springer: Berlin, 2005. (15) Wencka, M.; Jagodič, M.; Gradišek, A.; Kocjan, A.; Jagličić, Z.; McGuiness, P. J.; Apih, T.; Yokoyama, Y.; Dolinšek, J. Physical Properties of Zr50Cu40-xAl10Pdx Bulk Glassy Alloys. J. Alloys Compd. 2010, 504, 16−21. (16) Kimmich, R.; Unrath, W.; Schnur, G.; Rommel, E. NMR Measurement of Small Self-Diffusion Coeficients in the Fringe Field of Superconducting Magnets. J. Magn. Reson. 1991, 91, 136−140. (17) Bowman, R. C., Jr. Preparation and Properties of Amorphous Hydrides. Mater. Sci. Forum 1988, 31, 197−228. (18) Richter, D.; Hempelmann, R.; Bowman, R. C., Jr. Dynamics of Hydrogen in Intermetallic Hydrides. Top. Appl. Phys. 1992, 97−163. (19) Skripov, A. V.; Soloninin, A. V.; Stepanov, A. P.; Kozhanov, V. N. Hydrogen Diffusion in C15- type HfMo2H0.4: Nuclear Magnetic Resonance Evidence of Two Frequency Scales of H Hopping. J. Phys.: Condens. Matter 1999, 11, 10393−10400. (20) Noack, F. NMR Field-Cycling Spectroscopy: Principles and Applications. Prog. Nucl. Magn. Reson. Spectrosc. 1986, 18.3, 171−276. (21) Apih, T.; Domenici, V.; Gradišek, A.; Hamplová, V.; Kaspar, M.; Sebastião, P. J.; Vilfan, M. 1H NMR Relaxometry Study of a Rod-Like Chiral Liquid Crystal in its Isotropic, Cholesteric, TGBA*, and TGBC* Phases. J. Phys. Chem. B 2010, 114, 11993−12001. (22) Gradišek, A.; Apih, T.; Domenici, V.; Novotna, V.; Sebastião, P. J. Molecular Dynamics in a Blue Phase Liquid Crystal: a 1H Fast FieldCycling NMR Relaxometry Study. Soft Matter 2013, 9, 10746−10753. (23) Slichter, C. P. Principles of Magnetic Resonance; Springer: Berlin, 1996. (24) Kocjan, A.; Gradišek, A.; Daneu, N.; Apih, T.; McGuiness, P. J.; Kobe, S. Structural and Magnetic Changes in Hydrogenated TiFe1xNix Alloys. J. Magn. Mag. Mater. 2012, 324, 2043−2050. (25) Bloembergen, N.; Purcell, E. M.; Pound, R. V. Relaxation Effects in Nuclear Magnetic Resonance Absorption. Phys. Rev. 1948, 73, 679− 715. (26) Torrey, H. C. Nuclear Spin Relaxation by Translational Diffusion. Phys. Rev. 1953, 92, 962−969. (27) Sholl, C. A. Nuclear Spin Relaxation by Translational Diffusion in Solids. J. Phys. C 1974, 7, 3378−3386. (28) Wolf, D. Determination of Self-Diffusion Mechanisms from High-Field Nuclear-Spin-Relaxation Experiments. Phys. Rev. B 1974, 10, 2710−2723. (29) Switendick, A. C. Band Structure Calculations for Metal Hydrogen Systems. Z. Phys. Chem. N. F. 1979, 117, 89−112.

CONCLUSIONS We analyzed the hydrogen dynamics in a partially quasicrystalline alloy Zr69.5Cu12Ni11Al7.5. This system exhibits an aperiodic structure that results in a wide variety of different interstitial sites. As a consequence, we cannot describe the system with a single value of activation energy for proton hopping but have to consider a distribution of energies instead. The use of the fast field-cycling relaxometry technique presents a significant experimental advantage over the conventional measurements at fixed magnetic fields since it allows measurements over several orders of magnitude of magnetic field strength. As demonstrated, a good fit using a single activation energy model at a sole magnetic field at a relatively narrow temperature interval does not necessarily reflect a narrow distribution of activation energies. Instead, in the case of a broad distribution of correlation times for proton jumps, the analysis of a T1 temperature dependence at a single magnetic field can produce misleading results. The proton spin−lattice relaxation measurements in partially quasicrystalline Zr69.5Cu12Ni11Al7.5 were best described using a Gaussian distribution of activation energies, with Ea = 367 meV and σ = 46 meV, with the Ea value closely matching the value obtained independently from the direct diffusion measurements. Using the relation that connects diffusion with the correlation times and jump distances, it is possible to estimate the average distance for proton jumps, which is around 4.1 Å. As a potential continuation of the work, quasielastic neutron scattering measurements could provide an NMR-independent estimate of the average jump distance.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: + 386 1 477 3967. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Professor Uwe Köster from Dortmund for sample synthesis and hydrogenation.

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REFERENCES

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DOI: 10.1021/acs.jpcc.5b01047 J. Phys. Chem. C 2015, 119, 10677−10681