Diffusion of hydrogen in cubic Laves phase Ho1-xMmxCo2 (x=0 , 0.2 and 0.4) alloys

International Journal of Hydrogen Energy 32 (2007) 2965 – 2970 www.elsevier.com/locate/ijhydene

Diffusion of hydrogen in cubic Laves phase Ho1−x Mmx Co2 (x = 0, 0.2 and 0.4) alloys G. Srinivas a,b , V. Sankaranarayanan a , S. Ramaprabhu b,∗ a Low Temperature Laboratory, Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India b Alternative Energy Technology Laboratory, Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India

Received 14 November 2006; received in revised form 5 January 2007; accepted 5 January 2007 Available online 22 February 2007

Abstract The diffusion of hydrogen in cubic (C15-type) Laves phase Ho1−x Mmx Co2 (x = 0, 0.2 and 0.4, Mm = mischmetal) alloys was measured in the -phase (solid solution) region over the temperature range of 500.800 ◦ C using Sieverts-type apparatus. The alloys and its hydrides have been characterized by powder X-ray diffraction (XRD) Rietveld method. The diffusion constants have been determined from the gas–solid reaction, where the gas pressure dependence on time has been measured at fixed temperature. The results have been discussed on the basis of Fick’s law of diffusion. The dependence of diffusion constant on alloy composition and initial pressure has been evaluated. Activation energy is obtained from the temperature dependence of diffusion using Arrhenius relation. 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: Cubic Laves phase AB2 type; Rare earth and mischmetal; Kinetics of hydrogen absorption; Diffusion constant; Activation energy

1. Introduction The Laves phase AB2 .H system is one of the most intensively studied materials suitable for the chemical storage of gaseous hydrogen. Diffusion of hydrogen in metals is a fundamental process in hydrogen storage in metal hydrides, hydrogen purification by metal membranes and in hydrogen embrittlement. The rate at which hydrogen atoms diffuse amongst interstitial sites in metals is of vital importance in several technological areas [1–4]. However, in the lattice expansion and the embrittlement during hydrogen absorption, the bulk samples break up into hydride powders. For this reason, several reports on diffusion studies have been carried out by two-step process, in which the material has been hydrogenated first and then the diffusion process has been estimated in hydrides using quasielastic neutron scattering (QENS) nuclear magnetic resonance (NMR) and ultrasonic methods [5–14]. In addition, the diffusion measurements were successfully carried out by singlestep process, in which the diffusion of hydrogen atoms in the interstitials has been determined during hydrogen absorption ∗ Corresponding author. Tel.: + 91 44 22574862; fax: + 91 44 22570509.

E-mail address: [email protected] (S. Ramaprabhu).

(electrochemical or gaseous) process at dilute hydrogen loadings, where the lattice expansion and embrittlement of alloys are certainly avoided [15–23]. In the Laves phases, all of the hydrogen interstitial sites are tetrahedral, with four metal–atom nearest neighbors. In the cubic structure there are 12 interstitials (g sites) with two A and two B nearest neighbors per AB2 formula unit. In addition, there are four interstitials (e sites) with one A and three B nearest neighbors and one interstitial (b site) with four B nearest neighbors [24,25]. It has been found that in a number of cubic (C15-type) Laves phases at low hydrogen concentrations, the hydrogen atoms occupy only tetrahedral sites of g type (A2 B2 ) and the other two types of tetrahedral sites e (AB3 ) and b (B4 ) being empty [24,26,27]. In order to study the mechanism and parameters of hydrogen diffusion in the cubic (C15-type) Laves phase Ho1−x Mmx Co2 (x = 0, 0.2 and 0.4, Mm = mischmetal, it is a natural mixture of the light rare earth metals and it mainly contains 50% Ce, 35% La, 8% Pr, 5% Nd and 1.5% other rare earth elements and 0.5% Fe [28]) alloys, we have performed hydrogen absorption kinetics in the single spherical shape samples in -phase (solid solution) region using Sieverts-type apparatus. It is also of interest that, at small hydrogen concentrations the Laves phase–hydrogen system is expected to retain the host–lattice structure (MgCu2

0360-3199/$ - see front matter 䉷 2007 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2007.01.003

G. Srinivas et al. / International Journal of Hydrogen Energy 32 (2007) 2965 – 2970

type) in -phase and provides an opportunity to study the behavior of hydrogen in the single phase over a wide range of temperatures. The experimental data have been analyzed on the basis of Fick’s law of diffusion in spherical particles. The temperature dependence of diffusion process and activation energy has been evaluated. 2. Experimental details About 0.7 g of each Ho1−x Mmx Co2 alloys were prepared by arc melting of stoichiometric amounts of constituting elements Ho, Mm and Co with a purity better than 99.9% under protective argon atmosphere. A 6 wt% excess of Ho and Mm were taken in order to prevent the formation of Co-rich phases. The ingots were melted several times to ensure homogeneity. The spherical alloy buttons were obtained by grounding the as melted ingots. The samples thus obtained were spherical polycrystalline of diameters about 5–5.2 mm. Samples were sealed in an evacuated quartz tube and homogenized at 850 ◦ C for 4 days. Hydrogen absorption kinetics of Ho1−x Mmx Co2 alloys were performed using Sieverts-type apparatus in temperature range of 500.850 ◦ C. A controlled amount of hydrogen gas has been admitted into the reaction chamber that holds a specimen and the pressure change has been monitored while maintaining constant temperature of the reaction chamber. Diffusivity is obtained from the change in pressure in the hydrogen reservoir with time. Before the measurements the samples were heated to about 800 ◦ C for more than 5 h in a vacuum of less than 10−5 mbar. This heat treatment ensures measurement of the diffusivity free from the effect of surface contamination. The amount of hydrogen absorbed by the specimen is determined by calculating the amount of pressure change after the reaction. The structural characterization of the Ho1−x Mmx Co2 and its hydrides was carried out by powder X-ray diffraction (XRD) (X’pert PRO, PANalytical diffractometer) using nickel-filtered Cu K radiation scanning in the 2 range of 15.90◦ in steps of 0.05◦ . 3. Results and discussion Powder XRD patterns analyzed with Rietveld method revealed that Ho1−x Mmx Co2 (x = 0, 0.2 and 0.4) alloys crystallize in the cubic Laves phase C15 (MgCu2 type with space group F d3m) structure. For example, Fig. 1 represents the Rietveld XRD pattern of Ho0.6 Mm0.4 Co2 . The data markers stand for the observed intensities and the solid line is the calculated pattern. The XRD data are refined by assuming a statistical distribution of atomic positions at 18 , 18 , 18 for Ho, Mm (8a site) and 21 , 21 , 21 for Co (16d site), in accordance with the neutron powder diffraction results obtained for cubic Laves phase by Paolasini and Hennion [29]. The quality of the fit is evaluated by the two parameters, Rwp and Re . The most meaningful is Rwp (R-weighted pattern), which measures the weighted difference between the calculated and measured intensities. The Re (Rexpected) value is an estimation of the minimum possible value of Rwp [30,31]. Table 1 summarizes the structural parameters obtained from the Rietveld refinement for these alloys. The val-

Ho0.6Mm0.4Co2 Counts X10E 4

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1.0

5.0

0.0 20.0

30.0

40.0

50.0 60.0 2θ (deg)

70.0

80.0

90.0

Fig. 1. Powder XRD pattern of Ho0.6 Mm0.4 Co2 alloy analyzed with Rietveld method. +: the experimental intensity, upper solid line: calculated intensity, lower solid line: the intensity difference, vertical bars “|”: Bragg diffraction peaks.

ues in Table 1 are indicative of the fact that the substituted Mm preferentially occupies Ho sites. Cell parameters increase linearly with increasing Mm concentration. Since the mischmetal is an ore of light rare earths, which are having larger radius than the Ho, the lattice constants of Ho1−x Mmx Co2 alloys increase with increasing Mm concentration, similar to that of multi-element Laves phase AB2 -type alloys [32,33]. The cubic (C15) Laves phase structure of Ho1−x Mmx Co2 alloys is found up to x = 0.4. When x 0.5, the system shows the precipitation of secondary C14 Laves phase and it increases with increasing Mm content. The alloys hydrogenated in the -phase region exhibit single-phase solid solutions having the cubic C15-type host–alloy structure with almost negligible change in their lattice parameters. The time-dependent hydrogen absorption measurements have been carried out over the temperature range of 500.850 ◦ C and at different initial pressures. These conditions correspond to hydrogen concentrations in the range of 0.1–0.2 hydrogen atoms per formula unit (H/f.u.), which is well within in the solid-solution region. In the diffusivity measurement by the method of absorption at lower temperatures, in many cases the surface acts as a barrier to the flow of hydrogen. In the hydrogenation process, the hydrogen molecules have to dissociate and to penetrate the surface of the particles to be hydrogenated. Therefore surface barrier energy arises. The surface barrier effects are negligible when experiments are carried out at higher temperatures. If the particle flux through the surface barrier is smaller than the possible diffusion flux under the surface layer the reaction rate is surface controlled. In the opposite case, the surface barrier can be neglected and the absorption of the hydrogen atoms in the bulk material is controlled by the bulk diffusion constant. On the other hand, the presence of hydride phase boundaries can cause large changes in diffusivity. To avoid these difficulties, the experiments have been carried out at elevated temperatures at hydrogen concentrations very less than the solubility limit of Ho1−x Mmx Co2 alloys. Moreover, at a composition of AB2 H0.1 there is only one H atom in

G. Srinivas et al. / International Journal of Hydrogen Energy 32 (2007) 2965 – 2970

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Table 1 ˚ ), weighted pattern, Rwp , expected pattern, Re ), diffusion constants and activation energies for Ho1−x Mmx Co2 The structural parameters (lattice constant, a (A (x = 0, 0.2 and 0.4) alloys Alloy

˚ a (A)

Rwp (%)

Re (%)

D (cm2 s−1 ) (at 600 ◦ C)

Ea (meV)

D0 (cm2 s−1 )

HoCo2 Ho0.8 Mm0.2 Co2

7.1781 (2) 7.1900 (1)

2.56 2.02

1.66 1.50

Ho0.6 Mm0.4 Co2

7.2040 (1)

2.55

1.82

(4.02 ± 0.02) × 10−6 (3.78 ± 0.04) × 10−5 (2.17 ± 0.05) × 10−5 (7.80 ± 0.05) × 10−6 (16.9 ± 0.05) × 10−5

414 ± 16 (190 mbar) 343 ± 4 (140 mbar) 379 ± 17 (125 mbar) 708 ± 7 (65 mbar) 364 ± 5 (140 mbar) 335 ± 7 (95 mbar)

1.0 × 10−3 (190 mbar) 3.6 × 10−3 (140 mbar) 3.7 × 10−3 (125 mbar) 91.0 × 10−3 (65 mbar) 2.1 × 10−3 (140 mbar) 6.5 × 10−3 (95 mbar)

Ho0.8Mm0.2Co2-H

P = 65 mbar

500 °C 600 °C 650 °C 700 °C 750 °C 800 °C

HoCo2-H P = 190 mbar

1.0

0.8

(190 mbar) (140 mbar) (125 mbar) (65 mbar) (140 mbar)

1.0 0.8

600 °C 700 °C 750 °C 800 °C 850 °C

0.6

Δp(t)/Δp0

0.4 0.6 0.2 0.0

0.4

0

500

1000

1500

2000

2500

3000

0.2 1.0 P = 125 mbar

0.8 0

2000

4000 Time (s)

6000

8000

Fig. 2. Normalized presentation of pressure decrease as a function of time for HoCo2 at initial pressure of 190 mbar and at different temperatures in the range of 500.800 ◦ C.

Δp(t)/Δp0

0.0

600 °C 700 °C 800 °C

0.6 0.4 0.2 0.0 0

every 10th unit cell, so that H–H interactions are virtually nonexistent. At these conditions the hydrogen absorption in the alloys is a diffusion controlled process. Figs. 2–4 represent the normalized presentation of pressure decrease with respect to time of Ho1−x Mmx Co2 for x = 0, 0.2 and 0.4, respectively, at different constant initial pressures and temperatures. It is clear that the hydrogen absorption rate increases with increasing temperature, as expected for a thermally activated diffusion process. The propagation of hydrogen into the interstitial sites of bulk spherical particles with radius R (cm) can be described by the well-known Fick’s law of diffusion [34–36]: ∞ c(t) 6  1 −m2 2 Dt/R 2 =1− e , c∞  m2

(1)

m=1

where c is the fractional concentration of H atoms in the interstitial sites in the intermetallic compound (0 c(H/f.u.) 1), c∞ is the hydrogen concentration for t → ∞ and D is the resulting diffusivity (cm2 s−1 ) which is concentration dependent. The decrease of pressure corresponds to an increase of concentration of hydrogen atoms in the bulk material, i.e., c(t) ∝ p0 − p(t) and c∞ ∝ p0 − p∞ , where p0 and p∞ represent the pressures for times t = 0 and ∞, respectively. Due to high

500

1000

1500

2000

2500

1.0 P = 140 mbar

0.8 500 °C 600 °C 700 °C 800 °C

0.6 0.4 0.2 0.0 0

500

1000 Time (s)

1500

2000

Fig. 3. Normalized presentation of pressure decrease as a function of time for Ho0.8 Mm0.2 Co2 at initial pressures of 65, 125 and 140 mbar and at different temperatures in the range of 500.850 ◦ C.

mobility of the hydrogen only the first term of the sum in Eq. (1) needs to be considered and we obtain p(t) − p∞ p(t) 6 2 2 = = 2 e− Dt/R . p0 − p ∞ p0 

(2)

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G. Srinivas et al. / International Journal of Hydrogen Energy 32 (2007) 2965 – 2970

1.0

0

Ho0.6Mm0.4Co2-H

600 °C 700 °C 750 °C 800 °C 850 °C linear fit

Ho0.8Mm0.2Co2-H P = 65 mbar

P = 95 mbar 0.8 650 °C 700 °C 750 °C 800 °C 850 °C

0.6 0.4

-1

0.2 Δp(t)/Δp0

0

500

1000

1500

0.0 0

1.0 0.8

ln(Δp(t)/Δp0)

P = 140 mbar 500 °C 600 °C 700 °C 800 °C

0.6

P = 125 mbar

600 °C 700 °C 800 °C linear fit

-1

-2

0.4 0.2

0

200

400

600

800

0.0 0

100

200 300 Time (s)

400

500 °C 600 °C 700 °C 800 °C linear fit

P = 140 mbar

0 500 -1

Fig. 4. Normalized presentation of pressure decrease as a function of time for Ho0.6 Mm0.4 Co2 at initial pressures of 95 and 140 mbar and at different temperatures in the range of 500.850 ◦ C.

1000

-2 -3

HoCo2-H P = 190 mbar

ln(Δp(t)/Δp0)

0

0

500 °C 600 °C 650 °C 700 °C 750 °C 800 °C linear fit

-1

-3

2000

4000 Time (s)

6000

400 Time (s)

600

800

Fig. 6. ln(p(t)/p0 ) vs. t plots for Ho0.8 Mm0.2 Co2 at initial pressures of 65, 125 and 140 mbar and at different temperatures in the range of 500.850 ◦ C.

-2

0

200

8000

Fig. 5. ln(p(t)/p0 ) vs. t plots for HoCo2 at initial pressure of 190 mbar and at different temperatures in the range of 500.800 ◦ C.

The diffusion constant can be determined from a plot ln(p(t)/p0 ) as a function of time, where a straight line is expected. The slope of the straight line gives the diffusion constant, D. The ln(p(t)/p0 ) vs. t plots of Ho1−x Mmx Co2

for x = 0, 0.2 and 0.4 are shown in Figs. 5–7, respectively. At each pressure and temperature, the experimental data are well described by straight line fit, which is represented by a solid line suggesting that the absorption process is controlled by the diffusion process without surface barrier effects. The slope of the fit increases with increasing temperature which represents the thermally activated diffusion processes. The activation energy can be obtained from the temperature dependence of the diffusion constant and is given by D = D0 e−Ea /kB T ,

(3)

where D0 is exponential pre-factor and kB is the Boltzmann constant. The activation energy Ea as well as D0 are obtained from the slope and intercept of Arrhenius plot (ln D vs. 1/T ) shown in Fig. 8. Resulting Ea and D0 along with lattice parameters and diffusion constants of Ho1−x Mmx Co2 .H (x = 0, 0.2 and 0.4) are given in Table 1. The obtained diffusivity parameters are in good agreement with that of previously reported diffusion results for Laves phase AB2 -type and AB5 -type

G. Srinivas et al. / International Journal of Hydrogen Energy 32 (2007) 2965 – 2970

0

650 °C 700 °C 750 °C 800 °C 850 °C linear fit

Ho0.6Mm0.4Co2-H P = 95 mbar

-1

-2

ln(Δp(t)/Δp0)

-3

-4

0

500 °C 600 °C 700 °C 800 °C linear fit

P = 140 mbar

-1

-2

-3

-4 0

50

100 150 Time (s)

200

250

Fig. 7. ln(p(t)/p0 ) vs. t plots for Ho0.6 Mm0.4 Co2 at initial pressures of 95 and 140 mbar and at different temperatures in the range of 500.850 ◦ C.

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lower temperatures by decreasing the diffusion constant resulting in deviations from Arrhenius behavior. It is clear from the comparison that the diffusivity of hydrogen in the interstitials of alloys greatly increases with increasing Mm concentration; however, negligible change in the activation energy is observed. It is also observed that the diffusivity and activation energy change with initial hydriding pressures. The increase in diffusivity and variations in the activation energy of Ho1−x Mmx Co2 .H with increasing Mm concentration and hydrogenation pressure (or concentration) may be due to the changes in the intersite distances, since substitution of Mm increases lattice parameters thereby increasing interstitial hole size and intersite distances. In fact, it is reported that the H hopping rates in the Laves phase alloys and other intermetallics strongly depend on distances between the corresponding interstitial sites [13,37,38]. Further, the distribution of the elements on A and B sites of the AB2 structure and the nearest-neighbor interactions are the other factors to cause changes in the diffusivity and activation energy. In the cubic AB2 Laves phase, hydrogen atoms mainly occupy two kinds of interstitial sites: A2 B2 and AB3 . After Mm substitution, there are two kinds of A atoms: Ho and Mm. Thus, in the alloy there exist various environments of interstitial sites, for example, interstitials with HoHoCo2 , HoMmCo2 , MmMmCo2 , HoCo3 and MmCo3 , and have different hydrogen affinities. On the other hand, the rate at which the hydrogen atoms at the surface move into the bulk is related to the concentration of the hydrogen atoms at the surface. At very lower pressures (concentrations) the diffusivity obtained from the absorption rate is pressure dependent. 4. Conclusion

-7

Ho1−x Mmx Co2 .H (x = 0, 0.2 and 0.4) alloys crystallize in cubic (C15) Laves phase MgCu2 -type structure and the lattice parameters increase with increasing Mm concentration. The hydrides in the solid-solution region retain their cubic Laves host structure. The hydrogen absorption kinetics in the -phase region are found to be rate limited by diffusion of atomic H into the bulk. The diffusivity greatly depends on the Mm concentration. Obtained diffusion constant and activation energy are in the range of 4 × 10−6 .40 × 10−5 cm2 s−1 and 335.708 meV, respectively.

Ho0.6Mm0.4Co2-H -8

P = 140 mbar P = 95 mbar

ln(D)

-9 -10 -11 HoCo2-H

-12

P = 190 mbar

Ho0.8Mm0.2Co2-H -13

Acknowledgment

P = 140 mbar P = 125 mbar P = 65 mbar

-14 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1000/ T (K-1) Fig. 8. Arrhenius plots of hydrogen diffusion in Ho1−x Mmx Co2 (x = 0, 0.2 and 0.4) alloys at different initial pressures in the solid-solution region and at temperatures in the range of 500.850 ◦ C.

hydrogen systems [16,17]. The variation of the diffusion constants with temperature clearly exhibits an Arrhenius behavior. Surface barrier effects are expected to be more influenced at

The authors are grateful to the DRDO and DST for supporting this work. One of the authors (G. Srinivas) is grateful to IIT Madras for financial support. References [1] Kamakoti P, Morreale BD, Ciocco MV, Howard BH, Killmeyer RP, Cugini AV. et al. Science 2005;307:569. [2] Hauback BC, Brinks HW, Jensen CM, Murphy K, Maeland AJ. J Alloys Compd 2003;358:142. [3] Vajo JJ, Mertens F, Ahn CC, Bowman RC, Fultz B. J Phys Chem B 2004;108:13977. [4] Lunarska E, Chernyaeva O. Mater Sci 2004;40:399.

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