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Hydrogen diffusion in Mg–H and Mg–Ni–H alloys
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Acta Materialia 56 (2008) 2677–2686 www.elsevier.com/locate/actamat
Hydrogen diffusion in Mg–H and Mg–Ni–H alloys ˇ erma´k *, L. Kra´l J. C Institute of Physics of Materials, AS CR v. v. i., Zˇizˇkova 22, CZ-616 62 Brno, Czech Republic Received 25 October 2007; received in revised form 29 January 2008; accepted 3 February 2008 Available online 14 March 2008
Abstract Coefficients of hydrogen diffusion in Mg2NiH4 (DI), MgH2 (DM), and in (Mg + Mg2Ni)H eutectic (DE) were measured in the temperature interval 449–723 K. Experimental material was prepared by two techniques: by melting and casting and by ball-milling and compacting into pellets. Hydrogen charging was carried out from the hydrogen gas phase at high temperature and pressure. The Mg2NiH4 pellets were prepared in different regimes resulting either in a structure with a high fraction or with a low fraction of twinned low-temperature phase LT2. It was found that the LT2 slows down the hydrogen desorption rate considerably – values of DI in lowtemperature untwinned phase LT1 are by a multiplication factor of about 20 higher than those in the twinned phase LT2. Obtained values of DM are significantly lower than the literature values reported for the pure Mg. Hydrogen diffusion coefficients in interphase boundary were estimated from DE. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Intermetallic compounds; Magnesium alloys; Hydrogen diffusion; Hydrogen-storage materials
1. Introduction Hydrogen is a prospective fuel both for direct combustion and in electrochemical batteries and fuel cells. Therefore, there is an extended field of problems that are intensively studied, ranging from ecology of hydrogen production itself up to special materials for new hydrogen technologies. One of the partial problems of utmost importance is hydrogen storage in a solid media. There is a broad variety of materials considered as hydrogen-storage materials (HSM) (for review see, for example, Refs. [1–3]). It is interesting to note that – in some materials – the density of stored hydrogen reaches even higher values than the density of liquid hydrogen [4]. The main problems that should be solved in the field are sufficient storage capacity, high-cycle durability, resistance against contaminant gases, and sufficient rate of hydrogen charging/decharging (C/D) at moderate conditions (below 450 K and 2 bar). *
Corresponding author. Tel.: +420 532 290 422; fax: +420 541 218 657. ˇ erma´k). E-mail address: [email protected] (J. C
Magnesium-based alloys belong to most frequently studied HSM because of two main reasons: first, magnesium is a very cheap and abundant element on the Earth; and second, the light Mg-based matrix enables to achieve the best (up to now) weight storage ratio. However, pure Mg is not suitable HSM because of poor kinetics of C/D cycle. Therefore, it is alloyed with other elements, frequently with nickel. Before all, eutectic mixtures Mg + Mg2Ni and pure Mg2Ni intermetallic compound are in the focus of interest as base materials. Although the other intermetallic compound MgNi2 in the Mg – Ni binary system [5] shows a certain solubility of hydrogen [6], it is commonly considered as a not prospective HSM at present. Even alloyed, Mg-based HSMs need temperatures of about 470 K for C/D, which makes them somewhat unsuitable for energy sources in personal and household appliances. Considerable effort is, therefore, constantly devoted to lowering the stability of Mg-based hydrides and, at the same time, to preserve their favorable storage capacity (see, for example, Refs. [7–11]). Although there are some studies of C/D kinetics applicable to Mg-based alloys [12–20], the rate constants are
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.02.003
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known only. The theory of the C/D kinetics is often based on Johnson–Mehl–Avrami model (see, for example, Ref. [21]). Contrary to the often-drawn conclusion, namely that the process of desorption is controlled by diffusion [12,13,16,21], quantitative data describing hydrogen diffusion itself are very sparse in the literature. In Ref. [15], the authors declare the a/b (a – base matrix with hydrogen dissolved, b – hydride) interphase motion at high temperatures, nucleation-and-growth at ‘‘early stages” and diffusion at ‘‘later stages” as respective controlling mechanisms. In Refs. [16,18], the authors tested a number of known rate equations and chose ‘‘the best one” for their materials studied. It should be noted, however, that the choice of the optimal equation (and the probable kinetic mechanism governing the respective phase change) is, in this way, very difficult. It is known that Mg2NiH4 compound undergoes a phase change between the room temperature and the melting point, which complicates the kinetic study of C/D processes in the material. The history of the phase analysis in Mg2NiH4 begins in 1979 when Gavra and Mintz [22] identified the cubic high-temperature phase above Ttr = 508 K. In the 1980s a series of studies was started (see, for example, Refs. [23–32]), which can be summarized as follows: the high-temperature (HT) phase is face-centered cubic (fcc), derived from the CaF2-type structure. The magnesium ions form a cube around the [Ni0H4] complex (Ni0 – effectively zero-valent Ni atom; H atoms occupy six of the eight vertices of octahedral centering in Ni atom), building an anti-fluorite structure (anions occupy the fcc lattice points, complexes reside in four tetrahedral sites). Exact location of hydrogen atoms by Ni center can be specified only approximately. It can be said [30] that H atoms are ˚ . Somewhat more located at a sphere with a radius of 1.5 A detailed information on the H location can be found in Ref. [33]: a square planar order of H atoms in the complex implies metallic properties, whereas regular tetrahedron leads to semiconductor-like character of the compound (for step-like changes of electric conductivity – see also Ref. [30]). Upon cooling, the HT transforms into monoclinically distorted low-temperature (LT) phase with slightly distorted tetrahedral [Ni0H4] complex. LT exists in two modifications – untwinned (LT1) and microtwinned (LT2). Microtwinning occurs on the basic cell level. The ratio of LT1/LT2 depends sensitively on the thermomechanical history of the sample and, it influences to a certain extent, the electrical conductivity and the color of the LT [30]. The presence of LT2 may be indicated by typical peak in the XRD diffraction spectra at 2h = 23.7° (with Cr Ka1 radiation) [25,30,31]. The aim of the present study is to obtain diffusion coefficients of hydrogen in hydrogen-charged Mg2Ni intermetallic (i.e., in Mg2NiH4), in hydrogen-charged Mg (i.e., in MgH2), and in hydrogen-charged eutectic (Mg + Mg2Ni)H. The results enable the rate of hydrogen diffusion-controlled processes running in these materials to be quantified, which are often used as a base of hydrogen-storage media.
2. Experimental 2.1. Preparation of experimental materials Experimental alloys were prepared from pure components 3N6 Ni and 3N8 Mg. Splinters of pure components for preparation of intermetallic and eutectic alloys were ball-milled in air using a Fritsch-Pulverisette6. The composition was Mg – 54.5 wt.%Ni and Mg – 23.5 wt.%Ni respectively. Splinters (0.1 mm thick) of both Mg and Ni were ball-milled under the following conditions: 10 min milling +50 min relaxation 20 times repeated. Mass ratio of balls to the milled mixture was rm = 25. Milled powder was pressure-compacted at room temperature into pellets with diameter 20 mm 5 mm in height. Samples from pure Mg and from cast modification of intermetallic and eutectic alloys were prepared by induction-melting in the MgO crucible under Ar protective atmosphere. Ingots were cut into slices about 2 mm thick that were ground with metallographic papers down to foils of final thickness 2l lying between 100 and 703 lm. An overview of experimental materials is given in Table 1. 2.2. Hydrogen charging Hydrogen charging followed immediately after the pellets/foils preparation by isothermal annealing in a pressure vessel. Pressure of pure (5N3) hydrogen was 30 bar and the charging temperature Tc was 423 and 673 K. The time of charging was several hours by pellets and 14 days by foils. Hydrogen concentration in the charged samples was determined by precise weighing the samples before and after the charging. The samples were charged up to the state of complete charging, which was detected as a state with saturated weight of respective sample. 2.3. SEM observation 2.3.1. Pellets The structure of samples was checked by SEM JEOL JSM 6460 equipped with EDAX/WEDAX Oxford Instruments analyzer. Samples were porous and consisted of Table 1 Experimental materials Designation
Composition
Prepared as
Temperature of hydrogen charging
I
Intermetalic Mg2Ni (Mg–54.5 wt.%Ni)
Pelletsa
Tc = 426 K Tc = 623 K Tc = 623 K
c
M E
a
Mg Eutectic Mg + Mg2Ni (Mg–23.5 wt.%Ni)
Castingsb Castingsb Pelletsa Castingsb
Compacted into cylinders of diameter 20 mm height 5 mm. Machined to foils of diameter 20 mm thickness 2l = 100–703 lm. c Besides hydrogen-charged cast magnesium (MgH2), also MgH2 powder was measured purchased in ALFA AESAR. Mean grain size of the powder particles was about 2a = 100 lm. b
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compact grains of mean size 2q most frequently between 10 and 50 lm, as is illustrated in Fig. 1. Mean grain size of hydrogen-charged I and E pellets was reduced somewhat due to fragmentation of the largest grains. Chemical composition of grains coincided well with the intended average composition of respective alloy. 2.3.2. Foils The structure of cast modifications of alloys I and E is shown in Figs. 2 and 3. Due to incongruent solidification [5], there are three components present in alloy I. As the first one, the MgNi2 compound precipitates that form agglomerates of rectangular crystallites in the melt (see the light rectangular particles in Fig. 2). This phase participates on the hydrogen C/D process to a negligible extent only [6]. Below 1033 K, Mg2Ni starts to precipitate and the rest of the Mg-enriched melt solidifies between the grains of grown Mg2Ni as fine eutectic.
Fig. 3. SEM micrograph of cast alloy E after the hydrogen charging. Light particles and lamellae, Mg2NiH4.
During the hydrogen charging, the grains transform to Mg2NiH4 and in the eutectic, the MgH2 is nucleated. The latter phase grows and forms rows of individual crystallites in I, decorating the grain boundaries. Progressive hydrogen charging brings about the growth of internal stress and partial fragmentation of grains. The microstructure of cast eutectic alloy E is shown in Fig. 3. It consists of oblong Mg2Ni particles (size about 40 3 lm) in lamellar eutectic matrix (inter-lamellar distance is about 2 lm). Due to strain accommodation of (Mg) matrix between the Mg2NiH4 lamellae, hydrogen charging of alloy E does not lead to cracking. Grain size of Mg foils was of the order of tens of mm. Hence, it can be presumed that the presence of grain boundaries in M does not influence significantly the kinetics of the C/D process. Fig. 1. Structure of compacted pellets of alloy E after the hydrogen charging.
2.4. XRD phase analysis
Fig. 2. SEM micrograph of cast alloy I before the hydrogen charging. Grain interior, Mg2Ni; light rectangular particles, MgNi2; fine eutectic Mg+/Mg2Ni at grain boundaries.
X-ray profiles were obtained by X’Pert Pro MPD device (PANanalytical B.V., Almelo, The Netherlands) using Co Ka radiation and interpreted by the HighScore Plus software with commercial databases [34–36]. The results obtained for alloy I can be illustrated by the most significant reflections marked in XRD pattern shown in Fig. 4. It is clear that the prevailing phase in charged samples is Mg2NiH4. In cast sample (Fig. 4a) and in the pellets charged at temperature below the Ttr (Fig. 4c), also MgH2 phase as well as a certain amount of Mg2NiH0.3 is present. It is interesting to compare the amount of the twinned LT2 phase (typical line at 2h = 27.3° [25,29–31]) in the charged I samples. Whereas the pellets charged above Ttr (Fig. 4b) contain twinned LT2 phase to a considerable extent, in the cast sample charged above Ttr (Fig. 4a) and in the pellets charged below Ttr (Fig. 4c), the LT1 phase prevails. In the decharged samples, the a phase is present only, which is illustrated in Fig. 4d.
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Fig. 4. XRD pattern of alloy I. (1) Mg2NiH4 (LT1 – untwinned); 1TW, (LT2 – twinned); (2) Mg2NiH0.3; (3) MgH2; (4) Mg2Ni. Tc – charging temperature, Td – decharging temperature.
Fig. 5. XRD pattern of alloys M and E. (1) Mg2NiH4; (2) Mg2NiH0.3; (3) MgH2; (4) Mg2Ni; (5) Mg. Tc – charging temperature, Td – decharging temperature.
The same phases are identified in samples E as can be seen in Fig. 5 (Fig. 5c – hydrogen-charged M; Fig. 5d – decharged E). Hydrogen-charged M foils (Fig. 5a) contain exclusively Mg and MgH2 phases, whereas decharged M samples (Fig. 5b) show Mg lines only. No traces of magnesium oxide and magnesium hydroxides were detected in experimental samples. 2.5. Hydrogen desorption The desorption experiments were carried out in a vacuum chamber of calibrated volume enabling heating the sample isothermally at chosen temperatures Td and measuring the time dependence of desorbed hydrogen pressure p(t). The thermocouple Pt/PtRh was in contact with the sample, the mass of which was typically 3 g. The arrangement is shown schematically in Fig. 6. 3. Results and discussion 3.1. Desorption curves The measurement of desorption curves p = p(t) was done in isothermal regime since the temperature increase of the sample (after it is put into the tempered furnace) is
Fig. 6. Experimental apparatus – schematically. (1) Sample; (2), furnace; (3) vacuum chamber; (4) hydrogen inlet; (5) vacuum pump; (6) mV-meter; (7) vacuum gauge; (8) PC; (9) venting and (10) thermocouple Pt PtRh.
negligibly short comparing with the time of decharging. Examples of measured desorption curves are plotted in Figs. 7–9 in co-ordinates relative pressure r = (p ps)/ (pf ps) vs. time t. The starting pressure ps was always 2 mbar and the maximum pressure pf reached during the
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Fig. 7. Examples of desorption curves (cast alloy I) charged at Tc = 623 K and decharged at Td = 495–576 K. Full lines, Eqs. (1) and (4).
Fig. 8. Examples of desorption curves with two branches (alloy I pellets) charged at Tc = 623 K and decharged at Td = 485–511 K. Full lines, Eqs. (1), (4) and (5).
desorption ranged from 80 to 200 mbar. It is illustrated that all the curves had a sigmoid character. It was observed that the character of the curves measured with alloy I changed close to the HT/LT transformation temperature Ttr (Ttr = 508 K according to Ref. [37]; Ttr = 518 K according to Ref. [23]). At higher temperatures well above Ttr, the curves consist of one branch only, as it is shown in Fig. 7, whereas below Ttr, two distinguishable branches were observed (Figs. 8 and 9).
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Fig. 9. Examples of desorption curves with reversed sequence of two branches (cast alloy I) charged at Tc = 623 K and decharged at Td = 474 K. Full lines, Eqs. (1), (4), and (5).
To resolve the problem why two branches were observed in alloy I at lower temperatures, a series of several anneals with subsequent XRD measurements were done. The results are illustrated in Fig. 10. The observation was carried out at seven stages indicated with arrows in Fig. 10a. In Fig. 10b–d, three most instructive parts of X-ray spectra are shown. It was easy to conclude that the slow branch appears when the LT2 phase is present in a prevailing amount. The phase composition during this stage changes considerably, but it is always dominated by LT2. The fast branch appears in a situation where the LT phase contains little or no LT2 component. Breakpoint between the two branches (indicated in Fig. 10a) occurs in a moment when the a phase (Mg2NiH0.3) is nucleated – compare XRD patterns at stages (iv) and (v), especially in position close to 2h = 27.5° and 2h = 46.5°. The phase composition did not change during the time when the fast branch was observed (cf. XRD pattern at stages (v–vii)). It contains Mg2NiH0.3 and LT1 phases. The latter one prevails especially in samples where LT2 is not present in the initial state (see, efor example, Fig. 4a). In such a case, the fast branch is the first one, which is observed (Fig. 9). It is also interesting to mention a slight shift of peaks Nos. 2 and 4 related to a-phase Mg2NiH00.3 towards higher values of 2h during the desorption (cf. XRD pattern at stages (v–vii)). It is caused by lowering of the mean lattice parameter due to hydrogen desorption. The time sequence of branches (dominance of slow diffusion at the beginning, followed by the fast one as shown in Figs. 8 and 10a, or reverse situation, which is the case illustrated in Fig. 9) is determined by the ratio of amounts of LT1 and LT2 present in the sample at the beginning of the desorption experiment.
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Fig. 10. XRD pattern (Co Ka) measured at stages (i–vii) documenting the time evolution of phase composition in sample with a great content of LT2. Alloy I pellet. Peak labeling is the same as in Fig. 4. (a) Definition of sampling points; (b–d) instructive parts of XRD spectra.
3.2. Evaluation of diffusion coefficients 3.2.1. Controlling mechanism of hydrogen desorption The present experiments were done at hydrogen pressure p lying well below the equilibrium pressure peq calculated for each desorption temperature from the van’t Hoff equation [38]. This ensures that the driving force for the transformation is high enough during desorption and mobile hydrogen atoms are released in the whole volume of the hydride (homogeneous nucleation of a phase: b ? a + H). Under such conditions, the hydrogen evolution from the samples is controlled by hydrogen bulk diffusion in
hydride phase rather than the kinetics of the reaction b ? a + H. 3.2.2. Shape of particles To evaluate hydrogen diffusion coefficients, simple geometrical shapes must approximate hydrogen-releasing bodies. It was observed that both pellets and fragmented hydrogen-charged castings of alloy I are porous agglomerates of uneven but approximately equiaxed particles that can be characterized by their mean size q. For pellets, it is illustrated in Fig. 1. In the present work, the real structure was modeled by agglomerate of particles with equal
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size q. It was justified by the fact that prevailing fraction of volume was formed by particles with not too different size lying between q/1.5 and 1.5q. Cubes of edge q and spheres of diameter q were tested as the simplest model bodies that may approximate the real particles. Numerical simulation of respective analytic solutions [39,40] led to a conclusion that the difference between the amount of hydrogen desorbed from a sphere and that desorbed from a cube at the same desorption time is smaller than uncertainty of measured amount of desorbed hydrogen due to the variation of particle size q within the limits q/1.5 and 1.5 q. Therefore, the spherical shape was chosen that enables easier fitting of analytic solution to experimental data than the solution for the cubic shape. In the case of foils (cast alloy M), known analytic solution for out-diffusion from a planar slab [40] was used for the data fitting. 3.2.3. Analytic solution and data evaluation A relative amount of hydrogen r = (p ps)/(pf ps), desorbed from the pellets and fragmented cast alloy I was fitted by equations derived in Refs. [39,40] for the case of out-diffusion from spheres into a big but finite ‘‘well stirred” volume: Z t 1 X 1 Dp2 2 r ¼1A GðsÞ exp 2 n ðt sÞ ds ð1Þ n2 0 q n¼1 where A is a constant, D is the hydrogen diffusion coefficient and the function G describes the rate of hydrogen evolution. In the case of hydrogen diffusion from foils (cast alloy M), equation: Z t 1 X 1 GðsÞ r ¼1A 2 0 n¼0 ð2n þ 1Þ Dp2 2 exp 2 ðn þ 1=2Þ ðt sÞ ds ð2Þ l was used [39,40], derived for out-diffusion from plan-parallel slab of thickness l into great but finite ‘‘well stirred” volume [39,40]. Convolution in Eqs. (1) and (2) accounts for the fact that not all hydrogen atoms are free for diffusion at t = 0 [39]. We propose following representation of G:
Eq. (3), where d (0) is the Dirac’s delta function in s = 0, leads to the case known as instantaneous diffusion source [40]. It means that all hydrogen atoms in the volume of the particle are free for diffusion at t = 0. Eq. (4) with small k approaches the so-called constant source [40], i.e., continual generation of mobile hydrogen atoms, and medium values of k allow for initial generation of mobile hydrogen atoms, which fades out with time s.
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The desorption curves with two branches were fitted to linear combination of two terms formally identical to that in Eqs. (1) and (2): rðtÞ ¼ f1 r1 ðD1 ; to1 ; A1 ; k1 Þ þ ð1 f1 Þr2 ðD2 ; to2 ; A2 ; k2 Þ
ð5Þ
where fi is relative fraction of the ith component in the sum (i.e., to the mean relative amount of respective phase and to the mean hydrogen concentration in it) and to1, to2 are times of onset of the respective branch. The ith term ri in Eq. (5) is zero for ti = t toi < 0. Diffusion coefficients D and parameters k obtained as fitting parameters, are listed in Tables 2 and 3. 3.3. Temperature dependence of D and k Temperature dependence of diffusion coefficients is shown in Fig. 11, where the error bar denotes a typical accuracy of experimental points. It can be seen that by hydrogen diffusion in charged alloy I, the transition temperature Ttr (Ttr = 508–518 K [23,38]) between the HT and LT phases divides the set of the data distinctly: above the Ttr, one branch only on desorption curves was observed giving one effective diffusion coefficient characterizing the hydrogen diffusion in a phase mixture dominated by diffusion in HT b-phase (Mg2NiH4). Below Ttr, two branches observed on desorption curves enabled two diffusion coefficients, D1 and D2, to be evaluated. Both of them characterize effective hydrogen diffusion in a mixture of phases; the higher one, D1, describes the diffusion in mixtures with LT1 phase, the presence of which is a determining factor of the overall, macroscopically observable rate of diffusion process. The lower one, D2, is its counterpart for a mixture of phases containing LT2. It is worth of noting that values of D1 and D2 do not depend significantly on the sequence of desorption branches. Hydrogen diffusion coefficients measured in charged M foils and those measured in powder of MgH2 (purchased in Alfa Aesar; average diameter of grains 2a 100 lm,) agree reasonably one with another. It can be seen in Fig. 11 that the extrapolation of the data to lower temperatures is close to values of hydrogen diffusion coefficients measured in low-temperature untwinned modification of Mg2NiH4 compound (ILT1). Further, the values of hydrogen diffusion coefficients in M are much smaller compared to values reported for hydrogen diffusion in pure Mg [41– 43] – cf. the present data with literature values marked as Mg-1,2,3 in Fig. 11. This supports the idea that the present data characterize the hydrogen diffusion in hydride bphase, not in the a-solid solution. Hydrogen diffusion coefficients measured in the hydrogen-charged alloy E prepared by ball-milling and compacting (in pellets E) agree well with values obtained for alloy I. They differ significantly, however, from much higher values of effective hydrogen diffusion coefficients measured in foils of heterogeneous cast alloy E. It can also be seen in Fig. 11 that an extrapolation of effective diffusion coefficients in cast alloy E to lower
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Table 2 Hydrogen diffusion coefficients in hydrogen-charged alloy I and values of k obtained by fitting of Eqs. (1–5) Material
Cast Tc = 623 K; q = 7 lm
Pellets Tc = 623 K; q = 10 lm
Pellets Tc = 426 K; q = 5 lm
Td
LT1, HT
K
D1 1014 m2 s1
k1 s1
576 556 516 495 474
11.4 7.70 4.72 2.16 0.152
25 17 11.0 4.6 0.90
574 552 537 523 511 507 496 485
10.2 10.1 5.59 4.47 3.57 3.24 2.90
9.0 9.0 5.0 4.0 3.8 2.7 2.7
514 494 475 461 449
2.74 1.2 0.405 0.225 0.127
LT2
11.5 5.2 1.4 0.90 0.35
D2 1016 m2 s1
k2 s1
2.93
0.050
11.2 3.13 1.12
0.090 0.016 0.0022
1.52 0.431 0.759
0.0010 0.00045 0.00025
2q, mean size of particles or fragments; LT1, untwinned low-temperature modification; LT2, twinned low-temperature modification; HT, high-temperature modification.
Table 3 Hydrogen diffusion coefficients and values of k in hydrogen-charged alloys E and M obtained by fitting of Eqs. (1–5) Material
Td K
D 1011 m2 s1
E foils; l = 352 lm
723 673 623
17.4 8.76 4.76
2.3 1.8 0.7
E foils; l = 198 lm
678 627
6.79 2.79
5.1 2.1
E pellets; a = 22 lm
628 596 579 552
0.0295 0.0197 0.0148 0.00786
6.4 4.0 3.0 1.3
M foil; l = 49 lm
698 673 648
1.58 0.901 0.414
15 10 3.8
M powder; a = 50 lm
693 663 650 628 594 578
0.583 0.278 0.215 0.101 0.0607 0.0380
27 12 9 11 2.4 1.5
k s1
2l = thickness of the foil, 2a = mean size of particles. Hydrogen charging temperature Tc = 623 K.
temperatures is reasonably close to the literature data reported in Refs. [37,44,45] for the hydrogen diffusion in a mixture of hydride phases. Bearing in mind that the diffusion coefficients of hydrogen in both hydride phases – MgH2 (charged alloy M) and Mg2NiH4 (charged alloy I) – are lower than the obtained effective diffusion coefficient Deff = DE in charged cast alloy E, it is clear that fast hydro-
Fig. 11. Arrhenius diagram of hydrogen diffusion coefficients. Mg2NiH4 – [37]; Mg2NiH0.31 – [44]; Mg2NiH0.32 – [45]; Mg-1 – [41]; Mg-2 – [42]; Mg-3 – [43]. Error bar – typical experimental error.
gen diffusion along interphase boundaries in charged cast E must significantly contribute to the overall hydrogen diffusion flux. Effective diffusion coefficient in a two-phase alloy influenced by the diffusion along interphase boundaries is theoretically estimated in Ref. [46]. The final relation proposed in Ref. [46] describing the hydrogen effective
J. Cˇerma´k, L. Kra´l / Acta Materialia 56 (2008) 2677–2686 Table 4 Arrhenius parameters of hydrogen diffusion in hydrogen-charged experimental alloys Matrix
Q kJ mol1
–ln D0 D0 in m2 s1
IHT + E pellets ILT1 ILT2 M E Interphase boundary
54.4 ± 3.6 109 ± 12a
18.34 ± 0.79 5.3 ± 8 8.73 ± 0.24 8.8 ± 2.3 13.0 ± 2.4 3.4 ± 2.4b
96 ± 12 57 ± 13
a Due to scatter of experimental points, one value only for ILT1 and ILT2 was evaluated. b Calculated from Eq. (6).
diffusion can be simplified if: (i) the diffusion coefficient in interphase boundary, Di, is much greater than that in the both phases (Di DI, DM); and (ii) if the segregation of hydrogen to interphase boundaries is negligible (s d 1; s is the segregation coefficient and d is the thickness of the interphase boundary). The simplification leads to an approximate relation enabling an estimation of hydrogen diffusion coefficient in interphase boundary: Di ¼
3Deff 1:5 104 Deff 2sgi
ð6Þ
In Eq. (6), gi 1.5 104 stands for the volume fraction of interphase boundaries, which was estimated with d 5 1010 m [47] and s 1. Since it can be expected that both the above conditions, (i) and (ii), are fulfilled, Eq. (5) can be used for the estimation of Di. The calculated values of D were fitted to the Arrhenius equation D = D0 exp (Q/RT) (R is the gas constant) and frequency factor D0 and activation enthalpy Q were evaluated for all experimental alloys. Results are summarized in Table 4. It is obvious from Tables 2 and 3 that obtained values of k increase with increasing desorption temperature Td, which accords with an expected fact that the decomposition rate of the hydride phase increases with increasing temperature.
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gen from the samples was controlled by out-diffusion from the hydride phase only. Conclusions of the present work can be summarized into following items. 1. Activation enthalpy Q of hydrogen desorption from cubic alloy I above the transition temperature Ttr is lower than Q in monoclinically distorted structure below the Ttr. 2. Two modes of desorption from I were observed below the Ttr, which are manifested by two distinct branches of desorption curve and, consequently, by two different hydrogen diffusion coefficients. 3. Presence of LT2 (twinned low-temperature Mg2NiH4 phase) in I causes very slow hydrogen desorption rate. It was observed that samples with initial excess of LT2 show very slow hydrogen desorption rate unless the amount of LT2 and LT1 phases becomes about the same. Then, bustling hydrogen evolution occurs. 4. On the other hand, if the LT1 phase prevails the LT2 at the start of the desorption from in I, hydrogen desorbs rapidly unless the amounts of LT1 and LT2 are roughly equilibrated. After that, the rest of the hydrogen desorbs with dramatically slowed-down rate. 5. The findings listed above may be important for the optimization of structure of the material for hydrogen-storage cells with rapid C/D characteristic: the presence of LT2 phase in I seems to be undesirable. 6. LT2 phase in I can be avoided, e.g., by the melting-andcasting technology and/or by the charging at temperatures below the Ttr. 7. Coefficients of hydrogen diffusion in charged M are much lower than values reported in the literature for the hydrogen diffusion in pure Mg. 8. Coefficients of hydrogen diffusion in cast E seem to be effective coefficients characterizing the effective diffusion in a two-phase alloy with high-diffusivity interphase boundaries. Hydrogen diffusion coefficients in interphase boundaries, DI, were estimated.
Acknowledgements 4. Summary In the present paper, the kinetics of hydrogen desorption from intermetallic compounds Mg2NiH4 and MgH2, and from hydrogen-charged eutectic (Mg + Mg2Ni)H and relevant phase changes were studied. Two different techniques of intermetallic preparation were used: (i) melting and casting and (ii) ball-milling and compacting the powder into pellets. Hydrogen charging of experimental materials followed in a pressure vessel at elevated pressure and temperature. Charging conditions of I pellets were chosen in order to prepare (a) great or (b) low portion of LT2 phase. The hydrogen desorption was done far from the equilibrium, so that the driving force for hydride decomposition was high enough and desorption of hydro-
This work was supported by the Czech Science Foundation, Contract No. 106/07/0010, and by the Czech Academy of Sciences, Project No. AV0Z20410507. The authors would like to thank Mr. B. David, PhD, for XRD measurements. References [1] Trudeau ML. MRS Bull 1999;24:23. [2] Ross DK. Vacuum 2006;80:1084. [3] Be´rube´ V, Radtke G, Dresselhaus M, Chen G. Int J Energy Res 2007;31:637. [4] Schwarz RB. MRS Bull 1999;24:40. [5] Massalski TB. Binary Alloy Phase Diagrams CD ROM. Materials Park (OH): ASM International, ASM/NIST; 1996.
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[6] Kusadome Y, Ikeda K, Nakamori Y, Orimo S, Horita Z. Scr Mater 2007;57:751. [7] Barkhordarian G, Klassen T, Borman R. Scr Mater 2003;49:213. [8] Blomqvist H, Ro¨nnebro E, Nore´us D, Kuji T. J Alloys Compd 2002;268:330–2. [9] Kojima Y, Kawai Y, Haga T. J Alloys Compd 2006;424:294. [10] Montone A, Antisari MV, Abazovic´ N, Novakovic´ JG, Pasquini L, Bonetti E, et al. Mater Sci Forum 2007;555:335. [11] Gao RG, Tu JP, Wang XL, Zhang XB, Chen CP. J Alloys Compd 2003;356:649. [12] Martin M, Gomel C, Borkhart C, Fromm E. J Alloys Compd 1996;238:193. [13] Ferna´ndez GE, Rodrı´guez D, Mayer G. Int J Hydrogen Energy 1998;23:1193. [14] Fang S, Zhou Z, Zhang J, Yao M, Feng F, Northwood DO. J Alloys Compd 1999;293:10. [15] Liang G, Huot J, Boily S, Schulz R. J Alloys Compd 2000;305:239. [16] Fernandez JF, Sanchez CR. J Alloys Compd 2002;340:189. [17] Gabis IE, Voit AP, Evard EA, Zaika YuV, Chernov IA, Yartis VA. J Alloys Compd 2005;404:312. [18] Li Q, Lin Q, Chou KCh, Jiang L. J Mater Sci 2004;39:61. [19] Chou KCh, Xu K. Intermetallics 2007;15:767. [20] Chou KCh, Li Q, Lin Q, Jiang LJ, Xu KD. Int J Hydrogen Energy 2005;30:301. [21] Rudman PS. J Appl Phys 1979;50:7195. [22] Gavra Z, Mintz MH. Inorg Chem 1979;18:3595. [23] Hayakawa H, Ishido Y, Nomura K, Uruno H, Ono S. J LessCommon Metals 1984;103:277. [24] Nore´us D, Kihlborg L. J Less-Common Metals 1986;123:233. [25] Zolliker P, Yvon K, Bearlocher Ch. J Less-Common Metals 1986;115:65. [26] Post LM, Murray JJ. J Less-Common Metals 1987;134:15. [27] Selvam P, Viswanathan B, Swamy CS, Srinivasan V. Int J Hydrogen Energy 1988;13:749.
[28] Hayashi S, Hayamizu K. J Less-Common Metals 1989;155:31. [29] Darnaudery JP, Pezat M, Darriet B, Hagenmuller P. MRS Bull 1981;16:1237. [30] Blomqvist H, Nore´us D. J Appl Phys 2002;91:5141. [31] Blomqvist H, Nore´us D, Babushkin O, Nion F, Vourien E. J Mater Sci Lett 2003;22:1487. [32] Kim WG, Ur SC, Lee YG, Kim YJ, Hong TW. Mater Sci Forum 2007;544:311. [33] Garcı´a GN, Abriata JP, Sofo JO. Phys Rev 1999;B59:11746. [34] ICSD Databse release 2007/1, FIZ Karlsruhe, Germany. [35] JCPDS PDF-4 Full File 2004 Database. Newton Square, PA: ICDD. [36] X’Pert HighScore Plus 2.0a, PANanalytical BV, Almelo, The Netherlands. [37] Senegas J, Mikou A, Pezat M, Dariet B. J Solid State Chem 1984;52:1. [38] Sandrock GD, Suda S, Schlapbach L. In: Schlapbach L, editor. Hydrogen in intermetallic compounds, vol. II. Berlin: Springer-Verlag; 1992 [chapter 5]. [39] Carslaw HS, Jaeger JC. Conduction of heat in solids. Oxford: Clarendon Press; 1959. pp. 130, 184, 240. [40] Crank J. Mathematics of diffusion. Oxford: Clarendon Press; 1957. p. 88. [41] Renner J, Grabke HJ. Z Metallkde 1978;69:639. [42] Schimmel HG, Kearley GJ, Huot J, Mulder FM. J Alloys Compd 2005;404:235. [43] Nishimura C, Komaki M, Amano M. J Alloys Compd 1999;293:329. [44] Toepler H, Buchner H, Saeufferer K, Knorr K, Prandl W. J LessCommon Met 1982;88:397. [45] Hayashi S, Hayamizu K, Yamamoto O. J Phys Chem Solids 1984;45:555. [46] Belova IV, Murch GE. Philosophical Magazine 2004;84:17. [47] Kaur I, Mishin Y, Gust W. Fundamentals of Grain and Interphase Boundary Diffusion. New York: John Wiley; 1995.
Acta Materialia 56 (2008) 2677–2686 www.elsevier.com/locate/actamat
Hydrogen diffusion in Mg–H and Mg–Ni–H alloys ˇ erma´k *, L. Kra´l J. C Institute of Physics of Materials, AS CR v. v. i., Zˇizˇkova 22, CZ-616 62 Brno, Czech Republic Received 25 October 2007; received in revised form 29 January 2008; accepted 3 February 2008 Available online 14 March 2008
Abstract Coefficients of hydrogen diffusion in Mg2NiH4 (DI), MgH2 (DM), and in (Mg + Mg2Ni)H eutectic (DE) were measured in the temperature interval 449–723 K. Experimental material was prepared by two techniques: by melting and casting and by ball-milling and compacting into pellets. Hydrogen charging was carried out from the hydrogen gas phase at high temperature and pressure. The Mg2NiH4 pellets were prepared in different regimes resulting either in a structure with a high fraction or with a low fraction of twinned low-temperature phase LT2. It was found that the LT2 slows down the hydrogen desorption rate considerably – values of DI in lowtemperature untwinned phase LT1 are by a multiplication factor of about 20 higher than those in the twinned phase LT2. Obtained values of DM are significantly lower than the literature values reported for the pure Mg. Hydrogen diffusion coefficients in interphase boundary were estimated from DE. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Intermetallic compounds; Magnesium alloys; Hydrogen diffusion; Hydrogen-storage materials
1. Introduction Hydrogen is a prospective fuel both for direct combustion and in electrochemical batteries and fuel cells. Therefore, there is an extended field of problems that are intensively studied, ranging from ecology of hydrogen production itself up to special materials for new hydrogen technologies. One of the partial problems of utmost importance is hydrogen storage in a solid media. There is a broad variety of materials considered as hydrogen-storage materials (HSM) (for review see, for example, Refs. [1–3]). It is interesting to note that – in some materials – the density of stored hydrogen reaches even higher values than the density of liquid hydrogen [4]. The main problems that should be solved in the field are sufficient storage capacity, high-cycle durability, resistance against contaminant gases, and sufficient rate of hydrogen charging/decharging (C/D) at moderate conditions (below 450 K and 2 bar). *
Corresponding author. Tel.: +420 532 290 422; fax: +420 541 218 657. ˇ erma´k). E-mail address: [email protected] (J. C
Magnesium-based alloys belong to most frequently studied HSM because of two main reasons: first, magnesium is a very cheap and abundant element on the Earth; and second, the light Mg-based matrix enables to achieve the best (up to now) weight storage ratio. However, pure Mg is not suitable HSM because of poor kinetics of C/D cycle. Therefore, it is alloyed with other elements, frequently with nickel. Before all, eutectic mixtures Mg + Mg2Ni and pure Mg2Ni intermetallic compound are in the focus of interest as base materials. Although the other intermetallic compound MgNi2 in the Mg – Ni binary system [5] shows a certain solubility of hydrogen [6], it is commonly considered as a not prospective HSM at present. Even alloyed, Mg-based HSMs need temperatures of about 470 K for C/D, which makes them somewhat unsuitable for energy sources in personal and household appliances. Considerable effort is, therefore, constantly devoted to lowering the stability of Mg-based hydrides and, at the same time, to preserve their favorable storage capacity (see, for example, Refs. [7–11]). Although there are some studies of C/D kinetics applicable to Mg-based alloys [12–20], the rate constants are
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2008.02.003
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known only. The theory of the C/D kinetics is often based on Johnson–Mehl–Avrami model (see, for example, Ref. [21]). Contrary to the often-drawn conclusion, namely that the process of desorption is controlled by diffusion [12,13,16,21], quantitative data describing hydrogen diffusion itself are very sparse in the literature. In Ref. [15], the authors declare the a/b (a – base matrix with hydrogen dissolved, b – hydride) interphase motion at high temperatures, nucleation-and-growth at ‘‘early stages” and diffusion at ‘‘later stages” as respective controlling mechanisms. In Refs. [16,18], the authors tested a number of known rate equations and chose ‘‘the best one” for their materials studied. It should be noted, however, that the choice of the optimal equation (and the probable kinetic mechanism governing the respective phase change) is, in this way, very difficult. It is known that Mg2NiH4 compound undergoes a phase change between the room temperature and the melting point, which complicates the kinetic study of C/D processes in the material. The history of the phase analysis in Mg2NiH4 begins in 1979 when Gavra and Mintz [22] identified the cubic high-temperature phase above Ttr = 508 K. In the 1980s a series of studies was started (see, for example, Refs. [23–32]), which can be summarized as follows: the high-temperature (HT) phase is face-centered cubic (fcc), derived from the CaF2-type structure. The magnesium ions form a cube around the [Ni0H4] complex (Ni0 – effectively zero-valent Ni atom; H atoms occupy six of the eight vertices of octahedral centering in Ni atom), building an anti-fluorite structure (anions occupy the fcc lattice points, complexes reside in four tetrahedral sites). Exact location of hydrogen atoms by Ni center can be specified only approximately. It can be said [30] that H atoms are ˚ . Somewhat more located at a sphere with a radius of 1.5 A detailed information on the H location can be found in Ref. [33]: a square planar order of H atoms in the complex implies metallic properties, whereas regular tetrahedron leads to semiconductor-like character of the compound (for step-like changes of electric conductivity – see also Ref. [30]). Upon cooling, the HT transforms into monoclinically distorted low-temperature (LT) phase with slightly distorted tetrahedral [Ni0H4] complex. LT exists in two modifications – untwinned (LT1) and microtwinned (LT2). Microtwinning occurs on the basic cell level. The ratio of LT1/LT2 depends sensitively on the thermomechanical history of the sample and, it influences to a certain extent, the electrical conductivity and the color of the LT [30]. The presence of LT2 may be indicated by typical peak in the XRD diffraction spectra at 2h = 23.7° (with Cr Ka1 radiation) [25,30,31]. The aim of the present study is to obtain diffusion coefficients of hydrogen in hydrogen-charged Mg2Ni intermetallic (i.e., in Mg2NiH4), in hydrogen-charged Mg (i.e., in MgH2), and in hydrogen-charged eutectic (Mg + Mg2Ni)H. The results enable the rate of hydrogen diffusion-controlled processes running in these materials to be quantified, which are often used as a base of hydrogen-storage media.
2. Experimental 2.1. Preparation of experimental materials Experimental alloys were prepared from pure components 3N6 Ni and 3N8 Mg. Splinters of pure components for preparation of intermetallic and eutectic alloys were ball-milled in air using a Fritsch-Pulverisette6. The composition was Mg – 54.5 wt.%Ni and Mg – 23.5 wt.%Ni respectively. Splinters (0.1 mm thick) of both Mg and Ni were ball-milled under the following conditions: 10 min milling +50 min relaxation 20 times repeated. Mass ratio of balls to the milled mixture was rm = 25. Milled powder was pressure-compacted at room temperature into pellets with diameter 20 mm 5 mm in height. Samples from pure Mg and from cast modification of intermetallic and eutectic alloys were prepared by induction-melting in the MgO crucible under Ar protective atmosphere. Ingots were cut into slices about 2 mm thick that were ground with metallographic papers down to foils of final thickness 2l lying between 100 and 703 lm. An overview of experimental materials is given in Table 1. 2.2. Hydrogen charging Hydrogen charging followed immediately after the pellets/foils preparation by isothermal annealing in a pressure vessel. Pressure of pure (5N3) hydrogen was 30 bar and the charging temperature Tc was 423 and 673 K. The time of charging was several hours by pellets and 14 days by foils. Hydrogen concentration in the charged samples was determined by precise weighing the samples before and after the charging. The samples were charged up to the state of complete charging, which was detected as a state with saturated weight of respective sample. 2.3. SEM observation 2.3.1. Pellets The structure of samples was checked by SEM JEOL JSM 6460 equipped with EDAX/WEDAX Oxford Instruments analyzer. Samples were porous and consisted of Table 1 Experimental materials Designation
Composition
Prepared as
Temperature of hydrogen charging
I
Intermetalic Mg2Ni (Mg–54.5 wt.%Ni)
Pelletsa
Tc = 426 K Tc = 623 K Tc = 623 K
c
M E
a
Mg Eutectic Mg + Mg2Ni (Mg–23.5 wt.%Ni)
Castingsb Castingsb Pelletsa Castingsb
Compacted into cylinders of diameter 20 mm height 5 mm. Machined to foils of diameter 20 mm thickness 2l = 100–703 lm. c Besides hydrogen-charged cast magnesium (MgH2), also MgH2 powder was measured purchased in ALFA AESAR. Mean grain size of the powder particles was about 2a = 100 lm. b
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compact grains of mean size 2q most frequently between 10 and 50 lm, as is illustrated in Fig. 1. Mean grain size of hydrogen-charged I and E pellets was reduced somewhat due to fragmentation of the largest grains. Chemical composition of grains coincided well with the intended average composition of respective alloy. 2.3.2. Foils The structure of cast modifications of alloys I and E is shown in Figs. 2 and 3. Due to incongruent solidification [5], there are three components present in alloy I. As the first one, the MgNi2 compound precipitates that form agglomerates of rectangular crystallites in the melt (see the light rectangular particles in Fig. 2). This phase participates on the hydrogen C/D process to a negligible extent only [6]. Below 1033 K, Mg2Ni starts to precipitate and the rest of the Mg-enriched melt solidifies between the grains of grown Mg2Ni as fine eutectic.
Fig. 3. SEM micrograph of cast alloy E after the hydrogen charging. Light particles and lamellae, Mg2NiH4.
During the hydrogen charging, the grains transform to Mg2NiH4 and in the eutectic, the MgH2 is nucleated. The latter phase grows and forms rows of individual crystallites in I, decorating the grain boundaries. Progressive hydrogen charging brings about the growth of internal stress and partial fragmentation of grains. The microstructure of cast eutectic alloy E is shown in Fig. 3. It consists of oblong Mg2Ni particles (size about 40 3 lm) in lamellar eutectic matrix (inter-lamellar distance is about 2 lm). Due to strain accommodation of (Mg) matrix between the Mg2NiH4 lamellae, hydrogen charging of alloy E does not lead to cracking. Grain size of Mg foils was of the order of tens of mm. Hence, it can be presumed that the presence of grain boundaries in M does not influence significantly the kinetics of the C/D process. Fig. 1. Structure of compacted pellets of alloy E after the hydrogen charging.
2.4. XRD phase analysis
Fig. 2. SEM micrograph of cast alloy I before the hydrogen charging. Grain interior, Mg2Ni; light rectangular particles, MgNi2; fine eutectic Mg+/Mg2Ni at grain boundaries.
X-ray profiles were obtained by X’Pert Pro MPD device (PANanalytical B.V., Almelo, The Netherlands) using Co Ka radiation and interpreted by the HighScore Plus software with commercial databases [34–36]. The results obtained for alloy I can be illustrated by the most significant reflections marked in XRD pattern shown in Fig. 4. It is clear that the prevailing phase in charged samples is Mg2NiH4. In cast sample (Fig. 4a) and in the pellets charged at temperature below the Ttr (Fig. 4c), also MgH2 phase as well as a certain amount of Mg2NiH0.3 is present. It is interesting to compare the amount of the twinned LT2 phase (typical line at 2h = 27.3° [25,29–31]) in the charged I samples. Whereas the pellets charged above Ttr (Fig. 4b) contain twinned LT2 phase to a considerable extent, in the cast sample charged above Ttr (Fig. 4a) and in the pellets charged below Ttr (Fig. 4c), the LT1 phase prevails. In the decharged samples, the a phase is present only, which is illustrated in Fig. 4d.
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Fig. 4. XRD pattern of alloy I. (1) Mg2NiH4 (LT1 – untwinned); 1TW, (LT2 – twinned); (2) Mg2NiH0.3; (3) MgH2; (4) Mg2Ni. Tc – charging temperature, Td – decharging temperature.
Fig. 5. XRD pattern of alloys M and E. (1) Mg2NiH4; (2) Mg2NiH0.3; (3) MgH2; (4) Mg2Ni; (5) Mg. Tc – charging temperature, Td – decharging temperature.
The same phases are identified in samples E as can be seen in Fig. 5 (Fig. 5c – hydrogen-charged M; Fig. 5d – decharged E). Hydrogen-charged M foils (Fig. 5a) contain exclusively Mg and MgH2 phases, whereas decharged M samples (Fig. 5b) show Mg lines only. No traces of magnesium oxide and magnesium hydroxides were detected in experimental samples. 2.5. Hydrogen desorption The desorption experiments were carried out in a vacuum chamber of calibrated volume enabling heating the sample isothermally at chosen temperatures Td and measuring the time dependence of desorbed hydrogen pressure p(t). The thermocouple Pt/PtRh was in contact with the sample, the mass of which was typically 3 g. The arrangement is shown schematically in Fig. 6. 3. Results and discussion 3.1. Desorption curves The measurement of desorption curves p = p(t) was done in isothermal regime since the temperature increase of the sample (after it is put into the tempered furnace) is
Fig. 6. Experimental apparatus – schematically. (1) Sample; (2), furnace; (3) vacuum chamber; (4) hydrogen inlet; (5) vacuum pump; (6) mV-meter; (7) vacuum gauge; (8) PC; (9) venting and (10) thermocouple Pt PtRh.
negligibly short comparing with the time of decharging. Examples of measured desorption curves are plotted in Figs. 7–9 in co-ordinates relative pressure r = (p ps)/ (pf ps) vs. time t. The starting pressure ps was always 2 mbar and the maximum pressure pf reached during the
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Fig. 7. Examples of desorption curves (cast alloy I) charged at Tc = 623 K and decharged at Td = 495–576 K. Full lines, Eqs. (1) and (4).
Fig. 8. Examples of desorption curves with two branches (alloy I pellets) charged at Tc = 623 K and decharged at Td = 485–511 K. Full lines, Eqs. (1), (4) and (5).
desorption ranged from 80 to 200 mbar. It is illustrated that all the curves had a sigmoid character. It was observed that the character of the curves measured with alloy I changed close to the HT/LT transformation temperature Ttr (Ttr = 508 K according to Ref. [37]; Ttr = 518 K according to Ref. [23]). At higher temperatures well above Ttr, the curves consist of one branch only, as it is shown in Fig. 7, whereas below Ttr, two distinguishable branches were observed (Figs. 8 and 9).
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Fig. 9. Examples of desorption curves with reversed sequence of two branches (cast alloy I) charged at Tc = 623 K and decharged at Td = 474 K. Full lines, Eqs. (1), (4), and (5).
To resolve the problem why two branches were observed in alloy I at lower temperatures, a series of several anneals with subsequent XRD measurements were done. The results are illustrated in Fig. 10. The observation was carried out at seven stages indicated with arrows in Fig. 10a. In Fig. 10b–d, three most instructive parts of X-ray spectra are shown. It was easy to conclude that the slow branch appears when the LT2 phase is present in a prevailing amount. The phase composition during this stage changes considerably, but it is always dominated by LT2. The fast branch appears in a situation where the LT phase contains little or no LT2 component. Breakpoint between the two branches (indicated in Fig. 10a) occurs in a moment when the a phase (Mg2NiH0.3) is nucleated – compare XRD patterns at stages (iv) and (v), especially in position close to 2h = 27.5° and 2h = 46.5°. The phase composition did not change during the time when the fast branch was observed (cf. XRD pattern at stages (v–vii)). It contains Mg2NiH0.3 and LT1 phases. The latter one prevails especially in samples where LT2 is not present in the initial state (see, efor example, Fig. 4a). In such a case, the fast branch is the first one, which is observed (Fig. 9). It is also interesting to mention a slight shift of peaks Nos. 2 and 4 related to a-phase Mg2NiH00.3 towards higher values of 2h during the desorption (cf. XRD pattern at stages (v–vii)). It is caused by lowering of the mean lattice parameter due to hydrogen desorption. The time sequence of branches (dominance of slow diffusion at the beginning, followed by the fast one as shown in Figs. 8 and 10a, or reverse situation, which is the case illustrated in Fig. 9) is determined by the ratio of amounts of LT1 and LT2 present in the sample at the beginning of the desorption experiment.
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Fig. 10. XRD pattern (Co Ka) measured at stages (i–vii) documenting the time evolution of phase composition in sample with a great content of LT2. Alloy I pellet. Peak labeling is the same as in Fig. 4. (a) Definition of sampling points; (b–d) instructive parts of XRD spectra.
3.2. Evaluation of diffusion coefficients 3.2.1. Controlling mechanism of hydrogen desorption The present experiments were done at hydrogen pressure p lying well below the equilibrium pressure peq calculated for each desorption temperature from the van’t Hoff equation [38]. This ensures that the driving force for the transformation is high enough during desorption and mobile hydrogen atoms are released in the whole volume of the hydride (homogeneous nucleation of a phase: b ? a + H). Under such conditions, the hydrogen evolution from the samples is controlled by hydrogen bulk diffusion in
hydride phase rather than the kinetics of the reaction b ? a + H. 3.2.2. Shape of particles To evaluate hydrogen diffusion coefficients, simple geometrical shapes must approximate hydrogen-releasing bodies. It was observed that both pellets and fragmented hydrogen-charged castings of alloy I are porous agglomerates of uneven but approximately equiaxed particles that can be characterized by their mean size q. For pellets, it is illustrated in Fig. 1. In the present work, the real structure was modeled by agglomerate of particles with equal
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size q. It was justified by the fact that prevailing fraction of volume was formed by particles with not too different size lying between q/1.5 and 1.5q. Cubes of edge q and spheres of diameter q were tested as the simplest model bodies that may approximate the real particles. Numerical simulation of respective analytic solutions [39,40] led to a conclusion that the difference between the amount of hydrogen desorbed from a sphere and that desorbed from a cube at the same desorption time is smaller than uncertainty of measured amount of desorbed hydrogen due to the variation of particle size q within the limits q/1.5 and 1.5 q. Therefore, the spherical shape was chosen that enables easier fitting of analytic solution to experimental data than the solution for the cubic shape. In the case of foils (cast alloy M), known analytic solution for out-diffusion from a planar slab [40] was used for the data fitting. 3.2.3. Analytic solution and data evaluation A relative amount of hydrogen r = (p ps)/(pf ps), desorbed from the pellets and fragmented cast alloy I was fitted by equations derived in Refs. [39,40] for the case of out-diffusion from spheres into a big but finite ‘‘well stirred” volume: Z t 1 X 1 Dp2 2 r ¼1A GðsÞ exp 2 n ðt sÞ ds ð1Þ n2 0 q n¼1 where A is a constant, D is the hydrogen diffusion coefficient and the function G describes the rate of hydrogen evolution. In the case of hydrogen diffusion from foils (cast alloy M), equation: Z t 1 X 1 GðsÞ r ¼1A 2 0 n¼0 ð2n þ 1Þ Dp2 2 exp 2 ðn þ 1=2Þ ðt sÞ ds ð2Þ l was used [39,40], derived for out-diffusion from plan-parallel slab of thickness l into great but finite ‘‘well stirred” volume [39,40]. Convolution in Eqs. (1) and (2) accounts for the fact that not all hydrogen atoms are free for diffusion at t = 0 [39]. We propose following representation of G:
Eq. (3), where d (0) is the Dirac’s delta function in s = 0, leads to the case known as instantaneous diffusion source [40]. It means that all hydrogen atoms in the volume of the particle are free for diffusion at t = 0. Eq. (4) with small k approaches the so-called constant source [40], i.e., continual generation of mobile hydrogen atoms, and medium values of k allow for initial generation of mobile hydrogen atoms, which fades out with time s.
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The desorption curves with two branches were fitted to linear combination of two terms formally identical to that in Eqs. (1) and (2): rðtÞ ¼ f1 r1 ðD1 ; to1 ; A1 ; k1 Þ þ ð1 f1 Þr2 ðD2 ; to2 ; A2 ; k2 Þ
ð5Þ
where fi is relative fraction of the ith component in the sum (i.e., to the mean relative amount of respective phase and to the mean hydrogen concentration in it) and to1, to2 are times of onset of the respective branch. The ith term ri in Eq. (5) is zero for ti = t toi < 0. Diffusion coefficients D and parameters k obtained as fitting parameters, are listed in Tables 2 and 3. 3.3. Temperature dependence of D and k Temperature dependence of diffusion coefficients is shown in Fig. 11, where the error bar denotes a typical accuracy of experimental points. It can be seen that by hydrogen diffusion in charged alloy I, the transition temperature Ttr (Ttr = 508–518 K [23,38]) between the HT and LT phases divides the set of the data distinctly: above the Ttr, one branch only on desorption curves was observed giving one effective diffusion coefficient characterizing the hydrogen diffusion in a phase mixture dominated by diffusion in HT b-phase (Mg2NiH4). Below Ttr, two branches observed on desorption curves enabled two diffusion coefficients, D1 and D2, to be evaluated. Both of them characterize effective hydrogen diffusion in a mixture of phases; the higher one, D1, describes the diffusion in mixtures with LT1 phase, the presence of which is a determining factor of the overall, macroscopically observable rate of diffusion process. The lower one, D2, is its counterpart for a mixture of phases containing LT2. It is worth of noting that values of D1 and D2 do not depend significantly on the sequence of desorption branches. Hydrogen diffusion coefficients measured in charged M foils and those measured in powder of MgH2 (purchased in Alfa Aesar; average diameter of grains 2a 100 lm,) agree reasonably one with another. It can be seen in Fig. 11 that the extrapolation of the data to lower temperatures is close to values of hydrogen diffusion coefficients measured in low-temperature untwinned modification of Mg2NiH4 compound (ILT1). Further, the values of hydrogen diffusion coefficients in M are much smaller compared to values reported for hydrogen diffusion in pure Mg [41– 43] – cf. the present data with literature values marked as Mg-1,2,3 in Fig. 11. This supports the idea that the present data characterize the hydrogen diffusion in hydride bphase, not in the a-solid solution. Hydrogen diffusion coefficients measured in the hydrogen-charged alloy E prepared by ball-milling and compacting (in pellets E) agree well with values obtained for alloy I. They differ significantly, however, from much higher values of effective hydrogen diffusion coefficients measured in foils of heterogeneous cast alloy E. It can also be seen in Fig. 11 that an extrapolation of effective diffusion coefficients in cast alloy E to lower
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Table 2 Hydrogen diffusion coefficients in hydrogen-charged alloy I and values of k obtained by fitting of Eqs. (1–5) Material
Cast Tc = 623 K; q = 7 lm
Pellets Tc = 623 K; q = 10 lm
Pellets Tc = 426 K; q = 5 lm
Td
LT1, HT
K
D1 1014 m2 s1
k1 s1
576 556 516 495 474
11.4 7.70 4.72 2.16 0.152
25 17 11.0 4.6 0.90
574 552 537 523 511 507 496 485
10.2 10.1 5.59 4.47 3.57 3.24 2.90
9.0 9.0 5.0 4.0 3.8 2.7 2.7
514 494 475 461 449
2.74 1.2 0.405 0.225 0.127
LT2
11.5 5.2 1.4 0.90 0.35
D2 1016 m2 s1
k2 s1
2.93
0.050
11.2 3.13 1.12
0.090 0.016 0.0022
1.52 0.431 0.759
0.0010 0.00045 0.00025
2q, mean size of particles or fragments; LT1, untwinned low-temperature modification; LT2, twinned low-temperature modification; HT, high-temperature modification.
Table 3 Hydrogen diffusion coefficients and values of k in hydrogen-charged alloys E and M obtained by fitting of Eqs. (1–5) Material
Td K
D 1011 m2 s1
E foils; l = 352 lm
723 673 623
17.4 8.76 4.76
2.3 1.8 0.7
E foils; l = 198 lm
678 627
6.79 2.79
5.1 2.1
E pellets; a = 22 lm
628 596 579 552
0.0295 0.0197 0.0148 0.00786
6.4 4.0 3.0 1.3
M foil; l = 49 lm
698 673 648
1.58 0.901 0.414
15 10 3.8
M powder; a = 50 lm
693 663 650 628 594 578
0.583 0.278 0.215 0.101 0.0607 0.0380
27 12 9 11 2.4 1.5
k s1
2l = thickness of the foil, 2a = mean size of particles. Hydrogen charging temperature Tc = 623 K.
temperatures is reasonably close to the literature data reported in Refs. [37,44,45] for the hydrogen diffusion in a mixture of hydride phases. Bearing in mind that the diffusion coefficients of hydrogen in both hydride phases – MgH2 (charged alloy M) and Mg2NiH4 (charged alloy I) – are lower than the obtained effective diffusion coefficient Deff = DE in charged cast alloy E, it is clear that fast hydro-
Fig. 11. Arrhenius diagram of hydrogen diffusion coefficients. Mg2NiH4 – [37]; Mg2NiH0.31 – [44]; Mg2NiH0.32 – [45]; Mg-1 – [41]; Mg-2 – [42]; Mg-3 – [43]. Error bar – typical experimental error.
gen diffusion along interphase boundaries in charged cast E must significantly contribute to the overall hydrogen diffusion flux. Effective diffusion coefficient in a two-phase alloy influenced by the diffusion along interphase boundaries is theoretically estimated in Ref. [46]. The final relation proposed in Ref. [46] describing the hydrogen effective
J. Cˇerma´k, L. Kra´l / Acta Materialia 56 (2008) 2677–2686 Table 4 Arrhenius parameters of hydrogen diffusion in hydrogen-charged experimental alloys Matrix
Q kJ mol1
–ln D0 D0 in m2 s1
IHT + E pellets ILT1 ILT2 M E Interphase boundary
54.4 ± 3.6 109 ± 12a
18.34 ± 0.79 5.3 ± 8 8.73 ± 0.24 8.8 ± 2.3 13.0 ± 2.4 3.4 ± 2.4b
96 ± 12 57 ± 13
a Due to scatter of experimental points, one value only for ILT1 and ILT2 was evaluated. b Calculated from Eq. (6).
diffusion can be simplified if: (i) the diffusion coefficient in interphase boundary, Di, is much greater than that in the both phases (Di DI, DM); and (ii) if the segregation of hydrogen to interphase boundaries is negligible (s d 1; s is the segregation coefficient and d is the thickness of the interphase boundary). The simplification leads to an approximate relation enabling an estimation of hydrogen diffusion coefficient in interphase boundary: Di ¼
3Deff 1:5 104 Deff 2sgi
ð6Þ
In Eq. (6), gi 1.5 104 stands for the volume fraction of interphase boundaries, which was estimated with d 5 1010 m [47] and s 1. Since it can be expected that both the above conditions, (i) and (ii), are fulfilled, Eq. (5) can be used for the estimation of Di. The calculated values of D were fitted to the Arrhenius equation D = D0 exp (Q/RT) (R is the gas constant) and frequency factor D0 and activation enthalpy Q were evaluated for all experimental alloys. Results are summarized in Table 4. It is obvious from Tables 2 and 3 that obtained values of k increase with increasing desorption temperature Td, which accords with an expected fact that the decomposition rate of the hydride phase increases with increasing temperature.
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gen from the samples was controlled by out-diffusion from the hydride phase only. Conclusions of the present work can be summarized into following items. 1. Activation enthalpy Q of hydrogen desorption from cubic alloy I above the transition temperature Ttr is lower than Q in monoclinically distorted structure below the Ttr. 2. Two modes of desorption from I were observed below the Ttr, which are manifested by two distinct branches of desorption curve and, consequently, by two different hydrogen diffusion coefficients. 3. Presence of LT2 (twinned low-temperature Mg2NiH4 phase) in I causes very slow hydrogen desorption rate. It was observed that samples with initial excess of LT2 show very slow hydrogen desorption rate unless the amount of LT2 and LT1 phases becomes about the same. Then, bustling hydrogen evolution occurs. 4. On the other hand, if the LT1 phase prevails the LT2 at the start of the desorption from in I, hydrogen desorbs rapidly unless the amounts of LT1 and LT2 are roughly equilibrated. After that, the rest of the hydrogen desorbs with dramatically slowed-down rate. 5. The findings listed above may be important for the optimization of structure of the material for hydrogen-storage cells with rapid C/D characteristic: the presence of LT2 phase in I seems to be undesirable. 6. LT2 phase in I can be avoided, e.g., by the melting-andcasting technology and/or by the charging at temperatures below the Ttr. 7. Coefficients of hydrogen diffusion in charged M are much lower than values reported in the literature for the hydrogen diffusion in pure Mg. 8. Coefficients of hydrogen diffusion in cast E seem to be effective coefficients characterizing the effective diffusion in a two-phase alloy with high-diffusivity interphase boundaries. Hydrogen diffusion coefficients in interphase boundaries, DI, were estimated.
Acknowledgements 4. Summary In the present paper, the kinetics of hydrogen desorption from intermetallic compounds Mg2NiH4 and MgH2, and from hydrogen-charged eutectic (Mg + Mg2Ni)H and relevant phase changes were studied. Two different techniques of intermetallic preparation were used: (i) melting and casting and (ii) ball-milling and compacting the powder into pellets. Hydrogen charging of experimental materials followed in a pressure vessel at elevated pressure and temperature. Charging conditions of I pellets were chosen in order to prepare (a) great or (b) low portion of LT2 phase. The hydrogen desorption was done far from the equilibrium, so that the driving force for hydride decomposition was high enough and desorption of hydro-
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