Sorption hysteresis

3. Hydrogen sorption in intermetallic compounds 1. Pressure-composition isotherms

3.5. Sorption hysteresis

The thermodynamic efficiency of rechargable metal hydrides is reduced not only by the phenomenon of surface poisoning mentioned above but also, though to a smaller extent, by the occurrence of a sorption hysteresis.

The sorption process mentioned in connection with the isotherms shown in fig. 9 is not strictly reversible. The occurrence of a sorption hysteresis has been observed by many authors (van Mal, 1976; Kuijpers, 1973; Lundin and Lynch, 1978;

Bowerman et al., 1980). Results obtained by Kuijpers and van Mal (1971) on the hydride SmCosHx are schematically represented in fig. 15. The sorption hysteresis

(Ap)

increases with temperature, but then the ratio

Ap/p

seems to remain nearly constant. Kuijpers and van Mal relate the occurrence of a hysteresis to the volume expansion and postulate that the extent of the hysteresis is proportional to the hydrogen-to-metal (H/M) ratio of the corresponding hydride. The nature of the sorption hysteresis was investigated by Lundin and Lynch (1978). They argue that in the absorption isotherms the « phase and the/~ phase are compressively stra!ned, whereas, in the desorption isotherms both phases are more or less strain-free. Owing to the microplastic deformation of the « and/~ phases in the absorption process the hysteresis is irreversible (see the minor hysteresis loops in fig. 15). This would mean that the high-pressure absorption isotherm cannot be regarded as representing a metastable condition. In order to account thermodynamically for the two separate paths in the sorption process, Lundin and Lynch modified the phase rule by

3O

B 20 600

"O 7 -

I I

0 ] 2 3

×

Fig. 15. Schematic representation of the sorption hysteresis observed in SmC%H~ at 60°C (upper) and 40°C (lower). In the set of curves pertaining to 60°C a minor hysteresis loop is included (after Kuijpers and ran Mal, 1971).

incorporating a strain term:

F = C - P + 2 + rc(strain).

In some respects this analysis is analogous to that used by Scholtus and Hall (1963) to explain the hysteresis in the P d - H system. The Lundin and Lynch approach provides more directly a rationale pertaining to the pressure differential, in particular to that o f the plateau region. According to these authors the plateau pressure increase is a consequence of the decrease in size of the interstitial holes in the uncharged material. The interstitial sites in either the a or the fl phase, which phases are compressively strained during the absorption, are relatively smaller than the sites in either of the unstrained « and fl phases during desorption. Accordingly, the pressure observed in the absorption isotherms is higher than in the desorption isotherms.

Although the explanation in terms of compressive strain seems to be generally valid, one has to be careful in relating the pressure difference between the two isotherms to strain-induced changes in interstitial hole sizes, since Busch et al. (1978a) showed that the linear relationship between the plateau pressures of various RCosHx and RNi»Hx systems (R = rare earth) is difficult to explain in terms ofelastic deformation of the interstitial volume.

Interesting results with regard to the hysteresis phenomenon were also found by Flanagan and Biehl (1981), who showed that there is a marked increase in the plateau absorption pressure o f LaNi»Hx if this material is annealed (1025 K) after desorption.

F r o m this the authors conclude that at least two effects may be of importance: the occurrence of some mechanical disruption required in the more perfect sample (annealed sample), and the greater ease with which dislocations are formed in the less perfect sample (activated sample).

28 K.H.J. BUSCHOW

Hysteresis effects are extremely pronounced in hydrides based on intermetallic compounds containing Ce (van Vucht et al., 1970; Huang et al., 1978; Dayan et al., 1980). Here one has to take account of the fact that the valence state of the Ce ions in the hydride can be different from that in the starting material. A reduction in hysteresis was found upon substitution of elements of group 3 or 4 of the periodic table for Ni in LaNi5 (Mendelsohn et al., 1979).

Finally we mention that the occurrence of hysteresis in the sorption isotherms was used by Bowerman et al. (1980) to determine the relative partial molar enthalpies of H2 solution in the two coexisting phases in LaNisHx. Their calorimetric mea- surements comprised absorption hysteresis scans starting from the desorption plateau pressure and ending near the absorption plateau pressure. The single-phase value obtained for the relative partial molar enthalpy of the hydrogen-saturated LaNi 5 is slightly less negative ( - 1 3 . 5 kJ/mol H) than the « ~ f l reaction enthalpy ( - 14.8 kJ/mol H), whereas the single-phase value for the hydride phase is slightly more negative ( - 1 6 . 8 kJ/molH). From these results it was concluded that small discontinuities in the thermodynamic parameters must exist at the phase boundaries.

3.6. Diffusion o f hydrogen a t o m s

The diffusion of hydrogen atoms in ternary hydrides can be most conveniently studied by means of proton nuclear magnetic resonance (see for instance Barnes et al., 1976). By applying different pulse sequences, experimental information can be obtained about the spin-lattice relaxation time T 1 and the spin-spin relaxation time T2m. By means of the relation T ~ I = T 2 I - T { 1 it is possible to derive the dipolar reläxation time T2d , which is related to the mean time between H atom jumps Zc:

T~ 1 = 7 2 M 2 d ' C c • (8)

In this expression Vu is the proton gyromagnetic moment and M2d the dipolar second moment. This latter quantity is determined by the arrangement of the protons in the crystal structure and can be calculated if structural data are available for a given ternary hydride. It is also possible to derive the dipolar second moment from the NMR line shape. For a random walk diffusion process the mean jump time ~c is related to the diffusion constant D via the expression (Cotts, 1972)

D = d 2 / n % , (9)

where d is the mean jump distance and n the number of possible jump paths in the crystal strueture. The diffusion constant D is usually written in a typical Arrhenius expression:

D = D0 e x p ( - E A / k T ) , (10)

where E A is an activation energy and k is Boltzmann's constant. Combining relations (8)-(10) one has

T2« = D o ( n / d 2 ) 7 ~ 2 M ~ ~ exp(-- E A / k T ) . (11)

Plots of T2« versus 1 I T are expected to be linear. From their slope the corresponding

100500 357 50

10

A

1.0 0.5

(f)

°12.o 2'.~. 2.8

T(!Z)

278 227

i i I

(a) LaNis.oH~2 ( b)LaNi4.sA[o5H5 32 (c)LaNi43A[07 H46z,

~ (e(d)LaNi4.0 All 0 H~.33 )LaNi3aA[12 HL.oz, '~f)LclNi31sAt15 H377

(e)(d) (c) (bi (o)

103/T(K 4)

Fig. 16. Arrhenius plot of the dipolar proton relaxation time T2d in various LaNi»_yAlyH x alloys (after Bowman et al., 1980).

values of the activation energy EÄ can be derived, while from the intercepts on the vertical axis values of D0 can be obtained (provided values for the other quantities in eq. (11) are known). A typical set of such plots is shown for various LaNi» base materials in fig. 16 (Bowman et al., 1979). The activation energies are of the order of 0.3 eV. The room temperature diffusion constants derived from the N M R data are plotted versus A1 content in fig. 17. Bowman et al. were able to show in this way that the room temperature diffusion constant decreases by more than two orders of magnitude upon substitution of A1 for about 25}/o of the Ni in LaNi»

Apart from the spin-spin relaxation time orte can also use the spin-lattice relaxation time to obtain information on the proton jump frequencies. For com- pleteness it is mentioned that in current N M R investigations the spin lattice relaxation time is studied either in the laboratory reference frame (Tl) or in the rotating reference frame (Tip). A method of measuring D directly has been described by Karlicek and Lowe (1980), using an alternating pulsed field gradient technique (APFG). The results obtained on a number of ternary hydrides by means of various methods are compared in table 3. Also given in the table are data obtained by means of the quasi-elastic neutron scattering technique (QNS). In this technique the quasi-elastic line width F is determined as a function of momentum transfer Q. The diffusion constant D can be derived from the initial slope of a plot of F versus Q2.

Comparison of the data collected for LaNi»Hx in the table shows that there is satisfactory agreement between most of them. Furthermore, the diffusion of H atoms at room temperature is seen to be considerably faster in the LaNi5 hydride than in the Ti-base materials.

30 K.H.J. BUSCHOW

ùJ ',h c~ i=

8 co 121

10 4

10 -9

I 0 -1°

' ~ " T~p(NMR)

(NMR)

LaNis_yA[y H×

0 0'.2 ;.4 o'.6 0.8 110 112 1.~

Fig. 17. Influence of the A1 concentration (y) on the room temperature hydrogen diffusion coefficients in LaNi5 yAlyH x. For the various measuring techniques indicated in the figure, see text (after Bowman et al., 1979).

Apart from the La(Ni, A1)5 ternaries, diffusion of H atoms was also studied in several La(Ni, Cu)5 ternaries and in LaCu». Shinar et al. (1980) found that increasing Cu concentration leads to an increase in the activation energy EA, the value in LaCusHI.» being almost twice as high as in LaNi»H6.

In more detailed investigations Karlicek and Lowe (1980), Achard et al. (1982) and Noréus et al. (1983) found that the assumption of a single thermally activated diffusion process in the LaNi» hydride is an oversimplification. According to their results the hydrogen motion in the LaNi5 hydride is rather complicated and involves at least two different diffusion processes (with activation energies differing by more than a factor of two). They ascribe this to the possibility that the movement of hydrogen involves the crossing of several potential energy wells of different depths.

In this connection they point to the crystal structure of the LaNi» deuteride (see section 5) where the deuterium atoms occupy more than one inequivalent lattice position. These lattice positions are interconnected by a multitude of different jump paths.

Shinar et al. (1981) found experimental evidence indicating that an analysis of the diffusion-related experimental data in terms of a simple Arrhenius type of activation law is an over-simplification for other reasons as weil. For a number of hydrides based on binary and pseudobinary compounds they show that the activation energy E A cannot be taken to be temperature independent, as is usually done.

«! ,~;

0

efl

«

I

H

~ . ~ ~ . ~ ~ ~ ~

~ Z Z Z Z Z Z ~ Z

o ' & , o g g & , ' o o "

X X X X X X X X X X X

X X X X X X X X X

: ~ ~ . 7 7 7 7 '--

32 K.H.J. BUSCHOW