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Solvus data and dilute phase hydrogen solubilities for the intermetallic compound-hydrogen systems LaNi5-H and ErFe2-H
Journal
of the Less-Common Metals, 91(1983) 107-117
107
SOLVUS DATA AND DILUTE PHASE HYDROGEN SOLUBILITIES FOR THE INTERMETALLIC COMPOUN=HYDROGEN SYSTEMS LaNi,-H AND ErFe,-H
TED B. FLANAGAN,
N. B. MASON
and G. E. BIEHL
Department of Chemistry, University of Vermont, Burlington,
VT 05405 (U.S.A.)
(Received August X3,1982)
Summary The utility of employing solvus data for the derivation of thermodynamic parameters for miscibility gap intermetallic compound-hydrogen systems is discussed. It is shown that solvus data can be employed to determine whether complicating features, e.g. trapping, are present in the dilute solubility range. The solvus data can be employed to estimate the partial H-H interaction free energy. The thermodynamic development is applied to experimental data obtained for the LaNi,-H and ErFe,-H systems.
1. Introduction The solvus composition a is the dilute phase composition which coexists at a given temperature with the hydride phase. The variation in the solvus composition with temperature has been employed to help to characterize pure metal-hydrogen and alloy-hydrogen systems thermodynamically [l]. Solvus data have not been employed for the determination of thermodynamic data for intermetallic compound-hydrogen systems. These are the systems of most interest for practical applications of hydrides. The purpose of the present research is to examine the usefulness of solvus measurements for miscibility gap intermetallic compound-hydrogen systems. Measurements will be described for the LaNi,-H and ErFe,-H systems.
2. Solvus thermodynamics A free energy for the solvus can be defined as [2]
AGsolv@) = - RTln 2, = AHwlv@)- TAS,,,,“’
(1)
where 2, = a/(/3 - a) where a is the ratio n of hydrogen atoms to formula units in 0022-5088/83/oooO-0/$03.00
0 Elsevier Sequoia/Printed
in The Netherlands
108
the dilute phase coexisting with the hydride phase and /? is the structurally limiting value of n for the dilute phase. Values of a will differ depending upon whether the hydride phase is formed or decomposed. In the present discussion the solvus composition will simply be referred to as a with the understanding that hysteresis may affect the values of a and of the derived thermodynamic parameters [2]. For the purposes of discussion we shall consider hydride formation throughout because the experimental data are for hydride formation. From eqn. (1) we obtain -
a(AGoP) = aT
RlnZ,,+RTF=
a(ln -5J
As
(=) SOlV
and
WG,,,“‘YT aT-1
= -
R
a(ln 2,) = AH&
~
aT- ’
In the ideal dilute limit at a + 0 eqns. (2) and (3) reduce to ASsO,v(=~o’ = -AS&
+ AS,’
(4)
and AH_,,v(z* ‘) = -AH&= + AHa’
(5)
’ refer to the thermodynamic parameters for the reaction where ASplato and AHplat $I,(g,latm)+e
MH
= MHb(b - a)
(6)
where b refers to n for the hydride phase coexisting with the dilute phase. If eqns. (4) and (5) were to be expressed for hydride decomposition instead of formation, the negative signs in front of the flrst terms on the right-hand sides of eqns. (4) and (5) would be changed to positive signs. AS,’ and AH,.,’ are the standard values of solution for 0.5 mol H,(g) into the infinitely dilute interstitial solution without the configurational contribution for ASno. For finite values of a, where non-ideality is a factor, eqn. (1) can be written as AGsolv@) = AHsolv(=) - TAS&=) = AHsolv(=. O)- TASsolv@. O)+ /~“‘~‘(a)
(7)
where ~“‘~‘(a) contains the non-ideal contributions.
3. Hydrogen solubility in intermetallic compounds In contrast with pure metals or alloys, intermetallic compounds are activated before use. They are subjected to hydride formation at elevated pressures and then decomposed; this activation treatment results in a material which rapidly equilibrates with hydrogen. However, activation frequently leads to complex solubility behavior in the dilute phase as compared with that of pure metal-hydrogen systems. The reasons for this are not completely understood
109
but in the very dilute region the behavior can sometimes be described phenomenologically as if hydrogen traps are present [3]. It has been realized recently that the anomalous solubility behavior can be partially or completely removed by annealing of the activated material [4, 51. Figure 1 shows an example of this behavior for LaNi,-H. Another possible complexity in the dilute phase solubility of certain intermetallic compound-hydrogen systems follows from a model proposed by Kierstead [S, 73. For those systems which exhibit multiplateau behavior Kierstead has suggested that there are a series of groups of interstices with different enthalpies and entropies for hydrogen solution. It follows from his model that in the dilute phase region hydrogen dissolves simultaneously in several different groups of sites. The solvus concentration would then contain contributions from the various groups of interstices having different enthalpies and entropies. The next section will deal with the question of how these complexities will affect the derived solvus thermodynamic parameters. 4. Solvus parameters for intermetallic
compound-hydrogen
systems
Let us consider a system which does not exhibit the complexities in the dilute phase referred to above. If the dilute ideal solubility data at n + 0 are extrapolated to intersect the plateau pressure for hydride formation, the corresponding value of n is an ideal solvus composition a*. If ideal values are determined in this way at a series of temperatures, AHso,v(z*o)and ASsOlv(z*o) can be obtained from eqns. (2) and (3) and these will be identical with values calculated from eqns. (4) and (5) using the standard thermodynamic parameters for the dilute phase and the plateau reaction. This will not lead to any new thermodynamic information because the values of AHso,,,@~o)and ASsOIV(z*o) determined in this way must satisfy eqns. (4) and (5). However, if the dilute phase solubility data exhibit anomalous behavior, the values of AHso,v(z~o) and ASsolV(z* O) determined from a* values will not agree with the values predicted from eqns. (4) and (5). We consider an experimental situation where only a limited amount of very dilute solubility data are available and it is not clear from these data whether or not trapping is a factor. If these dilute data are assumed to represent ideal behavior and are extrapolated to the plateau pressure, the “ideal” solvus values which are obtained will be anomalous. They could, for example, be greater than the experimental solvus values which is impossible for a miscibility gap system without traps. The erroneous “ideal” solvus values could also lead to negative values of AHsOIV(z) because, owing to trapping, the apparent value of AHHo in eqn. (5) could be more negative than AHplato;such a result is impossible for a miscibility gap system which is free from complications in the dilute phase. It follows from the model proposed by Kierstead [S, 71 for ErFe,-H that the ideal solvus value is a* = a,+Cn, I
(3)
110
where the ni are the n values of the other contributing groups atp,,,,(I), i.e. only group I interstices lead to the first plateau pressure. The ideal value of a* is then given by a* = a*+Cni i
=~,et”2(I)~BiexP i
where pi is the number of interstices per formula unit for group i and Ap,“(i) = AHHo - TAS,“(i). Differentiation of In a* in eqn. (9) with respect to T - 1 gives AHso,V(z*o) = - AH&‘(I)
+
~~HoW~T)I XiBiexp{ -hW/~T)
XiCBiAHa”(i)exp{ -
(10)
and from eqns. (2) and (9) we obtain ASso,V(z~o) = -AS,,,“(I)
+
A~H”W~T}I+ xi8iew.4- bH”GY~T)
xi[Bi ASn”(i)exp{ -
, {-AJg(“}]-Rln/& +Rln [iCB.exp
(11)
where B, is the value of /I which is assumed to apply. According to this model AHsO,v(z* ‘) and ASso,v(z* O)will exhibit a temperature dependence arising from the summation terms. Similarly the experimental values of AHHo and AS,’ will exhibit a more marked temperature dependence than would be expected for a normal miscibility gap system.
5. Non-ideal
solvus behavior
In contrast with the solvus compositions determined from extrapolation of the ideal solubility relationships to the plateau pressures, the experimental solvus compositions must reflect non-ideality at finite values of a. In the dilute region eqn. (7) can be written as AGsolv(‘) = - RTln 2, = AHso,V(z~o)-TASso,V~Z*o)+g,u where g, is a free-energy coefficient for the H-H interaction. ideal solvus free energy from eqn. (12) gives
(12) Subtraction
of the
(13) where the last expression on the right-hand side of eqn. (13) is obtained for fl B u,u*. ,In the absence of information about the value of /?, the approximate form of eqn. (13) given on the right-hand side is useful for determining g,. Generallyg, is determined from plots of AG aCE)(= RTln{p’/2(Bn)/n}) against n [S] but this method is somewhat more dependent upon the magnitude of B than is eqn. (13).
111
6. Experimental
details
LaNi, and ErFe, were prepared by arc melting the pure components under argon. A slight excess of nickel was present in the LaNi,. This ensures that only LaNi, and a small amount of nickel precipitates will be present after annealing [5]. The latter does not affect the hydrogen solubility data. Buschow and van Ma1 have given a correlation between desorption plateau pressures at 313 K and the stoichiometry of the LaNi, [9]. They observed a value of 3.38 atm (313 K) and the present sample gives 3.2 atm at the same value of F. This suggests that the stoichiometry of the sample is very close to LaNi,,,. ErFe, was annealed in uucuo after preparation. The X-ray powder pattern gave a = 7.283 A (C15) in good agreement with the published values of 7.292 A [lo], 7.28 A [11] and 7.28 A [12]. Pressure-composition-temperature data were obtained using a conventional all-metal vacuum system.
6
0.2
0.4
0.6
0
0.05
0.10
015
3
n (=[tj/[LaNid)
Fig. 1. Plot of absorption isotherms for LaNi, (activated) in the dilute region at 273K following annealing at the following temperatures: 0,298 K; A, 1023 K. Fig. 2. Plot of absorption isotherms for annealed (1023 K) LaNi, in the dilute phase: ---, plateau pressures for hydride formation; 0, 0, 298.2 K; 0.273.2 K; A, 253.2 K; V, 233.2 K; A, 223.2 K; 0, 213.2 K. A small value of n (d 0.02) has been subtracted from the experimental data in order for these data to intersect the origin; this may arise in part from chemisorption of hydrogen at these low temperatures.
112
7. Results and discussion 7.1. LaN&-H It has been shown that annealing of activated LaNi, removes evidence of the trapping of hydrogen in the dilute phase [4, 51. Data determined here are shown in Fig. 2. The sample was annealed at about 1000 K following each isotherm determination. The ideal and experimental values of a can clearly be seen. A plot of the temperature dependence of the solubility data in the dilute region is shown in Fig. 3 which also shows the temperature dependence of the plateau pressures for hydride formation. The following values are obtained from the data in Fig. 3: AHHo= -5.4 kJ (mol H)-‘, AS,” = -52.6 J K-’ (mol H)-’ (B = 3), AHplato= - 14.6 kJ (mol H)- ’ and ASplato= - 55.7 J K- ’ (mol H)-‘. The value of AHa” is much less exothermic than that found for activated unannealed LaNi, 113,141. The same phenomenon occurs for FeTi where the observed AH,” changes from exothermic to endothermic [15]. This difference in the values of AH,” is due to the removal of hydrogen traps by annealing.
Fig. 3. Plotsofln Ks(K, = f~H2i~2~/[H]/~LaNiS])fa_o)andlnp,,~1B1izagainst T-‘forannealed(lO23 K) LaNi,: 0, In K,; 0, lnpm_.B1’*.
The solvus data are plotted in Fig. 4 from which we obtain AHS,,v(zVo) = 9.2 kJ (mol H)-‘. These values are close to those predicted by eqns. (4) and (5), as expected. The problem of multiple plateaux does not exist for LaNi,-H, but trapping can be a factor. There is no evidence that trapping occurs in the present sample after the annealing treatment because the values of a* obtained are quite reasonable. The effect of non-ideality on the solvus plot is shown in Fig. 4 where the degree of non-linearity is seen to increase with increase of temperature. Equation (13) has been used to calculate values of g1 from these solvus data and the results are shown in Table 1, fourth column. The sixth column shows the values of gI. as determined from plots of AGntE)against n using j3 = 3. The agreement is reasonable.
113
I
3.4
3.0
3.8 IO3 K/T
4.6
4.2
Fig. 4. Solvus plot for annealed (1023 K) LaNi,: solvus compositions. TABLE
0, experimental
solvus compositions;
0, ideal
1
Partial H-H interaction a
free energies for LaNi,-H a*
8
and ErFe,-H
g, b
g,
(kJ (mol H)-‘)
f
(kJ (mol H)-‘)
g1 (kJ (mol H)-‘)
-4.6 - 5.4 -4.0
LaNi5-H 298 273 253
0.1025 0.067 0.046
0.0835 0.061 0.0425
-4.9 -3.2 -3.6
-
ErFerH 423.2 421.8 403.2 389.8 373.2
0.215 0.192 0.155 0.135 0.1075
0.113 0.100 0.091 0.085 0.071
- 10.5 -11.7 - 11.5 -11.1 - 12.0
-
^Obtained from eqn. (13). “Calculated from eqn. (13) after correction
11.9 13.8 15.3 14.3 16.6
- 12.4 - 14.2 -14.5 - 14.6 - 16.0
for a small initial region where Sieverts’
law holds
exactly. ’ Obtained from plots of AC,,(s) against n.
The value of g, is rather small, but if n were to be expressed as hydrogen atoms per mole of metal rather than per formula unit it would be about - 26 kJ (mol H)- l which is of comparable magnitude with the H-H partial free energy for the group Vb metal-hydrogen systems [16]. It seems clear from these data on annealed activated LaNi, that this system behaves as a miscibility gap system;
114
this is consistent with the most recent structural evidence [17, IS]. This was not clear, however, from the solubility data for unannealed activated LaNi, [13,14]. 7.2. ErFezH In contrast with LaNi,-H, this system does not show any evidence for significant trapping of hydrogen in the dilute phase as a result of the activation process. Also in contrast with LaNi, [4], ErFe, does not show a change in the plateau pressure for hydride formation following annealing of the activated material. It seems that there is a connection between the two phenomena, i.e. in the LaNi,-H systemp, is increased and hydrogen trapping in the dilute phase is eliminated by annealing [4] whereas neither effect is noted in the dilute phase and first coexistence region of the ErFe,-H system. Some typical absorption isotherms in the dilute phase are shown for ErFe,-H in Fig. 5 where it can be seen that the solubility is appreciable before the hydride phase forms in this temperature range. The sample was annealed at 950 K between measurements of the isotherms because it has been observed that disproportionati-on can~occur above about 473 K and the annealing treatment restores the original ErFe,. The ideal and experimental solvus compositions were determined from these data as was done for LaNi,-H. Thermodynamic data for this system have also been obtained by keeping the amount of hydrogen in the sample constant and following the pressure changes as a function of temperature. The amount of hydrogen in the sample was kept nearly constant by employing a large sample and a small dead volume. The relatively low equilibrium pressures over the sample also contribute to maintaining an almost invariant hydrogen content. The results are shown in I
I
I
I ---
/----
----A--* .
5G--_o--_-_
a*---------/ /A
n Fig. 5. Dilute phase solubility plots for ErFe,-H: A, 432.2 K; 0,412.8 353.2 K.
K; A, 389.8 K;
l,373.2 K; V,
115
-1.0
I
28
3.0
I
3.2 3.4 103K/T
3.6
Fig. 6. Plots in the dilute phase of ErFe,-H of lnp,,1’2 against T- ’ at constant hydrogen contents (0, n = 0.055; A, n = 0.041; A,n = 0.031; V, n = 0.026; V, n = 0.019) and of lnp,,81’2 against Tm ‘,
Fig. 6 where the variation of the two-phase pressure with temperature is also shown. Values of the relative thermodynamic parameters for solution of hydrogen in the dilute solution can be obtained from the slopes and intercepts of the constant-content dilute phase data, and the two-phase parameters can be obtained from the slope and intercept of the two-phase pressure plot. In addition thermodynamic data were obtained from plots of lnp,.,21/2 against T-i using the data shown in Fig. 5 and from separate determinations of the variation of iI* against T l. The results from the two methods are in good agreement lnRa,, and we obtain AHHo = -15.8 kJ (mol H)-‘, AS,” = -61.3 J (mol H)-’ K-l, AH,,,” = -27.0 kJ (mol H)-’ and AS,,,” = -49.0 J (mol H))’ K-l. Besides allowing the determination of the relative thermodynamic parameters, the data in Fig. 6 allow the determination of solvus compositions from the intersection of the dilute single-phase data with the two-phase pressure plot. These values and those determined in Fig. 5 are plotted in Fig. 7. It can be seen that there are large deviations between the ideal values and the experimental values. This is to be expected because the temperature range is somewhat higher than that for LaNi,-H (Fig. 4) and consequently the solubilities and the nonideality are greater. From the ideal solvus values we obtain AHso,v(z*o)= 10.7 kJ (mol H)-’ as compared with the expected value of 11.2 kJ (mol H))’ calculated from the experimental values of the parameters in eqn. (4). The thermodynamic parameters of Kierstead’s original model [S] give a value of 8.6 kJ (mol H)- ’ for AHsolv(=* ‘) and his most recent model [7] gives 10.6 kJ (mol H)-’ (350 K). Both of his values exhibit some temperature dependence. The corresponding experimental value of ASsolv(GO)obtained from the ideal solvus compositions is - 13.9 J K-i (mol H)- 1 compared with the expected value of - 12.3 J K- ’ (mol H)- ’ which can be regarded as satisfactory agreement.
116
Fig. 7. Solvus data for ErFe,-H: 0, experimental values from data such as those shown in Fig. 5; A, experimental values from Fig, 6; 0, ideal values.
Values ofg, have been calculated from the solvus values using eqn. (13) and these are shown in Table 1. They are compared with values determined from plots of AGntE)against n using /.l = 12. The agreement is not very good especially at low temperatures. The reason for this may be due to the fact that the solubility data in the very dilute range appear to follow Sieve& law almost exactly. Hence if g, is determined from the slope of the AGstE) against n plots the initial portion will have almost zero slope and thereforeg, must be determined from the data at higher contents. The reason for this may be due to some chemisorption of hydrogen which may depress the values of pH2. If eqn. (13) is corrected for the initial solubility region (0 < n < 0.03) by division of the right-hand side of eqn. (13) by a-6, where 6 x 0.03, instead of by a, the values of g, shown in Table 1, fifth column, are found. These corrected values of g, are consistent with those values given in Table 1, sixth column, since in both cases the initial region has been removed. The agreement of the two sets of values of g, is reasonably good. The decrease in the values of g, with increase of temperature is due to the fact that g, contains a significant entropic contribution. If /I is chosen to be 1.26 [S] instead of 12, the values ofg, which are obtained from plots of AGHCE) against n are about 2 kJ (mol H))’ more negative than those shown in Table 1, sixth column, and therefore are in poorer agreement with the values of g, derived from eqn. (13) which is more independent of the selected value of j?. This argues that j3is greater than 1.26. The exact value of jl cannot be evaluated from these thermodynamic data but the value of fl= 12 has been selected from structural information [19, 201. A detailed analysis of the dilute
117
phase data for ErFe,-H presented elsewhere.
and a comparison
with Kierstead’s
models will be
8. Conclusion Solvus thermodynamic parameters for hydride formation for LaNi,-H (annealed) and ErFe,-H are consistent with the other thermodynamic data derived for these systems. Consequently the dilute phase solubility data for these systems are not anomalous, i.e. there is no evidence for trapping of hydrogen or multigroup solubility.
Acknowledgment The National research.
Science Foundation
is thanked for financial support of this
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
S. Kishimoto, W. A. Oates and T. B. Flanagan, J. Less-Common Met., 88 (1982) 459. T. B. Flanagan, W. A. Oates and S. Kishimoto, Actu Metall., 31(1983) 199. T. B. Flanagan, C. A. Wulff and B. S. Bowerman, J. Solid State Chem., 34 (1980) 215. T. B. Flanagan and G. E. Biehl, J. Less-Common Met., 82(1981) 385. J. F. Lynch and J. J. Reilly, J. Less-Common Met., 87(1982) 225. H. A. Kierstead, J. Less-Common Met., 71(1980) 303. H. A. Kierstead, J. Less-Common Met., 77(1981) 281. T. B. Flanagan and W. A. Oates, Ber. Bunsenges. Phys. Chem., 76(1972) 706. K. H. J. Buschow and H. H. van Mal, J. Less-Common Met., 29(1972) 203. D. M. Gualtieri, K. S. V. L. Narasimhan and W. E. Wallace, AIP Conf. Proc., 34(1976) 219. G. E. Fish, J. J. Rhyne, S. G. Sankar and W. E. Wallace, J. Appl. Phys., 50(1979) 2003. H. A. Kierstead, P. J. Viccaro, G. K. Shenoy and B. D. Dunlap, J. Less-Common Met., 66 (1979) 219. B. S. Bower-man, C. A. Wulff and T. B. Flanagan, 2. Phys. Chem. N.F., 116(1979) 197. J. J. Murray, M. L. Post and J. B. Taylor, J. Less-Common Met., 80(1981) 211. G. Arnold and J.-M. Welter, J. Less-Common Met., 74 (1980) 465. 0. J. Kleppa, P. Dantzer and M. E. Melnichak, J. Chem. Phys., 61(1974) 4048. A. Percheron-Guegan, C. Lartigue, J. C. Achard, P. Germi and F. Tasset, J. LessCommon Met., 74 (1980) 1. J. C. Achard, C. Lartigue, A. Percheron-Guegan, J. C. Mathieu, A. Pasture1 and F. Tasset, J. Less-Common Met., 79 (1981) 161. J. J. Didisheim, K. Yvon, D. Shaltiel, P. Fischer, P. Bujard and E. Walker, Solid State Commun., 32(1979) 1087.
20
J.-J. Didisheim, K. Yvon, P. Fischer and D. Shaltiel, J. Less-Common Met., 73 (1980) 355.
of the Less-Common Metals, 91(1983) 107-117
107
SOLVUS DATA AND DILUTE PHASE HYDROGEN SOLUBILITIES FOR THE INTERMETALLIC COMPOUN=HYDROGEN SYSTEMS LaNi,-H AND ErFe,-H
TED B. FLANAGAN,
N. B. MASON
and G. E. BIEHL
Department of Chemistry, University of Vermont, Burlington,
VT 05405 (U.S.A.)
(Received August X3,1982)
Summary The utility of employing solvus data for the derivation of thermodynamic parameters for miscibility gap intermetallic compound-hydrogen systems is discussed. It is shown that solvus data can be employed to determine whether complicating features, e.g. trapping, are present in the dilute solubility range. The solvus data can be employed to estimate the partial H-H interaction free energy. The thermodynamic development is applied to experimental data obtained for the LaNi,-H and ErFe,-H systems.
1. Introduction The solvus composition a is the dilute phase composition which coexists at a given temperature with the hydride phase. The variation in the solvus composition with temperature has been employed to help to characterize pure metal-hydrogen and alloy-hydrogen systems thermodynamically [l]. Solvus data have not been employed for the determination of thermodynamic data for intermetallic compound-hydrogen systems. These are the systems of most interest for practical applications of hydrides. The purpose of the present research is to examine the usefulness of solvus measurements for miscibility gap intermetallic compound-hydrogen systems. Measurements will be described for the LaNi,-H and ErFe,-H systems.
2. Solvus thermodynamics A free energy for the solvus can be defined as [2]
AGsolv@) = - RTln 2, = AHwlv@)- TAS,,,,“’
(1)
where 2, = a/(/3 - a) where a is the ratio n of hydrogen atoms to formula units in 0022-5088/83/oooO-0/$03.00
0 Elsevier Sequoia/Printed
in The Netherlands
108
the dilute phase coexisting with the hydride phase and /? is the structurally limiting value of n for the dilute phase. Values of a will differ depending upon whether the hydride phase is formed or decomposed. In the present discussion the solvus composition will simply be referred to as a with the understanding that hysteresis may affect the values of a and of the derived thermodynamic parameters [2]. For the purposes of discussion we shall consider hydride formation throughout because the experimental data are for hydride formation. From eqn. (1) we obtain -
a(AGoP) = aT
RlnZ,,+RTF=
a(ln -5J
As
(=) SOlV
and
WG,,,“‘YT aT-1
= -
R
a(ln 2,) = AH&
~
aT- ’
In the ideal dilute limit at a + 0 eqns. (2) and (3) reduce to ASsO,v(=~o’ = -AS&
+ AS,’
(4)
and AH_,,v(z* ‘) = -AH&= + AHa’
(5)
’ refer to the thermodynamic parameters for the reaction where ASplato and AHplat $I,(g,latm)+e
MH
= MHb(b - a)
(6)
where b refers to n for the hydride phase coexisting with the dilute phase. If eqns. (4) and (5) were to be expressed for hydride decomposition instead of formation, the negative signs in front of the flrst terms on the right-hand sides of eqns. (4) and (5) would be changed to positive signs. AS,’ and AH,.,’ are the standard values of solution for 0.5 mol H,(g) into the infinitely dilute interstitial solution without the configurational contribution for ASno. For finite values of a, where non-ideality is a factor, eqn. (1) can be written as AGsolv@) = AHsolv(=) - TAS&=) = AHsolv(=. O)- TASsolv@. O)+ /~“‘~‘(a)
(7)
where ~“‘~‘(a) contains the non-ideal contributions.
3. Hydrogen solubility in intermetallic compounds In contrast with pure metals or alloys, intermetallic compounds are activated before use. They are subjected to hydride formation at elevated pressures and then decomposed; this activation treatment results in a material which rapidly equilibrates with hydrogen. However, activation frequently leads to complex solubility behavior in the dilute phase as compared with that of pure metal-hydrogen systems. The reasons for this are not completely understood
109
but in the very dilute region the behavior can sometimes be described phenomenologically as if hydrogen traps are present [3]. It has been realized recently that the anomalous solubility behavior can be partially or completely removed by annealing of the activated material [4, 51. Figure 1 shows an example of this behavior for LaNi,-H. Another possible complexity in the dilute phase solubility of certain intermetallic compound-hydrogen systems follows from a model proposed by Kierstead [S, 73. For those systems which exhibit multiplateau behavior Kierstead has suggested that there are a series of groups of interstices with different enthalpies and entropies for hydrogen solution. It follows from his model that in the dilute phase region hydrogen dissolves simultaneously in several different groups of sites. The solvus concentration would then contain contributions from the various groups of interstices having different enthalpies and entropies. The next section will deal with the question of how these complexities will affect the derived solvus thermodynamic parameters. 4. Solvus parameters for intermetallic
compound-hydrogen
systems
Let us consider a system which does not exhibit the complexities in the dilute phase referred to above. If the dilute ideal solubility data at n + 0 are extrapolated to intersect the plateau pressure for hydride formation, the corresponding value of n is an ideal solvus composition a*. If ideal values are determined in this way at a series of temperatures, AHso,v(z*o)and ASsOlv(z*o) can be obtained from eqns. (2) and (3) and these will be identical with values calculated from eqns. (4) and (5) using the standard thermodynamic parameters for the dilute phase and the plateau reaction. This will not lead to any new thermodynamic information because the values of AHso,,,@~o)and ASsOIV(z*o) determined in this way must satisfy eqns. (4) and (5). However, if the dilute phase solubility data exhibit anomalous behavior, the values of AHso,v(z~o) and ASsolV(z* O) determined from a* values will not agree with the values predicted from eqns. (4) and (5). We consider an experimental situation where only a limited amount of very dilute solubility data are available and it is not clear from these data whether or not trapping is a factor. If these dilute data are assumed to represent ideal behavior and are extrapolated to the plateau pressure, the “ideal” solvus values which are obtained will be anomalous. They could, for example, be greater than the experimental solvus values which is impossible for a miscibility gap system without traps. The erroneous “ideal” solvus values could also lead to negative values of AHsOIV(z) because, owing to trapping, the apparent value of AHHo in eqn. (5) could be more negative than AHplato;such a result is impossible for a miscibility gap system which is free from complications in the dilute phase. It follows from the model proposed by Kierstead [S, 71 for ErFe,-H that the ideal solvus value is a* = a,+Cn, I
(3)
110
where the ni are the n values of the other contributing groups atp,,,,(I), i.e. only group I interstices lead to the first plateau pressure. The ideal value of a* is then given by a* = a*+Cni i
=~,et”2(I)~BiexP i
where pi is the number of interstices per formula unit for group i and Ap,“(i) = AHHo - TAS,“(i). Differentiation of In a* in eqn. (9) with respect to T - 1 gives AHso,V(z*o) = - AH&‘(I)
+
~~HoW~T)I XiBiexp{ -hW/~T)
XiCBiAHa”(i)exp{ -
(10)
and from eqns. (2) and (9) we obtain ASso,V(z~o) = -AS,,,“(I)
+
A~H”W~T}I+ xi8iew.4- bH”GY~T)
xi[Bi ASn”(i)exp{ -
, {-AJg(“}]-Rln/& +Rln [iCB.exp
(11)
where B, is the value of /I which is assumed to apply. According to this model AHsO,v(z* ‘) and ASso,v(z* O)will exhibit a temperature dependence arising from the summation terms. Similarly the experimental values of AHHo and AS,’ will exhibit a more marked temperature dependence than would be expected for a normal miscibility gap system.
5. Non-ideal
solvus behavior
In contrast with the solvus compositions determined from extrapolation of the ideal solubility relationships to the plateau pressures, the experimental solvus compositions must reflect non-ideality at finite values of a. In the dilute region eqn. (7) can be written as AGsolv(‘) = - RTln 2, = AHso,V(z~o)-TASso,V~Z*o)+g,u where g, is a free-energy coefficient for the H-H interaction. ideal solvus free energy from eqn. (12) gives
(12) Subtraction
of the
(13) where the last expression on the right-hand side of eqn. (13) is obtained for fl B u,u*. ,In the absence of information about the value of /?, the approximate form of eqn. (13) given on the right-hand side is useful for determining g,. Generallyg, is determined from plots of AG aCE)(= RTln{p’/2(Bn)/n}) against n [S] but this method is somewhat more dependent upon the magnitude of B than is eqn. (13).
111
6. Experimental
details
LaNi, and ErFe, were prepared by arc melting the pure components under argon. A slight excess of nickel was present in the LaNi,. This ensures that only LaNi, and a small amount of nickel precipitates will be present after annealing [5]. The latter does not affect the hydrogen solubility data. Buschow and van Ma1 have given a correlation between desorption plateau pressures at 313 K and the stoichiometry of the LaNi, [9]. They observed a value of 3.38 atm (313 K) and the present sample gives 3.2 atm at the same value of F. This suggests that the stoichiometry of the sample is very close to LaNi,,,. ErFe, was annealed in uucuo after preparation. The X-ray powder pattern gave a = 7.283 A (C15) in good agreement with the published values of 7.292 A [lo], 7.28 A [11] and 7.28 A [12]. Pressure-composition-temperature data were obtained using a conventional all-metal vacuum system.
6
0.2
0.4
0.6
0
0.05
0.10
015
3
n (=[tj/[LaNid)
Fig. 1. Plot of absorption isotherms for LaNi, (activated) in the dilute region at 273K following annealing at the following temperatures: 0,298 K; A, 1023 K. Fig. 2. Plot of absorption isotherms for annealed (1023 K) LaNi, in the dilute phase: ---, plateau pressures for hydride formation; 0, 0, 298.2 K; 0.273.2 K; A, 253.2 K; V, 233.2 K; A, 223.2 K; 0, 213.2 K. A small value of n (d 0.02) has been subtracted from the experimental data in order for these data to intersect the origin; this may arise in part from chemisorption of hydrogen at these low temperatures.
112
7. Results and discussion 7.1. LaN&-H It has been shown that annealing of activated LaNi, removes evidence of the trapping of hydrogen in the dilute phase [4, 51. Data determined here are shown in Fig. 2. The sample was annealed at about 1000 K following each isotherm determination. The ideal and experimental values of a can clearly be seen. A plot of the temperature dependence of the solubility data in the dilute region is shown in Fig. 3 which also shows the temperature dependence of the plateau pressures for hydride formation. The following values are obtained from the data in Fig. 3: AHHo= -5.4 kJ (mol H)-‘, AS,” = -52.6 J K-’ (mol H)-’ (B = 3), AHplato= - 14.6 kJ (mol H)- ’ and ASplato= - 55.7 J K- ’ (mol H)-‘. The value of AHa” is much less exothermic than that found for activated unannealed LaNi, 113,141. The same phenomenon occurs for FeTi where the observed AH,” changes from exothermic to endothermic [15]. This difference in the values of AH,” is due to the removal of hydrogen traps by annealing.
Fig. 3. Plotsofln Ks(K, = f~H2i~2~/[H]/~LaNiS])fa_o)andlnp,,~1B1izagainst T-‘forannealed(lO23 K) LaNi,: 0, In K,; 0, lnpm_.B1’*.
The solvus data are plotted in Fig. 4 from which we obtain AHS,,v(zVo) = 9.2 kJ (mol H)-‘. These values are close to those predicted by eqns. (4) and (5), as expected. The problem of multiple plateaux does not exist for LaNi,-H, but trapping can be a factor. There is no evidence that trapping occurs in the present sample after the annealing treatment because the values of a* obtained are quite reasonable. The effect of non-ideality on the solvus plot is shown in Fig. 4 where the degree of non-linearity is seen to increase with increase of temperature. Equation (13) has been used to calculate values of g1 from these solvus data and the results are shown in Table 1, fourth column. The sixth column shows the values of gI. as determined from plots of AGntE)against n using j3 = 3. The agreement is reasonable.
113
I
3.4
3.0
3.8 IO3 K/T
4.6
4.2
Fig. 4. Solvus plot for annealed (1023 K) LaNi,: solvus compositions. TABLE
0, experimental
solvus compositions;
0, ideal
1
Partial H-H interaction a
free energies for LaNi,-H a*
8
and ErFe,-H
g, b
g,
(kJ (mol H)-‘)
f
(kJ (mol H)-‘)
g1 (kJ (mol H)-‘)
-4.6 - 5.4 -4.0
LaNi5-H 298 273 253
0.1025 0.067 0.046
0.0835 0.061 0.0425
-4.9 -3.2 -3.6
-
ErFerH 423.2 421.8 403.2 389.8 373.2
0.215 0.192 0.155 0.135 0.1075
0.113 0.100 0.091 0.085 0.071
- 10.5 -11.7 - 11.5 -11.1 - 12.0
-
^Obtained from eqn. (13). “Calculated from eqn. (13) after correction
11.9 13.8 15.3 14.3 16.6
- 12.4 - 14.2 -14.5 - 14.6 - 16.0
for a small initial region where Sieverts’
law holds
exactly. ’ Obtained from plots of AC,,(s) against n.
The value of g, is rather small, but if n were to be expressed as hydrogen atoms per mole of metal rather than per formula unit it would be about - 26 kJ (mol H)- l which is of comparable magnitude with the H-H partial free energy for the group Vb metal-hydrogen systems [16]. It seems clear from these data on annealed activated LaNi, that this system behaves as a miscibility gap system;
114
this is consistent with the most recent structural evidence [17, IS]. This was not clear, however, from the solubility data for unannealed activated LaNi, [13,14]. 7.2. ErFezH In contrast with LaNi,-H, this system does not show any evidence for significant trapping of hydrogen in the dilute phase as a result of the activation process. Also in contrast with LaNi, [4], ErFe, does not show a change in the plateau pressure for hydride formation following annealing of the activated material. It seems that there is a connection between the two phenomena, i.e. in the LaNi,-H systemp, is increased and hydrogen trapping in the dilute phase is eliminated by annealing [4] whereas neither effect is noted in the dilute phase and first coexistence region of the ErFe,-H system. Some typical absorption isotherms in the dilute phase are shown for ErFe,-H in Fig. 5 where it can be seen that the solubility is appreciable before the hydride phase forms in this temperature range. The sample was annealed at 950 K between measurements of the isotherms because it has been observed that disproportionati-on can~occur above about 473 K and the annealing treatment restores the original ErFe,. The ideal and experimental solvus compositions were determined from these data as was done for LaNi,-H. Thermodynamic data for this system have also been obtained by keeping the amount of hydrogen in the sample constant and following the pressure changes as a function of temperature. The amount of hydrogen in the sample was kept nearly constant by employing a large sample and a small dead volume. The relatively low equilibrium pressures over the sample also contribute to maintaining an almost invariant hydrogen content. The results are shown in I
I
I
I ---
/----
----A--* .
5G--_o--_-_
a*---------/ /A
n Fig. 5. Dilute phase solubility plots for ErFe,-H: A, 432.2 K; 0,412.8 353.2 K.
K; A, 389.8 K;
l,373.2 K; V,
115
-1.0
I
28
3.0
I
3.2 3.4 103K/T
3.6
Fig. 6. Plots in the dilute phase of ErFe,-H of lnp,,1’2 against T- ’ at constant hydrogen contents (0, n = 0.055; A, n = 0.041; A,n = 0.031; V, n = 0.026; V, n = 0.019) and of lnp,,81’2 against Tm ‘,
Fig. 6 where the variation of the two-phase pressure with temperature is also shown. Values of the relative thermodynamic parameters for solution of hydrogen in the dilute solution can be obtained from the slopes and intercepts of the constant-content dilute phase data, and the two-phase parameters can be obtained from the slope and intercept of the two-phase pressure plot. In addition thermodynamic data were obtained from plots of lnp,.,21/2 against T-i using the data shown in Fig. 5 and from separate determinations of the variation of iI* against T l. The results from the two methods are in good agreement lnRa,, and we obtain AHHo = -15.8 kJ (mol H)-‘, AS,” = -61.3 J (mol H)-’ K-l, AH,,,” = -27.0 kJ (mol H)-’ and AS,,,” = -49.0 J (mol H))’ K-l. Besides allowing the determination of the relative thermodynamic parameters, the data in Fig. 6 allow the determination of solvus compositions from the intersection of the dilute single-phase data with the two-phase pressure plot. These values and those determined in Fig. 5 are plotted in Fig. 7. It can be seen that there are large deviations between the ideal values and the experimental values. This is to be expected because the temperature range is somewhat higher than that for LaNi,-H (Fig. 4) and consequently the solubilities and the nonideality are greater. From the ideal solvus values we obtain AHso,v(z*o)= 10.7 kJ (mol H)-’ as compared with the expected value of 11.2 kJ (mol H))’ calculated from the experimental values of the parameters in eqn. (4). The thermodynamic parameters of Kierstead’s original model [S] give a value of 8.6 kJ (mol H)- ’ for AHsolv(=* ‘) and his most recent model [7] gives 10.6 kJ (mol H)-’ (350 K). Both of his values exhibit some temperature dependence. The corresponding experimental value of ASsolv(GO)obtained from the ideal solvus compositions is - 13.9 J K-i (mol H)- 1 compared with the expected value of - 12.3 J K- ’ (mol H)- ’ which can be regarded as satisfactory agreement.
116
Fig. 7. Solvus data for ErFe,-H: 0, experimental values from data such as those shown in Fig. 5; A, experimental values from Fig, 6; 0, ideal values.
Values ofg, have been calculated from the solvus values using eqn. (13) and these are shown in Table 1. They are compared with values determined from plots of AGntE)against n using /.l = 12. The agreement is not very good especially at low temperatures. The reason for this may be due to the fact that the solubility data in the very dilute range appear to follow Sieve& law almost exactly. Hence if g, is determined from the slope of the AGstE) against n plots the initial portion will have almost zero slope and thereforeg, must be determined from the data at higher contents. The reason for this may be due to some chemisorption of hydrogen which may depress the values of pH2. If eqn. (13) is corrected for the initial solubility region (0 < n < 0.03) by division of the right-hand side of eqn. (13) by a-6, where 6 x 0.03, instead of by a, the values of g, shown in Table 1, fifth column, are found. These corrected values of g, are consistent with those values given in Table 1, sixth column, since in both cases the initial region has been removed. The agreement of the two sets of values of g, is reasonably good. The decrease in the values of g, with increase of temperature is due to the fact that g, contains a significant entropic contribution. If /I is chosen to be 1.26 [S] instead of 12, the values ofg, which are obtained from plots of AGHCE) against n are about 2 kJ (mol H))’ more negative than those shown in Table 1, sixth column, and therefore are in poorer agreement with the values of g, derived from eqn. (13) which is more independent of the selected value of j?. This argues that j3is greater than 1.26. The exact value of jl cannot be evaluated from these thermodynamic data but the value of fl= 12 has been selected from structural information [19, 201. A detailed analysis of the dilute
117
phase data for ErFe,-H presented elsewhere.
and a comparison
with Kierstead’s
models will be
8. Conclusion Solvus thermodynamic parameters for hydride formation for LaNi,-H (annealed) and ErFe,-H are consistent with the other thermodynamic data derived for these systems. Consequently the dilute phase solubility data for these systems are not anomalous, i.e. there is no evidence for trapping of hydrogen or multigroup solubility.
Acknowledgment The National research.
Science Foundation
is thanked for financial support of this
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
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20
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