J. Phys. Chem. B 2006, 110, 8087-8093
8087
Thermodynamics of Hydrogen Solution and Hydride Formation in Pd-Mn Alloys. 2. Ordered Alloys S. Luo, A. Craft, and Ted B. Flanagan* Chemistry Department, UniVersity of Vermont, Burlington, Vermont 05405 ReceiVed: October 26, 2005; In Final Form: February 28, 2006
There are marked differences in H2 solubilities between ordered and disordered Pd-Mn alloys with the largest difference found between the L12 and the disordered form of the Pd3Mn alloy. The thermodynamics of H2 solution have been determined for the L12 form, the long-period superstructure (lps), and the disordered forms of the Pd0.80Mn0.20 and Pd0.75Mn0.25(Pd3Mn) alloys. Relative partial molar enthalpies and entropies were determined mainly by reaction calorimetry over the range of H contents accessible from pH2 ≈ 10 Pa to ≈ 0.3 MPa (303 K). The enthalpies for absorption of H2 are more exothermic over most of the range of H contents for the L12 forms of the Pd3Mn and Pd0.80Mn0.20 alloys than for their other forms. The reaction enthalpies are constant across a relatively wide range of H contents for the L12 form of the Pd0.80Mn0.20 and Pd3Mn alloys indicating that there are two-phase coexistence regions (303 K). The H-H attractive interaction, which leads to hydride formation, is much greater for the L12 than for the other forms of the Pd3Mn alloy and for Pd itself. It has been found that the H-H interaction always decreases in magnitude and, accompanying this, the THS (terminal hydrogen solubility) always increases by alloying Pd.1 The L12 ordered Pd3Mn alloy is an exception to this, and therefore, the generalization about THS must be restricted to disordered face centered cubic (fcc) Pd alloys.
Introduction When a Pd3Mn (Pd0.75Mn0.25) alloy is slowly cooled from above 800 K, a long-period superstructure (lps)2,3 forms or, more accurately, an ordered tetragonal structure of the Al3Zr type,4 but for convenience, this will be referred to as lps with the understanding that there is a small tetragonal distortion resulting in the Al3Zr-type structure. The Pd3Mn alloy will be referred to by its stoichiometric formula to emphasize that it is stoichiometric, but when its H content is specified, it will be referred to Pd0.75Mn0.25, for example, r ) (H/Pd0.75Mn0.25), in order for the denominator to be 1 mol metal. It has been found that the L12 structure of Pd3Mn can be prepared by equilibration of the disordered alloy with g10 bar H2 at temperatures above ≈550 K.5,6 Thus the L12 form is an H-stabilized structure which, when heated at 550 K in the absence of hydrogen, changes into the lps. A disordered form of this alloy can be prepared by quenching from above 700 K. Thus, the Pd3Mn alloy can be prepared with three different structures (Figure 1): disordered, a ZrAl3-type long-range superstructure lps, and a L12 ordered structure. There are no other known examples of an alloy which can be prepared with three different structures each of which absorbs significant amounts of H2 at readily accessible pH2. Alloys with smaller amounts of Mn can also be ordered into the two forms but the ordering is incomplete. It should be noted that hydrogen solubilities may be more sensitive to the degree of order than other, often-employed physical parameters.7 The Pd3Mn alloy offers a unique opportunity to examine H2 solubilities in three different structures with the same stoichiometry, Pd3Mn, and such determinations may provide insight into the effect of the local interstice environment on H2 solution. It was shown by Wallace and co-workers that the electronic * To whom correspondence should be addressed. E-mail: flanagan@ emba.uvm.edu.
Figure 1. Ordered structures of the Pd3Mn alloy (a) lps and (b) L12 structure where (O) Mn and (b) Pd.
specific heat of a Pd3Fe alloy is the same for its ordered (L12) and disordered forms8 suggesting that the global electronic structure is independent of ordering, and therefore, any changes in H2 solubilities may, to a first approximation, be attributed to differences in local octahedral interstice environments. The long-
10.1021/jp0582787 CCC: $30.25 © 2006 American Chemical Society Published on Web 03/25/2006
8088 J. Phys. Chem. B, Vol. 110, No. 15, 2006 ranged elastic interaction9 which is a feature of metal-H systems should be nearly the same in the three forms of the Pd3Mn alloy because their elastic constants and partial molar volumes of H are similar. Using neutron diffraction, Andersson and co-workers4 have shown that in the lps superstructure, Pd3MnD0.61, D occupies mainly (85%) the Pd6 octahedral interstices with the remainder in the octahedral Pd5Mn (Pd5Mn) interstices. For the L12 structure, Pd3MnD0.67, only the Pd6 interstices are occupied at least up to Pd3MnD0.67 (0.2 MPa).10 The L12 form of the Pd3Mn alloy does not have any Pd5Mn interstices (Figure 1), and therefore, there will be a greater relative preference for the Pd6 interstices in this form than in the lps form which does have Pd5Mn interstices; these presumably become occupied at higher pH2. The fractions of Pd6 interstices in the Pd3Mn alloy are (H/ (Pd0.75Mn0.25)) ) 0.125, 0.178, and 0.250 for the lps, disordered, and the L12 structures, respectively (Figure 1). These fractions are equal to the H/(Pd0.75Mn0.25) ratios if only these Pd6 interstices are fully occupied. The fraction of Pd6 interstices in the disordered form has been calculated assuming random occupation of the nearest neighbor metal atoms around an octahedral site, that is, a binomial distribution. To explain their results, Phutela and Kleppa11 concluded that only interstices surrounded by Pd nearest neighbors, Pd6, were occupied at the small H contents which were obtained in their high-temperature studies. They were the first to observe a difference between H2 solubilities in the lps and disordered forms of the Pd3Mn alloy by following its dilute phase solubility through the ordering temperature. The L12 form was unknown at the time of their investigation. The thermodynamics of H2 absorption in these three structures have been determined in this research employing the equilibrium pressure-composition-temperature (p-c-T) technique for the Pd3Mn, Pd0.80Mn0.20, and Pd0.85Mn0.15 alloys and reaction calorimetry (303 K) for the first two alloys. The thermodynamics coupled with the known structures will hopefully provide some insight into H2 absorption, and the results will be useful for comparison with future theoretical calculations such as those recently carried out for the energy of H2 absorption by several Pd3M alloys in the L12 form where MdCu, Ag.12 Experimental Section The alloys were prepared by arc-melting and rolling into thin foil. They were then treated appropriately to obtain the desired states of order. The disordered forms were prepared by heating to 1200 K in quartz ampules and then quenched into ice water while simultaneously breaking their quartz ampule containers. The lps forms were prepared by heating in vacuo to 1200 K and then cooling slowly, that is, ≈2 K/h, and the L12 forms were prepared by exposing the alloys to 5.0 MPa H2 and holding at 473-523 K for 24 h and then cooling in H2 to 373 K and evacuating. These different types of order have been verified from their electron diffraction patterns.5 Since the degrees of order for different preparations were not always identical, there were small differences in the H2 solubilities for the ordered forms because the solubilities are very sensitive to the degree of order. The H2 solubilities were measured in a Sieverts’ type apparatus. ∆HH and ∆SH can be obtained from p-c-T data from the slopes and intercepts of plots of ln pH21/2 against 1/T at given H contents. Most of the thermodynamic data were, however, obtained calorimetrically. The calorimeter employed has been described elsewhere13 and is capable of measuring heats of absorption/desorption of small increments of H2 such that
Luo et al.
Figure 2. H2 isotherms (393 K) for the L12 and lps forms and an estimated isotherm for the disordered form of the Pd0.85Mn0.15 alloy.
(δq/δnH) ≈ (∂∆H/∂nH)T,ni*nH ) ∆HH where the ∆ indicates relative to H2 (g, 1 bar) although, in practice, pH2 differed from 1 bar but ∆HH does not depend on pH2 in this low, ideal pH2 range. Results and Discussion The nonstoichiometric Pd0.85Mn0.15 and Pd0.80Mn0.20 alloys cannot be ordered completely because they do not have the stoichiometry needed for complete ordering, that is, Pd3Mn, but they can be partially ordered as shown by their H2 solubility changes, electrical resistance changes, and electron diffraction patterns.14,15 The isotherm results will be described first and then the calorimetric results. H2 Isotherms. Pd0.85Mn0.15 Alloy. The difference between the isotherms for the lps and the L12 ordered forms is relatively small with the solubility in the latter greater than that in the former form. Both solubilities are greater than the solubility in the disordered form (Figure 2). Pd0.80Mn0.20 Alloy. The differences between isotherms for the ordered forms of this alloy are significant (Figure 3) with the L12 form having a greater solubility than the lps form which has a greater solubility than the disordered alloy. The equilibrium pH2 values for the L12 form are small from r ) 0 to about 0.15. Generally, for metal-H systems, the relative chemical potential of H can be written as16
1 ∆µH ) µH - µ°(H2,1bar) ) ∆µ°H + RT ln[r/(β - r)] + µEH(r) 2 (1) where µEH(r) is the excess or nonideal µH and r ) (H/(Pd1-xMnx)). The slopes of plots of RT ln((β - r)p1/2/r) against r give g1 at small r where µEH(r) ≈ g1 × r and g1 is the first term in a series expansion of µEH(r) as a function of r.16 From plots of RT ln((β - r)p1/2/r) against r for the Pd0.80Mn0.20 alloy, it has been found that g1 is the most negative, that is, a greater attractive interaction, for the L12 form, the lps is next, and the least negative is the disordered form. Such plots will be shown below for the stoichiometric alloy. Pd0.75Mn0.25 Alloy. Hydrogen solubility isotherms are shown in Figure 4 (303 K) for the three forms of both the Pd3Mn and Pd0.80Mn0.20 alloys. There are large differences in solubilities between the lps forms for the two alloys and also between the
Pd-Mn Alloys Part 2
J. Phys. Chem. B, Vol. 110, No. 15, 2006 8089 TABLE 1: Enthalpies and Entropies for Ordered and Disordered Pd-Mn Alloys in kJ/mol H and J/K mol H, Respectively, from p-c-T Data form
Figure 3. H2 isotherms (303 K) for the three forms of the Pd0.80Mn0.20 alloy. The open and filled symbols represent absorption and desorption, respectively.
Figure 4. H2 isotherms (303 K) for the three forms of the Pd3Mn alloy and for the Pd0.80Mn0.20 alloy. The open and filled symbols represent absorption and desorption, respectively.
disordered forms but a relatively small difference between their L12 forms. For the stoichiometric Pd3Mn alloy, the solubilities appear to be approaching (H/Pd0.75Mn0.25) ) r ) 0.125 and 0.25 for the lps and L12 forms, respectively, which are the fractions of Pd6 interstices in each. The H content found for the disordered form is much smaller than the fraction of Pd6 interstices, 0.188. If only isolated Pd6 interstices were accessible to the H atoms, then the fraction would be ≈0.09 which is closer to the value approached (Figure 4) although the occupation is still much smaller. The greater H content of the L12 form of the Pd0.80Mn0.20 compared to the stoichiometric alloy can be explained if the Pd0.80Mn0.20 alloy has the same fraction of Pd6 interstices as the L12 form of Pd3Mn but it also has some Pd5 interstices. It
alloy
∆H°H
∆S°H, using ∆S°H, β ) 1 β ) fract. of Pd6 in eq 2
dis.
Pd0.85Mn0.15 -12.5 Pd0.80Mn0.20 -15.0 Pd3Mn -22 ( 2
-60 -66 -76 ( 5
-52 -55 -62 ( 5
lps
Pd0.85Mn0.15 -22 Pd0.80Mn0.20 -24 Pd3Mn -28
-60 -77 -69
-58
L12
Pd0.85Mn0.15 -20 Pd0.80Mn0.20 -23 Pd3Mn -26
-68 -66 -68
-56
was found for the lps form of the stoichiometric alloy that 15% of the Pd5 interstices were occupied.4 If this also holds for the Pd0.80Mn0.20 alloy, then the limiting H/(Pd0.80Mn0.20) ratio would be fPd6 + fPd5 ) 0.25 + 0.15 × 0.187 ) 0.28 which is consistent with the results (Figure 4). The rising portion of the isotherm for the L12 form of the Pd0.80Mn0.20 alloy (Figure 4) is not as steep as that for the Pd3Mn alloy indicating that some Pd5 interstices may become occupied in this region. The L12 form of the Pd3Mn alloy does not have Pd5 interstices, and its Pd4 interstices must have significantly higher energies than the Pd6 ones and therefore their occupation requires higher pH2 to occupy them which may explain the very steep rise in the pH21/2 - r plot in this region. The neutron diffraction results showing only the Pd6 interstices occupied were carried out on a Pd3MnD0.67 alloy or r ) 0.167 and apparently in the steeply rising part of the isotherm, and Pd4 interstices may be occupied in the hydride phase region (Figure 4). To see the differences more clearly between the three forms of Pd3Mn, hydrogen isotherms were measured at a higher temperature, 503 K (Figure 5), than in Figure 4. The solubility differences at pH2 ) 6.4 kPa show a marked increase from disordered f lps f L12, but at low pH2, the solubility in the lps form exceeds that of the L12 form which is consistent with values of ∆H°H (Table 1). The large solubility in the L12 form at 6.4 kPa is mainly due to the local environment of the interstices rather than to any global electronic effect since, as mentioned above, the electronic specific heats are similar for the ordered and disordered Pd3Fe alloy.8 This indicates that electronic models where H donates electrons to the d-band of palladium17 may not be a determining factor in the limiting solubilities of Pd alloys. Representative plots of RT ln((β - r)p1/2/r) against r for the three forms of the Pd3Mn alloy along with a plot at the same temperature for Pd are shown in Figure 6 (443 K). The slopes give g1, and the most notable feature is the very negative slope for the L12 form demonstrating that it has a significantly larger H-H attractive interaction than the others and pure Pd. Such plots for the Pd0.80Mn0.20 alloy are similar, and the slopes for the various forms are the same sequence as those for the Pd3Mn alloy. β has been taken as 1 but the same trend is also found if β is taken as the fraction of Pd6 interstices. The energy of H2 absorption can be divided into configurational and nonconfigurational terms.18 The latter is of elastic origin arising from a long-range H-H attractive interaction which does not depend on the configurations of the H atoms. The former is a chemical term arising from the interaction of the H atoms and vacancies.18 Although there is a small change in the elastic constants upon ordering, they should not be large enough to significantly affect the elastic H-H interaction energy which depends on the volume changes and the elastic constants9
8090 J. Phys. Chem. B, Vol. 110, No. 15, 2006
Luo et al.
Figure 5. Plot of the H2 isotherms for the three forms of the Pd3Mn alloy at 393 K.
Figure 7. H2 isotherms for the disordered Pd-Mn alloys together with the isotherm for the L12 form of the Pd3Mn alloy (303 K).
Figure 6. Plots of (∆µ°H + µEH(r)) ) RT ln[p1/2(1 - r)/r] against r for the three forms of the Pd3Mn alloy and for Pd at 443 K.
and therefore, to a first approximation, the nonconfigurational term would be expected to be independent of order in these alloys. On this basis, the large apparent H-H interaction for the L12 form of Pd3Mn must be attributed to the configurational energy term which leads to an H-H interaction. In the L12 form, the H atoms occupy only Pd6 interstices with a closest H-H distance of 0.390 nm whereas in pure Pd nearest neighbor interstices may also be occupied which are 0.276 nm apart. The larger H-H separation may be optimal for a net H-H attraction. At r ) 0.02 (373 K), ∆SH ) -22 J/K mol H for Pd and -46 J/K mol H for the Pd3Mn alloy (L12) which shows that there are significantly fewer interstices available in the latter. In this low r range, for pH2 to be very low as found for the L12 form of the Pd3Mn-H system (Figure 4), ∆HH must be quite negative since ∆SH is relatively unfavorable, and much of its exothermicity arises from the large H-H attractive interaction. For PdH, ∆SH is more favorable than for the alloy in this r range, but the H-H interaction is less negative in Pd-H perhaps because
some of the time H atoms occupy some nearest neighbor interstices. Thermodynamic values at infinite dilution of H are shown in Table 1 for the three forms of the Pd0.85Mn0.15, Pd0.80Mn0.20, and Pd3Mn alloys from p-c-T data. After correction for the fraction of Pd6 interstices, the ∆S°H values are reasonably close to -55 J/K mol H, that is, the value for Pd-H16 using eq 2. Figure 7 shows the marked difference between an isotherm for an ordered alloy, the L12 form of Pd3Mn, and the disordered alloys. H Solubilities during Heating and Cooling of a Pd0.75Mn0.25 Alloy. Figure 8 shows the solubilities of H2 in the initially disordered and the L12 form of the Pd3Mn alloy during heating from room temperature to ≈900 K (2 K/h) and also during its subsequent cooling. The data points at each temperature correspond to the solubilities measured at pH2 ) 133 Pa, which is in the dilute phase region, where the H solution should be nearly ideal for most all of the temperatures. The data are plotted as ln(H solubility) against 1/T, that is, as van’t Hoff-like plots. Deviation from a given linear plot indicates some change in the ordering. The initial solubility in the disordered form is the smallest of the three forms, and its solubility is seen to increase at about 550 K where it undergoes ordering to the lps form and then decreases at ≈803 K where it starts to disorder. When this alloy is subsequently cooled, it starts to order to the lps form at slightly below 803 K and then, during its subsequent cooling, it follows the van’t Hoff relation for the lps form. The L12 form has smaller H2 solubilities at low temperatures than the lps form in this dilute region; this was also found by measurements of isotherms for these forms (Figure 5). Upon heating, the L12 form starts to transform to the lps form at a somewhat greater temperature 670 K than the disordered alloy transforms to lps, 550 K, indicating that the transition: L12 f lps has a smaller driving force than the disordered f lps transition. This agrees with the results in ref 19.
Pd-Mn Alloys Part 2
J. Phys. Chem. B, Vol. 110, No. 15, 2006 8091
Figure 9. Calorimetrically determined ∆HH values as a function of r for the Pd0.80Mn0.20 alloy. Figure 8. Dilute phase H2 solubilities as a function of temperature during heating and cooling for the three forms of the Pd3Mn alloy plotted according to van’t Hoff relations. The direction of the arrows indicates heating or cooling, and the empty and filled symbols indicate heating and cooling, respectively.
The L12 form undergoes disordering during heating at ≈803 K (Figure 8) and then, during its subsequent cooling, it reorders to the lps form. Figure 8 illustrates the sensitivity of H2 solubilities to the degree of order. If the H solution is ideal, then the slopes and intercepts of the plots of ln r against 1/T in Figure 8 correspond to -∆H°H/R and (∆S°H/R + ln pH21/2 + ln β), respectively. This follows from the law of ideal solubility
RT ln pH21/2 ) ∆µ°H + RT ln r + RT ln β
(2)
and, when pH21/2 is constant as in Figure 8, the plots give the thermodynamic parameters at infinite dilution. The slopes in Figure 8 give ∆H°H ) -26.7 kJ/ mol H (lps), -23.6 kJ/ mol H (disordered), and -24.2 kJ/mol H (L12). The trend of the ∆H°H values derived from Figure 8 for the three forms are similar to those in Table 1, but they differ somewhat because those in the table are based on the average of several determinations for each. The ∆S°H values derived from Figure 8 are -72.4 (lps), -77.7 J/K mol H (disordered), and -66.7 (L12) for β ) 1 in eq 2. These entropies are in reasonably good agreement with those in Table 1 which are again based on more data. Calorimetric Results Relative partial enthalpies, ∆HH, have been measured calorimetrically, and the accompanying ∆SH values have been determined as a function of r using ∆HH and pH2 at the corresponding r values. ∆HH and ∆SH are negative for H2 absorption and positive for desorption. If ∆HH and ∆SH are
constant over a significant range of r, then this indicates the presence of a two-phase coexistence region. Pd0.85Mn0.15 Alloy. Only the disordered form of this stoichiometry has been measured calorimetrically, and it is reported in part 1. Pd0.80Mn0.20 Alloy. Partial enthalpies as a function of r are shown in Figure 9 for the three different forms of this alloy. There are clearly no plateau regions for the disordered and lps forms. For the latter, there is a maximum in |∆HH| at about r ) 0.05 and then the values decline steadily with r falling to |∆HH| ) 7.5 kJ/mol H at r ) 0.23. The enthalpies for the L12 form are reasonably constant from r ≈ 0.02 to about 0.19 after which there is a sharp falloff. Isotherms measured at higher temperatures, ≈373 to 498 K, exhibit nearly constant pH2 from about r ) 0.04 to 0.16, and plots of ln pH2 against 1/T for this region evaluated at several different r values give approximately constant |∆H| values indicative of a two-phase region. On this basis, the L12 form of this alloy appears to have a two-phase coexistence region, or plateau, at e373 K. The |∆HH| values are generally larger for the L12 structure than for the other two forms by about 11 kJ/mol H except in the very dilute region, which is not shown in Figure 9, where solution in the lps structure is more exothermic (Table 1). It can be assumed that the very negative enthalpies (Figure 9) reflect the occupation of only Pd6 interstices for the L12 form.10 ∆SH values can be calculated from ∆HH and pH2 using
∆SH ) ∆HH/T - R ln pH21/2
(3)
The ∆SH values derived from eq 3 are for the reaction with H2 at 1 bar. At low H contents, no ∆SH values (Figure 10) have been given for the L12 form because of the low pH2 and because the ∆HH values also have considerable scatter (Figure 9). The plateau value, |∆Splat| ) 47 J/K mol H, has been determined from a van’t Hoff plot of isotherm measurements at higher
8092 J. Phys. Chem. B, Vol. 110, No. 15, 2006
Luo et al.
Figure 10. Calorimetrically determined ∆SH values using eq 3 as a function of r for the Pd0.80Mn0.20 alloy.
temperatures (373-433 K). For r g 0.2, interstices other than those for the Pd6 may be occupied for the L12 form as indicated by the fall of |∆SH| for r g 0.2. Pd3Mn Alloy. This stoichiometric composition is the most interesting one because the fraction of each type of interstice is known for the completely ordered structures. The |∆HH| values are shown in Figure 11 for the three forms. There is considerable scatter for the plateau region of the L12 alloy. A value of 32.4 kJ/ mol H was obtained with a different Pd3Mn alloy preparation which is slightly greater than that shown in Figure 11. The value from the van’t Hoff plot of absorption isotherms is 32.5 kJ/ mol H which is quite close to the calorimetric value. The |∆H| values increase in magnitude as disordered < lps < L12 forms. There are regions of r at relatively high pH2 for each form where |∆HH| falls off nearly linearly and this starts at a relatively high r value, ≈0.2, for the L12 form. ∆SH values for the L12 form (Figure 12) could not be determined for r e 0.18 because of the small pH2 at 303 K, for example, 0.20 force occupation of Pd4 interstices even though they are energetically
Figure 11. Calorimetrically determined ∆HH values as a function of r for the Pd3Mn alloy.
Figure 12. Calorimetrically determined ∆SH values using eq 3 as a function of r for the Pd3Mn alloy.
unfavorable. The large decrease in |∆HH| values reflects occupation of some Pd4 interstices. Both the Pd6 and Pd4 interstices become occupied in this region, and the fraction of the former decreases as the latter increases leading to the observed changes of |∆HH| and |∆SH| with r. The ∆SH - r relations for the lps and disordered forms are shown in the low H content region (Figure 12) because of the
Pd-Mn Alloys Part 2
J. Phys. Chem. B, Vol. 110, No. 15, 2006 8093 for the L12 form of the Pd0.80Mn0.20 alloy. This greater H-H attraction accounts for the very low plateau pH2 of the L12 form and its small THS relative to Pd-H. The question of why the H-H attractive interaction is so negative for the L12 form is important for the understanding of M-H systems. It is surely related to the interstitial sites occupied by the H atoms in the L12 form, that is, they are not nearest neighbors but next nearest neighbors which must lead to a large net attractive interaction. A general result is that alloys with the same stoichiometry have larger H capacities in the ordered than in the disordered state illustrating the important role of the local environment as opposed to a global electronic effect such as d-band filling. Acknowledgment. We wish thank Drs. H. Noh and T. Kuji for obtaining some of these data. The NSF is thanked for financial support of some of this research.
Figure 13. Isotherms showing the terminal hydrogen solubilities (THS) (arrows) at 373 K for the L12 form of Pd3Mn, Pd, and a Pd0.90Ag0.10 alloy.
higher pH2. There is a greater difference between the L12 and the other two forms for the Pd3Mn than for the Pd0.80Mn0.20 alloy. The appearance of a plateau in the L12 form of the Pd3Mn alloy at quite low pH2 is consistent with its small terminal hydrogen solubility (THS) because both depend on the H-H attractive interaction. The THS for the L12 form is compared to Pd-H and to a Pd0.90Ag0.10-H alloy in Figure 13. The Pd0.90Ag0.10 alloy is an expanded alloy with a lower plateau pressure than Pd.1 In the regular interstitial solution model, RT ln THS ) (1/2)h1 22 and h1 is the linear term in the enthalpy for the polynomial expansion of HEH in r and g1 ) h1 - Ts1. This gives a direct relation between the THS and the H-H interaction enthalpy which seems to be valid qualitatively because the latter is very negative and the THS is small for Pd3Mn (L12). Conclusions Very significant thermodynamic differences have been found between H2 solution in the three forms of the Pd-Mn alloys, that is, L12, lps, and disordered for the stoichiometric alloy, Pd3Mn, and also for the nonstoichiometric one, Pd0.80Mn0.20. The differences between the three forms are greatest for the stoichiometric alloy. The attractive H-H interaction is much more negative for the L12 form of the Pd3Mn alloy than for Pd-H or for the other forms of this alloy. It is also very negative
References and Notes (1) Sakamoto, Y.; Chen, F.; Ura, M.; Flanagan, T. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 807. (2) Kren, K.; Kadar, G. Phys. Lett. A 1969, 29, 340. (3) Iwasaki, H.; Okamura, K.; Ogawa, S. J. Phys. Soc. Jpn. 1971, 31, 497. (4) Ahlze`n, P.; Andersson, Y.; Tellgren, R.; Rodic, D.; Flanagan, T.; Sakamoto, Y. Z. Phys. Chem. N. F. 1989, 163, 213. (5) Flanagan, T.; Craft, A.; Kuji, T.; Baba, K.; Sakamoto, Y. Scr. Met. 1987, 20, 1745. (6) Baba, K.; Niki, Y.; Sakamoto, Y.; Flanagan, T.; Craft, A. Scr. Met. 1987, 21, 299. (7) Flanagan, T.; Sakamoto, Y. Platinum Met. ReV. 1993, 37, 26. (8) Bechman, C.; Wallace, W. E.; Craig, R. S. Philos. Mag. 1973, 37, 1249. (9) Alefeld, G. Ber. Bunsen-Ges. Phys. Chem. 1972, 76, 746. (10) O ¨ nnerud, P.; Andersson, Y.; Tellgren, R.; Nordblad, P.; Boure´e, F.; Andre´, G. Solid State Commun. 1997, 101, 433. (11) Phutela, R.; Kleppa, O. J. Chem. Phys. 1982, 76, 1525. (12) Ke, X.; Kramer, G.; Lo´vvik, O. J. Phys.: Condens. Mater. 2004, 16, 6267. (13) Flanagan, T.; Luo, W.; Clewley, J. J. Less-Common Met. 1991, 172-174, 42. (14) Baba, K.; Niki, Y.; Sakamoto, Y.; Flanagan, T. J. Alloys Compd. 1991, 172-174, 246. (15) Flanagan, T.; Craft, A.; Niki, Y.; Baba, K.; Sakamoto, Y. J. Alloys Compd. 1992, 184, 69. (16) Oates, W.; Flanagan, T. Prog. Solid State Chem. 1981, 13, 193. (17) Brodowsky, H.; Poeschel, E. Z. Phys. Chem. 1965, 43, 1965. (18) Mohri, T.; Oates, W. J. Alloys Compd. 2003, 330-332, 14. (19) Baba, K.; Niki, Y.; Sakamoto, Y.; Craft, A.; Flanagan, T. J. Mater. Sci. Lett. 1988, 7, 1160. (20) Noh, H.; Clewley, J.; Flanagan, T.; Craft, A. J. Alloys Compd. 1996, 240, 235. (21) Zhang, W.; Luo, S.; Flanagan, T. J. Alloys Compd. 1999, 293295, 1. (22) Oates, W.; Flanagan, T. J. Mater. Sci. 1981, 16, 3235.
