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Stoichiometries and interstitial site occupation in the hydrides of zrni and other isostructural intermetallic compounds
177
Journal of the Less-Common Metals, 75 (1980)177 - 185 0 Elsevier Sequoia S.A.,Lausanne - Printed in the Netherlands
~TOICHI~METRI~S AND INTERSTITIAL SITE OCCUPATION IN THE HYDRIDES OF ZrNi AND OTHER ISOSTRUCTURAL INTERMETALLIC COMPOUNDS
D. G. WESTLAKE Me~erials Science Division,
Argonne
rational
Laboratory,
Argonne,
Klf. 60439 (U.S.A.)
(Received January 3, 1980)
Summary Criteria of interstitial hole size and H-H interatomic distance were used to predict the stoichiometries and the hydrogen-occupied sites in hydrides of the intermetallic compound ZrNi and other isostructural compounds. With only these simple considerations of geometry it was possible to rationalize most of the experimental observations available for such compounds. A number of neutron diffraction experiments are recommended to test some of the predictions presented.
1. Introduction Switendick [lf has recently studied the relation between minimum H-H interatomic distance and the stability of metal hydrides. His theoretical considerations predict a minimum distance of about 2.1 ,4 for a stable hyd~de and his review of the st~ctures of known hydrides seems to confirm the prediction. Lundin et ~1. [Z] have shown a correlation between the size of the holes at tetrahedral interstitial sites and the stability of hydrides. They considered both AB5 and AB intermetallic compounds. For both cIasses of compounds they found that an increase in hole size was accompanied by greater stability. In the present work we applied these two principles to the intermetallic compound ZrNi in order to predict which stoichiometric hydrides should exist and which interstitial sites should be occupied in each. Several isostructural hydrides of other intermet~lic compounds were also considered. Where possible the predictions are compared with experimental obse~ations. These include both pressure-composition-temperature (p-C-2’) equilibria and determinations of crystal structure.
Fig. 1. Structure of ZrNi [3,4] with examples of the interstitial sites possibly available for occupation by hydrogen shown as solid symbols: 6, a sites;A, b sites; v, c sites; 0, d sites; *, e sites, The symbols 0 and •Irepresent zirconium and nickel respectively. As an aid in perspective, four face centers are shown as 0.
2. Structure
of ZrNi and its hydrides
The structure of ZrNi [3,4] is shown in Fig. 1. The lattice parameters are a = 3.258 A, b = 9.941 A and c = 4.094 A [4]. Except for small changes in positional parameters and a lattice expansion, the metal sublattice remains unchanged with addition of hydrogen, even at H/Zr ratios as great as 2.98 [ 3 - 61. For H/Zr = 2.7, Korst [4] using X-ray diffraction has determined the structure of the metal sublattice to be orthorhombic (space group Cmcm with a = 3.53 A, b = 10.48 a and c = 4.30 A). Peterson et al. [5] have been able to locate the hydrogen atoms from neutron diffraction experiments. The following refinements of the positional parameters for this compound have been suggested by Irodova et al. [6] : four nickel and four zirconium atoms occupy the positions (0 0 0;f f 0) + (0 y i) with yNi = - 0.429 and yzr = - 0.140; four hydrogen atoms are located in sites equivalent to (0 y 4 ) with y = 0.067; eight hydrogen atoms are located in sites equivalent to (0 y z) with y = - 0.312 and z = 0.509. The metal sublattices in the trihydrides of HfCo and HfNi, both of which will be discussed later, are isostructural with that of ZrNi and the lattice parameters (as measured in air) for all three compounds are nearly identical [4,7] . This latter fact is probably not surprising because the relative differences in atomic radii between hafnium and zirconium and between nickel and cobalt are both less than 1%. As mentioned previously, the metal sublattice expands as hydrogen is added. According to Korst [4] , the absorption of hydrogen by ZrNi to give ZrNiH, ., results in a lattice expansion which can be described by Au/a = 8.3%, Ah/b = 5.4% and AC/C = 5.0%. If the crude approximation that the increase in lattice parameter is proportional to the hydrogen concentration is made, then the parameters for ZrNiH would be a = 3.359 A, b = 10.141 A and c = 4.170 8. In the calculations of the H-H distances and the radii of interstitial holes we used these lattice parameters and the positional parameters specified for ZrNiH,. In order to estimate the radii of holes we used the approximations 1.60 and 1.25 _&for the atomic radii of zirconium and nickel respectively.
179
TABLE
1
Hole sizes and metal-hydrogen and H-H designated interstitial sites in ZrNiH Sitea
Number of sites per Zr atom
Nearest-neighbor metal atoms (Fig. 1)
:
1
1, l’, 1, l’,
:
2
e
2
1, 2, 394 10 2’, 3’, 4’, 3’, 9, 4’, 10
2, 3 7 5, 6,
aSites a to e refer to Fig. 1. bNumbers in parentheses denote
3. The monohydride
nearest-neighbor
the number
Interatomic
distances
for hydrogen
Hole
distanceb
radius
(A)
(A) Zr-H
Ni-H
H-H
2.22(4) 2.23( 2) 2.03( 1) 2.02(3) 1.90(2) 1.92(2)
-1.68( 2)
2.49 2.76
zo.43 0.62
1.67(l) 1.55( 2) 1.57(2)
1.08 1.95
0.30 0.42
1.84
0.32
of metal
in
atoms
at the given distance.
of ZrNi
In Table 1 we show our calculated H-H distances and hole sizes for the occupation of interstitial sites represented by solid symbols in Fig. 1. For both d and e sites the hole radii are shorter than those often observed [ 21 (0.37 - 0.39 A) f or stable hydrides, but for a, b and c the hole radii are more than adequate. Each of the species a and b has exactly the right number of sites, i.e. one site per zirconium atom, and the H-H distances are much greater than the criterion of 2.1 A. Occupation of the c sites cannot be ruled out solely on the basis of the nearest-neighbor H-H distance of 1.95 A. This is because there are twice as many sites as are required. If each filled site had its one nearest-neighbor site empty, stoichiometric ZrNiH could still be realized. The next nearestneighbor site, however, lies at a distance of only 2.03 A, which is also less than the required value. Because of the large hole radius, relaxation of the hydrogen atom to an off-center position could easily allow for an H-H distance of 2.1 A. The shortest H-H distances for a and b sites are much greater, however, and these sites would seem to be favored over c sites. The a site obviously rates highest on both criteria and may have still another factor favoring its occupation in ZrNiH. Because zirconium metal absorbs hydrogen exothermically whilst the reaction with nickel is endothermic, it may be important that all four metal atoms at this tetrahedrally coordinated site are zirconium atoms. Furthermore, both the H-H distance and the hole radius for a sites (Table 1) are greater than those of the very stable dihydride of zirconium (2.38 and 0.47 8, respectively). However, it is conceivable that for the species a the hole radius could be too large, i.e. the mean time of stay for hydrogen in such a site may be very short.
180
From the foregoing simple considerations it is predicted that a monohydride of ZrNi exists with full occupancy of a or b sites. Further, it is predicted from the following that little or no solubility for hydrogen will be observed in ZrNiH if the a site is occupied. Hole size (Table 1) augurs against the occupation of either d or e, and H-H distances preclude coincidental occupation of either a and b or a and c. The a-b and a-c distances are only 1.57 and 1.34 A respectively. However, if b sites are occupied in ZrNiH, then occupation of some c sites could be allowed because the b-c distance is 2.42 A. Studies of P-C-T equilibria indicate the existence of monohydrides for both ZrNi [3] and HfNi [7]. In both cases the solubility for hydrogen in the monohydride appears to be negligible in accord with the expectations for occupation of a sites. To our knowledge there has been no experimental determination of the site occupied by hydrogen in these compounds. 4. The dihydride of ZrNi If a dihydride of ZrNi were to exist, according to the approximation described earlier, it can be calculated that a = 3.46 A, b = 10.34 A and c = 4.25 A, The expansion with respect to ZrNiH is not nearly great enough to allow coincidental occupation of a and b sites, the combination of which would give the necessary two sites per zirconium atom. The necessary number of sites could also be provided by either d or e sites. Whilst the hole radii for d and e sites would be 0.34 and 0.36 A respectively (nearly adequate for a stable hydride [2] ), full occupation of either d or e sites would not be likely because newest-neighbor H-H distances would be only 1.07 and 1.91 A respectively. The c sites, with two sites per zirconium atom, would seem to be the only other possibility. The hole radius of 0.48 A is very adequate but the H-H distance would be only 1.95 A. From these considerations it is predicted that there should be no dihydride of ZrNi or of other isostructural intermetallic compounds. The conclusion that there should be no dihydride of ZrNi is in full accord with the experimental evidence. P-C-Z’ equilibria provide no indication for a dihydride of ZrNi [3] or of HfNi [7]. The prediction is not contradicted by the known formation of ZrCoH, [8] because, whilst ZrCo is obviously a related compound, it is not isostructural with ZrNi; ZrCo has the CsCl structure. In fact with the known lattice parameters for ZrCo, sites can be readily selected, either octahedral or tetrahedral, for which both criteria being used here are easily met. Thus with only geometric considerations, the existence of ZrCoH, could have been predicted, just as it has been predicted that neither ZrNi nor the isostructural compound HfNi should form a dihydride. 5. The trihydride of ZrNi The estimated expanded lattice parameters of ZrNiHa are a = 3.561 A, b = 10.541 A and c = 4.322 A. From these, we calculated the H-H distances
TABLE 2 Hole sizes and H-H nearest-neigh bar distances for hydrogen in designated interstitial sites in ZrNiH, Sitea
Hole radius (A)
H-Hdistance
(.&)
a
b
C
d
e
:
eO.55 0.72
I.61 2.87
1.61 2.58
2.46 1.43
2.39 2.23
2.67 1.52
Tt e
=0.50 0.38 0.39
2.23 1.43 2.67
2.46 2.39 1.52
2.08 1.30 2.21
1.30 1.07 1.38
2.21 1.38 1.97
%ites a to e refer to Fig. 1
and the hole radii listed in Table 2. It can be seen that, at this concentration of hydrogen, the hole radius for d and e sites, 0.38 8, is that typically observed in stable hydrides. Still, the radii of these sites are considerably smaller than those of the other three sites. Furthermore, the H-H distance for nearest-neighbor d sites is only 1.07 .& and for e sites it is somewhat less than Switendick’s ]l] minimum value of 2.1 8. The trihydride probably requires, therefore, occupation of some combination of a, b and c sites. As was pointed out earlier, however, occupation of a sites precludes occupation of the other two. It can only be concluded that the trihydrides of ZrNi and other isostructural intermetallic compounds must have all b and c sites occupied by hydrogen even though the H-H distance for c sites barely meets the requ~ement. Again, the foregoing conclusion, reached from consideration of geometry only, is in complete accord with reported experimental results. The positional parameters for hydrogen in ZrNiH, [ 5,6], given in Section 2, and for hydrogen in ZrCoH, 161 are those of the b and c sites. 6. Hyperstoichiomet~
in the trihydride of ZrNi
There is ample evidence in the literature from which it can be concluded that some stoichiometric hydrides have considerable solubility for still more hydrogen. For example GdHa,, at 400 “C and at a hydrogen pressure of 7 X lo2 Pa absorbs hydrogen to a ~oncen~ation of GdHs t5 when the pressure is increased by a factor of 10 [9]. ZrCoHs at 365 “C’increases its hydrogen content to ZrCoH2.as when the pressure changes from 1.3 X lo5 to 4.3 X lo5 Pa [8]. No phase transformation is involved in either case. We will consider now the likelihood of hypers~ichiomet~ in the trihydride of ZrNi. To do this we will begin by examining the geometry of a known hyperstoichiometric hydride GdH2 fx. GdH2 has the fluorite structure [9] ; essentially all the tetrahedral ft) interstices of the f,c.e. metal sublattice are filled with hydrogen atoms. As the hydrogen pressure is increased at a given temperature more hydrogen atoms are absorbed in solid solution, but these
32
34
HYDROGEN CONCENTRATION lH/Zf[tlf]l
Fig. 2. Pressure-composition isotherms for the systems ZrNi-H, HfNi-H and HfCo-H. The broken lines are postulated.
must be accommodated in octahedral (0) sites. The H-H distances in GdH,,, can be readily calculated from the lattice parameter given in ref. 9. For t-t sites the shortest distance is 2.65 8, but for o--t sites the distance is only 1.8’7 8. Seemingly, then, some H-H distances shorter than 2.1 a are tolerated for x less than 0.15. For x greater than 0.15 precipitation of a new phase, hexagonal GdH,, is initiated. In this compound all t and o sites are occupied; each hydrogen occupying a t site has three neighbors in o sites at a distance 2.26 A and one neighbor in a t site at a distance 1.97 a, still slightly less than that predicted by Switendick [l] for stable hydrides. These values, however, are the distances between centers of interstitial sites. We estimate the radius of the t site in GdHs to be quite large, 0.57 a, so the hydrogen atoms could relax to off-center positions resulting in minimum distances greater than 2.1 A, in conformity with Switendick’s rule. In the case of ZrNiHs, it can be seen from Table 2 that partial occupancy of a sites in addition to full occupancy of b and c sites would lead to some H-H distances as short as 1.43 SI. Similarly, the filling of d or e sites would result in H-H distances of only 1.30 and 1.52 a respectively. Obviously these are very much shorter than the calculated value of 1.87 ,& in hyperstoichiometric GdHs and the minimum distance in a stable hydride (2.1 a). Such sites would seemingly not be occupied except under extremely high Hz pressure, so little, if any, hydrogen solubility is expected in ZrNiH, . As discussed later, the available P-C-T results seem to provide some, but not complete, conflation. In Fig, 2 we show pressure-composition isotherms for ZrNi-H at 100 “C and for HfNi-H at 50 “C. With increasing pressure both curves appear in agreement with our to approach the composition H/Zr = 3 asymptotically,
183
expectation. Also plotted in Fig. 2, however, are three other pieces of information. One of these is the isotherm for HfCo-H. Obviously no phase change is indicated over a wide range of compositions above, as well as below, 3.0. This combined with the fact that the metal sublattice of HfCoHs is reported [7] to be isostructural with that of ZrNiH,, would seem to constitute a contradiction of our expectation that occupation of all b and c sites precludes the easy occupation of other sites. However, we do not know whether b and c sites are occupied in HfCoH,; we are unaware of any neutron diffraction experiments on this compound. HfCo has the CsCl structure and the P-C-T plot [7] suggests that the first hydride forms with an H/Hf ratio somewhat greater than 2. It is during hydride formation that the metal sublattice transforms to the CrB-type structure [ 71. We would like to suggest the possibility that this compound may be the hypostoichiometric variation of HfCoH, instead of HfCoH,. If the positional parameters are somewhat different for the metal atoms in this sublattice than they are in ZrNiH,, it is not inconceivable that a combination of c and e sites could become occupied. This combination affords four sites per zirconium atom and could, therefore, account for the range of composition observed (Fig. 2). Until the complete structure of HfCoH, has been specified, attempts to explain the observed P-C-T behavior on the basis of geometry are strictly conjectural.
7. Higher hydrides
of ZrNi
As intimated in the preceding section, a careful examination of Table 2 leads us to suspect that, if a higher hydride of ZrNi forms without a transformation of the metal sublattice, that hydride would probably be ZrNiH*. The nearest-neighbor distances a-b, a-c, b-e, c-d, d-d and d-e are all much too short to allow full occupation of these combinations of sites. In addition, each of the species a and b offers only one site per zirconium atom. Occupation of a combination of c and e sites appears to be most likely. The hole radii are large, 0.56 i$ for c and 0.43 a for e. The H-H distances for c-c, c-e and e-e are 1.95, 2.33 and 2.04 a respectively. When the hydrogen atoms are allowed to relax to off-center positions the criterion of 2.1 a is easily met with the effective hole radii being reduced only slightly, to 0.51 a for c sites and to 0.42 a for e sites. It is tempting to postulate that ZrNiH, does form at high H, pressure, because its existence would help to explain two pieces of information plotted on Fig. 2. First, let us consider the circle, which represents the reported [7] preparation of HfNiH,., at 50 “C and an Hz pressure of 2 X lo6 Pa. Given the shape of the experimental P-C-T curve [ 71 for HfNi-H, we submit that one logical explanation for the seeming mismatch between the point and the curve is that the formation of a higher hydride has been initiated. This proposal is indicated by the broken line connecting the point to the experimental P-C-T curve. The point would represent equilibrium between the trihydride and a higher hydride. Relieving the H2 pressure might very well allow evolution of hydro-
184
gen from the higher hydride, so that X-ray examination in air at room temperature would reveal no evidence of its prior existence. The experimental P-C-T plot for ZrNi-H at 100 “C, shown in Fig. 2 as a solid line, was mentioned in Section 6. Up to a pressure of 8 X lo4 Pa there is no indication that H/Zr ratios in excess of 3.0 can be achieved. Baron et al. [lo] , however, have reported the preparation of ZrNiHs.s, at 25 “C with an Hz pressure of 4 X lo5 Pa. This is shown as a square (Fig. 2). One possible explanation is represented as a broken curve. The asterisk is to remind the reader that the curve is only postulated. Whilst no experimental results have been provided in refs. 3 and 10 for the temperature 25 Y!, those having experience with P-C-T diagrams will recognize that the broken curve, whilst not unequivocally indicated, is not an unreasonable extrapolation from the results reported [3] for 250,200 and 100 “C. The reported [lo] ZrNiHs.,, could be, therefore, a mixture of ZrNiHs and a higher hydride. Baron et al. [lo] have observed the lattice parameters of their hydride, as measured in air, to be the same as those reported by Korst [4] for ZrNiH,., . By way of explanation, they have speculated that the initial product might have evolved some of its hydrogen between its preparation and the X-ray measurements. We conclude that, whilst no concrete evidence for the existence of a compound ZrNiH, _ Y has been reported, its postulated existence does not lead to any contradiction of the known P-C-T results and in fact allows some heretofore anomalous results to be explained.
8. Conclusion For intermetallic compounds known to react exothermically with hydrogen it appears that, armed only with the geometry of the metal sublattice, criteria of hole size and minimum H-H distance can be used to make some reasonable predictions of the occurrence of specific hydride stoichiometries and of the interstitial sites occupied by hydrogen. Neutron diffraction experiments should be performed on the monohydrides of ZrNi and HfNi to test the present prediction of hydrogen site selection. Similar studies on the hyperstoichiometric trihydrides of ZrNi and HfCo would be equally valuable.
Acknowledgment This work was supported
by the U.S. Department
of Energy.
References 1 A. C. Switendick, prospects, SAND
Theoretical study 78-0250, 1978.
of hydrogen
in metals:
current
status
and further
18.5
2 3 4 5 6 7 8 9 10
C. E. Lundin, F. E. Lynch and C. B. Magee, J. Less-Common Mel., 56 (1977) 19. G. G. Libowitz, H. F. Hayes and T. R. P. Gibb, Jr,, J. Phys. Chem., 62 (I 958) 76. W. L. Korst, J. Phys. Chem., 66 (1962) 370. S. W. Peterson, V. N. Sadana and W. L. Korst, J. Phys. (Paris), 25 (1964) 451. A. V. Irodova, V. A. Somenkov, S. Sh. Shil’shtein, L. N. Padurets and A. A. Chertkov, Sou. Phys. - Crystollogr., 23 (1978) 591. H. M. Van Essen and K. H. J. Buschow, J. Less-Common Met., 64 (1979) 277. H. W. Newkirk, A literature study of metallic ternary and quaternary hydrides, UCRL-51244 RQU. 1, 1975. G. E. Sturdy and R. N. R. Mulford, J. Am. Chem. Sot.. 78 (1956) 1083. J.-L. Baron, A. Virot and J. delaplace, J. Nucl. Mafer., 83 (1979) 286.
Journal of the Less-Common Metals, 75 (1980)177 - 185 0 Elsevier Sequoia S.A.,Lausanne - Printed in the Netherlands
~TOICHI~METRI~S AND INTERSTITIAL SITE OCCUPATION IN THE HYDRIDES OF ZrNi AND OTHER ISOSTRUCTURAL INTERMETALLIC COMPOUNDS
D. G. WESTLAKE Me~erials Science Division,
Argonne
rational
Laboratory,
Argonne,
Klf. 60439 (U.S.A.)
(Received January 3, 1980)
Summary Criteria of interstitial hole size and H-H interatomic distance were used to predict the stoichiometries and the hydrogen-occupied sites in hydrides of the intermetallic compound ZrNi and other isostructural compounds. With only these simple considerations of geometry it was possible to rationalize most of the experimental observations available for such compounds. A number of neutron diffraction experiments are recommended to test some of the predictions presented.
1. Introduction Switendick [lf has recently studied the relation between minimum H-H interatomic distance and the stability of metal hydrides. His theoretical considerations predict a minimum distance of about 2.1 ,4 for a stable hyd~de and his review of the st~ctures of known hydrides seems to confirm the prediction. Lundin et ~1. [Z] have shown a correlation between the size of the holes at tetrahedral interstitial sites and the stability of hydrides. They considered both AB5 and AB intermetallic compounds. For both cIasses of compounds they found that an increase in hole size was accompanied by greater stability. In the present work we applied these two principles to the intermetallic compound ZrNi in order to predict which stoichiometric hydrides should exist and which interstitial sites should be occupied in each. Several isostructural hydrides of other intermet~lic compounds were also considered. Where possible the predictions are compared with experimental obse~ations. These include both pressure-composition-temperature (p-C-2’) equilibria and determinations of crystal structure.
Fig. 1. Structure of ZrNi [3,4] with examples of the interstitial sites possibly available for occupation by hydrogen shown as solid symbols: 6, a sites;A, b sites; v, c sites; 0, d sites; *, e sites, The symbols 0 and •Irepresent zirconium and nickel respectively. As an aid in perspective, four face centers are shown as 0.
2. Structure
of ZrNi and its hydrides
The structure of ZrNi [3,4] is shown in Fig. 1. The lattice parameters are a = 3.258 A, b = 9.941 A and c = 4.094 A [4]. Except for small changes in positional parameters and a lattice expansion, the metal sublattice remains unchanged with addition of hydrogen, even at H/Zr ratios as great as 2.98 [ 3 - 61. For H/Zr = 2.7, Korst [4] using X-ray diffraction has determined the structure of the metal sublattice to be orthorhombic (space group Cmcm with a = 3.53 A, b = 10.48 a and c = 4.30 A). Peterson et al. [5] have been able to locate the hydrogen atoms from neutron diffraction experiments. The following refinements of the positional parameters for this compound have been suggested by Irodova et al. [6] : four nickel and four zirconium atoms occupy the positions (0 0 0;f f 0) + (0 y i) with yNi = - 0.429 and yzr = - 0.140; four hydrogen atoms are located in sites equivalent to (0 y 4 ) with y = 0.067; eight hydrogen atoms are located in sites equivalent to (0 y z) with y = - 0.312 and z = 0.509. The metal sublattices in the trihydrides of HfCo and HfNi, both of which will be discussed later, are isostructural with that of ZrNi and the lattice parameters (as measured in air) for all three compounds are nearly identical [4,7] . This latter fact is probably not surprising because the relative differences in atomic radii between hafnium and zirconium and between nickel and cobalt are both less than 1%. As mentioned previously, the metal sublattice expands as hydrogen is added. According to Korst [4] , the absorption of hydrogen by ZrNi to give ZrNiH, ., results in a lattice expansion which can be described by Au/a = 8.3%, Ah/b = 5.4% and AC/C = 5.0%. If the crude approximation that the increase in lattice parameter is proportional to the hydrogen concentration is made, then the parameters for ZrNiH would be a = 3.359 A, b = 10.141 A and c = 4.170 8. In the calculations of the H-H distances and the radii of interstitial holes we used these lattice parameters and the positional parameters specified for ZrNiH,. In order to estimate the radii of holes we used the approximations 1.60 and 1.25 _&for the atomic radii of zirconium and nickel respectively.
179
TABLE
1
Hole sizes and metal-hydrogen and H-H designated interstitial sites in ZrNiH Sitea
Number of sites per Zr atom
Nearest-neighbor metal atoms (Fig. 1)
:
1
1, l’, 1, l’,
:
2
e
2
1, 2, 394 10 2’, 3’, 4’, 3’, 9, 4’, 10
2, 3 7 5, 6,
aSites a to e refer to Fig. 1. bNumbers in parentheses denote
3. The monohydride
nearest-neighbor
the number
Interatomic
distances
for hydrogen
Hole
distanceb
radius
(A)
(A) Zr-H
Ni-H
H-H
2.22(4) 2.23( 2) 2.03( 1) 2.02(3) 1.90(2) 1.92(2)
-1.68( 2)
2.49 2.76
zo.43 0.62
1.67(l) 1.55( 2) 1.57(2)
1.08 1.95
0.30 0.42
1.84
0.32
of metal
in
atoms
at the given distance.
of ZrNi
In Table 1 we show our calculated H-H distances and hole sizes for the occupation of interstitial sites represented by solid symbols in Fig. 1. For both d and e sites the hole radii are shorter than those often observed [ 21 (0.37 - 0.39 A) f or stable hydrides, but for a, b and c the hole radii are more than adequate. Each of the species a and b has exactly the right number of sites, i.e. one site per zirconium atom, and the H-H distances are much greater than the criterion of 2.1 A. Occupation of the c sites cannot be ruled out solely on the basis of the nearest-neighbor H-H distance of 1.95 A. This is because there are twice as many sites as are required. If each filled site had its one nearest-neighbor site empty, stoichiometric ZrNiH could still be realized. The next nearestneighbor site, however, lies at a distance of only 2.03 A, which is also less than the required value. Because of the large hole radius, relaxation of the hydrogen atom to an off-center position could easily allow for an H-H distance of 2.1 A. The shortest H-H distances for a and b sites are much greater, however, and these sites would seem to be favored over c sites. The a site obviously rates highest on both criteria and may have still another factor favoring its occupation in ZrNiH. Because zirconium metal absorbs hydrogen exothermically whilst the reaction with nickel is endothermic, it may be important that all four metal atoms at this tetrahedrally coordinated site are zirconium atoms. Furthermore, both the H-H distance and the hole radius for a sites (Table 1) are greater than those of the very stable dihydride of zirconium (2.38 and 0.47 8, respectively). However, it is conceivable that for the species a the hole radius could be too large, i.e. the mean time of stay for hydrogen in such a site may be very short.
180
From the foregoing simple considerations it is predicted that a monohydride of ZrNi exists with full occupancy of a or b sites. Further, it is predicted from the following that little or no solubility for hydrogen will be observed in ZrNiH if the a site is occupied. Hole size (Table 1) augurs against the occupation of either d or e, and H-H distances preclude coincidental occupation of either a and b or a and c. The a-b and a-c distances are only 1.57 and 1.34 A respectively. However, if b sites are occupied in ZrNiH, then occupation of some c sites could be allowed because the b-c distance is 2.42 A. Studies of P-C-T equilibria indicate the existence of monohydrides for both ZrNi [3] and HfNi [7]. In both cases the solubility for hydrogen in the monohydride appears to be negligible in accord with the expectations for occupation of a sites. To our knowledge there has been no experimental determination of the site occupied by hydrogen in these compounds. 4. The dihydride of ZrNi If a dihydride of ZrNi were to exist, according to the approximation described earlier, it can be calculated that a = 3.46 A, b = 10.34 A and c = 4.25 A, The expansion with respect to ZrNiH is not nearly great enough to allow coincidental occupation of a and b sites, the combination of which would give the necessary two sites per zirconium atom. The necessary number of sites could also be provided by either d or e sites. Whilst the hole radii for d and e sites would be 0.34 and 0.36 A respectively (nearly adequate for a stable hydride [2] ), full occupation of either d or e sites would not be likely because newest-neighbor H-H distances would be only 1.07 and 1.91 A respectively. The c sites, with two sites per zirconium atom, would seem to be the only other possibility. The hole radius of 0.48 A is very adequate but the H-H distance would be only 1.95 A. From these considerations it is predicted that there should be no dihydride of ZrNi or of other isostructural intermetallic compounds. The conclusion that there should be no dihydride of ZrNi is in full accord with the experimental evidence. P-C-Z’ equilibria provide no indication for a dihydride of ZrNi [3] or of HfNi [7]. The prediction is not contradicted by the known formation of ZrCoH, [8] because, whilst ZrCo is obviously a related compound, it is not isostructural with ZrNi; ZrCo has the CsCl structure. In fact with the known lattice parameters for ZrCo, sites can be readily selected, either octahedral or tetrahedral, for which both criteria being used here are easily met. Thus with only geometric considerations, the existence of ZrCoH, could have been predicted, just as it has been predicted that neither ZrNi nor the isostructural compound HfNi should form a dihydride. 5. The trihydride of ZrNi The estimated expanded lattice parameters of ZrNiHa are a = 3.561 A, b = 10.541 A and c = 4.322 A. From these, we calculated the H-H distances
TABLE 2 Hole sizes and H-H nearest-neigh bar distances for hydrogen in designated interstitial sites in ZrNiH, Sitea
Hole radius (A)
H-Hdistance
(.&)
a
b
C
d
e
:
eO.55 0.72
I.61 2.87
1.61 2.58
2.46 1.43
2.39 2.23
2.67 1.52
Tt e
=0.50 0.38 0.39
2.23 1.43 2.67
2.46 2.39 1.52
2.08 1.30 2.21
1.30 1.07 1.38
2.21 1.38 1.97
%ites a to e refer to Fig. 1
and the hole radii listed in Table 2. It can be seen that, at this concentration of hydrogen, the hole radius for d and e sites, 0.38 8, is that typically observed in stable hydrides. Still, the radii of these sites are considerably smaller than those of the other three sites. Furthermore, the H-H distance for nearest-neighbor d sites is only 1.07 .& and for e sites it is somewhat less than Switendick’s ]l] minimum value of 2.1 8. The trihydride probably requires, therefore, occupation of some combination of a, b and c sites. As was pointed out earlier, however, occupation of a sites precludes occupation of the other two. It can only be concluded that the trihydrides of ZrNi and other isostructural intermetallic compounds must have all b and c sites occupied by hydrogen even though the H-H distance for c sites barely meets the requ~ement. Again, the foregoing conclusion, reached from consideration of geometry only, is in complete accord with reported experimental results. The positional parameters for hydrogen in ZrNiH, [ 5,6], given in Section 2, and for hydrogen in ZrCoH, 161 are those of the b and c sites. 6. Hyperstoichiomet~
in the trihydride of ZrNi
There is ample evidence in the literature from which it can be concluded that some stoichiometric hydrides have considerable solubility for still more hydrogen. For example GdHa,, at 400 “C and at a hydrogen pressure of 7 X lo2 Pa absorbs hydrogen to a ~oncen~ation of GdHs t5 when the pressure is increased by a factor of 10 [9]. ZrCoHs at 365 “C’increases its hydrogen content to ZrCoH2.as when the pressure changes from 1.3 X lo5 to 4.3 X lo5 Pa [8]. No phase transformation is involved in either case. We will consider now the likelihood of hypers~ichiomet~ in the trihydride of ZrNi. To do this we will begin by examining the geometry of a known hyperstoichiometric hydride GdH2 fx. GdH2 has the fluorite structure [9] ; essentially all the tetrahedral ft) interstices of the f,c.e. metal sublattice are filled with hydrogen atoms. As the hydrogen pressure is increased at a given temperature more hydrogen atoms are absorbed in solid solution, but these
32
34
HYDROGEN CONCENTRATION lH/Zf[tlf]l
Fig. 2. Pressure-composition isotherms for the systems ZrNi-H, HfNi-H and HfCo-H. The broken lines are postulated.
must be accommodated in octahedral (0) sites. The H-H distances in GdH,,, can be readily calculated from the lattice parameter given in ref. 9. For t-t sites the shortest distance is 2.65 8, but for o--t sites the distance is only 1.8’7 8. Seemingly, then, some H-H distances shorter than 2.1 a are tolerated for x less than 0.15. For x greater than 0.15 precipitation of a new phase, hexagonal GdH,, is initiated. In this compound all t and o sites are occupied; each hydrogen occupying a t site has three neighbors in o sites at a distance 2.26 A and one neighbor in a t site at a distance 1.97 a, still slightly less than that predicted by Switendick [l] for stable hydrides. These values, however, are the distances between centers of interstitial sites. We estimate the radius of the t site in GdHs to be quite large, 0.57 a, so the hydrogen atoms could relax to off-center positions resulting in minimum distances greater than 2.1 A, in conformity with Switendick’s rule. In the case of ZrNiHs, it can be seen from Table 2 that partial occupancy of a sites in addition to full occupancy of b and c sites would lead to some H-H distances as short as 1.43 SI. Similarly, the filling of d or e sites would result in H-H distances of only 1.30 and 1.52 a respectively. Obviously these are very much shorter than the calculated value of 1.87 ,& in hyperstoichiometric GdHs and the minimum distance in a stable hydride (2.1 a). Such sites would seemingly not be occupied except under extremely high Hz pressure, so little, if any, hydrogen solubility is expected in ZrNiH, . As discussed later, the available P-C-T results seem to provide some, but not complete, conflation. In Fig, 2 we show pressure-composition isotherms for ZrNi-H at 100 “C and for HfNi-H at 50 “C. With increasing pressure both curves appear in agreement with our to approach the composition H/Zr = 3 asymptotically,
183
expectation. Also plotted in Fig. 2, however, are three other pieces of information. One of these is the isotherm for HfCo-H. Obviously no phase change is indicated over a wide range of compositions above, as well as below, 3.0. This combined with the fact that the metal sublattice of HfCoHs is reported [7] to be isostructural with that of ZrNiH,, would seem to constitute a contradiction of our expectation that occupation of all b and c sites precludes the easy occupation of other sites. However, we do not know whether b and c sites are occupied in HfCoH,; we are unaware of any neutron diffraction experiments on this compound. HfCo has the CsCl structure and the P-C-T plot [7] suggests that the first hydride forms with an H/Hf ratio somewhat greater than 2. It is during hydride formation that the metal sublattice transforms to the CrB-type structure [ 71. We would like to suggest the possibility that this compound may be the hypostoichiometric variation of HfCoH, instead of HfCoH,. If the positional parameters are somewhat different for the metal atoms in this sublattice than they are in ZrNiH,, it is not inconceivable that a combination of c and e sites could become occupied. This combination affords four sites per zirconium atom and could, therefore, account for the range of composition observed (Fig. 2). Until the complete structure of HfCoH, has been specified, attempts to explain the observed P-C-T behavior on the basis of geometry are strictly conjectural.
7. Higher hydrides
of ZrNi
As intimated in the preceding section, a careful examination of Table 2 leads us to suspect that, if a higher hydride of ZrNi forms without a transformation of the metal sublattice, that hydride would probably be ZrNiH*. The nearest-neighbor distances a-b, a-c, b-e, c-d, d-d and d-e are all much too short to allow full occupation of these combinations of sites. In addition, each of the species a and b offers only one site per zirconium atom. Occupation of a combination of c and e sites appears to be most likely. The hole radii are large, 0.56 i$ for c and 0.43 a for e. The H-H distances for c-c, c-e and e-e are 1.95, 2.33 and 2.04 a respectively. When the hydrogen atoms are allowed to relax to off-center positions the criterion of 2.1 a is easily met with the effective hole radii being reduced only slightly, to 0.51 a for c sites and to 0.42 a for e sites. It is tempting to postulate that ZrNiH, does form at high H, pressure, because its existence would help to explain two pieces of information plotted on Fig. 2. First, let us consider the circle, which represents the reported [7] preparation of HfNiH,., at 50 “C and an Hz pressure of 2 X lo6 Pa. Given the shape of the experimental P-C-T curve [ 71 for HfNi-H, we submit that one logical explanation for the seeming mismatch between the point and the curve is that the formation of a higher hydride has been initiated. This proposal is indicated by the broken line connecting the point to the experimental P-C-T curve. The point would represent equilibrium between the trihydride and a higher hydride. Relieving the H2 pressure might very well allow evolution of hydro-
184
gen from the higher hydride, so that X-ray examination in air at room temperature would reveal no evidence of its prior existence. The experimental P-C-T plot for ZrNi-H at 100 “C, shown in Fig. 2 as a solid line, was mentioned in Section 6. Up to a pressure of 8 X lo4 Pa there is no indication that H/Zr ratios in excess of 3.0 can be achieved. Baron et al. [lo] , however, have reported the preparation of ZrNiHs.s, at 25 “C with an Hz pressure of 4 X lo5 Pa. This is shown as a square (Fig. 2). One possible explanation is represented as a broken curve. The asterisk is to remind the reader that the curve is only postulated. Whilst no experimental results have been provided in refs. 3 and 10 for the temperature 25 Y!, those having experience with P-C-T diagrams will recognize that the broken curve, whilst not unequivocally indicated, is not an unreasonable extrapolation from the results reported [3] for 250,200 and 100 “C. The reported [lo] ZrNiHs.,, could be, therefore, a mixture of ZrNiHs and a higher hydride. Baron et al. [lo] have observed the lattice parameters of their hydride, as measured in air, to be the same as those reported by Korst [4] for ZrNiH,., . By way of explanation, they have speculated that the initial product might have evolved some of its hydrogen between its preparation and the X-ray measurements. We conclude that, whilst no concrete evidence for the existence of a compound ZrNiH, _ Y has been reported, its postulated existence does not lead to any contradiction of the known P-C-T results and in fact allows some heretofore anomalous results to be explained.
8. Conclusion For intermetallic compounds known to react exothermically with hydrogen it appears that, armed only with the geometry of the metal sublattice, criteria of hole size and minimum H-H distance can be used to make some reasonable predictions of the occurrence of specific hydride stoichiometries and of the interstitial sites occupied by hydrogen. Neutron diffraction experiments should be performed on the monohydrides of ZrNi and HfNi to test the present prediction of hydrogen site selection. Similar studies on the hyperstoichiometric trihydrides of ZrNi and HfCo would be equally valuable.
Acknowledgment This work was supported
by the U.S. Department
of Energy.
References 1 A. C. Switendick, prospects, SAND
Theoretical study 78-0250, 1978.
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in metals:
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18.5
2 3 4 5 6 7 8 9 10
C. E. Lundin, F. E. Lynch and C. B. Magee, J. Less-Common Mel., 56 (1977) 19. G. G. Libowitz, H. F. Hayes and T. R. P. Gibb, Jr,, J. Phys. Chem., 62 (I 958) 76. W. L. Korst, J. Phys. Chem., 66 (1962) 370. S. W. Peterson, V. N. Sadana and W. L. Korst, J. Phys. (Paris), 25 (1964) 451. A. V. Irodova, V. A. Somenkov, S. Sh. Shil’shtein, L. N. Padurets and A. A. Chertkov, Sou. Phys. - Crystollogr., 23 (1978) 591. H. M. Van Essen and K. H. J. Buschow, J. Less-Common Met., 64 (1979) 277. H. W. Newkirk, A literature study of metallic ternary and quaternary hydrides, UCRL-51244 RQU. 1, 1975. G. E. Sturdy and R. N. R. Mulford, J. Am. Chem. Sot.. 78 (1956) 1083. J.-L. Baron, A. Virot and J. delaplace, J. Nucl. Mafer., 83 (1979) 286.