Deuterium site occupation in the oxygenstabilized ηcarbides Zr3V3OD x . II.Application of a geometric modelD. G. Westlake Citation: The Journal of Chemical Physics 79, 4532 (1983); doi: 10.1063/1.446367 View online: http://dx.doi.org/10.1063/1.446367 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/79/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Oxygen-stabilized glass formation in Zr 80 Pt 20 melt-spun ribbons Appl. Phys. Lett. 83, 69 (2003); 10.1063/1.1588371 Transitioning model potentials to real systems. II. Application to molecular oxygen J. Chem. Phys. 113, 2354 (2000); 10.1063/1.482050 Site occupancy of Zr in Nd(FeZr)B magnet during hydrogenation disproportionation desorption recombinationprocess Appl. Phys. Lett. 73, 2512 (1998); 10.1063/1.122499 The thermodynamic stability of clathrate hydrate. II. Simultaneous occupation of larger and smaller cages J. Chem. Phys. 98, 8110 (1993); 10.1063/1.464567 Deuterium site occupation in the oxygenstabilized ηcarbides Zr3V3OD x . I. Preparation and neutron powderdiffraction J. Chem. Phys. 79, 4522 (1983); 10.1063/1.446339

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Deuterium site occupation in the oxygen-stabilized 1J-carbides Zr 3 V 30Dx. II. Application of a geometric modela)

D. G. Westlake

Materials Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received 18 April 1983; accepted 29 July 1983)

A geometric model has been applied to the 17-carbides Zr3V30Dx ' which belong to space group Fd3m. With criteria of minimum hole size and minimum distance between deuterium atoms and with the assumption that the larger interstices are preferred, it was possible to rationalize the experimentally observed preference, in decreasing order, for 32e sites, 192i sites, 96g I' and 96g, sites. The respective numbers of coordinating metal atoms for these interstices are Zr3V, Zr,V" Zr3V, and ZrV3• The largest interstices, which are the octahedral 8a sites with Zr6 coordination, remain empty for x = 1.86, 2.85, and 4.93 because of their proximity to the more numerous 32e sites. The failure of deuterium atoms to occupy any 96g 1 (Zr,V) sites at x = 1.86 may indicate the existence of a short-range repulsive interaction between oxygen and deuterium. The possibilities for achieving higher values of x are also explored.

I. INTRODUCTION

A geometriC model developed recentlyl has had con­siderable success in rationalizing the observed hy­drogen sites and the stoichiometry for stable hydrides of some intermetallic compounds. The model depends on four generalizations drawn from surveys of pub­lished experimental results: (1) For the hydride at equilibrium in the plateau region of a pressure-com­position isotherm, the hydrogen atoms occupy only those interstices that can accommodate a sphere with radius?: 0.40 A. Even in solid solution, hydrogen atoms will not occupy sites with radii much shorter than that value. (2) Because of a Short-range repulsive interaction, two hydrogen atoms cannot simultaneously occupy sites that are separated by less than 2.10 A. (3) Interstices with the largest radii are preferentially occupied by hydrogen atoms. (4) The volume of the metallic lattice expands during hydrogenation at a rate between 2 and 3 A3 per hydrogen atom added.

The model has been shown to be applicable to hy­drides of several hexagonal C14 and cubic C15 Friauf­Laves phases, to hydrides of the Haucke compounds LaNi5, LaNi4AI, and LaNi4Mn,2 to hydrides of AeB23 compounds, 3,4 to hydrides of ZrNi, 5,6 and even to the hydride V2H (D). 7

The structure of deuterated Zr3V30, described in the preceding paper, 8 makes an important test of the model for several reasons: (1) The structure provides a good variety of potential sites for hydrogen occupa­tion; in one unit cell there are 456 tetrahedral inter­stices of six different types, and there are eight octa­hedral interstices. (2) In many cases, the various types of tetrahedral interstices in deuterated Zr3V30 have only small differences in radii. (3) This is the first ap­plication of the model to an intermetallic compound con­taining a nonmetallic element. (4) Both metallic ele­ments form very stable hydrides by exothermic re­action with hydrogen.

a)Work supported by the U. S. Department of Energy.

II. CALCULATIONS

For the purpose of the model, the hole radius r h is taken to be the radius of the largest sphere that can be accommodated in a given interstice. The computer program for tetrahedral holes is a general solution of a set of four equations which, together, state that the sphere is tangent to the spherical surfaces of all four coordinating metal atoms. The four unknowns are r h

and the position parameters for the center of the sphere. Distances between sites are taken as the distances be­tween the centers of the respective tangential spheres. Regardless of deuterium concentration, the atomic radii for Zr and V were taken to be 1.602 and 1.346 A, respectively, as reported in a compilationS of metallic radii for coordination number 12. The position pa­rameters for the metal atoms and the lattice param­eters at the various levels of deuterium concentration were those given in the preceding paper. 8

III. DESCRIPTION OF THE INTERSTICES

It is important to note that, throughout the following diSCUSSio~, we ref~~ to th_e Fd3r:z space !{~UP of Zr3V30 wlth the or1gm at 43m, 1. e., at 888 from the center of symmetry Sm. The present choice places the center of an octahedral site at the origin and sim­plifies the pictorial representation for some of the interstices. Figure 1 depicts the location of all Zr atoms associated with one-fourth of a unit cell, which for the purpose of this discussion will be called the "fundamental building blOCk" of the structure. This block consists of two cubes that measure ao/2 on an edge. It is apparent that all Zr atoms are at the ver­tices of regular octahedra whose centers are given in the figure caption.

In Fig. 2 are shown the locations of all oxygen atoms, along with all of the Zr atoms, All oxygen atoms occupy a second set of octahedral interstices also co­ordinated by six Zr atoms.

In the same quarter of a unit cell, all Zr and ° atoms were removed from Fig. 3(a) in order to show the po-

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D. G. Westlake: Deuterium site occupation in Zr3V30Dx' II 4533

r-----05 00-----+---0.5 oo,---~·I

I T

FIG. 1. All zirconium atoms in the fundamental building block of Zr3V30 (one-fourth of a unit cell). Sets of six Zr atoms (0)

form regular octahedral interstices with centers at ooo,!!i, !O!'OH,Ho.

sitions of V2 atoms. The tetrahedral sites having (V2), coordination will be referred to as D5. In Fig. 3(b), all VI atoms have been added. The tetrahedral inter­stices having (V2)3(VI)1 coordination will be called D6.

We note that the poSitions of the VI atoms in the cube on the right are analogous to those of the oxygen atoms in the cube on the left (Fig. 2). The unit cell is con­structed from the fundamental building blocks by stacking them such that the cubes containing no oxygen atoms and the cubes containing no VI atoms alternate in the x, y, and z directions.

Examples of DI, D3, and D4 sites are shown in Fig. 4. Their coordinations and Wyckoff notations are in Table I. Both DI and D3 are coordinated by three Zr atoms and one V2 atom, but the D3 site has a near neighbor oxygen atom in a I6c Site, while the analogous poSition near the DI site is the center of a vacant octa­hedral site (Sa).

Two examples of the D2-type site are given in Fig, 5.

.3D B88

f::,

o

I I 1

I ? 1

I I

-f'''<: -\-1+ - - - -0- - --I.--+--_ C\

FIG. 2. All zirconium (0) and oxygen (A) atoms in the funda­mental building block of Zr3V30. Sets of six zirconium atoms form slightly irregular octahedra centered on each oxygen atom. Shown here is the octahedron centered on the oxygen atom at Hi.

I I I I I I I I I I I BB8

- - - - "----::.::::: --x

1

I 1

I 1

1

-----1.. ---

FIG. 3. (a) Vanadium atoms of type V2 (e) forming regular tetrahedra centered at!OO, OlD, ool, H!, and!£!. For clarity, tetrahedra at 01! and! 10 are not shown. (b) Examples of D6 sites coordinated by three V2 atoms (e) and one VI atom (0). VlatomsareaqH, Ht H~, andHk. Sitesoftype D5 share all their faces with D6 sites.

This site is coordinated by two Zr atoms, one VI atom, and one V2 atom. The centers of both sites shown here lie close to the (020) plane; in Zr3VsOD,.93, for example, one has Y"'" 0.50, and the other has y"" O. 56. Projection of these sites onto their nearest cube faces (Fig. 6) allows easy visualization of the rings that they form.

000

I I I I I

01 I ------l;-+--, ,

FIG. 4. A fundamental building block of Z rs V sO showing only examples of three types of tetrahedral interstices. 0, Zr. e, V2; 0, VI. A, oxygen. The three zirconium atoms of the D3 site coordinate the oxygen atom at ~ ~ i, while the three zir­conium atoms of the Dl site coordinate the empty octahedral interstice at ! ! o.

J. Chern. Phys., Vol. 79, No.9, 1 November 1983

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4534 D. G. Westlake: Deuterium site occupation in ZrN30Dx. II

I I I I I I

I I -------~--------~~-

" "

FIG. 5. A fundamental building block of Zr3V30 showing only two examples of the type D2 site. D, Zr; ., V2; 0, VI.

Tetrahedral interstices Band E share a common face, as do Band D, and also H' and H. The tetrahedron H shares common edges with E and G, and D shares a Common edge with D' •

IV. ANALYSIS OF ZrN30

The radii of all the interstices available for possible occupation by hydrogen (deuterium) atoms are given in Table I. Calculated position parameters of the various types of sites are in Table II. Nearest-neighbor inter­site distances are given in Table III, and additional relevant intersite distances are given in Table IV.

Only the octahedral site has r h >0. 40 A, and without any other considerations, according to the model, it should be possible to form a stable hydride having the formula Z ra V aOHo. 5 by filling anSa octahedral inte rstices. We note, however, that these octahedral interstices share four faces with octahedra containing oxygen atoms and four faces with tetrahedral Dl sites. These latter sites are quite small, having radii less than 0,35 A (Table I). If hydrogen diffusion occurs by jumping through trigonal "saddle points, It then the octahedral interstices must remain empty so long as the Dl sites are too small to allow any solute hydrogen atoms to enter them. Similar arguments apply to occupation of some of the types of tetrahedral interstices.

D5 sites have rh =0.397 A, and, according to the model1 should be large enough to accept hydrogen in

-y

010

FIG. 6. Projections of D2 sites onto their nearest faces of the cube containing four VI atoms (cube on the right in Figs. 1-5). For clarity, projections of sites lying near the left, back, and bottom faces are not shown. The symbols 0, D, and t:. repre­sent interstices lying virtually in their respective faces (Table II), while the analogous solid symbols represent interstices ly­ing about O. 06ao away from their respective faces toward the in­terior of the cube. The projections of two D4 sites (0) are shown. These interstices lie about 0.10 ao inside the front face of the cube. The symbol 'V represents the actual location of a D4 site atx=0.47, y=0.97, z=0.15.

solid solution. These interstices are widely spaced rFig. 3(a)], however, and can be occupied only if hy­drogen atoms can diffuse to them through other types of sites. All faces of a D5 site are shared with D6 sites, which have r h =0.34 A. Because such a radius is considered l too small, even for hydrogen in solid solution, it is expected that the central region of the cube containing the VI atoms fFig. 3(b)] must remain devoid of hydrogen atoms.

D3 sites have r h "" 0.36 A and are, a priori, doubtful1

for occupancy by solute hydrogen atoms in Significant numbers. Both D2 and D4 sites have r h "" O. 375 A and would seem to be large enough to take some hydrogen atoms in solid solution. Furthermore, long range dif­fusion appears to be possible. As mentioned earlier, tetrahedral interstice B shares faces with E and D

TABLE I. Radii of the various interstices in Zr3V30, Zra V3ODj.ss, Zra V30D2.S5 , and Zra V3OD4•9a •

Site Wyckoff Hole radius, rh (A)

designation notation Coordination Zr3VaO Zr3 V3OD1.86 Zr3 V3OD2.S• Zra VaOD4•33

Dl 32ej (Zr)a(V2)j 0.348 0.440 0.437 0.444 D2 192i (Zr)2(Vl)j(V2)j 0.374 0.381 0.389 0.414 D3 96gj (Zr)a(V2)j 0.360 0.405 0.406 0.423 D4 96g2 (Z r)j (Vl)j (V2)2 0.375 0.349 0.368 0.401 D5 8b (V2)4 0.397 0.275 0.335 0.394 D6 32e2 (Vl)j(V2)3 0.339 0.267 0.307 0.351

Octahedral Sa (Zr)6 0.706 0.812 0.819 0.831

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D. G. Westlake: Deuterium site occupation in ZrN 300 x' "

TABLE n. Calculated position parameters for the interstices in Zr3V30 and in deuterated Zr3V30. Space group Fd3m with origin at 43m.

Wyckoff notation

32e1

192i

Site

D1

02

03

04

05

06

Octahedral

Parameter

x=y=z

x y z

x=y z

x=y z

x =y =z

x = y =z

x=y=z

0.9130

0.7484 0.8615 0.9424

0.9048 0.2783

0.9731 0.6525

1 3 ~, 4;

0.5451

0, i

0.9097

0.7496 0.8617 0.9380

0.9034 0.2848

0.9705 0.6512

0.5494

0, i

0.9115

0.7490 0.8619 0.9390

0.9032 0.2825

0.9712 0.6506 1 3 ~, ..

0.5479

0, !

0.9127

0.7488 0.8619 0.9402

0.9034 0.2805

0.9719 0.6509

0.5468

0, i

TABLE m. Calculated nearest-neighbor intersite distances for all the interstices in Zr3 V30 at four different deuterium concentrations.

Nearest neighbors Intersite distance (A)

Site No. Type Zr3V30 Zr3 V3OOI . 86 Zr3V3002.85 Zr3V3004.93

Dl 1 Oct. 1.834 1.926 1.898 1.894

3 03 1.368 1.294 1.328 1.370

1 02 1.018 1.121 1. 099 1.089

02 1 02 1.393 1.329 1.350 1.387 1 03 1.247 1.255 1.275 1.279 1 D4 1.190 1.166 1.184 1.207

1 D1 1.369 1.294 1.328 1.370 03 2 02 1.247 1.255 1. 275 1.279

1 Oxygen 1.935 2.030 2.012 2.012

2 02 1.190 1.166 1.184 1.207 D4 1 D4 0.926 1.028 1.009 0.996

1 D6 1.344 1.283 1.315 1.345

05 4 D6 0.951 0.994 1.027 1.015

06 3 04 1.360 1.301 1. 315 1.345 1 05 0.951 0.994 1. 027 1.015

Octahedral 4 D1 1.834 1.926 1.898 1.894 4 Oxygen 2.635 2.667 2.681 2.712

TABLE IV. Additional relevant near-neighbor distances between various types of interstices in ZrSV30 at four different deuterium concentrations.

Neighbor Intersite distance (A)

Site type Zr3V30 Zr3V30~.86 Zr3 V3OO2.85 Zr3V30D4.93

D1 D1 2.995 3.146 3.099 3.093 02 2.130 2.088 2.131 2.177

02 02 1.916 1.958 1.957 1.976 02 1.892 1.939 1.942 1.961

03 03 2.178 2.066 2.113 2.177 03 2.246 2.393 2.369 2.361

02 1.830 1.851 1.864 1.887 04 02 1.787 1.835 1.843 1.858

03 1.900 1.928 1.953 1.978

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4535

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4536 D. G. Westlake: Deuterium site occupation in Zr3V30Dx' II

(Fig. 6), and we note here that the distance E -H can be spanned by an intermediate jump to the neighboring 04 site whose projection on the nearest cube face is shown. The distances G-H and F-H could be traversed through the two 04 sites near the center of the ring. Finally, long range diffusion is pOSSible, because a hydrogen atom could escape from one ring of 02 sites to another by two different routes. Sites Hand H' (Fig. 6) share a face, and sites D and 0' are separated by a single D4 site (shown as an inverted triangle). It seems likely that whatever hydrogen enters Zr3V30 in solid solution must occupy some 02 and some D4 sites,

In earlier applications of the model to Friauf-Laves phases,l predictions of hydrogen-site preference and hydride stoichiometries were based on the assumption that position parameters of the metal atoms remain constant as the lattice expands with increasing hydrogen concentration. For Zr3V30, however, formation of a hydride (deuteride) causes changes in those position parameters, as can be seen in Table III of the preceding paper, We note that the value of x for the particular V2 atom represented in that table decreases when a small number (less than two) of deuterium atoms are added to the formula unit of Zr3V30, but further additions cause a monotonic increase in x. Similarly, the value of x for the particular Zr atom represented in that table decreases at first, but then increases monotonically with increasing deuterium concentration. These subtle changes in position parameters of the metal atoms have important effects on the relative and absolute sizes of the various types of interstices that lead to the inter­esting consequences in hydrogen-site selection dis­cussed below,

V. ANALYSIS OF Zr3 V30D1.86

The poSition parameters calculated for the centers of the various interstices in Zr3V300t.86 are shown in Table II. These agree very closely with the experi­mentally determined poSitions of the deuterium atoms (Table 1lI of the preceding paper8), Because of the changes in metal atom positions discussed above, the largest tetrahedral site (05) in Zr3VSO becomes the smallest site in ZrSV300t.B7 (Table I); the second to the smallest site (01) becomes the largest tetrahedral site; both the 01 and D3 sites have r h >0. 40; and the D2 sites expand only slightly, so rh remains somewhat less than 0.40 A, in the range where some deuterium atoms in solid solution might be expected to reside in such sites.

According to the model, the D1 sites should be pre­ferred on the basis of Size, and, in fact, the experi­ments in the preceding paperB confirm that preference. Because there are 32 01 sites and 48 Zr atoms per unit cell, full occupancy of the 01 sites could result in the formula Zr3V30~. Obviously, there are more than enough D1 sites to accommodate the deuterium atoms present in the sample considered here. No 01 sites need be excluded because nearest-neighbor 01 sites are separated by 3.146 A (Table IV). As mentioned above, the 02 sites are large enough to allow some occupation by solute deuterium atomS. In this respect, the model

can rationalize the experimental results of the pre­ceding paper: More than 96% of the deuterium atoms occupy 01 sites and the remainder occupy 02 sites. The null occupancy of octahedral Sa sites at this level of deuterium concentration is readily explicable. The distance between one of these 8a sites and its four nearest D1 sites is only 1. 926 A (Table III), Thus, for one 01 site to empty into the octahedral site would re­quire the simultaneous emptying of all three other Dl sites. Without further conSideration, however, the failure of deuterium to occupy any of the second largest tetrahedra, 03, is unexplained.

The D1 site has three nearest-neighbor 03 sites at a distance of 1. 294 A. Thus, if all Dl sites (32et) were filled, all D3 sites (96g t ) would have to be empty. In this alloy, however, 10% of the 01 sites are empty, so 10% of the second largest sites (D3) would seem to be available for occupancy. Despite the Slightly smaller size of the D2 site and its coordination by fewer zir­conium atoms, it appears to be preferred over D3 sites for occupation by deuterium atoms. This may be the first evidence in this system of a repulsion between the oxygen and deuterium atoms. Each tetrahedral 03 site shares a face with the octahedral site of an oxygen atom, and the separation of the two sites is only 2.030 A. In the absence of any other reason within the framework of the model for deuterium atoms to shun the D3 sites we are tempted to speculate that there may be a minimum 0· .. H distance, and, if so, that distance is greater than 2.030 A. It should be noted, however, that at some stage of the hydrogen-absorption process in Z r3 V30, hydrogen atoms must diffuse through 03 sites, because they are an essential part of the diffusion path to the occupied D1 sites.

The possible repulsion of oxygen and hydrogen atoms is reminiscent of a study of hydrogen trapping in oxygen­doped niobium reported by Magerl et al. tO Using neu­tron inelastic scattering, they studied the phonon spec­tra and concluded that hydrogen atoms are trapped in tetrahedral interstices by oxygen atoms occupying octa­hedral interstices. Very importantly, however, these two impurity atoms do not occupy nearest-neighbor sites separated by 0.825 A or even second-neighbor sites at 1.845 A. In fact, the fourth-neighbor distance of 2.976 A was thought to be the most likely separation of the oxygen atom and its trapped hydrogen atom.

Again, Dl sites are the largest (Table 1), and, with their wide separation (>3 A), they should be expected to be nearly fully occupied~ For this alloy, the 03 ... oxygendistance is still short, 2.011 A, but, 03 sites are excluded, also by their proximity (1. 328 'A) to the nearly fully occupied D1 sites. The radius of the 02 sites has increased slightly, and it is essential now, to ascertain whether these sites should be able to accommodate all the deuterium atoms not occupying 01 sites.

Full occupancy of D1 sites could account for two deuterium atoms per formula unit. In the preceding

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D. G. Westlake: Deuterium site occupation in Zr3V30Dx' II 4537

paper, the authors found 1.940 deuterium atoms in 01 sites, and they reported the remainder in 02 sites. In Fig. 6, the relevant distances between 02 sites are: O···H= 1.099 A; B···0=1.350 A; E···H=L942 A; G·ooH=1.942 A; B···H= 1.957 A; 0"'0'=1.942 A; and H· •. H' = 1. 350 A. Obviously, no ring of 02 sites can contain more than two deuterium atoms; i. e., one at each end of the oval-shaped ring, and neither 0·· '0' nor H .•. H' pairs are allowed to be occupied simultane­ously. One example of an ordered array in which ex­actly two deuterium atoms per ring would be allowed is to fill sites F,H,E',G',E",G" and the analogous sites near the other cube faces (Fig. 6). Nowhere is the 2.10 A criterion violated by this arrangement.

The availability of one-fourth of all 02 sites for simul­taneous hydrogen occupation could account for three hydrogen atoms per formula unit, considerably more than enough, unless some 01-02 distances were less than 2.10 A. In fact, the shortest 01-02 distance is 2.131 A, so, according to the model, occupied 01 sites do not block any of the 02 sites.

Summarizing the analysis of Zr3V300Z.85, we conclude that the model is in excellent agreement with the experi­mental results of the preceding paper as it predicts nearly full occupation of 01 sites with deuterium atoms in excess of two per formula unit being taken into solid solution by the occupation of 02 sites. 03 sites cannot be occupied because of their proximity to the fUled 01 sites, and all other tetrahedral interstices are too small for Significant occupation by deuterium.

VII. ANALYSIS OF Zr3V30D4.93

With the increase in lattice parameter accompanying the addition of about two more deuterium atoms per formula unit, the radius of a 01 site increases slightly, and it remains the largest tetrahedral site in the lattice (Table I). Again, therefore, we expect nearly full oc­cupation of the 01 sites by deuterium atoms. The dis­tance 03· .• oxygen is still only 2.012 A, and if there is a repulsive H· •• 0 interaction, it augurs against sig­nificant occupation of 03 sites, despite the fact that they are the second largest tetrahedral interstices. As mentioned earlier, diffusion in and out of a 01 site must occur through the 03 sites on three of its faces. On that baSiS, it is not surprising that the authors of the preceding paper8 found some 03 occupancy. According to the model, the number of occupied 03 sites would be limited to three times the number of vacant 01 sites. From their experimental work, Rotella et al. 8 reported 0.005±0.025 vacant 01 sites and 0.16±0.04 occupied 03 sites per formula unit. Thus, the experimental re­sult differs from the model by about two standard de­viations. A refinement11 with the number of occupied 03 sites constrained to be three times the number of vacant 01 sites gave a 03 occupancy of 0.12 ± O. 03 and a 01 occupancy of 1. 96 ± O. 01. The weighted profile R value was slightly higher (Rwp =2.6958); the uncon -strained model is preferred at a 75%-90% confidence level (based on R-value ratio tests). 11 This small dis­crepancy should not be considered a serious violation of the proposed model.

The shortest 01-02 distance is 2.177 A, so no 02 sites would be blocked by occupied 01 sites. The 02-02 distances E -H and G-H (Fig. 6) are both 1. 961 A, and the distance B-H is 1. 975 A, which means that only two deuterium atoms can be accommodated in a Single ring. There are, therefore, three fUlable 02 sites per formula unit. Between 01 and 02 sites there are five fillable sites per formula unit, i. e., more than enough to explain the stOichiometry of the present sample.

Sites of type 05 appear to be large enough for oc­cupancy by solute hydrogen atoms, but these sites are isolated from the rest of the lattice by the fact that they share all four faces with 06 sites, which have radii of only 0.35 A. The radii of 04 sites exceed 0.40 A, but occupancy is expected to be very limited. Each 04 site shares its faces with one 06 site, one 04 site and two 02 sites. In Fig. 6, these last two sites would be sites E and H for the 04 site in the lower right por­tion of the ring that is projected onto the front face of the cube. Furthermore, sites Band 0 are both at a dis­tance of only 1. 887 A from that 04 site, and sites F and G are even closer, at 1. 858 A. Thus, an occupied 04 site blocks six of the eight 02 sites in the oval ring surrounding it. As mentioned earlier, occupancy of 04 sites may be incidental to diffusion between the more important 02 sites. Certainly, this conjecture is not inconsistent with the experimentally observed values of 2.65 atoms of deuterium in 02 sites compared with 0.15 atoms of deuterium in 04 sites.

VIII. HIGHER HYDROGEN (DEUTERIUM) CONCENTRATIONS

The proximity of 01-03 pairs and of 02-04 pairs and the failure of relevant 02-02 distances (such as B-H, E -H, and G-H in Fig. 6) to elongate signifi -cantly with deuterium additions lead us to suspect that absorption at higher gas pressures probably would not greatly affect the number of hydrogen (deuterium) atoms that can be accommodated in these sites. The rapidly increaSing value of the radii of 06 sites (Table I), however, may allow them to accept some solute hydrogen atoms at elevated hydrogen pressures. While this should allow occupancy of 05 sites, the total in­crement in hydrogen capacity would be small. Occupa­tion of all 05 sites would add only 0.5 hydrogen atoms per formula unit, and, because the 05-06 distance is only 1. 015 A, no 06 sites could be occupied simul­taneously. Furthermore, occupation of 06 sites instead of 05 sites would not increase the capacity because the 06-06 distance for 06 sites surrounding a given 05 site is only 1.657 A. Thus, the maximum capacity for hy­drogen atoms in the combination of 05 and 06 sites is 0.5 hydrogen atoms per formula unit.

In the foregoing we have accounted for the possibility of two hydrogen atoms in 01 Sites, three hydrogen atoms in 02 sites and 0.5 hydrogen atoms in 05 and/or 06 sites. The authors of the preceding paper,8 however, have evidence of still higher hydrogen concentra­tions at elevated hydrogen pressures. Their observa­tion might be attributable to either of two possibilities:

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4538 D. G. Westlake: Deuterium site occupation in Zr3V30Dx' II

(1) If some sort of transformation occurs that allows distances G-H and B-H to exceed 2.10 A, then the number of fillable D2 sites woulq be doubled yielding a maximum total capacity of 8.5 hydrogen atoms per formula unit.

(2) If increased hydrogen pressure can cause some occupation of D3 sites (and that seems to be indicated by the experiments on Zr3V30Df.93), then at still higher pressures, the D1sites might empty, thereby allowing all D3 sites to fill, for a total of six hydrogen atoms per formula unit in D3 sites. In the ZrNi-H systemS,6 there is a precedent for the emptying of an initially preferred site. Each D3 site shares two faces with D2 sites at a distance of only about 1. 3 A, so all D2 sites would have to be empty. The D3-D4 distance increases only slightly from 1. 928 A in Zr3 V 30Dl.86 to 1. 978 A in Zr3 V 30D •• 93, so it is possible that all D4 sites could be blocked by full occupation of D3 sites, even at somewhat higher deuterium concentrations. With empty D1 sites, the octahedral sites become available, however, and as mentioned above, the D5 and D6 may be partially oc­cupied. This scenario yields a total capacity of 7.0 hydrogen atoms per formula unit, without the necessity of a transformation.

IX. SUMMARY

The geometric model cannot predict the minor ad­justments of the metal atom positions that are con­comitant with the transformation of Zr3V30 to its first hydride phase. Accepting these adjustments, however, we can use this model to rationalize the fact that es­sentially only D1 sites are occupied by hydrogen (deu­terium). After this one transformation, no two-phase

regions are to be expected in the phase diagram for the system. As D2 sites fill with solute hydrogen atoms, the lattice expands allowing D3 and D4 sites to playa role before D2 sites are filled to the capacity allowed by the 2.10 A criterion. The experimentally observed occupation of D1 and D2 sites at compositions up to Zr3V30D4.93 is consistent with this model. Minor oc­cupancy of D3 and D4 sites is probably incidental to diffusion between the more important D1 and D2 sites. Further expansion may allow the D3 sites to dominate at the expense of D1 and D2, and finally, some D5, D6, and octahedral sites may be occupied. After transfor­mation to the first hydride, with the successive avail­ability of new sites, no additional discontinuous changes in lattice parameter should be required to permit the continuation of absorption of hydrogen atoms under in­creasing hydrogen pressure. In such a solid solUtion, however, the maximum hydrogen concentration would be 7.0 atoms per formula unit.

10. G. Westlake, J. Less-Common Metals 90, 251 (1983) 2 • O. G. Westlake, J. Less-Common Metals 91, 275 (1983).

30. G. Westlake, Scripta Met. 16, 1049 (1982). 40. G. Westlake, J. Mat. Sci. 18, 605 (1983). :0. G. Westlake, J. Less-Common Metals 75,177 (1980), O. G. Westlake, J. Less-Common Metals 88, 17 (1982).

70 G. Westlake, Mat. Lett. 1, 107 (1982). 8F • J. Rotella, H. E. Flotow, O. M. Gruen, andJ. O. Jor­

gensen, J. Chem. Phys. 79, 4522 (1983). 9E. T. Teatum, K. A. Gschneidner, and J. T. Waber, Report

No. LA-4003, 1968. lOA. Magerl, J. J. Rush, J. M. Rowe, O. Richter, and H,

Wipf, Phys. Rev. B 27, 927 (1983), u F • J. Rotella (private communication, 1983).

J. Chem. Phys., Vol. 79, No.9, 1 November 1983

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