Novel oxidation of RbGa3 through substitution of gold for gallium—a reapportionment of the dodecahedral clusters

Journal of Alloys and Compounds 338 (2002) 4–12

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Novel oxidation of RbGa 3 through substitution of gold for gallium— a reapportionment of the dodecahedral clusters q Robert W. Henning, John D. Corbett* Department of Chemistry and Ames Laboratory-DOE, Iowa State University, Ames, IA 50011, USA Received 7 August 2001; accepted 26 November 2001

Abstract Exploratory syntheses in the rubidium–gallium–late transition metal systems have revealed a family of nonstoichiometric compounds are formed in RbGa 32x M x systems (M5Cu, Ag and Au) that remain isostructural with RbGa 3 (I4¯m2 ). Only the RbGa 32x Au x products could be obtained in high yields, and these have been structurally defined for x50.26(1) and 0.36(2) (saturation). Gold substitutes unequally on all three gallium positions in the structure of RbGa 3 , the anion of which consists of layers of interlinked Ga 8 dodecahedral clusters plus 4-bonded gallium spacers between the layers. The effects of the oxidation of the structure by Au are well focused on a 0.19 ˚ elongation of a short, evidently p-bond at the 4¯ extremes of the Ga 8 dodecahedron between x50 and x50.36. Extended Huckel ¨ A band calculations on the anion network provide insights into the distortion, which evidently reflects an unequal electron distribution of the bonding states in a deltahedron made of two types of cluster atoms.  2002 Elsevier Science B.V. All rights reserved. Keywords: Zintl phases; Chemical synthesis; Crystal structure; Electronic band structure; X-ray diffraction

1. Introduction The alkali-metal–group 13 (triel) systems are well known for the formation of many stoichiometric compounds with evidently closed electronic shells [1]. They are often classified as Zintl phases and are credited with filling some of the gap between intermetallic and valence (salt-like) compounds [2,3]. These characteristics may continue when late transition elements from the Ni, Cu or Zn families are introduced instead. Among the gallium systems, isolated clusters form in Na 10 Ga 10 Ni [4], but network structures, often complex, are much more common in others [5], e.g. for Na 35 Cd 24 Ga 56 [6], Na 21 K 14 Cd 17 Ga 82 [7], Na 128 Au 81 Ga 275 [8] and Na 36 Ag 7 Ga 73 [9]. Although many of the reported structures have electron counts consistent with closed electronic shells, or nearly so, the formation of phases that are also poor metals should not be unexpected inasmuch as these phases are on the border between valence and intermetallic compounds. In addition, a number of gallium compounds with unknown properties have been reported that apparentq

Dedicated to Professor H. Fritz Franzen as a colleague and in recognition of his long service to the Journal. *Corresponding author. E-mail address: [email protected] (J.D. Corbett).

ly contain disordered atoms or are nonstoichiometric. The simpler binary phase RbGa 3 of interest here has already been structurally characterized by Belin and Ling [10] as having a typical three-dimensional cluster network that is consistent with a closed shell compound, but the last condition has not been verified experimentally. When RbGa 3 is prepared in the presence of certain late transition metals, the third element is incorporated into the structure even though the resulting electron-poorer compounds may not be formally closed shell. This article reports on the nonstoichiometry achieved for RbGa 32x Au x and, to a much lesser extent, for the related copper and silver compounds. The single crystal X-ray structural results for two gold compositions will be described and ¨ discussed. Extended Huckel calculations on the RbGa 3 binary and on the gold derivative have been performed in order to gain a better understanding of the electronic structures and the reduction reactions.

2. Experimental

2.1. Syntheses The RbGa 32x Au x compounds can be prepared by allowing the elements to react above the melting point in the

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R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12

system (|600 8C) followed by slow cooling to 500 8C or below. The reactivity of the starting materials and products required the use of nitrogen or helium-filled gloveboxes. Tantalum tubing was used as an inert reaction container, as previously reported [11], whereas niobium is not suitable with gallium. The melting point of RbGa 3 is quite uncertain according to a standard compilation [12] because of conflicting results, and a later report contains yet a third value, with RbGa 3 melting much higher, near 621 8C [13]. The binary system is particularly difficult to work with because of the low melting points of the components. RbGa 3 appeared to be substantially a line phase as we could not find any line shifts in scanned patterns from samples with different Rb:Ga proportions. All of the reactions of RbGa 3 with a heterometal from the Cu and Zn families were troubled by multiple phase formation. Those with gold appeared to be most tractable. Phases that were RbGa 32x Au x (x50–0.36) in composition could be obtained in |85–90% yields but always with some small amounts of RbGa 7 [14] and AuGa 2 [15] as byproducts. Excess gold (up to x50.5) was always loaded because of the simultaneous formation of AuGa 2 , which also accounted for the additional formation of RbGa 7 . In addition, a small amount of rubidium metal could also be observed in one end of the Ta container. Such vaporization of some rubidium (b.p. 686 8C) is believed to hinder the formation of pure samples as well, but reactions loaded with excess rubidium produced similar results. In general, the physically mixed components would be prereacted, then this product ground and pressed into a pellet. A trial series, annealing separate pellets of RbGa 2.7 Au 0.3 for 1 month at 400, 450, 500 and 520 8C, failed to produce pure samples. Samples that were loaded with a still greater excess of gold, that is, for x>0.5, gave Guinier powder patterns that also showed a further unknown phase, its lines increasing in intensity as the gold content increased. Otherwise, all of the gold is present in the phase AuGa 2 and the target. These difficulties presumably arose because of complex, probably incongruent, melting relationships between RbGa 32x Au x and the other products that we could not unravel. Similar reactions loaded as RbGa 2.64 M 0.36 for M5Cu and Ag and slowly cooled (3 8C / h) from 650 8C also produced shifted lattice parameters for the same lattice ˚ c515.232(3), 15.050(2) A ˚ type: a56.2628(9), 6.314(3) A, ˚ c5 for Cu and Ag, respectively, vs. a56.3221(4) A, ˚ for RbGa 3 . These are consistent with the 15.007(2) A substitution of some Cu or Ag into the structure, less for the latter, but in each case another intermetallic phase formed in high yield, Ag 3 Ga (|50%) or an unidentified Cu–Ga product. These of course also altered the stoichiometry so that less Cu or Ag was available for substitution into the RbGa 3 structure. In fact, the lattice parameters for the silver phase did not shift very much because of the large amount of Ag 3 Ga that formed. Only a

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few reactions of this type were investigated so it is difficult to assess the extents of reaction. Parallel reactions of RbGa 3 in the presence of zinc, cadmium, or mercury produced smaller changes in lattice dimensions because of the competitive formation of additional intermetallic binary compounds such as RbCd 13 . Only the RbGa 32x Au x reactions were studied in detail because of the distinctly higher reaction yields and the ability to distinguish or analyze for mixed gallium and gold through single crystal X-ray structural refinements. Lattice parameter shifts for KGa 32x M x could be identified in the K–Ga–Zn,Cd systems, but these were not investigated further because of the additional formation of K 2 Ga 3 . The products of all Rb–Ga–Au reactions were brittle with a metal-like luster. Reactions loaded with an excess of gold (x>0.4) produced mixed-phase powder patterns in which the lines were very sharp while those with less gold gave patterns with broader lines, consistent with slightly nonhomogeneous samples. Annealing samples at 500 8C produced slightly sharper patterns but did not improve the yields of the desired phases.

2.2. Crystal structures Because of the multiphase nature of all products, the structures and stoichiometries of the higher-yield gold products were established by single crystal XRD means. Crystallites were selected from reactions loaded as RbGa 2.64 Au 0.36 and Rb 1.2 Ga 2.33 Au 0.67 and sealed into 0.3mm thin-walled capillary tubes. The crystals were checked for singularity by Laue photographs, and one crystal from each product was used for a single crystal X-ray data collection. Both data sets were collected at room temperature on a Rigaku AFC6R four-circle diffractometer with the aid of Mo Ka radiation. Twenty-five reflections obtained from a random search were used to index the crystals to body-centered-tetragonal unit cells. The diffractometer-based lattice parameters for the gold-richer phase were within 3s of those refined from an indexed Guinier powder pattern of the same sample. The diffractometer lattice parameters for the other crystal were not in such close agreement; the a-axis was nearly identical but the ˚ c-axis from the diffractometer was smaller by 0.075(7) A ˚ This may reflect a range of (15.403(4) vs. 15.478(6) A). stoichiometries present in this particular sample, especially considering that the lines in the powder pattern were a little broad. (The Guinier lattice parameters were more consistent with the lattice parameters of the other phases so they were used in the distance calculations.) Two octants of data (1h, 1k, 6l) were collected up to 708 in 2u for the first crystal and four octants (1h, 6k, 6l) up to 608 for the second crystal. The body-centering condition was confirmed for both crystals by initially collecting data for the primitive cell. Each data set was corrected for Lorentz and polarization effects and for absorption with the aid of three c-scans collected at

R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12

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different 2u angles. Systematic absences and the N(Z) distribution suggested the noncentrosymmetric space group I4¯m2 (no. 119), as was already known for RbGa 3 [10]. Application of direct methods [16] revealed two trial positions with separations appropriate for Rb–Rb contacts and three positions suitable for gallium. The refinement of the positional and isotropic displacement parameters for all five atoms yielded small, even slightly negative, values of the latter for all three gallium positions in both compounds. The R factors at these points were |9.5% for both compounds. A mixed occupancy of gallium and gold was then refined on all three gallium positions with the total occupancy of each fixed at unity. The anisotropic thermal parameters of the gallium and gold components in each were set equal to each other and allowed to refine along with the occupancy. This lowered R to |9.0% for each data set, and R ave (I > 3sI ) for the gold-richer sample was 13.0 vs. 9.4% for the other. The total gold contents of the gallium sites in the crystal obtained from the gold-richer sample corresponded to x50.36(2) in RbGa 32x Au x or |two Au atoms per unit cell (Z56), with 6.3(8), 16(1) and 20(1) atom% Au on Ga1, Ga2 and Ga3 sites, respectively. The other crystal gave x50.26(1) and 3.8(5), 12.9(6) and 10.3(8)% Au on the respective sites. All refinements were performed on a VAX workstation using the TEXSAN [17] crystallographic package. Details of data collection and

refinement for the two gold-containing samples are given in Table 1.

2.3. Band structure calculations The EHMACC program utilized originated with the group of R. Hoffmann at Cornell University.

3. Results and discussion

3.1. Structures The positional parameters, isotropic displacement parameters, and refined occupancies for the structures of RbGa 2.74( 1) Au 0.26( 1) and RbGa 2.64( 2) Au 0.36(2) are listed in Table 2. Anisotropic displacement parameters and interatomic distances are given in Tables 3 and 4, respectively, whereas lattice parameters obtained from diverse Rb–Ga– Au reactant compositions are in Table 5. The RbGa 32x Au x compounds are isotypic with the body-centered tetragonal AGa 3 binary phases, A5K, Rb, Cs, with substitution of gold on all gallium positions. The main building blocks in the anionic framework are interlinked Ga 8 dodecahedra and tetrahedrally coordinated gallium atoms that separate the former into layers, as

Table 1 Data collection and refinement parameters for two RbGa 32x Au x phases

Space group, Z Lattice parameters a ˚ a (A) ˚ c (A) ˚ 3) V (A d calc (g / cm 3 ) Crystal dimensions (mm) Diffractometer Radiation; 2umax Octants measured Scan method Temperature (8C) m (cm 21 ) (MoKa) Transm. coeff. range Number of reflections Measured Observed (I >3sI ) Unique obs. Number of variables R avg. (I > 3sI ) (%) Residuals R, R w b (%) Goodness of fit ˚ 3) Largest peaks in final DF map (e / A

Sec. ext. coeff (10 26 ) a b

˚ 23 8C. Guinier data with Si as an internal standard, l 51.540562 A, R5SuuFo u n uFc uu / SuFo u; R w 5[Sw(uFo u n uFc u)2 / Sw(Fo )2 ] 1 / 2 ; w5 s 22 F .

RbGa 2.74( 1 ) Au 0.26( 1 )

RbGa 2.64( 2 ) Au 0.36( 2 )

I4¯ m2 (No. 119), 6

I4¯ m2 (No. 119), 6

6.205(1) 15.478(6) 595.9(3) 5.478 0.1030.1830.21 Rigaku MoKa; 708 1h, 1k, 6l vB2u 23 395.6 0.202–1.00

6.195(1) 15.515(4) 595.6(2) 5.696 0.1430.1630.19 Rigaku MoKa; 608 1h, 6k, 6l v–2u 23 425.9 0.642–1.00

1617 939 392 25 9.4 3.9, 3.6 1.44 11.9 ˚ from Rb2) (0.5 A –2.8 2.75(6)

1890 1160 359 25 13.0 4.9, 4.7 1.19 13.9 ˚ from Rb2) (0.21 A 23.1 0.7(1)

R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12 Table 2 a Positional parameters for RbGa 2.74( 1 ) Au 0.26( 1 ) and RbGa 2.64( 1 ) Au 0.36( 1 ) Atom

Wykoff symbol

x

Rb1

2a

0 0

0 0

0 0

1.90(7) 1.3(1)

Rb2

4f

0 0

2 2

0.3713(1) 0.3711(2)

1.8(1) 1.3(1)

Ga1 /Au1

8i

0.2074(3) 0.2085(4)

0 0

0.21995(8) 0.2196(1)

1.21(7) 1.0(1)

3.8(5) 6.3(8)

Ga2 /Au2

8i

0.2919(4) 0.2876(5)

0 0

0.38775(7) 0.3870(1)

2.05(7) 1.6(1)

12.9(6) 16(1)

Ga3 /Au3

2b

0 0

0 0

2 2

1.79(9) 1.5(1)

10.3(8) 20(1)

a

y

z

Beq.

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Table 4 ˚ Selected bond distances in RbGa 32x Au x phases (d #4.0 A)

Au (at.%)

b

Ga1–Ga1 Ga1–Ga2 Ga1–Ga132 Ga1–Ga232 Ga1–Rb1 Ga1–Rb232 Ga2–Ga2 Ga2–Ga3 Ga2–Ga1 Ga2–Ga132 Ga2–Rb232 Ga2–Rb132 Ga2–Rb2 Ga3–Ga234 Ga3–Rb234 Rb1–Ga134 Rb1–Rb234 Rb1–Ga238 Rb2–Ga234 Rb2–Ga134 Rb2–Ga332 Rb2–Rb132 Rb2–Rb2 Rb2–Ga2

Data for RbGa 2.64( 1 ) Au 0.36( 1 ) are listed second.

shown in Fig. 1 for RbGa 2.74 Au 0.36 . The dodecahedra are generated by Ga1 and Ga2 atoms and have D 2d symmetry (Fig. 2). The four Ga1 atoms around the waist of the cluster each have five neighbors within the cluster plus an exo bond to a Ga1 atom in an adjacent cluster. The latter generate layers of dodecahedra with four-fold symmetry about the normal c axis, vertical in the figure. The Ga2 atoms each have four bonds (neighbors) within the cluster and an exo bond to a Ga3 atom that interconnect adjacent layers of dodecahedra through Ga3. The approximately tetrahedral coordination around the Ga3 atoms means that the clusters of one layer fall in the depressions of the neighboring layers within the body-centered tetragonal unit cell. The rubidium atoms have characteristic functions in this assembly; one of each is marked in Fig. 1. Each Rb1 (at the origin and body center) caps Ga1–Ga2–Ga2 trigonal faces on four different dodecahedra, whereas Rb2 (2mm) bridges a Ga2–Ga2 edge of one cluster and Ga1–Ga2 edges of four others. The anisotropic displacement parameters are close to spherical for all atoms, although the U11 value for Ga(Au)2 is twice as large as U22 . The larger value lies along the Ga2–Ga2 bond that lengthens on gold

a b

RbGa 3 a

RbGa 2.74( 1 ) Au 0.26( 1 )

RbGa 2.64( 2 ) Au 0.36( 2 )

2.612(9) 2.609(5) 2.741(6) 2.806(4) 3.590(3) 3.702(3) 2.442(8) 2.528(4) 2.609(5) 2.806(4) 3.716(2) 3.755(2) 3.749(5) 2.528(4) 3.695(2) 3.590(3) 3.695(2) 3.755(2) 3.716(2) 3.702(3) 3.695(2) 3.695(2) 3.660(9) 3.749(5)

2.574(4) 2.650(2) 2.731(3) 2.782(2) 3.640(2) 3.644(2) 2.583(5) 2.510(2) 2.650(1) 2.782(2) 3.602(1) 3.783(1) 3.947(3) 2.510(2) 3.687(1) 3.640(2) 3.687(1) 3.783(1) 3.602(1) 3.644(2) 3.687(1) 3.687(1) 3.754(4) 3.947(3)

2.583(5) 2.643(3) 2.722(4) 2.781(3) 3.645(2) 3.640(2) 2.632(6) 2.500(3) 2.643(2) 2.781(3) 3.582(2) 3.795(2) 3.977(3) 2.500(3) 3.687(2) 3.645(2) 3.687(2) 3.795(2) 3.582(2) 3.640(2) 3.687(2) 3.687(2) 3.759(2) 3.977(3)

Data from Ref. [8]. Exo-bond.

Table 5 Lattice parameters and volumes a of some RbGa 32x Au x reaction products Loaded composition

˚ a (A)

˚ c (A)

˚ 3) V (A

RbGa 3 RbGa 2.9 Au 0.1 RbGa 2.8 Au 0.2 RbGa 2.7 Au 0.3 RbGa 2.64 Au 0.36 b RbGa 2.6 Au 0.4 RbGa 2.5 Au 0.5 Rb 1.2 Ga 2.33 Au b0.67

6.3221(4) 6.283(7) 6.254(2) 6.261(4) 6.205(1) 6.202(1) 6.200(2) 6.195(1)

15.007(2) 15.17(1) 15.29(1) 15.304(9) 15.478(6) 15.485(6) 15.513(7) 15.515(4)

599.82(8) 598.9(6) 598.2(6) 599.9(6) 595.9(3) 595.6(3) 595.6(3) 595.6(2)

a ˚ From Guinier data with Si as an internal standard, l 51.540562 A, 23 8C. b Sources of data crystals RbGa 2.74( 1 ) Au 0.26( 1 ) and RbGa 2.64( 2 ) Au 0.36( 2 ) , respectively.

Table 3 Anisotropic thermal parameters for RbGa 2.74( 1 ) Au 0.26( 1 ) and RbGa 2.64( 1 ) Au 0.36( 1 ) a Atom

U11

U22

U33

U12

Rb1

0.030(2) 0.023(2)

0.030 0.023

0.012(1) 0.005(2)

0 0

0 0

0 0

Rb2

0.019(1) 0.012(2)

0.019(1) 0.011(2)

0.028(1) 0.027(2)

0 0

0 0

0 0

Ga1 /Au1

0.0091(9) 0.008(1)

0.017(1) 0.013(1)

0.0197(6) 0.017(1)

0 0

20.0008(6) 20.003(1)

0 0

Ga2 /Au2

0.040(1) 0.032(2)

0.0197(9) 0.015(1)

0.0184(6) 0.015(1)

0 0

0.0046(7) 0.006(1)

0 0

Ga3 /Au3

0.023(2) 0.017(2)

0.023 0.017

0.021(1) 0.022(3)

0 0

0 0

0 0

a

Data for RbGa 2.64( 1 ) Au 0.36( 1 ) are listed second.

U13

U23

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R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12

Fig. 1. Unit cell of tetragonal RbGa 2.74 Au 0.36 (KGa 3 type) with vertical. Gold substitutes on all gallium sites. The [Ga(Au)] 8 dodecahedra (D 2d ) form layers via intercluster bonds, and these are interconnected along via tetrahedral Ga(Au)3 atoms. The open circles are rubidium.

substitution (below), so that the U11 difference presumably reflects the presence of a statistical distribution of Au substitutions on the pair of positions and hence a range of Ga2–Ga2 distances. ¯ The dodecahedral cluster is a regular deltahedron (42m) in which the internal angles on the triangular faces vary

between 52 and 648 in RbGa 3 . It can readily be assigned a skeletal electron count of 18 (52n12) on the basis of Wade’s rules [18], as was earlier verified through EHMO calculations on the isolated cluster in RbGa 3 by Belin and Tillard-Charbonnel [5]. Their Ga–Ga bond distances within the clusters in RbGa 3 are typical of those in a delocal˚ ized system, with all but two in the range of 2.61–2.81 A. One variation might seem to be the somewhat shorter distances around the tetrahedrally-intercluster bridging ˚ but this is appropriate for what are usually Ga3, 2.53 A, viewed as normal two-electron–two-center bonds. The more remarkable exception is the unique Ga2–Ga2 bond ˚ in distance within the cluster which is a short 2.442(8) A the binary [8]. This is a particularly important feature in the present Ga–Au structures. (Direct comparison with published structural data for RbGa 3 seem reasonable as our lattice dimensions from Guinier powder pattern data are quite consistent with the earlier results [10]: a56.3221(4) ˚ and c515.007(2) vs. 15.000(2) A.) ˚ here vs. 6.315(2) A ˚ has been A similarly short Ga–Ga bond, 2.435 A, observed in a Ga 15 spacer in Na 22 Ga 39 [19]. Theoretical EH calculations regarding this by Burdett and Canadell [20] indicate that it corresponds to a double bond, the adjoining triangles each possessing a low lying, empty orbital on the close pair of Ga atoms. Similarly, MO calculations performed on an isolated dodecahedral Ga 8 cluster (with simulated exo bonds) indicate that some p-bonding is important in the pertinent Ga2–Ga2 interactions as well [5], the higher curvature of the cluster at the Ga2 position making the tangential orbitals project further above the surface of the cluster and thus contribute to an additional p-interaction. So this bond can perhaps be viewed as a fairly localized p bond even though it occurs in a cluster with largely delocalized s bonding. Cation packing does not appear to be involved in this anomaly, rather the short Ga2–Ga2 separation appears to be intrinsic to this network as it is also observed in KGa 3 (2.44(1) [21] ˚ and in CsGa 3 (2.47 A) ˚ according to and 2.436(5) [22] A) powder data refinement [23]. An interesting nonstoichiometry region may be present around KGa 3 as well, which we will return to after the effects of gold on the RbGa 3 system are considered.

3.2. Cluster distortion

Fig. 2. Substituted Ga 22 cluster with exo bonds to adjoining clusters 8 (Ga1) or the bridging Ga3. Displacement ellipsoids for RbGa 2.64 Au 0.36 are drawn at the 90% probability level.

Changes in the lattice parameters, a and V decreasing (by 1.9 and 0.7%) and c increasing (3.4%), are in parallel with the amount of gold present in the reaction mixture, Table 5, up to x|0.4–0.5 where the substitution evidently saturates. A parallel AuGa 2 formation occurred in all cases and altered the loaded stoichiometry of the samples, which made it necessary to quantify the amount of gold in the derivatives by crystallographic refinement of the structure and composition. Thus, reaction of a RbGa 2.64 Au 0.36 composition yielded crystals with x50.26(1), fairly con-

R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12

sistent with the approximate yields from this reaction, 85% RbGa 32x Au x , 10% AuGa 2 and 5% Rb. Gold substitutes for gallium in the structure up to about 12% (x50.36(1)) when the loaded x is 0.67, the former being distributed unequally on all three Ga positions, 6.3, 16 and 20 at.% at Ga1, Ga2, Ga3, respectively (Table 2). The distance changes accompanying the gold insertion are significant, see Table 4. The most striking change is seen for Ga(Au)2–Ga(Au)2, which increases from 2.442(8) ˚ in RbGa 3 to 2.582(5) A ˚ in RbGa 2.74( 1) Au 0.26( 1) (with 13 A ˚ (16% at.% Au on those particular sites) and to 2.632(6) A Au) in RbGa 2.64(2) Au 0.36(2 ) , an overall change of 0.19(1) ˚ The Ga(Au)–Ga(Au) distances in the rest of the A. ˚ or less, structure do not change as significantly, 60.03 A even though Au also substitutes significantly at Ga3 (Table 4). The changes in Ga2–Ga2 bond lengths naturally affect the rest of the structure, but they do not appear directly responsible for the shifts in lattice parameters. As the Ga2–Ga2 separation increases, the Ga2–Ga3 exo-bond ˚ lengths decrease slightly (20.028(5) A), as would be expected, so that the Ga2–Ga3–Ga2 bond angle (bridging between clusters within the same layer) is decreased by 9.9(2)8. This scissoring action is reflected in the overall ˚ (0.33%) increase in c, but in a marginal decrease in 0.51 A ˚ the intercluster Ga1–Ga1 distance at most (20.029(10) A). Internal cluster distortions dominate the overall 4.22% volume decrease as the Ga1 atoms move away from the basal plane (z50.25, Fig. 1) and nearly all internal distances become smaller. At the end the overall decrease ˚ (2.0%) dominates the 0.51 A ˚ increase in c in a by 0.127 A as the former change is weighted twice, and the cell volume decreases overall slightly, by 0.70%. Of course, some of the changes we see must be ˚ influenced by the larger size of gold, 1.34 vs. 1.25 A according to Pauling’s single bond metallic radii [24]. However, the radius effects become quite diluted as substitution occurs at all three Ga sites (Ga3.Ga2.Ga1, Table 2). Reported Au–Ga contacts in other phases, AuGa 2 [13], AuGa [25] and Au 2 Ga [26], are typical, 2.63, ˚ respectively, and are not very different 2.58 and 2.60 A, from d(Ga–Ga) in these delocalized bonding situations. Although the overall effects of gold are quite focused on the Ga2–Ga2 interactions, the site of a supposed unusual p-bond, the fact that gold substitutes over the whole gallium network makes its electronic effects still quite appropriate to a system with delocalized bonding.

9

atoms provide the requisite number of electrons to form a 12 closed-shell compound, (Rb 1 ) 3 Ga 22 ). Extended 8 (4b-Ga ¨ Huckel band calculations were carried out on the networks in the binary RbGa 3 as well as on the limiting RbGa 2.64( 2) Au 0.36( 2) in order to gain a better understanding of why the structure distorts during the two-electron oxidation produced by each gold atom. The calculations were performed on the full anionic framework, using 300 k-points in the irreducible wedge of the first Brillouin zone. Since the method cannot readily handle a mixture of gallium and gold on the same positions, all positions were assigned as gallium and only the distances and electron count were altered for the ternary phase calculation. The Hii parameters used for Ga were 214.58 and 26.75 for 4s and 4p, respectively [27]. The total densities-of-states (DOS) for the binary compound are shown in Fig. 3 (solid line), with the Ga2 p contributions also projected out. The total number of electrons available for bonding in RbGa 3 is 60 per cell (Z56), and the Fermi level falls at 26.40 eV, in the apparent band gap. This is characteristic for a compound with a closed electronic shell, but the present DOS does not afford a meaningful measure of the gap as the cations and thence the presumed major components of the conduction band, are not included in the calculation. COOP curves for both Ga–Ga interactions (solid line) and for Ga2–Ga2 (dashed) in RbGa 3 are shown in Fig. 4, the right

3.3. Electronic structure calculations The application of Wade’s rules to the dodecahedral cluster affords a skeletal electron count of 18 (2n12), and with all eight vertices exo-bonded, its formal cluster charge should be 22. The tetrahedrally coordinated Ga3 atom presumably follows the octet rule, and so it is assigned a formal charge of 12. Thus, the three rubidium

Fig. 3. Total densities-of-states (DOS) for the anionic network in RbGa 3 with the Ga2 projection drawn in. The two Fermi levels (dashed) correspond to the binary phase and the end result of the gold oxidation (see text).

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R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12

Fig. 4. Total Ga–Ga COOP curve (solid line) for the RbGa 3 results in Fig. 3 with the Ga2–Ga2 contribution as a dashed line. Values to the right of the midpoint are bonding; to the left, antibonding.

and left sides of the vertical axis representing bonding and antibonding totals at those energies, respectively. All bonding states are filled in the anion lattice, as expected for and customary with many Zintl (valence) compounds. Gold substitution means that two fewer electrons are available per atom, which puts EF for RbGa 2.64( 2) Au 0.36( 2)

at 256 electrons per cell (55.7(2) more accurately), corresponding to 28.10 eV for the binary DOS, in the middle of a large DOS peak. A closer look at the orbitals contributing at this point indicates that these are mainly Ga2 p (Fig. 3). The COOP curve for the Ga2–Ga2 bond also given in Fig. 4 (dashed line) confirms that a decreased electron count from simulated gold substitution will especially weaken the Ga2–Ga2 bond. The COOP curves for the gold-saturated compounds, that is, for the RbGa 3 structure with positions and distances observed for RbGa 2.64( 2) Au 0.36( 2) , are shown in Fig. 5. As shown in Fig. 5a, bonding between the Ga2 atoms (dashed line) dominates near the Fermi level for 56 electrons, with a small ˚ Ga1–Ga2 bond within contribution from the 2.643(3) A the cluster (dotted). Thus, the distortion of the structure does not change the DOS or COOP curves significantly for the all-gallium model. The first four electrons removed from the cell are primarily involved in cluster bonding, effectively oxidizing each cluster by two electrons and converting the apparent ‘double’ bond into a more typical delocalized single bond. But it is probably better to refer to the strong Ga2–Ga2 bonding in RbGa 3 as a particularly strong pairwise portion in a delocalized system that has an irregular distribution of neighbors in a distorted deltahedron with two independent types of atoms rather than in terms of a more localized p bond. Fig. 5b shows the COOP curves for the intercluster Ga2–Ga3 (dashed line) and Ga1–Ga1 bonds (dotted). Both of these bond types appear to be formal two-center2two-electron bonds that interlink the clusters into a three-dimensional network, and optimum bonding has already been achieved for both with approximately 56 electrons in the unit cell. Further lowering of the number of electrons would not be expected, although, as a matter of fact, the observed reduction limit

˚ Fig. 5. COOP curves for RbGa 3 with the dimensions and positions of RbGa 2.74 Au 0.36 (a) total Ga–Ga (solid), Ga2–Ga2 (dashed), Ga1–Ga2, 2.643 A (dotted); (b) intercluster Ga2–Ga3 (dashed), Ga1–Ga1 (dotted) bonds, total Ga–Ga (solid). The EF levels are marked for RbGa 3 (60 e 2) and for the gold-rich compound (56 e 2).

R.W. Henning, J.D. Corbett / Journal of Alloys and Compounds 338 (2002) 4 – 12

achieved with gold is probably determined by its equilibration with other competing phases containing Ga and Au. The Mulliken overlap populations (OP) are also tabulated in Table 6 for all Ga–Ga contacts in both RbGa 3 and in the ternary structure with the lattice parameters, positions and electron count refined for RbGa 2.64(2) Au 0.36(2 ) . The greatest reduction in bonding found on oxidation is, as expected, between the two Ga2 atoms, the so-called OP decreasing from 0.81 to 0.50. Other changes are small and negative except for one Ga1–Ga2 value. The real effects of gold are better judged by substituting two of the Ga2 and Ga3 atoms by gold in several variations, taking care to avoid adjoining atoms. Such calculations produced the same general results as with the pure gallium framework with altered dimensions with respect to the critical variations already discussed. Another manifestation of the interesting effects that oxidation of RbGa 3 by gold has on the cluster shapes, cell parameters, and bond distances, especially the particularly short one attributed to a double bond, may be contained in a report by van Vucht [23]. He observed in passing that the cell parameters of KGa 3 (from powder data) depended significantly on composition between 20 at.% potassium (K-poor) and 40 at.%. An increased reduction (K fraction) ˚ (2.3%) decrease in a, no significant led to a 0.145 A ˚ 3 (4.8%) decrease in V (recalcuchange in c, and a 27 A lated). These are in the opposite sense from the observations made here, that is, the parallel reduction of the gold-saturated phase would increase V and a and give a sizable decrease in c. A repeat examination of the KGa 3 system seems warranted together with some crystallographic studies. In contrast, we were unable to find any hint of nonstoichiometry in RbGa 3 according to lattice dimensions. Instead, our systems exhibited only substitution reactions. This seeming reduction of KGa 3 would seem to require, in some continuous way, either the introduction of cations at new sites or the elimination of some gallium and ultimately the formation of a new anion lattice. (It is not stated whether all foreign lines accompanying the rather large composition variations in KGa 3 could be accounted for by other known phases.) The addition of more cations seems totally inconsistent with the observed dimensional changes, so only a continuous reconstruction into a smaller anion network would be Table 6 ˚ and overlap populations (OP) for Ga–Ga contacts in Distances (A) RbGa 3 and RbGa 2.64( 2 ) Au 0.36( 2 ) (RbGa 3 model) RbGa 3

Ga2–Ga2 Ga2–Ga3 Ga1–Ga2 Ga1–Ga1 Ga1–Ga1 Ga1–Ga2

RbGa 2.64( 2 ) Au 0.36( 2 )

d

Overlap pop.

d

Overlap pop.

2.442 2.528 2.609 2.612 2.741 2.806

0.81 0.78 0.57 0.75 0.40 0.34

2.632 2.500 2.643 2.583 2.722 2.781

0.50 0.78 0.48 0.67 0.40 0.39

11

possible. Such a process, if true, would seem unprecedented, but that is one reason why one does research.

3.3. Further thoughts The reasons why gold can be incorporated into the structure are not well understood, but part of this depends on the stabilities of alternate phases. A closer look at binary phase diagrams for gallium with the late transition metals [12] shows that several more intermetallic-like phases seem to have large phase widths. Heteroatoms mix on the same sites in these structures, and so it may not be too surprising to find the same occur in ternary compounds, e.g. Na 35 Cd 24 Ga 56 [6] and Na 128 Au 81 Ga 275 [8]. The late transition elements do not routinely form related deltahedral clusters. Many of the compounds formed in alkali-metal2 gallium systems are reported to be stoichiometric, but since these compounds are closely related to intermetallic phases, careful analysis may reveal that more nonstoichiometric examples exist. This is especially true in the ternary systems with late transition metals wherein their substitution for gallium is very common. Compounds that contain unusual clusters or spacers may be more susceptible to this type of behavior, as we have observed in Na 30.5 Ga 602x Ag x [28] which contains an unusual hexacapped hexagonal prism. Nonstoichiometry has also been noted in several compounds containing twinned icosahedra, e.g. Li 9 K 3 Ga 28.83 [29] and Na 6.25 Rb 0.6 Ga 20.02 [30]. Structures containing regular deltahedra evidently tend to occur more often as stoichiometric closed shell compositions.

Acknowledgements This research was supported by the Office of the Basic Energy Sciences, Materials Sciences Division, US Department of Energy. The Ames Laboratory is operated by DOE by Iowa State University under Contract No. W-7405-Eng82.

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