Ternary K₂Zn₅As₄-type pnictides Rb₂Cd₅As₄ and Rb₂Zn₅Sb₄, and the solid solution Rb₂Cd₅(As,Sb)₄

Dirubidium penta­cadmium tetra­arsenide, Rb₂Cd₅As₄, di­rubid­ium penta­zinc tetra­antimonide, Rb₂Zn₅Sb₄, and the solid-solution phase dirubidium penta­cadmium tetra(arsen­ide/antimonide), Rb₂Cd₅(As,Sb)₄ [or Rb₂Cd₅As_3.00(1)Sb_1.00(1)], have been prepared by direct reaction of the component elements at high temperature. These com­pounds are charge-balanced Zintl phases and adopt the ortho­rhom­bic K₂Zn₅As₄-type structure (Pearson symbol oC44), featuring a three-dimensional [M₅Pn₄]^2- framework [M = Zn or Cd; Pn is a pnicogen or Group 15 (Group V) element] built of linked MPn₄ tetra­hedra, and large channels extending along the b axis which host Rb⁺ cations. The As and Sb atoms in Rb₂Cd₅(As,Sb)₄ are randomly disordered over the two available pnico­gen sites. Band-structure calculations predict that Rb₂Cd₅As₄ is a small-band-gap semiconductor and Rb₂Zn₅Sb₄ is a semimetal.

S1. Comment

Research interest in ternary A–M–Pn systems [where A is an electropositive alkali, alkaline earth or rare earth metal, M is a d metal and Pn is a pnictogen, i.e. Group 15 (Group V) element] was boosted by the discovery of superconductivity in doped BaFe₂As₂ and related iron arsenides (Rotter et al., 2008; Mandrus et al., 2010). The recent discovery that Yb₁₄MSb₁₁ and AZn₂Sb₂ can be used for power generation (Kauzlarich et al., 2007; Toberer et al., 2010) promoted even greater interest in A–M–Pn systems. These renewed efforts have provided access to many more new compounds composed of these elements, most of which can be regarded as Zintl phases with complex anionic frameworks (Kauzlarich et al., 2007). Such materials are typically small-band-gap semiconductors or semimetals and represent a new thrust in modern thermoelectrics development (Toberer et al., 2010).

So far, the ternary systems A–Cd–As and A–Zn–Sb containing alkali metals have been sporadically investigated and research in this area has not been systematic. There are several basic structures that have been known since the 1970's; examples include ACdAs (A = Na and K; Kahlert & Schuster, 1976; Krenkel et al., 1979), K₄CdAs₂ (Eisenmann et al., 1991), AZnSb (A = Li, Na and K; Schuster & Schröder, 1972; Kahlert & Schuster, 1976; Savelsberg & Schäfer, 1978) and Li₂ZnSb (Schröder & Schuster, 1977). More recently, the first example of an antimony-based type-I clathrate phase Cs₈Zn₁₈Sb₂₈ (Liu et al., 2009) was reported, followed by a report on Rb₂Cd₅Sb₄ and Cs₂Cd₅Sb₄ (Zheng et al., 2010). Concurrently, our teams have contributed to the field by several recent discoveries, which comprise Cs₄CdAs₁₄, featuring a notricyclane-like [As₇]^3- cluster (He et al., 2011a), ACd₄As₃ (A = Na, K, Rb and Cs; He et al., 2011b), Cs₈Cd₁₈As₂₈, the first example of an arsenide type-I clathrate (He et al., 2012), and K₂Zn₅As₄ (Stoyko et al., 2012). Here, we expand on the latter report and discuss the crystal and electronic structures of dirubidium pentacadmium tetraarsenide, Rb₂Cd₅As₄, dirubidium pentazinc tetraantimonide, Rb₂Zn₅Sb₄, and the solid-solution phase dirubidium pentacadmium tetra(arsenide/antimonide), Rb₂Cd₅(As,Sb)₄Rb₂Cd₅As₄.

Since the prototype and three isostructural representatives known to date, namely Rb₂Zn₅As₄ (Stoyko et al., 2012), and Rb₂Cd₅Sb₄ and Cs₂Cd₅Sb₄ (Zheng et al., 2010), have already been discussed in detail, we will only briefly introduce the structures of Rb₂Cd₅As₄ and Rb₂Zn₅Sb₄ here. Both compounds feature [M₅Pn₄]^2- frameworks, with large channels running along the b axis and accommodating Rb⁺ cations (Fig. 1a). The basic building block of this framework is a heterocubane [M₄Pn₄] structure unit with additional Pn atoms in the corners. [M₄Pn₄] units are linked together by the interleaving M3 atoms to form infinite columns along the b axis. These columns alternate along the a axis and are related by the translation 1/2a+1/2b (Fig. 1b). The structural relationship with another complex structure, K₂Cu₂Te₅ (Chen et al., 2001), was previously drawn based on the topology of flat nets extending parallel to the ab plane (Stoyko et al., 2012). At the same time, some relationship with the ubiquitous CaAl₂Si₂-type structure (Gladyshevskii et al., 1967) can also be shown, based on the presence of [M₂Pn₂] fragments in Rb₂M₅Pn₄ structures, linked together to form infinite chains along the c axis (Fig. 1b). Closer inspection of the [M₄Pn₄] unit in polyhedral representation reveals a unit called a stella quadrangula, which is formed by two types of tetrahedra centred by M1 and M2 atoms (Fig. 1c). Stellae are connected along the c axis through edge-sharing and within the ab plane through corner-sharing. Tetrahedra with M3 atoms at the centre share common edges with stellae and serve to link them along the b axis.

The preferential site occupancy by Sb atoms in Rb₂Cd₅(As,Sb)₄ can be understood if the coordination environment of the Pn atoms is considered. Although both atoms As1 and As2 in the parent Rb₂Cd₅As₄ compound are coordinated by seven metal atoms, their coordination polyhedra are slightly different in size. The average distances from As1 and As2 to the Cd atoms are equal (~2.7 Å). Meanwhile, atoms As1 are located further away (~3.7 Å) than atoms As2 (~3.6 Å) from two neighbouring Rb atoms. Since the same geometry is preserved in Rb₂Cd₅(As,Sb)₄, the size difference between Sb and As atoms (Pauling metallic radii of 1.39 Å for Sb and 1.21 Å for As; Pauling, 1960) dictates that the former prefer the Pn1 site.

The bonding in Rb₂Cd₅As₄ and Rb₂Zn₅Sb₄ can be readily rationalized applying the Zintl concept. The assumption of complete transfer of valence electrons from electropositive to electronegative elements results in the charge-balanced formulations (Rb⁺)₂(Cd²⁺)₅(As^3-)₄ and (Rb⁺)₂(Zn²⁺)₅(Sb^3-)₄, respectively. To understand further the electronic structure of the title compounds, tight-binding linear muffin-tin orbital band-structure calculations were performed on Rb₂Cd₅As₄ and Rb₂Zn₅Sb₄ within the local density and atomic spheres approximation, using the Stuttgart TB-LMTO-ASA program (Tank et al., 1998). The basis sets included Rb 5s/5p/4d, Zn 4s/4p/3d, Cd 5s/5p/4d, As 4s/4p/4d and Sb 5s/5p/5d orbitals, with the Rb 5p/4d, As 4d and Sb 5d orbitals being downfolded. Integrations in reciprocal space were carried out with an improved tetrahedron method over 172 irreducible k points within the first Brillouin zone.

The density of states (DOS) diagram for Rb₂Cd₅As₄ (Fig. 2a) shows the separation of the valence band from the conduction band by a small gap, indicating that the compound would be a semiconductor and confirming expectations for the charge-balanced formulation obtained by applying the Zintl concept. The valence band is dispersed over the region down to -5.2 eV and corresponds to Cd 5s and Cd 5p states mixed with As 4p states throughout the entire range. Cd 5s states contribute mostly to the lower energy region (from -2.7 to -5.2 eV) and Cd 5p states to the higher energy one (from 0 to -2.7 eV). Not shown in the diagram are the narrow bands of the As 4s and Cd 4d states, located in the regions from -10.7 to -11.4 eV and from -7.8 to -9.3 eV, respectively. On progressing to Rb₂Zn₅Sb₄, the band structure changes slightly (Fig. 2b). The valence band, which is composed of Zn 4s, Zn 4p and Sb 5p states, widens in energy dispersion, and the overlap with the conduction band is noticeable (total DOS of 1.5 states eV^-1 cell^-1 at the Fermi level). Thus, semimetallic behaviour is expected for Rb₂Zn₅Sb₄. In its valence band, Zn 4p and Sb 5p states are predominant from 0 to -3 eV, where the Zn 4p states fall off, and the contribution from the Zn 4s states increases from -3 to -5.7 eV while mixing with further dispersed Sb 5p states. Zn 3d and Sb 5s states are found as narrower bands in the regions from -7.1 to -8.2 eV and from -9.3 to -10.9 eV, respectively. There is a contribution of Rb-based states to the valence bands of both compounds, suggesting that the Zintl concept oversimplifies the interaction between cations and anions as being electrostatic only, and that the actual bonding picture in these compounds can be more complicated. The predictions of the electrical transport properties for Rb₂Cd₅As₄, and more particularly for Rb₂Zn₅Sb₄, should be verified experimentally due to possible underestimation of the band gap by LMTO calculations. Nevertheless, it is obvious for both compounds that the p orbitals in Cd and As (or Zn and Sb) should play an important role in electrical transfer and that the charge carriers will move mostly in the three-dimensional framework built by Cd and As (or Zn and Sb).

Inspection of crystal orbital Hamilton population (COHP) curves reveals that the heteroatomic Cd–As (Fig. 2a) and Zn–Sb (Fig. 2b) interactions are fully optimized, with all bonding and no antibonding levels filled. These interactions are strong (-ICOHP of 1.24 eV per bond and 14.9 eV per cell for Cd–As, and -ICOHP of 0.95 eV per bond and 11.4 eV per cell for Zn–Sb) and define the overall structure stability, in contrast with weak contacts Rb–As (-ICOHP of 0.02 eV per bond and 0.2 eV per cell), Cd–Cd (-ICOHP of 0.12 eV per bond and 0.5 eV per cell), Rb–Sb (-ICOHP of 0.02 eV per bond and 0.2 eV per cell) and Zn–Zn (-ICOHP of 0.07 eV per bond and 0.3 eV per cell). In this regard, the Zintl formalism works well to account for the mostly electrostatic interactions between Rb and Cd–As or Zn–Sb frameworks.

The band structure of Rb₂Cd₅As₄ was also examined, in order to understand the preferred occupancy of Sb atoms between two pnictogen sites, Pn1 and Pn2, in Rb₂Cd₅(As,Sb)₄. The QVAL value, which represents the integrated electron density within a Wigner–Seitz sphere around a specified site, is slightly lower for As1 (4.75) than for As2 (4.80), indicating a slight preference for the more electropositive Sb atoms (Pauling electronegativities of 1.9 for Sb and 2.0 for As; Pauling, 1960) to occupy the former. This prediction is consistent with the structure refinement results for Rb₂Cd₅(As,Sb)₄, in which the larger fraction of Sb atoms is found on the Pn1 site.

To conclude, the successful preparation of the ternary Rb₂Cd₅As₄ and Rb₂Zn₅Sb₄ pnictides demonstrates that the anionic [Zn₅As₄]^2- framework in the K₂Zn₅As₄-type structure is flexible for substitutions if the parent Rb₂Zn₅As₄ compound is considered. The fact that we tried, and successfully obtained, the solid-solution phase Rb₂Cd₅(As,Sb)₄ confirms this line of thinking and suggests the existence of a wide homogeneity range, not only for Cd-based compounds, but likely for Zn-based compounds as well. This could prove useful for the tuning of the electronic and transport properties of these materials. Band-structure calculations support, in principle, the bonding scheme derived for these compounds from the Zintl concept.

Related literature

For related literature, see: Chen et al. (2001); Eisenmann et al. (1991); Gelato & Parthé (1987); Gladyshevskii et al. (1967); He et al. (2011a, 2011b, 2012); Kahlert & Schuster (1976); Kauzlarich et al. (2007); Krenkel et al. (1979); Liu et al. (2009); Mandrus et al. (2010); Pauling (1960); Rotter et al. (2008); Savelsberg & Schäfer (1978); Schröder & Schuster (1977); Schuster & Schröder (1972); Stoyko et al. (2012); Tank et al. (1998); Toberer et al. (2010); Zheng et al. (2010).

S2. Experimental

Starting materials were pure elements obtained from Alfa or Aldrich with a nominal purity greater than 99.9 wt%. All reagents and products were handled within an argon-filled glove-box, with controlled oxygen and moisture levels below 1 p.p.m. Stoichiometric mixtures of the elements were loaded into niobium tubes, which were then sealed with an arc welder under high-purity argon gas. The niobium tubes were subsequently jacketed within fused-silica tubes, which were evacuated and sealed. The reaction mixtures were held either at 923 K for 7 d and subsequently quenched in icy water (Rb₂Cd₅As₄), or at 823 K for 10 d and then cooled to room temperature at a rate of 3 K h^-1 (Rb₂Zn₅Sb₄). These two different temperature profiles were determined experimentally and gave nearly quantitative yields of the title compounds. Rb₂Cd₅As₃Sb was prepared analogously and also in high yield.

S3. Refinement

Small good quality single crystals of Rb₂Cd₅As₄, Rb₂Zn₅Sb₄ and Rb₂Cd₅As₃Sb were isolated from crushed samples examined under an optical microscope. They were mounted on glass fibres using Paratone oil and then immediately transferred into a cold nitrogen gas stream (ca 200 K) on the diffractometer. The centrosymmetric orthorhombic space group Cmcm was chosen on the basis of the Laue symmetry, systematic absences and intensity statistics (mean |E² - 1| of 1.005 for Rb₂Cd₅As₄, 0.963 for Rb₂Zn₅Sb₄ and 0.978 for Rb₂Cd₅As₃Sb). The structures were solved by direct methods and refinements proceeded in a straightforward manner. The atomic positions were standardized using the STRUCTURE TIDY program (Gelato & Parthé, 1987).

Three models were considered for refinement to test the order/disorder of the As and Sb atoms in Rb₂Cd₅As₃Sb: (i) the Pn1 site (Wyckoff position 8g) is occupied by a mixture of As and Sb atoms and the Pn2 site (Wyckoff position 8f) is occupied by As atoms; (ii) the Pn1 site is occupied by As atoms and the Pn2 site is occupied by a mixture of As and Sb atoms; and (iii) the Pn1 and Pn2 sites are occupied by mixtures of As and Sb atoms. Occupancy factors in model (i) converged at 0.733 (8) As/0.267 (8) Sb for the Pn1 site [R(F²) = 0.019] and correspond to the formula Rb₂Cd₅As_3.47 (2)Sb_0.53 (2). The refined values of the occupancy factors in model (ii) are 0.901 (12) As/0.099 (12) Sb for the Pn2 site [R(F²) = 0.025] and correspond to the formula Rb₂Cd₅As_3.80 (2)Sb_0.20 (2). Displacement parameters for the sites occupied solely by As atoms are lower than those for the sites occupied by As/Sb mixtures in both models [U_eq(Pn1) = 0.0139 (2) Ų and U_eq(Pn2) = 0.0107 (2) Ų in model (i); U_eq(Pn1) = 0.0080 (2) Ų and U_eq(Pn2) = 0.0142 (4) Ų in model (ii)], which is indicative of the presence of heavier Sb atoms. Indeed, the assumption of disorder of the As and Sb atoms over two sites [model (iii)] improved the refinement significantly, and it converged at a lower agreement factor and resulted in very similar values of the equivalent displacement parameters for both sites. The refined composition Rb₂Cd₅As_3.00 (1)Sb_1.00 (1) is in excellent agreement with the nominal composition of the sample.

The highest residual density peaks for Rb₂Cd₅As₄ and Rb₂Zn₅Sb₄ are located 0.75 Å from Cd3 and 1.17 Å from Sb1, respectively, and the deepest holes are located 1.90 Å from Cd2 and 0.75 Å from Zn2, respectively. For Rb₂Cd₅As₃Sb, the highest residual density peak is located 0.75 Å from Cd2, and the deepest hole is located 0.74 Å from Cd1.

Computing details

For all compounds, data collection: SMART (Bruker, 2002); cell refinement: SMART (Bruker, 2002); data reduction: SAINT (Bruker, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008b); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008b); molecular graphics: SHELXTL (Sheldrick, 2008b); software used to prepare material for publication: SHELXTL (Sheldrick, 2008b).

Figures

Fig. 1. The structure of Rb2M5Pn4 (M = Zn or Cd; Pn = As or Sb), viewed (a) down the b direction and (b) down the a direction. (c) Combined ball-and-stick and polyhedral representations of [M4Pn4] units capped by M3 atoms. The large circles (blue in the electronic version of the paper) are Rb atoms, the medium circles (lime) are M atoms and the small circles (pink) are Pn atoms. Structural fragments translated by 1/2a+1/2b are shown in grey. The unit cell is outlined by dashed lines (red). Wire-frame polyhedra are M1Pn4 tetrahedra, and dark (orange) and light (cyan) polyhedra are M2Pn4 and M3Pn4 tetrahedra, respectively.

Fig. 2. Band structures of (a) Rb2Cd5As4 and (b) Rb2Zn5Sb4. The density of states (DOS) and their atomic projections are shown in the left-hand panels. Crystal orbital Hamilton population (-COHP) curves for the average Cd–As and Zn–Sb interactions are shown in the right-hand panels. In each case, the Fermi level is marked by the horizontal line at 0 eV.

(I) Dirubidium pentacadmium tetraarsenide

Crystal data

Rb2Cd5As4	F(000) = 1784
Mr = 1032.62	Dx = 5.814 Mg m^−3
Orthorhombic, Cmcm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2c 2	Cell parameters from 1019 reflections
a = 12.432 (4) Å	θ = 3.2–25.7°
b = 7.587 (3) Å	µ = 28.14 mm^−1
c = 12.507 (4) Å	T = 200 K
V = 1179.7 (7) Å^3	Block, silver
Z = 4	0.04 × 0.03 × 0.03 mm

Data collection

Bruker SMART CCD area-detector diffractometer	754 independent reflections
Radiation source: fine-focus sealed tube	615 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.056
ϕ and ω scans	θmax = 27.7°, θmin = 3.2°
Absorption correction: multi-scan (SADABS; Sheldrick, 2008a)	h = −16→16
Tmin = 0.399, Tmax = 0.540	k = −9→9
7479 measured reflections	l = −16→16

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.021	Secondary atom site location: difference Fourier map
wR(F^2) = 0.043	w = 1/[σ^2(Fo^2) + (0.018P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.00	(Δ/σ)max < 0.001
754 reflections	Δρmax = 1.03 e Å^−3
34 parameters	Δρmin = −1.10 e Å^−3

Special details

Experimental. Data collection is performed with four batch runs at ϕ = 0.00° (456 frames), at ϕ = 90.00° (456 frames), at ϕ = 180.00° (456 frames) and at ϕ = 270.00° (456 frames). Frame width = 0.40° in ω. Data are merged, corrected for decay and treated with multi-scan absorption corrections.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Rb1	0.20949 (6)	0.0000	0.0000	0.02520 (19)
Cd1	0.14652 (4)	0.38073 (7)	0.2500	0.01936 (14)
Cd2	0.0000	0.65040 (7)	0.10604 (4)	0.01920 (14)
Cd3	0.0000	0.00729 (10)	0.2500	0.02174 (19)
As1	0.34328 (5)	0.25315 (10)	0.2500	0.01573 (17)
As2	0.0000	0.27439 (10)	0.09904 (6)	0.01520 (17)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0242 (4)	0.0260 (4)	0.0254 (4)	0.000	0.000	0.0029 (3)
Cd1	0.0130 (3)	0.0236 (3)	0.0215 (3)	0.0011 (2)	0.000	0.000
Cd2	0.0225 (3)	0.0223 (3)	0.0129 (3)	0.000	0.000	−0.0009 (2)
Cd3	0.0239 (4)	0.0147 (4)	0.0266 (4)	0.000	0.000	0.000
As1	0.0111 (4)	0.0163 (4)	0.0198 (4)	0.0014 (3)	0.000	0.000
As2	0.0189 (4)	0.0157 (4)	0.0110 (4)	0.000	0.000	−0.0001 (3)

Geometric parameters (Å, º)

Cd1—As1	2.6306 (12)	Cd3—As1^vii	2.7411 (11)
Cd1—As2	2.7447 (9)	Cd3—As1^viii	2.7411 (11)
Cd1—As2^i	2.7447 (9)	Cd3—As2^i	2.7697 (11)
Cd1—As1^ii	2.8284 (14)	Cd3—As2	2.7697 (11)
Cd1—Cd2	3.2781 (9)	Cd3—Cd2^ix	3.2517 (12)
Cd1—Cd2^i	3.2781 (9)	Cd3—Cd2^x	3.2517 (12)
Cd1—Cd3	3.3683 (12)	Cd3—Cd1^vi	3.3683 (12)
Cd2—As2^iii	2.6278 (12)	As1—Cd3^xi	2.7411 (11)
Cd2—As1^ii	2.7651 (9)	As1—Cd2^xii	2.7651 (9)
Cd2—As1^iv	2.7650 (9)	As1—Cd2^xiii	2.7651 (9)
Cd2—As2	2.8541 (13)	As1—Cd1^viii	2.8284 (14)
Cd2—Cd3^v	3.2517 (12)	As2—Cd2^iii	2.6278 (12)
Cd2—Cd1^vi	3.2781 (9)	As2—Cd1^vi	2.7447 (9)
As1—Cd1—As2	120.59 (3)	As1^vii—Cd3—As2	120.975 (19)
As1—Cd1—As2^i	120.59 (3)	As1^viii—Cd3—As2	120.975 (19)
As2—Cd1—As2^i	86.92 (4)	As2^i—Cd3—As2	85.95 (5)
As1—Cd1—As1^ii	109.02 (3)	As1^vii—Cd3—Cd2^ix	54.14 (2)
As2—Cd1—As1^ii	108.87 (2)	As1^viii—Cd3—Cd2^ix	54.14 (2)
As2^i—Cd1—As1^ii	108.87 (2)	As2^i—Cd3—Cd2^ix	170.65 (3)
As1—Cd1—Cd2	138.275 (19)	As2—Cd3—Cd2^ix	103.40 (3)
As2—Cd1—Cd2	55.73 (3)	As1^vii—Cd3—Cd2^x	54.14 (2)
As2^i—Cd1—Cd2	101.10 (3)	As1^viii—Cd3—Cd2^x	54.14 (2)
As1^ii—Cd1—Cd2	53.23 (2)	As2^i—Cd3—Cd2^x	103.40 (3)
As1—Cd1—Cd2^i	138.275 (19)	As2—Cd3—Cd2^x	170.65 (3)
As2—Cd1—Cd2^i	101.10 (3)	Cd2^ix—Cd3—Cd2^x	67.24 (4)
As2^i—Cd1—Cd2^i	55.73 (3)	As1^vii—Cd3—Cd1^vi	101.96 (3)
As1^ii—Cd1—Cd2^i	53.23 (2)	As1^viii—Cd3—Cd1^vi	167.44 (3)
Cd2—Cd1—Cd2^i	66.63 (3)	As2^i—Cd3—Cd1^vi	52.02 (2)
As1—Cd1—Cd3	101.15 (3)	As2—Cd3—Cd1^vi	52.02 (2)
As2—Cd1—Cd3	52.69 (2)	Cd2^ix—Cd3—Cd1^vi	134.462 (17)
As2^i—Cd1—Cd3	52.69 (2)	Cd2^x—Cd3—Cd1^vi	134.462 (17)
As1^ii—Cd1—Cd3	149.83 (3)	As1^vii—Cd3—Cd1	167.44 (3)
Cd2—Cd1—Cd3	102.97 (3)	As1^viii—Cd3—Cd1	101.97 (3)
Cd2^i—Cd1—Cd3	102.97 (3)	As2^i—Cd3—Cd1	52.02 (2)
As2^iii—Cd2—As1^ii	125.06 (2)	As2—Cd3—Cd1	52.02 (2)
As2^iii—Cd2—As1^iv	125.06 (2)	Cd2^ix—Cd3—Cd1	134.463 (16)
As1^ii—Cd2—As1^iv	89.60 (4)	Cd2^x—Cd3—Cd1	134.463 (16)
As2^iii—Cd2—As2	100.78 (3)	Cd1^vi—Cd3—Cd1	65.47 (3)
As1^ii—Cd2—As2	107.56 (2)	Cd1—As1—Cd3^xi	113.71 (4)
As1^iv—Cd2—As2	107.56 (2)	Cd1—As1—Cd2^xii	139.369 (18)
As2^iii—Cd2—Cd3^v	111.08 (3)	Cd3^xi—As1—Cd2^xii	72.39 (3)
As1^ii—Cd2—Cd3^v	53.46 (2)	Cd1—As1—Cd2^xiii	139.369 (18)
As1^iv—Cd2—Cd3^v	53.46 (2)	Cd3^xi—As1—Cd2^xiii	72.39 (3)
As2—Cd2—Cd3^v	148.14 (3)	Cd2^xii—As1—Cd2^xiii	81.26 (4)
As2^iii—Cd2—Cd1	132.20 (2)	Cd1—As1—Cd1^viii	114.16 (3)
As1^ii—Cd2—Cd1	55.02 (3)	Cd3^xi—As1—Cd1^viii	132.13 (3)
As1^iv—Cd2—Cd1	102.11 (3)	Cd2^xii—As1—Cd1^viii	71.75 (2)
As2—Cd2—Cd1	52.63 (2)	Cd2^xiii—As1—Cd1^viii	71.75 (2)
Cd3^v—Cd2—Cd1	102.45 (3)	Cd2^iii—As2—Cd1^vi	127.42 (3)
As2^iii—Cd2—Cd1^vi	132.20 (2)	Cd2^iii—As2—Cd1	127.42 (3)
As1^ii—Cd2—Cd1^vi	102.11 (3)	Cd1^vi—As2—Cd1	83.16 (4)
As1^iv—Cd2—Cd1^vi	55.02 (3)	Cd2^iii—As2—Cd3	145.52 (3)
As2—Cd2—Cd1^vi	52.63 (2)	Cd1^vi—As2—Cd3	75.29 (3)
Cd3^v—Cd2—Cd1^vi	102.45 (3)	Cd1—As2—Cd3	75.30 (3)
Cd1—Cd2—Cd1^vi	67.51 (3)	Cd2^iii—As2—Cd2	79.22 (3)
As1^vii—Cd3—As1^viii	90.60 (5)	Cd1^vi—As2—Cd2	71.65 (2)
As1^vii—Cd3—As2^i	120.975 (18)	Cd1—As2—Cd2	71.64 (2)
As1^viii—Cd3—As2^i	120.975 (18)	Cd3—As2—Cd2	135.27 (3)

Symmetry codes: (i) x, y, −z+1/2; (ii) −x+1/2, y+1/2, −z+1/2; (iii) −x, −y+1, −z; (iv) x−1/2, y+1/2, z; (v) x, y+1, z; (vi) −x, y, −z+1/2; (vii) x−1/2, y−1/2, z; (viii) −x+1/2, y−1/2, −z+1/2; (ix) x, y−1, z; (x) x, y−1, −z+1/2; (xi) x+1/2, y+1/2, z; (xii) x+1/2, y−1/2, −z+1/2; (xiii) x+1/2, y−1/2, z.

(II) Dirubidium pentazinc tetraantimonide

Crystal data

Rb2Zn5Sb4	F(000) = 1712
Mr = 984.79	Dx = 5.611 Mg m^−3
Orthorhombic, Cmcm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2c 2	Cell parameters from 1010 reflections
a = 12.3975 (11) Å	θ = 3.2–28.2°
b = 7.5516 (7) Å	µ = 27.44 mm^−1
c = 12.4514 (11) Å	T = 200 K
V = 1165.71 (18) Å^3	Block, silver
Z = 4	0.05 × 0.04 × 0.04 mm

Data collection

Bruker SMART CCD area-detector diffractometer	797 independent reflections
Radiation source: fine-focus sealed tube	729 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.044
ϕ and ω scans	θmax = 28.3°, θmin = 3.2°
Absorption correction: multi-scan (SADABS; Sheldrick, 2008a)	h = −16→16
Tmin = 0.371, Tmax = 0.407	k = −10→10
7627 measured reflections	l = −16→16

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.018	w = 1/[σ^2(Fo^2) + (0.017P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.039	(Δ/σ)max < 0.001
S = 1.07	Δρmax = 0.66 e Å^−3
797 reflections	Δρmin = −1.01 e Å^−3
35 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00202 (6)

Special details

Experimental. Data collection is performed with four batch runs at ϕ = 0.00° (456 frames), at ϕ = 90.00° (456 frames), at ϕ = 180.00° (456 frames) and at ϕ = 270.00° (456 frames). Frame width = 0.40° in ω. Data are merged, corrected for decay and treated with multi-scan absorption corrections.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Rb1	0.22404 (5)	0.0000	0.0000	0.01652 (14)
Zn1	0.13985 (5)	0.39171 (9)	0.2500	0.01503 (16)
Zn2	0.0000	0.65688 (9)	0.11049 (5)	0.01772 (17)
Zn3	0.0000	0.00653 (12)	0.2500	0.0179 (2)
Sb1	0.34002 (3)	0.25996 (4)	0.2500	0.01097 (11)
Sb2	0.0000	0.27375 (5)	0.09762 (3)	0.01112 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0167 (3)	0.0172 (3)	0.0157 (3)	0.000	0.000	0.00194 (19)
Zn1	0.0110 (3)	0.0188 (3)	0.0153 (3)	−0.0007 (3)	0.000	0.000
Zn2	0.0155 (3)	0.0266 (4)	0.0111 (3)	0.000	0.000	−0.0011 (3)
Zn3	0.0160 (5)	0.0135 (5)	0.0242 (5)	0.000	0.000	0.000
Sb1	0.00910 (19)	0.01206 (19)	0.01176 (19)	0.00060 (13)	0.000	0.000
Sb2	0.01162 (19)	0.01295 (19)	0.00878 (18)	0.000	0.000	−0.00029 (13)

Geometric parameters (Å, º)

Zn1—Sb1	2.6736 (7)	Zn3—Sb1^vi	2.7204 (7)
Zn1—Sb2^i	2.7202 (5)	Zn3—Sb2	2.7699 (8)
Zn1—Sb2	2.7202 (5)	Zn3—Sb2^i	2.7699 (8)
Zn1—Sb1^ii	2.7921 (8)	Sb1—Zn3^vii	2.7204 (7)
Zn2—Sb2^iii	2.6436 (8)	Sb1—Zn2^viii	2.7490 (5)
Zn2—Sb1^ii	2.7490 (5)	Sb1—Zn2^ix	2.7490 (5)
Zn2—Sb1^iv	2.7490 (5)	Sb1—Zn1^vi	2.7921 (8)
Zn2—Sb2	2.8976 (8)	Sb2—Zn2^iii	2.6436 (8)
Zn3—Sb1^v	2.7204 (7)	Sb2—Zn1^x	2.7202 (5)
Sb1—Zn1—Sb2^i	118.018 (19)	Zn1—Sb1—Zn2^viii	140.808 (12)
Sb1—Zn1—Sb2	118.018 (19)	Zn3^vii—Sb1—Zn2^viii	70.599 (19)
Sb2^i—Zn1—Sb2	88.46 (2)	Zn1—Sb1—Zn2^ix	140.808 (12)
Sb1—Zn1—Sb1^ii	106.72 (2)	Zn3^vii—Sb1—Zn2^ix	70.599 (19)
Sb2^i—Zn1—Sb1^ii	112.526 (19)	Zn2^viii—Sb1—Zn2^ix	78.38 (2)
Sb2—Zn1—Sb1^ii	112.527 (19)	Zn1—Sb1—Zn1^vi	116.97 (2)
Sb2^iii—Zn2—Sb1^ii	124.281 (18)	Zn3^vii—Sb1—Zn1^vi	128.06 (2)
Sb2^iii—Zn2—Sb1^iv	124.281 (18)	Zn2^viii—Sb1—Zn1^vi	69.726 (19)
Sb1^ii—Zn2—Sb1^iv	92.35 (2)	Zn2^ix—Sb1—Zn1^vi	69.726 (19)
Sb2^iii—Zn2—Sb2	98.26 (2)	Zn2^iii—Sb2—Zn1	128.228 (17)
Sb1^ii—Zn2—Sb2	108.52 (2)	Zn2^iii—Sb2—Zn1^x	128.228 (17)
Sb1^iv—Zn2—Sb2	108.52 (2)	Zn1—Sb2—Zn1^x	79.19 (2)
Sb1^v—Zn3—Sb1^vi	93.62 (3)	Zn2^iii—Sb2—Zn3	144.66 (2)
Sb1^v—Zn3—Sb2	119.910 (7)	Zn1—Sb2—Zn3	76.159 (18)
Sb1^vi—Zn3—Sb2	119.910 (7)	Zn1^x—Sb2—Zn3	76.159 (18)
Sb1^v—Zn3—Sb2^i	119.911 (7)	Zn2^iii—Sb2—Zn2	81.74 (2)
Sb1^vi—Zn3—Sb2^i	119.911 (7)	Zn1—Sb2—Zn2	68.559 (18)
Sb2—Zn3—Sb2^i	86.47 (3)	Zn1^x—Sb2—Zn2	68.560 (18)
Zn1—Sb1—Zn3^vii	114.96 (2)	Zn3—Sb2—Zn2	133.59 (2)

Symmetry codes: (i) x, y, −z+1/2; (ii) −x+1/2, y+1/2, −z+1/2; (iii) −x, −y+1, −z; (iv) x−1/2, y+1/2, z; (v) x−1/2, y−1/2, z; (vi) −x+1/2, y−1/2, −z+1/2; (vii) x+1/2, y+1/2, z; (viii) x+1/2, y−1/2, −z+1/2; (ix) x+1/2, y−1/2, z; (x) −x, y, −z+1/2.

(III) Dirubidium pentacadmium tetra(arsenide/antimonide)

Crystal data

Rb2Cd5(As·Sb)4	F(000) = 1856
Mr = 1079.45	Dx = 5.869 Mg m^−3
Orthorhombic, Cmcm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2c 2	Cell parameters from 2999 reflections
a = 12.6086 (11) Å	θ = 3.1–27.5°
b = 7.6761 (6) Å	µ = 26.64 mm^−1
c = 12.6232 (11) Å	T = 200 K
V = 1221.74 (18) Å^3	Block, black
Z = 4	0.08 × 0.06 × 0.06 mm

Data collection

Bruker SMART CCD area-detector diffractometer	768 independent reflections
Radiation source: fine-focus sealed tube	728 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.027
ϕ and ω scans	θmax = 27.5°, θmin = 3.1°
Absorption correction: multi-scan (SADABS; Sheldrick, 2008a)	h = −16→16
Tmin = 0.237, Tmax = 0.317	k = −9→9
7711 measured reflections	l = −16→16

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.013	w = 1/[σ^2(Fo^2) + (0.0097P)^2 + 1.3211P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.026	(Δ/σ)max < 0.001
S = 1.09	Δρmax = 0.57 e Å^−3
768 reflections	Δρmin = −0.61 e Å^−3
37 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00060 (2)

Special details

Experimental. Data collection is performed with four batch runs at ϕ = 0.00° (456 frames), at ϕ = 90.00° (456 frames), at ϕ = 180.00° (456 frames) and at ϕ = 270.00° (456 frames). Frame width = 0.40° in ω. Data are merged, corrected for decay and treated with multi-scan absorption corrections.

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Rb1	0.20959 (3)	0.0000	0.0000	0.02233 (11)
Cd1	0.14478 (2)	0.38078 (4)	0.2500	0.02087 (10)
Cd2	0.0000	0.64870 (4)	0.10582 (2)	0.01853 (9)
Cd3	0.0000	0.00707 (6)	0.2500	0.02068 (12)
As1	0.34187 (3)	0.25362 (4)	0.2500	0.01467 (12)	0.680 (4)
Sb1	0.34187 (3)	0.25362 (4)	0.2500	0.01467 (12)	0.320 (4)
As2	0.0000	0.27231 (5)	0.09855 (3)	0.01495 (14)	0.822 (4)
Sb2	0.0000	0.27231 (5)	0.09855 (3)	0.01495 (14)	0.178 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0234 (2)	0.0213 (2)	0.0223 (2)	0.000	0.000	0.00341 (17)
Cd1	0.01903 (17)	0.02488 (18)	0.01871 (17)	−0.00181 (13)	0.000	0.000
Cd2	0.02065 (17)	0.01993 (17)	0.01501 (16)	0.000	0.000	−0.00032 (12)
Cd3	0.0230 (2)	0.0140 (2)	0.0250 (2)	0.000	0.000	0.000
As1	0.01220 (19)	0.01378 (19)	0.0180 (2)	0.00173 (14)	0.000	0.000
Sb1	0.01220 (19)	0.01378 (19)	0.0180 (2)	0.00173 (14)	0.000	0.000
As2	0.0204 (2)	0.0140 (2)	0.0104 (2)	0.000	0.000	0.00079 (14)
Sb2	0.0204 (2)	0.0140 (2)	0.0104 (2)	0.000	0.000	0.00079 (14)

Geometric parameters (Å, º)

Cd1—As1	2.6698 (5)	Cd2—Cd3^vi	3.2985 (5)
Cd1—As2	2.7714 (4)	Cd3—Sb1^vii	2.7858 (5)
Cd1—Sb2^i	2.7714 (4)	Cd3—As1^vii	2.7858 (5)
Cd1—As2^i	2.7714 (4)	Cd3—Sb1^viii	2.7858 (5)
Cd1—Sb1^ii	2.8669 (5)	Cd3—As1^viii	2.7858 (5)
Cd1—As1^ii	2.8669 (5)	Cd3—Sb2^i	2.7929 (5)
Cd1—Cd2	3.2976 (4)	Cd3—As2^i	2.7929 (5)
Cd1—Cd2^i	3.2976 (4)	Cd3—As2	2.7929 (5)
Cd1—Cd3	3.4002 (5)	Cd3—Cd2^ix	3.2985 (5)
Cd2—Sb2^iii	2.6501 (5)	Cd3—Cd2^x	3.2985 (5)
Cd2—As2^iii	2.6501 (5)	Cd3—Cd1^v	3.4002 (5)
Cd2—Sb1^ii	2.8172 (4)	As1—Cd3^xi	2.7858 (5)
Cd2—As1^ii	2.8172 (4)	As1—Cd2^xii	2.8172 (4)
Cd2—Sb1^iv	2.8172 (4)	As1—Cd2^xiii	2.8172 (4)
Cd2—As1^iv	2.8172 (4)	As1—Cd1^viii	2.8669 (5)
Cd2—As2	2.8906 (5)	As2—Cd2^iii	2.6501 (5)
Cd2—Cd1^v	3.2976 (4)	As2—Cd1^v	2.7714 (4)
As1—Cd1—As2	120.215 (12)	Cd1^v—Cd2—Cd3^vi	102.450 (11)
As1—Cd1—Sb2^i	120.215 (12)	Cd1—Cd2—Cd3^vi	102.450 (11)
As2—Cd1—Sb2^i	87.232 (16)	Sb1^vii—Cd3—Sb1^viii	91.41 (2)
As1—Cd1—As2^i	120.215 (12)	As1^vii—Cd3—Sb1^viii	91.41 (2)
As2—Cd1—As2^i	87.232 (16)	Sb1^vii—Cd3—As1^viii	91.41 (2)
As1—Cd1—Sb1^ii	108.079 (13)	As1^vii—Cd3—As1^viii	91.41 (2)
As2—Cd1—Sb1^ii	109.792 (12)	Sb1^vii—Cd3—Sb2^i	120.604 (7)
Sb2^i—Cd1—Sb1^ii	109.792 (12)	As1^vii—Cd3—Sb2^i	120.604 (7)
As2^i—Cd1—Sb1^ii	109.792 (12)	Sb1^viii—Cd3—Sb2^i	120.604 (7)
As1—Cd1—As1^ii	108.079 (13)	As1^viii—Cd3—Sb2^i	120.604 (7)
As2—Cd1—As1^ii	109.792 (12)	Sb1^vii—Cd3—As2^i	120.604 (7)
Sb2^i—Cd1—As1^ii	109.792 (12)	As1^vii—Cd3—As2^i	120.604 (7)
As2^i—Cd1—As1^ii	109.792 (12)	Sb1^viii—Cd3—As2^i	120.604 (7)
As1—Cd1—Cd2	138.011 (9)	As1^viii—Cd3—As2^i	120.604 (7)
As2—Cd1—Cd2	56.083 (11)	Sb1^vii—Cd3—As2	120.605 (7)
Sb2^i—Cd1—Cd2	101.739 (13)	As1^vii—Cd3—As2	120.605 (7)
As2^i—Cd1—Cd2	101.739 (13)	Sb1^viii—Cd3—As2	120.605 (7)
Sb1^ii—Cd1—Cd2	53.839 (9)	As1^viii—Cd3—As2	120.605 (7)
As1^ii—Cd1—Cd2	53.839 (9)	Sb2^i—Cd3—As2	86.40 (2)
As1—Cd1—Cd2^i	138.011 (9)	As2^i—Cd3—As2	86.40 (2)
As2—Cd1—Cd2^i	101.739 (13)	Sb1^vii—Cd3—Cd2^ix	54.377 (10)
Sb2^i—Cd1—Cd2^i	56.082 (11)	As1^vii—Cd3—Cd2^ix	54.377 (10)
As2^i—Cd1—Cd2^i	56.082 (11)	Sb1^viii—Cd3—Cd2^ix	54.377 (10)
Sb1^ii—Cd1—Cd2^i	53.839 (9)	As1^viii—Cd3—Cd2^ix	54.377 (10)
As1^ii—Cd1—Cd2^i	53.839 (9)	Sb2^i—Cd3—Cd2^ix	170.290 (14)
Cd2—Cd1—Cd2^i	66.997 (13)	As2^i—Cd3—Cd2^ix	170.290 (14)
As1—Cd1—Cd3	101.026 (14)	As2—Cd3—Cd2^ix	103.313 (11)
As2—Cd1—Cd3	52.619 (10)	Sb1^vii—Cd3—Cd2^x	54.377 (10)
Sb2^i—Cd1—Cd3	52.619 (10)	As1^vii—Cd3—Cd2^x	54.377 (10)
As2^i—Cd1—Cd3	52.619 (10)	Sb1^viii—Cd3—Cd2^x	54.377 (10)
Sb1^ii—Cd1—Cd3	150.895 (14)	As1^viii—Cd3—Cd2^x	54.377 (10)
As1^ii—Cd1—Cd3	150.895 (14)	Sb2^i—Cd3—Cd2^x	103.313 (12)
Cd2—Cd1—Cd3	103.234 (11)	As2^i—Cd3—Cd2^x	103.313 (12)
Cd2^i—Cd1—Cd3	103.234 (11)	As2—Cd3—Cd2^x	170.290 (14)
Sb2^iii—Cd2—Sb1^ii	124.297 (10)	Cd2^ix—Cd3—Cd2^x	66.977 (15)
As2^iii—Cd2—Sb1^ii	124.297 (10)	Sb1^vii—Cd3—Cd1	166.769 (14)
Sb2^iii—Cd2—As1^ii	124.297 (10)	As1^vii—Cd3—Cd1	166.769 (14)
As2^iii—Cd2—As1^ii	124.297 (10)	Sb1^viii—Cd3—Cd1	101.825 (11)
Sb2^iii—Cd2—Sb1^iv	124.297 (10)	As1^viii—Cd3—Cd1	101.825 (11)
As2^iii—Cd2—Sb1^iv	124.297 (10)	Sb2^i—Cd3—Cd1	52.047 (9)
Sb1^ii—Cd2—Sb1^iv	90.104 (15)	As2^i—Cd3—Cd1	52.047 (9)
As1^ii—Cd2—Sb1^iv	90.104 (15)	As2—Cd3—Cd1	52.047 (9)
Sb2^iii—Cd2—As1^iv	124.297 (10)	Cd2^ix—Cd3—Cd1	134.717 (6)
As2^iii—Cd2—As1^iv	124.297 (10)	Cd2^x—Cd3—Cd1	134.717 (6)
Sb1^ii—Cd2—As1^iv	90.104 (15)	Sb1^vii—Cd3—Cd1^v	101.825 (11)
As1^ii—Cd2—As1^iv	90.104 (15)	As1^vii—Cd3—Cd1^v	101.825 (11)
Sb2^iii—Cd2—As2	101.407 (14)	Sb1^viii—Cd3—Cd1^v	166.769 (14)
As2^iii—Cd2—As2	101.407 (14)	As1^viii—Cd3—Cd1^v	166.769 (14)
Sb1^ii—Cd2—As2	107.834 (11)	Sb2^i—Cd3—Cd1^v	52.047 (9)
As1^ii—Cd2—As2	107.834 (11)	As2^i—Cd3—Cd1^v	52.047 (9)
Sb1^iv—Cd2—As2	107.834 (11)	As2—Cd3—Cd1^v	52.047 (9)
As1^iv—Cd2—As2	107.834 (11)	Cd2^ix—Cd3—Cd1^v	134.717 (6)
Sb2^iii—Cd2—Cd1^v	132.841 (10)	Cd2^x—Cd3—Cd1^v	134.717 (6)
As2^iii—Cd2—Cd1^v	132.841 (10)	Cd1—Cd3—Cd1^v	64.943 (15)
Sb1^ii—Cd2—Cd1^v	102.330 (12)	Cd1—As1—Cd3^xi	114.258 (17)
As1^ii—Cd2—Cd1^v	102.330 (12)	Cd1—As1—Cd2^xii	139.753 (7)
Sb1^iv—Cd2—Cd1^v	55.246 (11)	Cd3^xi—As1—Cd2^xii	72.128 (11)
As1^iv—Cd2—Cd1^v	55.246 (11)	Cd1—As1—Cd2^xiii	139.753 (7)
As2—Cd2—Cd1^v	52.713 (9)	Cd3^xi—As1—Cd2^xiii	72.128 (12)
Sb2^iii—Cd2—Cd1	132.841 (10)	Cd2^xii—As1—Cd2^xiii	80.488 (15)
As2^iii—Cd2—Cd1	132.841 (10)	Cd1—As1—Cd1^viii	114.811 (15)
Sb1^ii—Cd2—Cd1	55.246 (10)	Cd3^xi—As1—Cd1^viii	130.931 (16)
As1^ii—Cd2—Cd1	55.246 (10)	Cd2^xii—As1—Cd1^viii	70.916 (10)
Sb1^iv—Cd2—Cd1	102.330 (12)	Cd2^xiii—As1—Cd1^viii	70.916 (10)
As1^iv—Cd2—Cd1	102.330 (12)	Cd2^iii—As2—Cd1	127.069 (12)
As2—Cd2—Cd1	52.713 (9)	Cd2^iii—As2—Cd1^v	127.069 (12)
Cd1^v—Cd2—Cd1	67.227 (13)	Cd1—As2—Cd1^v	82.401 (16)
Sb2^iii—Cd2—Cd3^vi	110.262 (14)	Cd2^iii—As2—Cd3	146.425 (18)
As2^iii—Cd2—Cd3^vi	110.262 (14)	Cd1—As2—Cd3	75.334 (12)
Sb1^ii—Cd2—Cd3^vi	53.495 (9)	Cd1^v—As2—Cd3	75.334 (12)
As1^ii—Cd2—Cd3^vi	53.495 (9)	Cd2^iii—As2—Cd2	78.593 (14)
Sb1^iv—Cd2—Cd3^vi	53.495 (9)	Cd1—As2—Cd2	71.204 (11)
As1^iv—Cd2—Cd3^vi	53.495 (9)	Cd1^v—As2—Cd2	71.204 (11)
As2—Cd2—Cd3^vi	148.331 (14)	Cd3—As2—Cd2	134.982 (16)

Symmetry codes: (i) x, y, −z+1/2; (ii) −x+1/2, y+1/2, −z+1/2; (iii) −x, −y+1, −z; (iv) x−1/2, y+1/2, z; (v) −x, y, −z+1/2; (vi) x, y+1, z; (vii) x−1/2, y−1/2, z; (viii) −x+1/2, y−1/2, −z+1/2; (ix) x, y−1, z; (x) x, y−1, −z+1/2; (xi) x+1/2, y+1/2, z; (xii) x+1/2, y−1/2, −z+1/2; (xiii) x+1/2, y−1/2, z.