An Unusual Triple-Decker Variant of the Tetragonal BaAl4-Structure

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

An Unusual Triple-Decker Variant of the Tetragonal BaAl4‑Structure Type: Synthesis, Structural Characterization, and Chemical Bonding of Sr3Cd8Ge4 and Eu3Cd8Ge4 Nian-Tzu Suen,† Linna Huang, John J. Meyers, and Svilen Bobev* Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, United States S Supporting Information *

ABSTRACT: Reported are the synthesis and the crystal structures of the new ternary phases Sr3Cd8Ge4 and Eu3Cd8Ge4. The structures of both compounds have been established by singlecrystal and powder X-ray diffraction methods. They crystallize in the tetragonal space group I4/mmm (No. 139, own structure type, Pearson symbol tI30) with Z = 2, and lattice parameters as follows: a = 4.4941(14) Å; c = 35.577(7) Å for Sr3Cd8Ge4, and a = 4.4643(12) Å; c = 35.537(9) Å for Eu3Cd8Ge4, respectively. The most prominent feature of the structure is the complex [Cd2Ge] polyanionic framework, derived by unique ordering of the Cd and Ge atoms in fragments that bear resemblance to the BaAl4 structure type. Temperature dependent DC magnetization measurements indicate that Eu3Cd8Ge4 displays Curie−Weiss paramagnetic behavior with no sign of magnetic ordering in the measured range. Theoretical considerations of the electronic structure on the basis of the tight-binding linear muffin-tin orbital (TB-LMTO-ASA) method are also presented and discussed.

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“cations” and “anions;” thereby, all atoms should contribute significantly to the overall bonding. In many (most) cases, a substantial degree of delocalization must also be considered. Several comprehensive papers such as those by Zheng and Hoffman,10,11 Miller and Burdett,12 Häussermann et al.,13 and Seo and Corbett14 are excellent treatises on the electronic structure of such compounds. The detailed studies show that despite the fact that the bonding is expected to be electronically most stable with 14 valence electrons per formula, the valence electron count in BaAl4-related structures can be varied significantly. In that regard, it is easy to understand why extended families of isostructural phases are possible with seemingly very different elements or why certain structure types have “ranges of electronic stability” and not “fixed electron count.” Today, examples of compounds with valence electrons per formula ranging between 12 and 16 are known, suggesting that factors beyond the basic valence electron count are also at play.12 This argument is also supported by the fact that CaAl4 and EuIn4 form as distorted derivates of BaAl4 (space group C2/m) regardless of the same number of valence electrons for all three.14−16 Another isoelectronic but not isotypic example is the already mentioned La3Al11 (=LaAl3.67).8 All these findings attest for the strong correlation between the crystal and electronic structure here, and in polar intermetallics in general.

INTRODUCTION Intermetallic compounds with the BaAl4 structure type have been studied extensively.1−21 To date, more than 2200 structures belonging to this family have been deposited in the Inorganic Crystal Structure Database (ICSD).22 Among those, specific mentions deserve the common ordered variants known as the ThCr2Si2 (I4/mmm),2 CaBe2Ge2 (P4/nmm),3 and BaNiSn3 (I4mm)4 types (Figure 1). Some distorted variants also occur within the BaAl4 family with a lower symmetry monoclinic space group.5 BaMg2Sn26 and BaCu2Sb2 (LT)7 can be considered as linear intergrowths of ThCr2Si2 and CaBe2Ge2; i.e., superstructures obtained by doubling or tripling the c axes. La3Al11□ (□ denotes a missing atom) is an ordered defect derivative of BaAl4.8 The structures of Dy3Co6Sn5, Yb3Au5.5Ga5.5, Rb5Hg19, U2Co3Si5, Eu2Au2Sn5, Ce3Pd6Sb5, Lu2Co3Si5, La2NiAl7, and CePt0.95Ga3.05 also have their roots in the BaAl4 structure and can be considered as superstructures of the latter via ordering of defects/missing atoms. A detailed review of the crystallographic relationships between the above-mentioned structures has been offered by Kußmann et al.9 Because the chemical bonding in this class of materials can be, at least in part, associated with the notion of covalent twocenter, two-electron bonds,10−14 simple chemical concepts such as the ideas of valency and the octet rule can be applied, although one must remember that closed-shell electronic configurations for all atoms may not be required. Simply put, the electronegativity differences between the constituting elements are insufficient to create ionic interactions between © XXXX American Chemical Society

Received: October 31, 2017

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DOI: 10.1021/acs.inorgchem.7b02781 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. A schematic representation of the BaAl4 structure and its most common ordered variants: BaNiSn3, CaBe2Ge2, and ThCr2Si2. All projections are approximately down the [100] direction. The broken lines in the ThCr2Si2 structure denote the lack of homoatomic bonding between adjacent layers in certain examples, emphasizing their 2D nature. evacuated tubes with the mixtures inside were kept upright and moved into programmable muffle furnaces. The elemental mixtures were heated to 973 K with a rate of 300 K per hour, allowed to equilibrate at this temperature for 5 h, and then cooled down to 773 K (rate of 30 K per hour). At this temperature, the sealed tubes were removed from the furnace, and the molten residual Cd metal (mp 595 K)26 was separated from the products. Crystals with plate-like morphology and silver−metallic luster were recovered upon opening the tubes in the glovebox, and follow-up diffraction work showed that the isolated crystals were of the title compounds. On this note, we specifically mention that Sr3Cd8Ge4 and Eu3Cd8Ge4 were not the only identified products of these reactions, although they were the major phases. SrCd11 and EuCd111a were minor phases, alongside unreacted Ge and Cd. After the structure and composition were established, attempts were made to synthesize Sr3Cd8Ge4 and Eu3Cd8Ge4 by fusing together the respective elements in Nb containers, which had been sealed on both ends with an arc welder. To avoid possible oxidation, the Nb containers were enclosed in evacuated fused silica jackets (ca. 10−5 Torr). The reactions were carried out at 1173 K (heating rate of 200 K/h) for 12 h, followed by cooling to room temperature over a period of 30 h. The reaction products were visibly inhomogeneous, and annealing them for 1 week at 773 K did not change the outcome. The respective powder X-ray diffraction patterns were generally consistent with the simulations from the single-crystal data for Sr3Cd8Ge4 and Eu3Cd8Ge4, but subtle differences in the peak positions and intensities could be noticed. Subsequent single-crystal X-ray diffraction work confirmed that the materials obtained from the on-stoichiometry reactions in sealed Nb containers are not exactly the same as the ones from the flux-growth process. Specifically, the refined formula of the sample with nominal composition SrCd2Ge2 was SrCd∼2.2Ge∼1.8, while the refined formula of the sample with nominal composition SrCd3Ge was SrCd∼2.7Ge∼1.3, both showing moderate to extensive Cd/Ge disorder (vide infra). Further attempts to optimize the reaction conditions (by varying the stroichiometric ratios and temperature) showed that all Sr−Cd−Ge samples obtained from the melt are nonstoichiometric SrCd2+xGe2−x (0.2 < x < 0.7). Similar work in sealed Nb containers in the system Eu−Cd−Ge was not carried out, although it is expected that EuCd2+xGe2−x will exist and will form with a similar phase width as that of SrCd2+xGe2−x. To complement our studies on cadmium germanides with divalent metals, we also explored the corresponding Ca−Cd−Ge, Ba−Cd−Ge, and Yb−Cd−Ge systems. These synthetic efforts did not yield phases isotypic with Sr3Cd8Ge4 and Eu3Cd8Ge4. Only binary compounds were identified from the reactions of Ca, Cd, and Ge (main product was CaCd6);1a the reactions of Ba, Cd, and Ge produced mostly BaCd2Ge2 (or rather BaCd2+xGe2−x, as discussed later on), while the reactions of Yb, Cd, and Ge produced mostly Yb2CdGe2.25 The failure to obtain the desired AE3Cd8Ge4 phases with Ca, Yb, or Ba (smallest and largest atomic size among the least electronegative metals in

Recently, the interest in compounds adopting the ThCr2Si2 and some other closely related structures has surged, and it has largely been instigated by the discovery of unconventional superconductivity in several classes of iron-arsenides.17,18 Though not related to research on superconductors, our group has studied related ternary transition metal pnictides and has identified unusual behavior, for example, in RENi2−xP2 (RE = La, Ce, Pr),19 which have been shown to accommodate a wide range of defects on the transition metal site, with the variation strongly dependent on the reaction conditions. Not surprisingly, perhaps, the Ni defects act as a means to alleviate unfavorable antibonding interactions within the structure, which is an artifact of the apparent electron-richness. However, in other cases worked out in our laboratory, such as AEAl4−xGex (AE = Sr, Ba, Eu; x ≈ 0.3−0.4)20 and BaGa4−xSnx (x ≈ 0.9),21 we have encountered rare examples of electronrich phases, whose parent structure is also the prototypical BaAl4. Over the course of studying these compounds, we naturally progressed toward the AE−Zn−Tt and AE−Cd−Tt systems (Tt = group 14 element, AE = Sr, Ba, Eu, hereafter). We expected to find phases isotypic to the above-mentioned aluminides and gallides, albeit on the electron-poor side. In this paper, we present the synthesis and the structural characterization of two such ternary phases with formulas Sr3Cd8Ge4 and Eu3Cd8Ge4. The structures of these compounds have been accurately established by single-crystal X-ray diffraction methods and are derived from the BaAl4 structure type by unique ordering of the Cd and Ge atoms. Structural relationships are discussed alongside electronic structure calculations and experimental evidence for previously overlooked phase width in the known compounds SrCd2Ge223 and BaCd2Ge2.24

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EXPERIMENTAL SECTION

Synthesis. The starting materials were stored and handled inside an argon-filled glovebox with controlled moisture and oxygen levels below 1 ppm. Sr and Ba (dendritic, Alfa), Eu (ingot, Ames Laboratory), Cd (shot, Alfa), and Ge (pieces, Alfa)all with stated purity greater than 99.9% metal basiswere used as received. The initial reactions were done in a manner reminiscent of the synthesis of RE2CdGe2 (RE = rare-earth element).25 A much larger (5 times) than stoichiometric amount of Cd metal was used deliberately with the aim for it to be a reactive flux. The elements were weighed in the glove-box and loaded into 2 cm3 alumina crucibles, which were then taken out and sealed in evacuated fused silica tubes. The B


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Inorganic Chemistry stable divalent states) indicates that besides electronic stability, geometric factors, i.e., crystal packing, are important for the realization of the structure in question. X-ray Powder Diffraction. X-ray powder diffraction data were taken at room temperature on a Rigaku MiniFlex powder diffractometer with filtered Cu Kα radiation. The powder X-ray diffraction patterns could be readily indexed with the body-centered tetragonal subcell (a ≈ 4.5 Å; c ≈ 11.9 Å) corresponding to the BaAl4type structure (Figure 2); reliable indexing of the powder patterns to

from unityalmost all were in the range of 98−102% within 3σ. For both Sr3Cd8Ge4 and Eu3Cd8Ge4 refinements, however, the Cd2 site showed larger deviations95% within the 5σ confidence range for the former and 96% within 7σ for the latter. This may indicate that Cd2 is partially substituted by Ge (in ca. 8:1 ratio), but since the eventual disorder is small, both Sr3Cd8Ge4 and Eu3Cd8Ge4 are hereafter referred to as line compounds. Relevant details of the crystallographic work for Sr3Cd8Ge4 and Eu3Cd8Ge4 are summarized in Table 1. Crystallographic data from the

Table 1. Crystallographic Data and Refinement Parameters for Sr3Cd8Ge4 and Eu3Cd8Ge4 (Tetragonal Crystal System with Space Group I4/mmm (No. 139))a empirical formula −1

fw, g mol Z a, Å c, Å V, Å3 ρcalcd, g cm−3 μ (Mo Kα), cm−1 GOF on F2 R1 [I > 2σ(I)]b wR2 [I > 2σ(I)]b R1 [all data]b wR2 [all data]b

Figure 2. Simulated powder X-ray diffraction patterns from the singlecrystal refinements of Eu3Cd8Ge4 (S.G. I4/mmm with a ≈ 4.5 Å; c ≈ 35.5 Å) and EuCd2+xGe2−x (x ≈ 0.6; S.G. I4/mmm with a ≈ 4.5 Å; c ≈ 11.9 Å). For further crystallographic details, the reader is referred to Table 1. The inset shows a magnified view of the 004, 101, 105, and 107 reflections for Eu3Cd8Ge4 (red arrows), which are expected to be the clearest indicators of the tripled periodicity along the c axis.

Sr3Cd8Ge4

Eu3Cd8Ge4

1452.42 2 4.4941(14) 35.577(7) 718.5(3) 6.71 307.7 1.126 0.0290 0.0709 0.0363 0.0775

1645.44 2 4.4643(12) 35.537(9) 708.3(3) 7.72 330.8 1.136 0.0333 0.0780 0.0400 0.0811

a

Both data collections are done at 120(2) K, using Mo Kα radiation with wavelength λ = 0.71073 Å. Both crystals were obtained from reactions carried out in Cd metal flux. bR1 = ∑∥Fo| − |Fc∥/∑|Fo|; wR2 = [∑[w(Fo2 − Fc2)2]/∑[w(Fo2)2]]1/2, and w = 1/[σ2Fo2 + (A·P)2 + B·P], P = (Fo2 + 2Fc2)/3; A and B are weight coefficients.

the true unit cell determined on the basis of the single-crystal X-ray work (a ≈ 4.5 Å; c ≈ 35.5 Å) could not be accomplished. The reason for this is that the observed intensities of many peaks are very low notice that the peak positions/intensities from simulations show that the four reflections at a low Bragg angle that will be the hallmark of the tripled unit cell are very weak (I/Imax is in the range 0.2−1.0%). A representative experimental powder diffraction pattern is shown in the Supporting Information (Figure S1). The powder X-ray diffraction patterns also indicated that all compounds described in this paper are stable in the air for at least 1 week. Single Crystal X-ray Diffraction. Crystals were selected under an optical microscope, cut to desired dimensions ( 2σ(I)]b wR2 [I > 2σ(I)]b R1 [all data]b wR2 [all data]b

485.5 2 4.5021(5) 11.917(3) 241.54(7) 6.68 304.5 1.152 0.0258 0.0561 0.0289 0.0573

467.6 2 4.5147(12) 11.593(6) 236.3(2) 6.57 319.7 1.125 0.0245 0.0534 0.0333 0.0566

527.2 2 4.6516(8) 11.711(4) 253.39(11) 6.91 265.8 1.299 0.0122 0.0271 0.0122 0.0271

511.3 2 4.6814(2) 11.3858(11) 249.53(3) 6.81 276.9 1.189 0.0087 0.0221 0.0087 0.0221

507.3 2 4.6831(7) 11.340(3) 248.71(9) 6.77 279.6 1.281 0.0145 0.0307 0.0147 0.0308

All data collections are done at 200(2) K, using Mo Kα radiation with wavelength λ = 0.71073 Å. The specimens are obtained from stoichiometric reactions with varied nominal compositions (between 1:2:2 and 1:3:1). bR1 = ∑∥Fo| − |Fc∥/∑|Fo|; wR2 = [∑[w(Fo2 − Fc2)2]/∑[w(Fo2)2]]1/2, and w = 1/[σ2Fo2 + (A·P)2 + B·P], P = (Fo2 + 2Fc2)/3; A and B are weight coefficients. a

follows: Ba = 2.33 Å; Sr = 2.29−2.35 Å; Cd = 1.42−1.74 Å; Ge = 1.38−1.49 Å. The basis sets included Ba 6s, 6p, and 5d orbitals; Sr 5s, 5p, and 4d orbitals; Cd 5s, 5p, and 4d orbitals; and Ge 4s and 4p orbitals. All relativistic effects except spin−orbit coupling were taken into account using a scalar relativistic approximation.35 The Ba 6p, Sr 5p, and Cd 4d were treated by the Löwdin downfolding technique. kSpace integrations were done with the tetrahedron method and 349 kpoints in the Brillouin zone.

Table 3. Atomic Coordinates and Equivalent Isotropic Displacement Parameters (Ueqa) for Sr3Cd8Ge4 and Eu3Cd8Ge4

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RESULTS AND DISCUSSION Structure. The isostructural Sr3Cd8Ge4 and Eu3Cd8Ge4 crystallize in the tetragonal space group I4/mmm (No. 139, Pearson symbol tI30). The asymmetric unit contains seven crystallographically unique atomstwo alkaline-earth metal/ europium atoms, three cadmium atoms, and two germanium atoms, all in special positions. The final positional and equivalent isotropic displacement parameters for Sr3Cd8Ge4 and Eu3Cd8Ge4 are listed in Table 3. Formally, this crystallographic order (Wyckoff sequence ge4da) corresponds to the structure of BaCu2Sb2;7 however, there are sufficient differences between the two (Figure 3), which is why we believe that Sr3Cd8Ge4 and Eu3Cd8Ge4 should be considered in a structure type of their own. As seen from the projection of the Sr3Cd8Ge4 structure presented in Figure 3, it bears a lot of similarities to the structure of BaCu2Sb2.7 Both are 1a × 1b × 3c superstructures of the BaAl4-related structure types (Figure 1). However, while BaCu2Sb27 can be precisely described as a 2:1 intergrowth of CaBe2Ge2 and ThCr2Si2 slabs, respectively (in the figure, CaBe2Ge2 and CaBe2Ge2′ differentiate a “normal” and an “inverted” slab), the same cannot be said for Eu3Cd8Ge4. In the latter case, the stacking sequence is also ABA′ABA′ but the atomic ordering within both slabs A and B is unique. From a group-subgroup point of view, the structure of Sr3Cd8Ge4 can be derived from the structure of BaAl4 by an isomorphic symmetry reduction of index 3 (i3) upon tripling the c axis (Figure 4). The same scheme applies to BaCu2Sb2 (=Ba3Cu6Sb6); however, the distribution of the Cu and Sb atoms is very different from the distribution of the Cd and Ge atoms in Sr3Cd8Ge4. First, because of the difference in the stoichiometry, there are two Cu positions (8g and 4e) in BaCu2Sb2 compared to three Cd sites (8g, 4e, and 4d) in Sr3Cd8Ge4. Second, the two transition metal sites in BaCu2Sb2 formally correspond to the Cd1 and Ge1 in Sr3Cd8Ge4, with

atom

Wyckoff Site

x

Sr1 Sr2 Cd1 Cd2b Cd3 Ge1 Ge2

4e 2a 8g 4e 4d 4e 4e

0 0 0 0 0 0 0

Eu1 Eu2 Cd1 Cd2b Cd3 Ge1 Ge2

4e 2a 8g 4e 4d 4e 4e

y

Sr3Cd8Ge4 0 0 1/2 0 1/2 0 0 Eu3Cd8Ge4 0 0 0 0 0 1/2 0 0 0 1/2 0 0 0 0

z

Ueq (Å2)

0.3301(1) 0 0.0818(1) 0.1304(1) 1/4 0.2037(1) 0.4647(1)

0.010(1) 0.009(1) 0.010(1) 0.013(1) 0.009(1) 0.009(1) 0.009(1)

0.3295(1) 0 0.0815(1) 0.1305(1) 1/4 0.2035(1) 0.4650(1)

0.011(1) 0.010(1) 0.011(1) 0.014(1) 0.010(1) 0.010(1) 0.010(1)

a

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. bUeq for Cd2 in both Sr3Cd8Ge4 and Eu3Cd8Ge4 is slightly larger than the Ueq for the remaining sites. Refining Cd2 with freed site occupation factor (or allowing a small admixture with Ge) leads to modest improvements, although the elongation of the thermal ellipsoid is still present (U11 = U22 = 0.0143; U33 = 0.0834). The results from these model refinements are tabulated in the Supporting Information (Table S4).

the Sb atoms occupying positions designated as Ge2, Cd2, and Cd3 in Figure 4, respectively. Considering another possible way for symmetry reduction with a tripled c axis, one might envision a primitive tetragonal Sr3Cd8Ge4 (Figure S2), a structure which is a linear intergrowth of BaNiSn3 and ThCr2Si2 fragments. To date, this arrangement remains hypothetical. Another triple-decker variant of the BaAl4 structure type that has not be realized experimentally so far would be Sr3Cd10Ge2 (Figure S3), a structure which is a 2:1 linear intergrowth of imaginary SrCd3Ge (BaNiSn3 type) and SrCd4 (BaAl4 type) fragments. Such unique coloring of the Cd and Ge positions in the structure accounts for a number of homo- and heteroatomic interactions (selected interatomic distances are tabulated in D


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Inorganic Chemistry Table 4. Selected Interatomic Distances (< 4 Å) in Sr3Cd8Ge4 and Eu3Cd8Ge4 Sr3Cd8Ge4

Eu3Cd8Ge4

atom pair

distance (Å)

atom pair

distance (Å)

Cd1−Ge2 (2×) Cd1−Cd2 (2×) Cd1−Cd1 (4×) Cd2−Ge1 Cd2−Cd1 (4×) Cd3−Ge1 (4×) Cd3−Cd3 (4×) Ge1−Cd2 Ge1−Cd3 (4×) Ge2−Ge2 Ge2−Cd1 (4×) Sr1−Ge1 (4×) Sr1−Cd2 (4×) Sr1−Cd3 (4×) Sr1−Cd1 (4×) Sr2−Ge2 (8×) Sr2−Cd2 (8×)

2.790(1) 2.836(1) 3.178(1) 2.609(2) 2.836(1) 2.785(1) 3.178(1) 2.609(2) 2.785(1) 2.511(3) 2.790(1) 3.398(1) 3.475(1) 3.628(1) 3.859(1) 3.417(1) 3.676(1)

Cd1−Ge2 (2×) Cd1−Cd2 (2×) Cd1−Cd1 (4×) Cd2−Ge1 Cd2−Cd1 (4×) Cd3−Ge1 (4×) Cd3−Cd3 (4×) Ge1−Cd2 Ge1−Cd3 (4×) Ge2−Ge2 Ge2−Cd1 (4×) Eu1−Ge1 (4×) Eu1−Cd2 (4×) Eu1−Cd3 (4×) Eu1−Cd1 (4×) Eu2−Ge2 (8×) Eu2−Cd2 (8×)

2.778(1) 2.830(1) 3.157(1) 2.596(2) 2.830(1) 2.777(1) 3.157(1) 2.596(2) 2.777(1) 2.486(3) 2.778(1) 3.368(1) 3.463(1) 3.600(1) 3.871(1) 3.393(1) 3.657(1)

surprisingly, the contribution of the Cd−Cd interactions to the overall bonding is not significant, as evident from the electronic structure calculations (vide infra). From an electronic structure standpoint, however, the Cd−Ge interactions appear to be far more important, and this conjecture is supported by both their integrated COHP values (Table S5), as well as the short Cd−Ge distances which measure from 2.6 to2.8 Å (Table 4). These numbers compare very well with the sum of the corresponding Pauling radii (rCd + rGe = 2.62 Å)36 and are slightly shorter, on average, than the distances in RE2CdGe2 (RE = Pr, Nd, Sm, Gd−Yb),25 which are in the range 2.84 Å to 2.97 Å. Having discussed the interactiomic distances in Sr3Cd8Ge4, a brief comment on the presumed line compound SrCd2Ge2 and the proposed by us reassessment of this structure as SrCd2+xGe2−x (Table 2 and Tables S3 and S4) is warranted. In the reported devoid of disorder SrCd2Ge2 structure,23 the following distances are found: dGe−Ge= 2.54 Å, dCd−Ge= 2.81 Å, and dCd−Cd= 3.22 Å. For the analogous BaCd2Ge2,24 dGe−Ge= 2.58 Å, dCd−Ge= 2.82 Å, and dCd−Cd= 3.31 Å are reported. Our experimental work suggests that these compounds have a finite phase width, which is strongly dependent on the reaction conditions. We already showed that recognizing the weak reflections that give rise to tripling of the unit cell is not easily accomplished by routine powder X-ray diffraction (Figure 2, Figure S1). Careful single-crystal work (or synchrotron powder work) is required to measure these Bragg peaks and integrate them properly. This point can also be easily underscored by comparing the refinement of Eu3Cd8Ge4 (Table 1) and the data from a trial solution/refinement of EuCd2.6Ge1.4 (Table S1), done in a BaAl4 subcell. The latter fit to the data results in extensive Ge/Cd disorder at the 4e site (ca. 2:1 ratio)the slightly high residuals for such a simple structure, coupled with the fact that a few relatively weak reflections need to be excluded, are a good indication that the chosen model in the BaAl4 subcell is deficient. These pointers can be easily disregarded, however, unless one recognizes that there are systematic variations of the unit cell volumes (Table 2), which are particularly important as they are the clear tell-tale sign of off-stoichiometry. Specifically,

Figure 3. Schematic representation of the structures of Sr3Cd8Ge4 (a) and BaCu2Sb2 (b). Unit cells are outlined, and the unique positions labeled. The two structures are linear intergrowths along the c-axis of BaAl4-like slabs. For Sr3Cd8Ge4, the slabs are denoted as A and B (A′ is the inverse of A) since they do not correspond to BaNiSn3, CaBe2Ge2, or ThCr2Si2. For BaCu2Sb2, the slabs are akin to the ordering in CaBe2Ge2 and ThCr2Si2, respectively.

Figure 4. Group-subgroup relationship within the Bärnighausen formalism between the structure of SrCd2.67Ge1.33 (BaAl4 type with Ge and Cd co-occupying the 4e site in a ratio 2:1) and its ordered 3fold superstructure Sr3Cd8Ge4.

Table 4). Judging from the length of the Ge2−Ge2 bonds (ca. 2.5 Å), a number that is very close to the sum of the Pauling’s radii (rGe = 1.242 Å),36 these homoatomic interactions are rather strong. Similar distances are observed in many other ternary germanides, such as RE2CdGe2 (dGe−Ge = 2.492(2)− 2.522(1) Å),25 RE2MgGe2 (dGe−Ge = 2.506(2)−2.548(1) Å),37 RE2InGe2 (dGe−Ge = 2.504(5)−2.512(2) Å),38 RE7Li8Ge10 (dGe−Ge = 2.528(2)−2.537(2) Å),39 RE3Li4Ge4 (dGe−Ge = 2.514(2)−2.524(2) Å),40 etc., which are typical for Ge−Ge single bonds in germanides. The shortest Cd−Cd distances measure ca. 2.83 Å, almost twice the Pauling’s single-bonded radius (rCd = 1.382 Å),36 which is indicative of potentially significant covalency of the Cd−Cd interactions. On the basis of distances, the Cd−Cd bonding might be speculated to be one of the driving forces for the formation of these triple-decker arrangements, but E


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Inorganic Chemistry

Sr3Cd8Ge4) can be considered as two-center, two-electron bonds, while the longer bonds within the square pyramids can be considered as five-center, six-electron interactions.1b,10−14 There are two five-center, six-electron bonds and one twocenter, two-electron bond per formula unit, which gives an optimal valence electron count of 14/f.u. For some ThCr2Si2 derivatives, interlayer separations are too large, for example, as in BaMn2Sb2 with dSb−Sb > 3.8 Å;42 therefore, the majority of the compounds with such layered structures have an optimal valence electron count of 16/f.u. From the above, it comes as a surprise that the number of valence electrons in Sr3Cd8Ge4 and Eu3Cd8Ge4 (Eu exists as Eu2+ as evidenced from the magnetic susceptibility data, vide infra) deviates from the ideal values. It is apparent that Sr3Cd8Ge4 = 2e− (Sr) × 3 + 2e− (Cd) × 8 + 4e− (Ge) × 4 = 38e− (or 12.67 electrons if formulated as SrCd2.67Ge1.33) is electron deficient. However, the deduced electron-poor nature of the bonding is not without a precedentthere are known examples of BaAl4-related phases with an even lower electron count, such as CaAu2Si2 (12 v.e.),43 SrMg1.7Ga2.3, and BaMg1.7Ga2.3 (12.3 v.e.),13 as well as EuMg1.7Ga2.3 (12.3 v.e.).44 It is also clear that if one were to try to assign oxidation numbers/formal charges, the application of the valence rules to the discussed structures will be questionable. Taking into account the Pauling electronegativity scale, χSr = 1.0, χGe = 1.8, and χCd = 1.7,36 it can be argued that the Sr−Ge or Sr−Cd interactions are mostly electrostatic. By doing so, the Sr3Cd8Ge4 structure can be partitioned to three Sr2+ cations and a polyanionic [Cd8Ge4]6− framework. This is implicitly done in Figure 3, where bonds are drawn between Cd and Ge atoms only, with the understanding that the notion of Sr2+ is an apparent exaggeration. Further, one should expect that the Ge2 dimer (bond length 2.5 Å) represents a strong homoatomic interaction and that the dimerized Ge atoms will require three additional electrons/each to satisfy their octets. The Cd atoms can be counted as closed shell species ([Kr]4d10 electron configuration) since the closest Cd−Cd contacts measure 2.83 Å and represent weak interactions. Although realistic, this approach leads to no plausible charge-balanced formula based on the description of 2:1 intergrowth of BaNiSn3 and ThCr2Si2 fragments (Figure S2), the electron count in Sr3Cd8Ge4 = (SrCd3Ge)2 + SrCd2Ge2 will be ([Sr2+][Cd2+]3[Ge4−])2([Sr2+][Cd2+]2[Ge3−]2), i.e., eight electrons short of being electron precise. Even ignoring the Ge−Ge bonding completely, the electron count is still vastly underestimated, e.g., [Sr2+]3[Cd2+]8[Ge4−]4, which is six electrons short of being electron precise. The failure to achieve a reasonable partitioning of the available electrons must be due to the somewhat nebulous role of Cd to the bondingCd for certain is not oxidized to Cd2+, and the contribution of the Cd−Cd interactions is not captured by the classic concepts.45 Electronic Structure. In order to better understand the above-mentioned problems of relevance to the bonding and the electron count in this new structure type, electronic structure calculations were performed on Sr3Cd8Ge4 using the TB-LMTO-ASA method.32 Total and partial density of states plots (TDOS and PDOS), together with the crystal orbital Hamilton population (COHP) curves for Sr−Ge, Cd−Ge, Cd−Cd, and Ge−Ge interactions, are presented in Figure 5. The integrated crystal orbital Hamilton populations (iCOHP) are tabulated in Table S5 (Supporting Information).

one will notice that the unit cell volumes of SrCd2+xGe2−x and BaCd2+xGe2−x increase as the amount of Cd (bigger atomic radius than Ge) increases (Table 3). Interestingly, the expansion is only in the c direction. In fact, a small contraction in the ab plane is evident when the metrics of SrCd2.66Ge1.34(2)41 are compared with SrCd2.24Ge1.76(5); the same is also observed on comparison between BaCd2.52Ge1.48(2) and BaCd2.14Ge1.86(1). Given the published unit cell data for SrCd2Ge2 (a = 4.56(2) Å; c = 11.63(2) Å23) and for BaCd2Ge2 (a = 4.6735(6) Å; c = 11.448(1) Å24), it can be argued that in both previous reports, the extent of the structural disorder has been overlooked. The sensitivity of the unit cell to small variations of the network polarity and/or the size of the constituent elements in the BaAl4 and related structures is a known issue. Previous theoretical considerations based on Mulliken population analyses10−12 have suggested that in ternary analogues of the BaAl4 structure, in particular the ordered ThCr2Si2 variant, the element with the greater electronegativity will prefer the 4e site, rather than the 4d site (dubbed apical and basal sites,1b respectively). The reported SrCd2Ge2 and BaCd2Ge2 are refined in the ThCr2Si2 structure type, and the more electronegative Ge is indeed in the apical position. In both SrCd2+xGe2−x and BaCd2+xGe2−x, the apical position is taken by randomly disordered Ge and Cd atoms up to what appears to be the limiting 2:1 ratio. Only in one refined structure, evidence was found for a small Cd/Ge disorder at the 4d site, although the noted preferential occupations hold true. As a result of the unit cell expansion, the separation between two apical corners is slightly enlarged from 2.54 Å in what has previously been known as SrCd2Ge2 (close to the value for the typical two-center two-electron Ge−Ge bonding) to 2.58 Å in the Cd-richest SrCd2.66Ge1.34(2). In the latter case, because of the co-occupation by Cd and Ge atoms of this position, unfavorably close Cd−Ge and even Cd−Cd distances might arise. Further, one can also see that the M−M distance in BaCd2.52Ge1.48(2) (M denotes the mixed occupied Ge/Cd, where the ratio is almost 3:1) is expanded to 2.63 Å. Since SrCd 2.66Ge1.34(2) is Cd-richer than its Ba counterpart BaCd2.52Ge1.48(2), the 0.05 Å difference in the M−M contacts must be due to the larger size of Ba relative to Sr. Given that, for SrCd2.66Ge1.34(2), c = 11.917(3) Å and, for BaCd2.52Ge1.48(2), c = 11.711(4) Å, the elongation in the M−M distances must be contributed by the significant increase of the a-axis parameter of the Ba- vs the Sr-analogs (a = 4.6516(8) Å vs a = 4.5021(5) Å; Table 2). Such geometric considerations might help explain why the triple-decker ordered variant is found for the Sr and Eu compounds, but not for the Ba one, a notion that is further corroborated by the calculations, discussed next. Chemical Bonding and Valence Electron Count. The bonding in BaAl4 and related structures has been studied in detail.10−14 We will only recall that at a basic level, the BaAl4 structure can be rationalized as two layers with PbO-like topology (the atom occupying the 4d site, i.e., the basal position is nearly tetrahedrally coordinated by four atom occupying the 4e site, i.e., the apical position), joined into a 3D-framework via bonds through the apical sites. The basal atoms can be also viewed forming 2D square nets, which are capped from both sides in an alternating fashion by the atoms in apical positions; the latter are coordinated by four basal atoms and one apical atom in a square pyramidal fashion. In terms of bonding, the bonds between the layers which are typically short (viz., the Ge2−Ge2 2.5 Å bonds in the case of F


Article

Inorganic Chemistry

relatively low DOS, EF for SrCd2Ge2 is situated at a peak. The bands at the Fermi level are mainly composed of Sr-4d, Cd-5p, and Ge-4p orbitals. These orbital contributions extend to ca. −5.5 eV below the Fermi level, where a distinct gap of over 1 eV opens up. Below it, in the energy window from ca. −7.0 eV to −8.5 eV, the states are dominated by Cd and Ge s-wave functions. The contributions in the lowest energy segment are primarily contributed by Cd-4d states. From the COHP calculations, the Sr−Ge and Cd−Cd interactions exhibit mostly bonding characters at the Fermi level, while the Cd− Ge and Ge−Ge interactions are antibonding. Approximately 1 eV above EF, all COHP curves show antibonding character, but remarkably, 1 eV below the Fermi level, there is a pseudogap in the DOS corresponding to slightly below 13 e−/f.u. Even though it has been argued before that the rigid-band approach to interpret the electronic structure of BaAl4-type compounds is not valid, the fact that both DOS and COHP curves indicate enhanced electronic stability at a lower valence electron count cannot be overlooked. Careful comparison of the COHP curves for all interactions in Figures 5 and 6 is suggestive of increased delocalization of the Ge s and p states. It is likely that this observation, together with the fact that a higher number of valence electrons will push the Fermi level up, both for Sr3Cd8Ge4 and for SrCd2Ge2, in regions of predominantly antibonding interactions explains our experimental finding that the phase is always SrCd2+xGe2−x with x > 0.2. On this note, it is useful to recall that based on the results from our synthetic and structural work presented in Table 2, the homogeneity range in BaCd2+xGe2−x appears to be different from the range in SrCd2+xGe2−x. Also, as mentioned earlier in the Experimental Section, only Sr3Cd8Ge4 could be made, while the experiments aimed at Ba3Cd8Ge4 produced BaCd2+xGe2−x, always crystallizing in the BaAl4-type subcell. A question naturally arises: why the differences between the Sr and Ba analogs? We reasoned that there could be a synergistic electronic/size effect at play; therefore, the electronic structure of an ordered BaCd2Ge2 (modeled in the ThCr2Si2 structure type) was also computed and summed up in Figure S4 (Supporting Information). The calculations for BaCd2Ge2 mirror, as expected, those for SrCd2Ge2 (Figure 6). The Fermi level is again located almost at a small peak of relatively high density of state. The interactions contributing to it are Cd−Ge (antibonding), Ge−Ge (antibonding), Ba−Ge (bonding), and Cd−Cd (bonding). The total of the antibonding states is slightly larger than the sum of bonding states at the Fermi level, which indicates the ordered BaCd2Ge2 may not be electronically stable. Lowering the Fermi level within the rigid band approximation moves it to a valley (ca. −0.4 eV), with an electron count of 13.6 e−/f.u. (∼BaCd2.2Ge1.8). In this configuration, all bonding interactions are nearly optimized and in bonding states. This electronic structure analysis supports the single-crystal refinements that show Ge is always substituted with Cd (even when the refined composition is very close to the nominal, the Ge/Cd mixing is still 10:1) in order to achieve a stable electronic structure. Since the pseudogap for BaCd2Ge2 is at slightly higher energy compared to the pseudo gap for SrCd2Ge2 (ca. −1 eV), the structure is stabilized with an electron count closer to the ideal for a BaAl4type compound. As a result, the Cd/Ge disorder in BaCd2+xGe2−x is smaller, which could be the reason that the 3-fold superstructure does not exist in the Ba−Cd−Ge system (Ba3Cd8Ge4 = 3× BaCd2.67Ge1.33 will require a higher level of Cd/Ge mixing).

Figure 5. Left panel: Calculated total density of states (DOS) and partial density of states (PDOS) curves for Sr3Cd8Ge4. Right panel: COHP curves for Sr−Ge, Cd−Ge, Cd−Cd, and Ge−Ge interactions. In the −COHP curves, the positive and negative regions represent bonding and antibonding states, respectively. The Fermi level is the energy reference at 0 eV.

As shown in Figure 5, the nonzero DOS at the Fermi level indicates that Sr3Cd8Ge4 should have metallic behavior. The bands at the Fermi level are mainly composed of an admixture of Sr-4d, Cd-5p, and Ge-4p orbitals. The shapes of the curves for the partial density of states for Sr, Cd, and Ge throughout all energy ranges are very similar, suggesting that there are appreciable bonding interactions between the atoms of each element in Sr3Cd8Ge4. The bands in the energy window from ca. −8.5 eV to −10.5 eV are dominated by the Cd-4d contribution. Just above, a segment primarily contributed by Cd and Ge s-states is observed. Below the Fermi level and down to ca. −5 eV, the Sr-4d, Cd-4p, and Ge-4p contribute mostly. From the COHP calculations, Sr−Ge, Cd−Ge, and Ge−Ge interactions exhibit mostly bonding characters below Fermi level, with only a small antibonding character for Ge− Ge. The COHP curves for Cd−Ge and Ge−Ge show antibonding character above EF, while the Sr−Ge interactions remain slightly under-optimized as their COHP shows few bonding states available just above EF. In an effort, from the electronic structure viewpoint, to understand why SrCd2Ge2 (14 e−/f.u.) is not preferred over SrCd2.67Ge1.33 (12.7 e−/f.u.), TB-LMTO calculations were carried out for an ordered SrCd2Ge2 (ThCr2Si2 structure type), and the results are shown in Figure 6. Again, nonzero DOS at the Fermi level indicates that SrCd2Ge2 is a metal. Notice that while EF for Sr3Cd8Ge4 (Figure 5) is in a valley, i.e., a region of

Figure 6. Left panel: Calculated total density of states (DOS) and partial density of states (PDOS) curves for SrCd2Ge2 (ThCr2Si2 structure type). Right panel: COHP curves for Sr−Ge, Cd−Ge, Cd− Cd, and Ge−Ge interactions. In the −COHP curves, the positive and negative regions represent bonding and antibonding states, respectively. The Fermi level is the energy reference at 0 eV. G


Article

Inorganic Chemistry Magnetism. The temperature dependent DC magnetization measurements were performed on a polycrystalline sample of Eu3Cd8Ge4 within the temperature range from 5 to 300 K in field cooling mode (Figure 7). The magnetic

thermal analyses coupled with exploratory work are currently ongoing with the goal to ascertain the phase width and to address the open question whether polymorphism can be the explanation for the behavior in these systems. In a concurrent effort to understand why these (apparently) electron-deficient SrCd2+xGe2−x/BaCd2+xGe2−x/EuCd2+xGe2−x phases form instead of their electron-precise SrCd2Ge2/ BaCd2Ge2/EuCd2Ge2 counterparts, we are considering a molecular orbital approach. In this context, as pointed out by Burdett and Miller,12 the highest valence bands can be viewed as based on antibonding orbitals. Thus, lowering the valence electrons from the ideal 14 electrons/f.u. will remove electrons from antibonding states, which in turn will be expected to enhance the strength of multiple bonds and to electronically stabilize the corresponding structures. While depopulating of antibonding states for SrCd2+xGe2−x may be a plausible explanation for the extensive Cd/Ge mixing and the eventual formation of the ordered Sr3Cd8Ge4 phase, this reasoning does not answer the question why BaCd2+xGe2−x favors higher electron count and why Ba3Cd8Ge4 could not be made. It is apparent that a delicate balance between electronic and geometric effects exists, and the unusual crystal chemistry is suggestive of an interplay between the electronegativity and the atomic sizes in these structures, calling for further studies on these and related systems.

Figure 7. Field-cooled magnetic susceptibility vs temperature of Eu3Cd8Ge4. The inset shows the temperature dependence of the inverse magnetic susceptibility. The red solid line is the linear fit of the data, according to the Curie−Weiss law.

response agrees with the local-moment 4f magnetism expected for Eu2+ (4f7), and the data follow the Curie−Weiss law χ(T) = C/(T − θp),46 where C is the Curie constant (NAμ2eff/3kB) and θp is the Weiss temperature. The effective magnetic moment derived from the Curie constant is 7.0 μB, close but not in perfect agreement with the theoretical value of free ion Eu2+ (for J = 7/2, expected value of 7.94 μB).46 This anomaly is not fully understood at the current stageanother measurement for a different batch also gave a similar value for the effective magnetic moment. We can argue that the sample contains a small amount of an impurity phase, likely Cd metal, which is nonmagnetic but contributed to an error in the determination of the correct mass of the measured sample. The presence of mixed-valent Eu2+/Eu3+ is also a possibility, albeit more distant. Given the stable Eu2+ ground state in intermetallics in general, it can be argued that the hypothesis for an impurity contribution seems more plausible. At very low temperatures, the inverse susceptibility deviates slightly from the linear fit, which is suggesting the presence of short-range magnetic correlations. There are no obvious magnetic orderings down to 5 K. The low, slightly positive value of the Weiss temperature (θp = 1.3 K) indicates that the magnetic interactions are weak, which likely is a consequence of the relatively long Eu−Eu distances (>4.4 Å, longer than those in the rare-earth elemental form1).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b02781. Tables with coordinates and interatomic distances for the reassessed structures of SrCd 2+x Ge 2−x and BaCd2+xGe2−x; table with crystallographic data for EuCd2.6Ge1.4 (same .hkl file used in the refinement of Eu3Cd8Ge4, but processed in a BaAl4-subcell); table with refined coordinates and equivalent displacement parameters for the model refinements on Sr3Cd7.7(1)Ge4.3 and Eu3Cd7.8(1)Ge4.2 (same .hkl files used in the refinement of Sr3Cd8Ge4 and Eu3Cd8Ge4 but refined against a model where Cd and Ge co-occupy the 4e site); integrated crystal orbital Hamilton populations (iCOHP); experimental X-ray powder diffraction pattern for Eu3Cd8Ge4; a precession image generated from the single-crystal data for Eu3Cd8Ge4 showing the h0l layer; structural representations for imaginary compounds derived from similar structural motifs; DOS and COHP curves for BaCd2Ge2 (ThCr2Si2 structure type) (PDF)

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CONCLUSION Polar intermetallics can be regarded as intermediate between the typical intermetallics (metallic bonding) and the typical Zintl phases (covalent and/or ionic bonding), often displaying unusual chemical and physical properties. As in the case of Sr3Cd8Ge4 and Eu3Cd8Ge4, whose structures can be regarded as variants of the common BaAl4 structure with a tripled periodicity constant in one (stacking) direction, the versatile nature of the Ge−Ge, Cd−Ge, and Cd−Cd interactions leads to very complicated bonding patterns. The discovery of these compounds in well-studied systems is another testament to the fact that the available “phase space” for further exploration is vast, and more investigations are warranted. Systematic

Accession Codes

CCDC 1583188−1583195 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (302) 831-8720. Fax: (302) 831-6335. E-mail: [email protected]. H


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Svilen Bobev: 0000-0002-0780-4787 Present Address †

College of Chemistry and Chemical Engineering, Yangzhou University, Yangzhou 225002, People’s Republic of China Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from the National Science Foundation, grants DMR-0743916 (CAREER) and DMR-1709813.

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Article

Inorganic Chemistry (39) Guo, S.-P.; You, T.-S.; Jung, Y.-H.; Bobev, S. Synthesis, crystal chemistry, and magnetic properties of RE7Li8Ge10 and RE11Li12Ge16 (RE = La−Nd, Sm): New members of the [REGe2]n[RELi2Ge]m homologous series. Inorg. Chem. 2012, 51, 6821−6829. (40) Guo, S.-P.; You, T.-S.; Bobev, S. Closely related rare-rarth metal germanides RE2Li2Ge3 and RE3Li4Ge4 (RE = La−Nd, Sm): Synthesis, crystal chemistry, and magnetic properties. Inorg. Chem. 2012, 51, 3119−3129. (41) Sample SrCd2.66Ge1.34(2) is a crystal obtained from a stoichiometric reaction of Sr, Cd, and Ge in a ratio 1:3:1. The Cd content is probably slightly underestimated in the refined composition, as the unit cell volume is somewhat higher than 1/3 of the unit cell volume of Sr3Cd8Ge4. Specifically, the c axis for SrCd2.66Ge1.34(2) is almost 0.2 Å longer than 1/3 of the c axis for Sr3Cd8Ge4, suggesting that the latter triple-decker structure is not realized for the melt-grown crystal. We speculate that annealing the sample for long periods of time (longer than the tried 1 week treatments) might lead to long-range crystallographic order in the tripled unit cell; i.e., the two might be LT/HT phases. Another possible explanation could be that Sr3Cd8Ge4 is a kinetic product (stabilized in the Cd flux). (42) Xia, S.-Q.; Myers, C.; Bobev, S. Combined experimental and density functional theory studies on the crystal structures and magnetic properties of Mg(Mg1−xMnx)2Sb2 (x ≤ 0.25) and BaMn2Sb2. Eur. J. Inorg. Chem. 2008, 2008, 4262−4269. (43) Doerrscheidt, W.; Niess, N.; Schäfer, H. Neue Verbindungen AB2X2 (A = Erdalkalimetall, B = Uebergangselement, X = Element(IV)) im ThCr2Si2-Typ. Z. Naturforsch. B 1976, 31, 890−891. (44) You, T.-S.; Miller, G. J. Phase width and site preferences in the EuMgxGa4−x series. Z. Anorg. Allg. Chem. 2008, 634, 2845−2852. (45) The formula of BaCd2Ge2 where Cd−Cd bonding is avoided can be readily broken down to [Ba2+][Cd2+]2[Ge3−]2; i.e., it is an electron precise phase. The same, but to a much lesser extent, is true for the Cd-leanest composition SrCd2.2Ge1.8 as well. (46) (a) Smart, J. S. Effective Field Theories of Magnetism; Saunders, Philadelphia, PA, 1966. (b) Kittel, C. Introduction to Solid State Physics, 7th ed.; John Wiley and Sons: Hoboken, NJ, 1996.

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An Unusual Triple-Decker Variant of the Tetragonal BaAl4-Structure

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