Open AccessArticle

β-Yb₂CdSb₂—A Complex Non-Centrosymmetric Zintl Polymorph

Spencer R. Watts

Larissa Najera

¹,

Michael O. Ogunbunmi

^2,3

Svilen Bobev

^2,*

and

Sviatoslav Baranets

^1,2,*

Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803, USA

Department of Chemistry and Biochemistry, University of Delaware, Newark, DE 19716, USA

Department of Physics and Computer Science, Xavier University of Louisiana, New Orleans, LA 70125, USA

Authors to whom correspondence should be addressed.

Crystals 2024, 14(11), 920; https://doi.org/10.3390/cryst14110920

Submission received: 1 October 2024 / Revised: 15 October 2024 / Accepted: 21 October 2024 / Published: 25 October 2024

(This article belongs to the Special Issue Crystalline Materials: Polymorphism)

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Figure 1
Ternary Yb−Cd−Sb compositional diagram. The newly identified Yb2CdSb2 polymorph is identified as a red star. Known binary and ternary phases are indicated as well. Note that Yb14CdSb11 and Yb10.5Cd0.5Sb9 have not yet been reported. "> Figure 2
Crystal structures of β-Yb2CdSb2 (a), β-Ca2CdSb2 (b), β-Ca2CdAs2 (c), and α-Yb2CdSb2 (d) viewed along the b-axis. The unit cell of β-Yb2CdSb2 is doubled along the c-axis for clarity. The Ca and Yb atoms are drawn as dark gray, Cd atoms are green, and Pn = Sb/As atoms are blue-gray. [CdPn4] tetrahedral units are drawn in dark green. The unit cells are outlined. Interatomic Cd–Sb contacts exceeding 3.10 Å are not displayed. "> Figure 3
The representation of the β-Yb2CdSb2 structure with the labeled ABC layers. The unit cell of β-Yb2CdSb2 is doubled along the c-axis. Cd atoms with less than 50% occupancy are avoided for clarity (a). Close-up view of the A layer in β-Yb2CdSb2 (b), ∞2[CdSb2]4– layer in β-Ca2CdSb2 (c), and [Cd3Sb10] units composing B/C layers (d). Typical six-coordinated octahedral coordination environment of [YbSb6] units (e) and five-coordinated square pyramidal [YbSb5] units (f). Completeness of the spheres visualizes SOFs. Similar structural units in β-Yb2CdSb2 and β-Ca2CdSb2 are highlighted by red tetrahedra. The color code is the same as in <a href="#crystals-14-00920-f002" class="html-fig">Figure 2</a>. "> Figure 4
Calculated (a) band structure, (b) total (DOS) density of states, and partial (PDOS) density of states for (d) Yb, (e) Cd, and (f) Sb for Yb2CdSb2. An enlarged view of the band structure at the Fermi level is provided in (c). The Fermi level is the energy reference at 0 eV. The second dashed line at 0.08 eV indicates a 2-electron shift per unit cell. ">

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Abstract

The ternary Zintl phase, Yb₂CdSb₂, was discovered to exist in two different polymorphic forms. In addition to the orthorhombic α-Yb₂CdSb₂ (space group Cmc2₁) known for its excellent thermoelectric properties, we present the synthesis and characterization of the crystal and electronic structure of its monoclinic variant, β-Yb₂CdSb₂. Structural characterization was performed with the single-crystal X-ray diffraction method. β-Yb₂CdSb₂ crystallizes in a monoclinic crystal system with the non-centrosymmetric space group Cm (Z = 33, a = 81.801(5) Å, b = 4.6186(3) Å, c = 12.6742(7) Å, β = 93.0610(10)°) and constitutes a new structure type. The complex crystal structure of β-Yb₂CdSb₂ contrasts with the previously studied β-Ca₂CdPn₂ (Pn = P, As, Sb) polymorphs, although it shares similar structural features. It consists of three different layers, made of corner-sharing [CdSb₄] tetrahedra and stacked in the ABC sequence. The layers are interconnected via [CdSb₃] trigonal planar units. Multiple Yb and Cd atomic sites exhibit partial occupancy, resulting in extensive structural disorder. Valence electron partitioning within the Zintl–Klemm formalism yields the formulation (Yb²⁺)_1.98(Cd²⁺)_1.01(Sb³⁻)₂(h⁺)_0.02, highlighting the nearly charge-balanced composition. Detailed electronic structure calculations reveal the closed band gap and presumably semimetallic nature of β-Yb₂CdSb₂ with the band structure features hinting at potential topological properties.

Keywords:

Zintl phases; single-crystal X-ray diffraction; charge balance; structural disorder; topological insulators

1. Introduction

The structural complexity within the family of polar intermetallic and Zintl phases is viewed as a frequently observed phenomenon that influences their physical properties and potential applications [1,2]. Complex compounds with large unit cells containing hundreds of atoms are often characterized by extensive disorder that originates from compositional and structural inhomogeneities. Materials with such complex structural arrangements often possess low glass-like thermal conductivity, offering a promising platform for the design of novel advanced functional materials, such as thermoelectrics [3,4,5,6]. In addition, superstructures with extended periodicity or ordering can induce localization of electronic states and alter band structure. With this in mind, enhancing complexity and promoting the formation of superstructures or complex polymorphs may be viewed as an efficient way to fine-tune the transport properties of the materials.

Zintl compounds are known for their complex bonding interactions, involving electron transfer from electropositive elements from groups 1 and 2 or lanthanides to more electronegative elements from groups 13–15, which, in turn, can result in complex covalently bonded anionic substructures [2,7]. Pronounced compositional and structural abundance within Zintl phases is often responsible for the formation of complex structures. Complex Zintl phases usually display a range of unprecedented physical properties, although the inherent complexity poses challenges in understanding structure–property relationships [8,9,10,11,12,13,14,15,16].

In recent years, we pushed the frontiers of complexity within the family of Zintl phases containing pnictogens, i.e., elements from group 15, by synthesizing and structurally characterizing complex and often disordered Zintl compounds with several hundreds of atoms in the unit cell, such as Ba₂Mn_1−xBi₂ [17], Eu₈Zn₂As₆O [18], Ba₁₆Sb₁₁ [19], Ca₉(Zn,In)₄Sb₉ [20], and Ca₂CdSb₂ [21], to name a few. The three latter compositions are particularly interesting, as they exemplify the existence of relatively rare Zintl polymorphs with enhanced structural complexity and substantially large unit cells.

Inspired by our recent discovery of polymorphism of the Ca₂CdSb₂ composition, which adopts a simpler orthorhombic modification (V ≈ 585 Å³) [22] and a more complex monoclinic modification (V ≈ 4398 Å³) [21], we investigated the amenability of compositionally and structurally related Yb₂CdSb₂ Zintl antimonide to host polymorphic modifications as well. The orthorhombic α-Yb₂CdSb₂ (space group Cmc2₁, ICSD 173171) phase was discovered in 2007 [22], and since then, materials crystallizing in its archetype have received noticeable attention due to their promising thermoelectric performance [23,24,25,26], optical properties [27,28,29], and interesting aspects of structural science [30,31,32,33]. Although several reports indicate the existence of polymorphs for the structurally related Ca₂CdPn₂ (Pn = P, As, Sb) phases [21,27,32], the polymorphism within the Yb-bearing Yb₂CdPn₂ family has not been reported to date.

In this manuscript, we report the discovery of a polymorph of the Yb₂CdSb₂ phase and provide a comprehensive characterization of its complex crystal and electronic structure, highlighting bonding aspects and the role of structural disorder in charge balance and its semiconducting nature. The reported modification crystallizes in the monoclinic space group Cm; therefore, we will notate it m-Yb₂CdSb₂ or β-Yb₂CdSb₂ hereafter to distinguish it from the original orthorhombic o-Yb₂CdSb₂, which will be notated as α-Yb₂CdSb₂ throughout this manuscript.

2. Materials and Methods

2.1. Synthesis

The monoclinic Yb₂CdSb₂ phase reported here was synthesized by the direct solid-state method, i.e., from melt. The reaction procedures involve loading stoichiometric amounts of the elements (Sigma-Aldrich or Alfa-Aesar with typical purity of ≥99.9 wt.%.) into a Nb tube. Handling of the starting materials was carried out in an Ar-filled glovebox. The tube was then properly shut and arc-welded using Ar plasma. The sealed Nb tube was further flame-sealed in the silica ampoule under vacuum. The ampoule was loaded into a programmable tube furnace which was heated to 1173 K at the rate of 100 K h⁻¹ and maintained at this temperature for 72 h before cooling to 873 K followed by immediate quenching in cold water. The silica ampoule was crack-opened, and the Nb tube with reacted material was returned to the glovebox. The product was a mixture of several binary phases, including the stable Yb₁₁Sb₁₀ composition [34]. Also found were the ternary o-Yb₂CdSb₂ phase previously reported [22], along with the monoclinic polymorph reported herein.

Safety Note. Extreme caution should be taken when executing high-temperature reactions with Cd metal. Experiments must be handled with extreme care in well-ventilated areas. The high vapor pressure of Cd at reaction temperatures exceeding its boiling point can cause sealed containers to rupture, creating potentially hazardous conditions. Slow heating is recommended to minimize these risks.

2.2. Structural Characterization

Single-crystal X-ray diffraction (SCXRD) data for m-Yb₂CdSb₂ were collected at 200 K using a Bruker APEX II diffractometer equipped with Mo Kα radiation (λ = 0.71073 Å) and a CCD detector. An inert atmosphere and low temperature were maintained by continuously flowing a nitrogen stream over the MiTeGen plastic loop holding the mounted crystal. The unit cell refinements, data reduction, and integration were completed with the SAINT program, whereas the SADABS program package was used for absorption corrections [35,36]. The structure was solved by the Intrinsic Phasing method using the SHELXT (version 2018/2) program and consequently refined with full-matrix least-squares methods on F² using SHELXL (version 2018/3) utilizing Olex2 software (version 1.5) as the GUI [37,38,39,40]. The STRUCTURE TIDY program was used to standardize coordinates [41]. Selected crystallographic data, atomic coordinates, displacement parameters, site occupancy factors (SOFs), and selected bond distances are presented in Table 1, Tables S1 and S2, respectively.

2.3. Electronic Structure Calculations

To better understand the properties and the potential of Yb₂CdSb₂ for applications, structural optimization and electronic structure calculations were performed with density functional theory (DFT) using Vienna Ab Initio Simulation Package (VASP) software (version 6.4.3.) [42]. The generalized gradient approximation (GGA) of PBEsol [43] was used for the exchange correlation functional, with both core and valence electrons treated using the projector-augmented wave (PAW) method [44]. k-point mesh and k-path for band structure were automatically generated using VASPKIT [45], with a Monkhorst-Pack mesh of 1 × 7 × 3 points in the Brillouin zone for self-consistency field calculations. The Fermi level was selected to be used as an energy reference (E_F = 0 eV).

3. Results and Discussions

3.1. Synthesis

In this section, we discuss additional details on aspects of the sample synthesis procedures presented in the experimental section. After the initial discovery of the m-Yb₂CdSb₂ polymorphic phase through a direct solid-state reaction, we explored several approaches to access the phase via a high-temperature flux technique. From previous synthesis experiences, where a polymorphic Ca₂CdSb₂ phase was identified from a Cd-flux method [21], we attempted to synthesize the title m-Yb₂CdSb₂ polymorph similarly by loading starting elements Yb:Cd:Sb at a 9:60:9.2 ratio and treating the mixture with the thermal treatment described in our previous report [21]. However, the observed products were predominantly needle-shaped crystals of the previously reported o-Yb₂CdSb₂ phase. Only a few of the checked crystals were indexed with lattice parameters that are shown in Table 1, i.e., m-Yb₂CdSb₂, although the quality was usually poor. Understandably, the powder patterns of both phases are very complex and hardly distinguishable, making it difficult to exhaustively confirm the presence of the monoclinic phase; however, weak superstructure peaks can presumably be identified from the high-resolution synchrotron data. Attempts to produce the title phase via Pb- or Sn-flux reactions also failed, yielding mainly the Yb₁₁Sb₁₀ phase [34].

Whereas the solid-state direct reaction synthetic route appears to be the best means of preparing the m-Yb₂CdSb₂ phase, this approach has its own challenges, specifically, the predominant occurrence of the o-Yb₂CdSb₂ phase. Also, the crystals obtained from this method are mostly of micron sizes that are mainly suitable for SCXRD data collection but not for transport and magnetic property measurements. It is therefore noted that further optimization of kinetic parameters of the synthesis is expected to grow larger crystals, and perhaps a better understanding of the homogeneity temperature range of this phase may be unraveled via the time-dependent in situ approach [46], which can provide useful information on the reaction pathways.

The compositional space within the Yb–Cd–Sb ternary system is not well populated, with only two reported compositions, o-Yb₂CdSb₂ [22] and YbCd₂Sb₂ [47,48], being known for a long time. Recently, we identified two (yet to be reported) other ternary compounds, Yb₁₄CdSb₁₁ and Yb₁₀CdSb₉ (note the real structure of the latter is heavily disordered and its composition is non-stoichiometric), significantly advancing the compositional landscape of this ternary system (Figure 1).

3.2. Crystal Structure and Structural Relationships

Ternary Zintl pnictides with A₂MPn₂ composition (A = Ca, Sr, Ba, Eu, Yb; M = Mn, Zn, Cd; Pn = P, As, Sb, Bi) represent a promising but still relatively underexplored class of functional materials with the potential for advancing various technologies [49,50,51]. This family of compounds offers a rich chemical diversity and complexity with more than a dozen structure types [17,21,22,27,32,52,53,54], including superstructure polymorphs of Ca₂CdP₂ [27], Ca₂CdAs₂ [32], and Ca₂CdSb₂ [21] phases. These β-Ca₂CdP₂ and β-Ca₂CdAs₂ polymorphs are isostructural and crystallize in the monoclinic space group Cm with unit cell parameters a ≈ 21.0/21.5 Å, b ≈ 4.2/4.3 Å, c ≈ 14.0/14.4 Å, and β ≈ 109.1/110.0°, respectively. The monoclinic structure of the β-Ca₂CdSb₂ is more complex (a ≈ 37.3 Å, b ≈ 4.6 Å, c ≈ 25.7 Å, and β ≈ 96.0°) and heavily disordered with multiple partially occupied Cd atoms.

As reported in this work, the title m-Yb₂CdSb₂ (β-Yb₂CdSb₂) phase also crystallizes in the non-centrosymmetric monoclinic space group Cm (No. 8) akin to all three listed Ca-bearing polymorphs. Still, its structure is notably different, being the largest (a ≈ 81.8 Å, b ≈ 4.6 Å, c ≈ 12.7 Å, β ≈ 93.0°) and the most complex with the enormous a lattice parameter (Table 1). Its asymmetric unit contains 33 crystallographically independent Yb atomic sites, 23 Cd sites, and 33 Sb sites, all occupying special positions (Wyckoff 2a) with the site symmetry m (Table S1). Similarly to the structure of β-Ca₂CdSb₂, multiple Cd atoms in β-Yb₂CdSb₂ are disordered with the site occupancy factors (SOFs) varying from 10% to 60% (Table S1). The disorder in β-Yb₂CdSb₂ is further exacerbated by the partial occupancy of two Yb atomic sites and the split of one Cd atomic position (Table S1). The latter type of disorder, however, was previously observed for the Lu-doped version of the β-Ca₂CdSb₂ phase and was considered an efficient mechanism to increase the dimensionality of the polyanionic substructure and, therefore, enhance transport properties [21].

The crystal structure of β-Yb₂CdSb₂ has no precedent and should be considered a novel structure type. Given the extensive disorder, assigning a proper Wyckoff sequence is complicated, although we tend to formally consider it as a⁸⁸ by neglecting the split on the Cd site. Formally, the Pearson symbol can be assigned as mS176, yet given the vacant Cd and Yb sites, it could also be viewed as mS165.

The disordered anionic substructure of β-Yb₂CdSb₂ shown in Figure 2a is much more complex than that of ordered α-Yb₂CdSb₂ (Figure 2d) and β-Ca₂CdPn₂ (Pn = P, As) (Figure 2c), but comparable to the β-Ca₂CdSb₂ (Figure 2b) and its Lu-doped variant [21]. All listed structure types lack inversion symmetry and crystallize in the non-centrosymmetric space group Cmc2₁ for α-Yb₂CdSb₂ or Cm for the rest of the compounds, which allows the identification of structural relationships across the series. α-Yb₂CdSb₂ and β-Ca₂CdSb₂ contain layers composed of the corner-sharing [CdSb₄] tetrahedra, which are stacked in the AAAA sequence, although with the 1/2-translation displacement along the shortest a- or b-axis, respectively. However, careful analysis of the β-Yb₂CdSb₂ structure reveals the presence of several different layers so that the stacking sequence can be denoted as ABC (Figure 3a). Similarly to the β-Ca₂CdSb₂, adjacent slabs of [ABC] layers are displaced by a translation halfway along the shortest b-axis, which corresponds to the viewing direction in Figure 2a and Figure 3a.

To better understand the compositional and structural configurations of each layer, we should consider the structural model with the partially reduced disorder. The crystal structure of the title β-Yb₂CdSb₂ phase contains eight partially occupied or split Cd atomic sites. All of them, but Cd22 with the SOF of ca. 58%, are coordinated by three Sb atoms in a trigonal planar arrangement, with the Cd atoms noticeably protruding from the plane. However, the coordination of these Cd sites cannot be extended to the tetrahedra through the fourth Cd−Sb contacts, as these distances exceed 3.12 Å, which is noticeably larger than the combined values of the covalent radii of Cd and Sb (2.83 Å) [55]. A reasonable structural model with well-separated layers (Figure 3a) can be obtained if we omit the Cd1, Cd2, Cd3, Cd4B, Cd5, Cd7, Cd8, and Cd9 atomic positions, i.e., those with SOFs ≤ 50% (Table S1).

Layer A, depicted in Figure 3b, can be described as consisting of seven unique Cd-centered (Cd10−Cd12, Cd19−Cd22) [CdSb₄] tetrahedra, which are corner-shared. Note that all Cd sites except Cd22 are fully occupied. Layer A features partially similar structural arrangements observed in α-Yb₂CdSb₂ (Figure 2d) and β-Ca₂CdSb₂ (Figure 3c), although they are not entirely identical. These complex infinite layers are located within the bc-plane.

Layers B and C can be viewed as 1D [Cd₃Sb₁₀] units composed of three [CdSb₄] tetrahedra interconnected via the same Sb atom. These three-fold units propagate along the b-axis by sharing corners of all three [CdSb₄] tetrahedra (Figure 3d). We have recently reported similar structural fragments in β-Ca₂CdAs₂ (Figure 2c) [32], Ca₈LaMn_4+xSb₉ [56], and Ca₉(Zn,In)₄Sb₉ [20]. Although the [Cd₃Sb₁₀] units composing B and C slabs are nearly identical in the structure of β-Yb₂CdSb₂ (Figure 3a), they consist of different sets of atoms: Cd16−Cd18-centered tetrahedra for B and Cd13−Cd15-centered tetrahedra for C. These units are slightly displaced along the c-axis and tilted differently for B and C with respect to the b-axis. Interatomic Cd−Sb contacts within all three described layers (Table S2) range from 2.75 Å to 3.09 Å and are consistent with the previously observed values for α-Yb₂CdSb₂, β-Ca₂CdSb_2, and similar materials [21,22].

Trigonal planar [CdSb₃] units composed of the partially occupied Cd atoms form 1D corner-sharing ribbons along the b-axis. Some of the interatomic contacts within these units are somewhat shortened, falling below the sum of covalent radii of Sb and Cd (2.83 Å, Table S2), which can be attributed to the partial SOFs of the Cd atoms. With some flexibility for allowed interatomic Cd–Sb contacts, we can consider these ribbons as linking fragments for the described layers, as can be seen in Figure 2a. Such structural features can contribute to the increased dimensionality of the anionic substructure and improve charge-carrier transport properties, as was recently shown for the β-Ca₂CdSb₂ and its Lu-doped variant [21].

The coordination environments of the Yb²⁺ cations in the β-Yb₂CdSb₂ structure are very similar to those observed in α-Yb₂CdSb₂ and β-Ca₂CdSb₂. Among all 33 Yb atomic sites, 16 are coordinated in a slightly distorted octahedral fashion with CN = 6 (Figure 3e), and 17 are in a distorted square pyramidal fashion with CN = 5 (Figure 3f). The observed interatomic Yb−Sb distances range from 3.08 to 3.58 Å, although considering longer contacts up to 3.79 Å, some of the [YbSb₅] square pyramids can be transformed into the heavily distorted [YbSb₆] octahedra.

Two Yb sites, Yb17 with square-pyramidal coordination and Yb22 with octahedral coordination, were refined as partially occupied with SOFs of ca. 80% and 86%, respectively. The Fourier difference map indicates negligible residual electron density peaks close to multiple Yb atoms, which were considered artifacts of the absorption correction. The presence of the multiple underoccupied Yb and Cd atomic sites in the structure of β-Yb₂CdSb₂ (Table S1) is explained by the charge balance and electron count considerations. Indeed, since all atomic sites have the same site symmetry (Wyckoff 2a), and given Z = 33, it is required to have 33 Yb sites, 33 Sb sites, and 16.5 Cd sites to maintain the charge-balanced Yb₂CdSb₂ composition. Instead, the crystal structure of the title compound features 22 Cd sites, 8 of which are partially occupied (Table S1). A hypothetical structural model in which all atomic sites are fully occupied is improbable as it would have a pronouncedly electron-rich composition (i.e., Yb₆₆Cd₄₄Sb₆₆(e⁻)₂₂ = Yb₂Cd_1.33(3)Sb₂(e⁻)_0.66, where e⁻ denotes the electrons). The reported refined formula with underoccupied Cd and Yb atoms is nearly charge-balanced and can be described according to the fully ionic approximation as (Yb²⁺)_1.98(Cd²⁺)_1.01(Sb³⁻)₂(h⁺)_0.02, where h⁺ denotes holes.

3.3. Electronic Structure

Given the moderate difference between the electronegativities of the constituted elements in Yb₂CdSb₂ and the sizable charge transfer, we anticipate observing a semiconducting behavior for the title compound as was previously reported for the Ca₂CdPn₂ (Pn = P, As, Sb) family of compounds [21,22,27,32]. However, Yb-bearing compounds are expected to be more metallic in nature and possess smaller band gaps due to the more diffuse and larger orbitals of Yb. This prediction is corroborated by the electronic structure calculations provided below.

As discussed in the experimental section, a simplified structure of Yb₂CdSb₂ can be generated by removing partially occupied atomic sites. To compose the structural model suitable for the electronic structure calculations, we further adjusted the structural model provided in Figure 3a. In particular, split Cd4A and Cd4B atomic sites were combined into the singular Cd4 position with an SOF of 1. Some Cd sites with low SOFs, such as Cd3 (SOF 36.9%), Cd5 (SOF 32.3%), Cd7 (SOF 9.7%), Cd8 (SOF 10.4%), and Cd9 (SOF 19.7%), were also removed, while Yb17 (SOF 80.3%), Yb22 (SOF 86.2%), Cd1 (SOF 50%), Cd2 (SOF 50%), and Cd22 (SOF 58.1%) were given full occupancy. This allowed for a nearly charge-balanced composition of Yb₆₆Cd₃₄Sb₆₆ = Yb₂Cd_1.03Sb₂ with 17 fully occupied Cd sites but resulted in a two-electron shift in the Fermi level according to the (Yb²⁺)₆₆(Cd²⁺)₃₄(Sb^3–)₆₆(e⁻)₂ charge partitioning, as indicated on the density-of-states plots below (Figure 4).

Figure 4a,c show the calculated band structure and the total (TDOS) and partial (PDOS) density of states within the energy range from −5 to 2 eV. The absence of a band gap opening in the β-Ca₂CdSb₂ phase indicates a semimetallic behavior. Specifically, an overlap of the conduction and valence bands is observed, which can result in a relatively low carrier concentration and high mobility. Here, the Fermi level lies very close to the point of overlap between the valence and conduction bands as opposed to those of semiconductors, where the Fermi level lies within the band gap. The features observed also likely indicate the anisotropic nature of the electron and hole masses in the title phase, which can play critical roles in its electronic and transport properties. A closer look at Figure 4a,c indicate the presence of what can be considered anti-crossing and band inversion features along the high-symmetry Г-points, which can be a signature of nontrivial topology. Although the observed features require further extensive investigation, it should be noted that the presented band structure in Figure 4c has no spin–orbit coupling (SOC). We speculate that the switching on of SOC and/or the strain effect in this phase can provide other interesting features, such as opening a band gap, which is expected for a topological insulator state. Here, the crossing of the valence and conduction bands brings about discrete touch points in momentum space as one would expect for Dirac and Weyl semimetals, which are characterized by massless fermions and nontrivial Berry curvature. Detailed band structure calculations and parity analysis of occupied bands are expected to provide additional insight into the electronic and transport properties of this material.

The correlation between the surface state properties of topological insulators and excellent thermoelectric properties in Zintl phases has been established [57,58]. If confirmed, the presence of nontrivial band topology in the title compound can also provide a window of opportunity to explore this material for excellent thermoelectric properties. The heavy disorder and intricate atomic bonding in the title phase are particularly expected to drive the realization of ultra-low thermal conductivity. The presence of multiple bands below the Fermi level and the generic view of the band structure appear to be very similar to the previously reported β-Ca₂CdP₂ and β-Ca₂CdAs₂ phases [27,32], although they are direct-gap semiconductors with relatively wide band gaps.

The total and partial density of states (DOS) plots (Figure 4) also show patterns similar to other ternary pnictides [22,54]. States between −5 and the valence band maxima (VBM) consist primarily of Sb-p states, with minimal contributions from Sb-s and Sb-d, indicating poor orbital mixing. Yb-p and Yb-d states both contribute to the range between −4 eV and the VBM, with Yb–d being the primary contributor. Cd-s orbitals contribute primarily to states below −5 eV, while Cd-p states contribute to the range between −4 eV and the VBM.

4. Conclusions

A novel complex monoclinic β-Yb₂CdSb₂ polymorph has been identified and studied, enriching the Yb–Cd–Sb phase diagram and highlighting the structural diversity of the A₂CdPn₂ (A = Ca, Yb; Pn = P, As, Sb) family of non-centrosymmetric compounds. β-Yb₂CdSb₂ has a disordered anionic substructure based on the distorted [CdSb₄] tetrahedral and [CdSb₃] trigonal planar units, being reminiscent of the related β-Ca₂CdSb₂ phase, although with significant differences in stacking sequences and interlayer interactions. Detailed structural and electronic characterizations highlight the influence of disorder on the charge-balanced nature of the material, which can be notated as the (Yb²⁺)_1.98(Cd²⁺)_1.01(Sb³⁻)₂(h⁺)_0.02. Its discovery underscores the potential for tailoring thermoelectric and optical properties through polymorphism and structural disorder and helps in understanding the relationships between structural complexity and material properties. Electronic structure calculations reveal a presumably semimetallic feature of β-Yb₂CdSb₂. In addition, features reminiscent of nontrivial topological properties are observed, although subsequent studies are expected to provide a clearer picture of this.

Future investigations could focus on fine-tuning the disorder through doping or substitutions, aiming to optimize thermoelectric performance and explore the tuning of possible topological properties. It should be noted that this compound may occur as an impurity phase in the synthesis of thermoelectric materials based on the orthorhombic α-Yb₂CdSb₂ polymorph, therefore posing a risk of misidentification and misinterpretation of the structure–property relationships. Subsequent studies will also benefit from optimizing the synthesis condition of this phase towards realizing larger single crystals and polycrystalline bulk synthesis, which will provide an opportunity for an exhaustive investigation of its thermoelectric and transport properties.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/cryst14110920/s1: Table S1: Refined atomic coordinates for β-Yb₂CdSb₂. Table S2: Selected bond distances for β-Yb₂CdSb₂.

Author Contributions

Validation, M.O.O.; formal analysis, S.R.W., M.O.O., and S.B. (Sviatoslav Baranets); data curation, S.R.W. and L.N.; writing—original draft preparation, visualization, S.R.W. and S.B. (Sviatoslav Baranets); writing—review and editing, M.O.O. and S.B. (Svilen Bobev); methodology, conceptualization, supervision, project administration, S.B. (Svilen Bobev) and S.B. (Sviatoslav Baranets), funding acquisition S.B. (Svilen Bobev). All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the United States Department of Energy, Office of Science, Basic Energy Sciences, under Award #DE-SC0008885. S. Baranets acknowledges financial support from the College of Science and Department of Chemistry at Louisiana State University (start-up funding).

Data Availability Statement

The corresponding crystallographic information files (CIFs) have been deposited with the Cambridge Crystallographic Database Centre (CCDC) and can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/ or by emailing [email protected] with the following depository number: 2387090.

Acknowledgments

S. Bobev acknowledges financial support from the United States Department of Energy, Office of Science, Basic Energy Sciences, under Award #DE-SC0008885. S. Baranets acknowledges financial support from the College of Science and Department of Chemistry at Louisiana State University (start-up funding). Julien Makongo is acknowledged for his preliminary work in the Yb–Cd–Sb system.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Ternary Yb−Cd−Sb compositional diagram. The newly identified Yb₂CdSb₂ polymorph is identified as a red star. Known binary and ternary phases are indicated as well. Note that Yb₁₄CdSb₁₁ and Yb_10.5Cd_0.5Sb₉ have not yet been reported.

Figure 2. Crystal structures of β-Yb₂CdSb₂ (a), β-Ca₂CdSb₂ (b), β-Ca₂CdAs₂ (c), and α-Yb₂CdSb₂ (d) viewed along the b-axis. The unit cell of β-Yb₂CdSb₂ is doubled along the c-axis for clarity. The Ca and Yb atoms are drawn as dark gray, Cd atoms are green, and Pn = Sb/As atoms are blue-gray. [CdPn₄] tetrahedral units are drawn in dark green. The unit cells are outlined. Interatomic Cd–Sb contacts exceeding 3.10 Å are not displayed.

Figure 3. The representation of the β-Yb₂CdSb₂ structure with the labeled ABC layers. The unit cell of β-Yb₂CdSb₂ is doubled along the c-axis. Cd atoms with less than 50% occupancy are avoided for clarity (a). Close-up view of the A layer in β-Yb₂CdSb₂ (b), _∞²[CdSb₂]^4– layer in β-Ca₂CdSb₂ (c), and [Cd₃Sb₁₀] units composing B/C layers (d). Typical six-coordinated octahedral coordination environment of [YbSb₆] units (e) and five-coordinated square pyramidal [YbSb₅] units (f). Completeness of the spheres visualizes SOFs. Similar structural units in β-Yb₂CdSb₂ and β-Ca₂CdSb₂ are highlighted by red tetrahedra. The color code is the same as in Figure 2.

Figure 4. Calculated (a) band structure, (b) total (DOS) density of states, and partial (PDOS) density of states for (d) Yb, (e) Cd, and (f) Sb for Yb₂CdSb₂. An enlarged view of the band structure at the Fermi level is provided in (c). The Fermi level is the energy reference at 0 eV. The second dashed line at 0.08 eV indicates a 2-electron shift per unit cell.

Table 1. Selected data collection and crystallographic details and structure refinement parameters for β-Yb₂Cd₂Sb₂ (monoclinic space group Cm; Z = 33; Mo Kα radiation (λ = 0.71073 Å); T = 200(2) K).

Empirical formula	Yb_1.98(1)Cd_1.01(1)Sb₂
Formula weight	699.62
a/Å	81.801(5)
b/Å	4.6186(3)
c/Å	12.6742(7)
β/°	93.0610(10)
V/Å³	4781.6(5)
ρ_calc g/cm³	8.018
μ/mm⁻¹	44.311
Collected/independent reflections	29,216/10,902
R₁ (I > 2σ_(I)) ^a	0.0333
wR₂ (I > 2σ_(I)) ^a	0.0589
R₁ (all data) ^a	0.0395
wR₂ (all data) ^a	0.0616
Δρ_max,min/e⁻ Å⁻³	2.35, −2.66

^a R₁ = Σ ∣ ∣F_o∣ − ∣F_c∣ ∣/Σ∣F_o∣. wR₂ = (Σ [w(F_o² − F_c²)²]/ΣwF_o⁴)^1/2, w = 1/[σ²(F_o²)].

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Watts, S.R.; Najera, L.; Ogunbunmi, M.O.; Bobev, S.; Baranets, S. β-Yb₂CdSb₂—A Complex Non-Centrosymmetric Zintl Polymorph. Crystals 2024, 14, 920. https://doi.org/10.3390/cryst14110920

AMA Style

Watts SR, Najera L, Ogunbunmi MO, Bobev S, Baranets S. β-Yb₂CdSb₂—A Complex Non-Centrosymmetric Zintl Polymorph. Crystals. 2024; 14(11):920. https://doi.org/10.3390/cryst14110920

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Watts, Spencer R., Larissa Najera, Michael O. Ogunbunmi, Svilen Bobev, and Sviatoslav Baranets. 2024. "β-Yb₂CdSb₂—A Complex Non-Centrosymmetric Zintl Polymorph" Crystals 14, no. 11: 920. https://doi.org/10.3390/cryst14110920

APA Style

Watts, S. R., Najera, L., Ogunbunmi, M. O., Bobev, S., & Baranets, S. (2024). β-Yb₂CdSb₂—A Complex Non-Centrosymmetric Zintl Polymorph. Crystals, 14(11), 920. https://doi.org/10.3390/cryst14110920

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β-Yb₂CdSb₂—A Complex Non-Centrosymmetric Zintl Polymorph

Abstract

1. Introduction